Zeng Xiancheng; Hu Hao; Hu Xiangqian; Yang Weitao
2009-01-01
A quantum mechanical/molecular mechanical minimum free energy path (QM/MM-MFEP) method was developed to calculate the redox free energies of large systems in solution with greatly enhanced efficiency for conformation sampling. The QM/MM-MFEP method describes the thermodynamics of a system on the potential of mean force surface of the solute degrees of freedom. The molecular dynamics (MD) sampling is only carried out with the QM subsystem fixed. It thus avoids 'on-the-fly' QM calculations and thus overcomes the high computational cost in the direct QM/MM MD sampling. In the applications to two metal complexes in aqueous solution, the new QM/MM-MFEP method yielded redox free energies in good agreement with those calculated from the direct QM/MM MD method. Two larger biologically important redox molecules, lumichrome and riboflavin, were further investigated to demonstrate the efficiency of the method. The enhanced efficiency and uncompromised accuracy are especially significant for biochemical systems. The QM/MM-MFEP method thus provides an efficient approach to free energy simulation of complex electron transfer reactions.
Minimum free-energy paths for the self-organization of polymer brushes.
Gleria, Ignacio; Mocskos, Esteban; Tagliazucchi, Mario
2017-03-22
A methodology to calculate minimum free-energy paths based on the combination of a molecular theory and the improved string method is introduced and applied to study the self-organization of polymer brushes under poor solvent conditions. Polymer brushes in a poor solvent cannot undergo macroscopic phase separation due to the physical constraint imposed by the grafting points; therefore, they microphase separate forming aggregates. Under some conditions, the theory predicts that the homogeneous brush and the aggregates can exist as two different minima of the free energy. The theoretical methodology introduced in this work allows us to predict the minimum free-energy path connecting these two minima as well as the morphology of the system along the path. It is shown that the transition between the homogeneous brush and the aggregates may involve a free-energy barrier or be barrierless depending on the relative stability of the two morphologies and the chain length and grafting density of the polymer. In the case where a free-energy barrier exists, one of the morphologies is a metastable structure and, therefore, the properties of the brush as the quality of the solvent is cycled are expected to display hysteresis. The theory is also applied to study the adhesion/deadhesion transition between two opposing surfaces modified by identical polymer brushes and it is shown that this process may also require surpassing a free-energy barrier.
A fast tomographic method for searching the minimum free energy path
Chen, Changjun; Huang, Yanzhao; Xiao, Yi; Jiang, Xuewei
2014-01-01
Minimum Free Energy Path (MFEP) provides a lot of important information about the chemical reactions, like the free energy barrier, the location of the transition state, and the relative stability between reactant and product. With MFEP, one can study the mechanisms of the reaction in an efficient way. Due to a large number of degrees of freedom, searching the MFEP is a very time-consuming process. Here, we present a fast tomographic method to perform the search. Our approach first calculates the free energy surfaces in a sequence of hyperplanes perpendicular to a transition path. Based on an objective function and the free energy gradient, the transition path is optimized in the collective variable space iteratively. Applications of the present method to model systems show that our method is practical. It can be an alternative approach for finding the state-to-state MFEP
On the normalization of the minimum free energy of RNAs by sequence length.
Edoardo Trotta
Full Text Available The minimum free energy (MFE of ribonucleic acids (RNAs increases at an apparent linear rate with sequence length. Simple indices, obtained by dividing the MFE by the number of nucleotides, have been used for a direct comparison of the folding stability of RNAs of various sizes. Although this normalization procedure has been used in several studies, the relationship between normalized MFE and length has not yet been investigated in detail. Here, we demonstrate that the variation of MFE with sequence length is not linear and is significantly biased by the mathematical formula used for the normalization procedure. For this reason, the normalized MFEs strongly decrease as hyperbolic functions of length and produce unreliable results when applied for the comparison of sequences with different sizes. We also propose a simple modification of the normalization formula that corrects the bias enabling the use of the normalized MFE for RNAs longer than 40 nt. Using the new corrected normalized index, we analyzed the folding free energies of different human RNA families showing that most of them present an average MFE density more negative than expected for a typical genomic sequence. Furthermore, we found that a well-defined and restricted range of MFE density characterizes each RNA family, suggesting the use of our corrected normalized index to improve RNA prediction algorithms. Finally, in coding and functional human RNAs the MFE density appears scarcely correlated with sequence length, consistent with a negligible role of thermodynamic stability demands in determining RNA size.
On the normalization of the minimum free energy of RNAs by sequence length.
Trotta, Edoardo
2014-01-01
The minimum free energy (MFE) of ribonucleic acids (RNAs) increases at an apparent linear rate with sequence length. Simple indices, obtained by dividing the MFE by the number of nucleotides, have been used for a direct comparison of the folding stability of RNAs of various sizes. Although this normalization procedure has been used in several studies, the relationship between normalized MFE and length has not yet been investigated in detail. Here, we demonstrate that the variation of MFE with sequence length is not linear and is significantly biased by the mathematical formula used for the normalization procedure. For this reason, the normalized MFEs strongly decrease as hyperbolic functions of length and produce unreliable results when applied for the comparison of sequences with different sizes. We also propose a simple modification of the normalization formula that corrects the bias enabling the use of the normalized MFE for RNAs longer than 40 nt. Using the new corrected normalized index, we analyzed the folding free energies of different human RNA families showing that most of them present an average MFE density more negative than expected for a typical genomic sequence. Furthermore, we found that a well-defined and restricted range of MFE density characterizes each RNA family, suggesting the use of our corrected normalized index to improve RNA prediction algorithms. Finally, in coding and functional human RNAs the MFE density appears scarcely correlated with sequence length, consistent with a negligible role of thermodynamic stability demands in determining RNA size.
Sparse RNA folding revisited: space-efficient minimum free energy structure prediction.
Will, Sebastian; Jabbari, Hosna
2016-01-01
RNA secondary structure prediction by energy minimization is the central computational tool for the analysis of structural non-coding RNAs and their interactions. Sparsification has been successfully applied to improve the time efficiency of various structure prediction algorithms while guaranteeing the same result; however, for many such folding problems, space efficiency is of even greater concern, particularly for long RNA sequences. So far, space-efficient sparsified RNA folding with fold reconstruction was solved only for simple base-pair-based pseudo-energy models. Here, we revisit the problem of space-efficient free energy minimization. Whereas the space-efficient minimization of the free energy has been sketched before, the reconstruction of the optimum structure has not even been discussed. We show that this reconstruction is not possible in trivial extension of the method for simple energy models. Then, we present the time- and space-efficient sparsified free energy minimization algorithm SparseMFEFold that guarantees MFE structure prediction. In particular, this novel algorithm provides efficient fold reconstruction based on dynamically garbage-collected trace arrows. The complexity of our algorithm depends on two parameters, the number of candidates Z and the number of trace arrows T; both are bounded by [Formula: see text], but are typically much smaller. The time complexity of RNA folding is reduced from [Formula: see text] to [Formula: see text]; the space complexity, from [Formula: see text] to [Formula: see text]. Our empirical results show more than 80 % space savings over RNAfold [Vienna RNA package] on the long RNAs from the RNA STRAND database (≥2500 bases). The presented technique is intentionally generalizable to complex prediction algorithms; due to their high space demands, algorithms like pseudoknot prediction and RNA-RNA-interaction prediction are expected to profit even stronger than "standard" MFE folding. SparseMFEFold is free
Hoehler, Tori M.; Alperin, Marc J.; Albert, Daniel B.; Martens, Christopher S.; DeVincenzi, Don (Technical Monitor)
2000-01-01
Among the most fundamental constraints governing the distribution of microorganisms in the environment is the availability of chemical energy at biologically useful levels. To assess the minimum free energy yield that can support microbial metabolism in situ, we examined the thermodynamics of H2-consuming processes in anoxic sediments from Cape Lookout Bight, NC, USA. Depth distributions of H2 partial pressure, along with a suite of relevant concentration data, were determined in sediment cores collected in November (at 14.5 C) and August (at 27 C) and used to calculate free energy yields for methanogenesis and sulfate reduction. At both times of year, and for both processes, free energy yields gradually decreased (became less negative) with depth before reaching an apparent asymptote. Sulfate reducing bacteria exhibited an asymptote of -19.1 +/- 1.7 kj(mol SO4(2-)(sup -1) while methanogenic archaea were apparently supported by energy yields as small as -10.6 +/- 0.7 kj(mol CH4)(sup -1).
Tomba, J. Pablo
2017-01-01
The use of free energy plots to understand the concept of thermodynamic equilibrium has been shown to be of great pedagogical value in materials science. Although chemical equilibrium is also amenable to this kind of analysis, it is not part of the agenda of materials science textbooks. Something similar is found in chemistry branches, where free…
Ascoli, Sergio; Malvestuto, Vincenzo
2004-01-01
For a fluid system, obeying a state equation of the van der Waals type, the gas and the liquid phases can coexist in equilibrium, at a given temperature, only if the volume of the system is kept fixed. Thus, in order to study the two-phase equilibria of a fluid system, it seemed quite natural to choose the molar volume as the independent variable, and, consequently, the Helmholtz free energy as the proper thermodynamic potential for the application of the minimum principle. Specific computations are here carried out for a single van der Waals fluid, namely, pure water at 300 0 C. As a result, the present treatment indicates a simple and effective way to identify the whole range of molar volumes where the equilibrium preferred by the system is a two-phase equilibrium. This range results to be wider than the interval of strict instability of the van der Waals isotherm. Finally, it is pointed out that all the results, obtained here for the van der Waals state equation, can be extended to all the state equations of the same type
Yoshida, Norio
2018-05-01
A new method for finding the minimum free energy pathway (MFEP) of ions and small molecule transportation through a protein based on the three-dimensional reference interaction site model (3D-RISM) theory combined with the string method has been proposed. The 3D-RISM theory produces the distribution function, or the potential of mean force (PMF), for transporting substances around the given protein structures. By applying the string method to the PMF surface, one can readily determine the MFEP on the PMF surface. The method has been applied to consider the Na+ conduction pathway of channelrhodopsin as an example.
van Gunsteren, WF; Daura, [No Value; Mark, AE
2002-01-01
Many quantities that are standardly used to characterize a chemical system are related to free-energy differences between particular states of the system. By statistical mechanics, free-energy differences may be expressed in terms of averages over ensembles of atomic configurations for the molecular
Free energy analysis of cell spreading.
McEvoy, Eóin; Deshpande, Vikram S; McGarry, Patrick
2017-10-01
In this study we present a steady-state adaptation of the thermodynamically motivated stress fiber (SF) model of Vigliotti et al. (2015). We implement this steady-state formulation in a non-local finite element setting where we also consider global conservation of the total number of cytoskeletal proteins within the cell, global conservation of the number of binding integrins on the cell membrane, and adhesion limiting ligand density on the substrate surface. We present a number of simulations of cell spreading in which we consider a limited subset of the possible deformed spread-states assumed by the cell in order to examine the hypothesis that free energy minimization drives the process of cell spreading. Simulations suggest that cell spreading can be viewed as a competition between (i) decreasing cytoskeletal free energy due to strain induced assembly of cytoskeletal proteins into contractile SFs, and (ii) increasing elastic free energy due to stretching of the mechanically passive components of the cell. The computed minimum free energy spread area is shown to be lower for a cell on a compliant substrate than on a rigid substrate. Furthermore, a low substrate ligand density is found to limit cell spreading. The predicted dependence of cell spread area on substrate stiffness and ligand density is in agreement with the experiments of Engler et al. (2003). We also simulate the experiments of Théry et al. (2006), whereby initially circular cells deform and adhere to "V-shaped" and "Y-shaped" ligand patches. Analysis of a number of different spread states reveals that deformed configurations with the lowest free energy exhibit a SF distribution that corresponds to experimental observations, i.e. a high concentration of highly aligned SFs occurs along free edges, with lower SF concentrations in the interior of the cell. In summary, the results of this study suggest that cell spreading is driven by free energy minimization based on a competition between decreasing
SOCIAL EQUIVALENT OF FREE ENERGY
Josip Stepanic
2004-06-01
Full Text Available Characterisation of unbounded resources of a social system within the sociological interpretation has resulted in a large number of different notions, which are relevant in different situations. From the view point of statistical mechanics, these notions resemble free energy. In this paper the concept of social free energy is introduced and first steps toward its development presented. The social free energy is a function equal to physical free energy appropriately determined for the social system, with intrinsically sociological interpretation as a measure of social action obtainable in a given social system without changes in its structure. Its construction is a consequence of response of a social system to recognised parts of environment dynamics. It is argued that development of a social system response resembles exciting the normal modes of a general, physical system.
Jensen, Henrik J.; Sibani, Paolo
2007-01-01
The term glassy dynamics is often used to refer to the extremely slow relaxation observed in several types of many component systems. The time span needed to reach a steady, time independent, state will typically be far beyond experimentally accessible time scales. When melted alloys are cooled...... down they typically do not enter a crystalline ordered state. Instead the atoms retain the amorphous arrangement characteristic of the liquid high temperature phase while the mobility of the molecules decreases very many orders of magnitude. This colossal change in the characteristic dynamical time...
Kurata, M.; Devanathan, R.
2015-01-01
Free energy and heat capacity of actinide elements and compounds are important properties for the evaluation of the safety and reliable performance of nuclear fuel. They are essential inputs for models that describe complex phenomena that govern the behaviour of actinide compounds during nuclear fuels fabrication and irradiation. This chapter introduces various experimental methods to measure free energy and heat capacity to serve as inputs for models and to validate computer simulations. This is followed by a discussion of computer simulation of these properties, and recent simulations of thermophysical properties of nuclear fuel are briefly reviewed. (authors)
Free Energy in Introductory Physics
Prentis, Jeffrey J.; Obsniuk, Michael J.
2016-01-01
Energy and entropy are two of the most important concepts in science. For all natural processes where a system exchanges energy with its environment, the energy of the system tends to decrease and the entropy of the system tends to increase. Free energy is the special concept that specifies how to balance the opposing tendencies to minimize energy…
Free energy of hydration of niobium oxide
Plodinec, M.J.
1996-01-01
Some of the glasses being formulated by SRTC researchers contain niobium oxide. In this report, the free energy of hydration of the oxide is calculated from the free energies of formation of the oxide, the hydroxide, and water. This value can be used in calculations of the free energy of hydration of glasses containing niobium
Microscopically derived free energy of dislocations
Kooiman, M.; Hütter, M.; Geers, M.G.D.
2015-01-01
The dynamics of large amounts of dislocations is the governing mechanism in metal plasticity. The free energy of a continuous dislocation density profile plays a crucial role in the description of the dynamics of dislocations, as free energy derivatives act as the driving forces of dislocation
Uncertainty Quantification in Alchemical Free Energy Methods.
Bhati, Agastya P; Wan, Shunzhou; Hu, Yuan; Sherborne, Brad; Coveney, Peter V
2018-05-02
Alchemical free energy methods have gained much importance recently from several reports of improved ligand-protein binding affinity predictions based on their implementation using molecular dynamics simulations. A large number of variants of such methods implementing different accelerated sampling techniques and free energy estimators are available, each claimed to be better than the others in its own way. However, the key features of reproducibility and quantification of associated uncertainties in such methods have barely been discussed. Here, we apply a systematic protocol for uncertainty quantification to a number of popular alchemical free energy methods, covering both absolute and relative free energy predictions. We show that a reliable measure of error estimation is provided by ensemble simulation-an ensemble of independent MD simulations-which applies irrespective of the free energy method. The need to use ensemble methods is fundamental and holds regardless of the duration of time of the molecular dynamics simulations performed.
Mechanism of active transport: free energy dissipation and free energy transduction.
Tanford, C
1982-01-01
The thermodynamic pathway for "chemiosmotic" free energy transduction in active transport is discussed with an ATP-driven Ca2+ pump as an illustrative example. Two innovations are made in the analysis. (i) Free energy dissipated as heat is rigorously excluded from overall free energy bookkeeping by focusing on the dynamic equilibrium state of the chemiosmotic process. (ii) Separate chemical potential terms for free energy donor and transported ions are used to keep track of the thermodynamic ...
The free energy principle, negative energy modes, and stability
Morrison, P.J.; Kotschenreuther, M.
1990-01-01
This paper is concerned with instability of equilibria of Hamiltonian, fluid and plasma dynamical systems. Usually the dynamical equilibrium of interest is not the state of thermodynamic equilibrium, and does not correspond to a free energy minimum. The relaxation of this type of equilibrium is conventionally considered to be initiated by linear instability. However, there are many cases where linear instability is not present, but the equilibrium is nonlinearly unstable to arbitrarily small perturbations. This paper is about general free energy expressions for determining the presence of linear or nonlinear instabilities. These expressions are simple and practical, and can be obtained for all equilibria of all ideal fluid and plasma models. By free energy, we mean the energy change upon perturbations of the equilibrium that respect dynamical phase space constraints. This quantity is measured by a self-adjoint quadratic form, called δ 2 F. The free energy can result in instability when δ 2 F is indefinite; i.e. there exist accessible perturbations that lower the free energy of the system. A primary purpose of this paper is to tie together three manifestations of what we will refer to as negative energy modes. The first is the conventional plasma physics notion of negative energy mode that is based on the definition of the energy in a homogeneous dielectric medium. A negative energy mode is a normal mode of the medium (plasma) that possesses negative dielectric energy. The second manifestation occurs in finite degree-of-freedom Hamiltonian normal form theory. The quadratic part of a Hamiltonian in the vicinity of an equilibrium point, which possesses only distinct oscillatory eigenvalues, has an invariant signature. Thus in cases where the quadratic form is indefinite, it is natural to refer to the modes corresponding to the negative signature as negative energy modes
Free Energy and Internal Combustion Engine Cycles
Harris, William D.
2012-01-01
The performance of one type (Carnot) of Internal Combustion Engine (ICE) cycle is analyzed within the framework of thermodynamic free energies. ICE performance is different from that of an External Combustion Engine (ECE) which is dictated by Carnot's rule.
Mass and free energy of Lovelock black holes
Kastor, David; Traschen, Jennie; Ray, Sourya
2011-01-01
An explicit formula for the ADM mass of an asymptotically AdS black hole in a generic Lovelock gravity theory is presented, identical in form to that in Einstein gravity, but multiplied by a function of the Lovelock coupling constants and the AdS curvature radius. A Gauss' law-type formula relates the mass, which is an integral at infinity, to an expression depending instead on the horizon radius. This and other thermodynamic quantities, such as the free energy, are then analyzed in the limits of small and large horizon radius, yielding results that are independent of the detailed choice of Lovelock couplings. In even dimensions, the temperature diverges in both limits, implying the existence of a minimum temperature for black holes. The negative free energy of sufficiently large black holes implies the existence of a Hawking-Page transition. In odd dimensions, the temperature still diverges for large black holes, which again have negative free energy. However, the temperature vanishes as the horizon radius tends to zero and sufficiently small black holes have positive specific heat.
Good Practices in Free-energy Calculations
Pohorille, Andrew; Jarzynski, Christopher; Chipot, Christopher
2013-01-01
As access to computational resources continues to increase, free-energy calculations have emerged as a powerful tool that can play a predictive role in drug design. Yet, in a number of instances, the reliability of these calculations can be improved significantly if a number of precepts, or good practices are followed. For the most part, the theory upon which these good practices rely has been known for many years, but often overlooked, or simply ignored. In other cases, the theoretical developments are too recent for their potential to be fully grasped and merged into popular platforms for the computation of free-energy differences. The current best practices for carrying out free-energy calculations will be reviewed demonstrating that, at little to no additional cost, free-energy estimates could be markedly improved and bounded by meaningful error estimates. In energy perturbation and nonequilibrium work methods, monitoring the probability distributions that underlie the transformation between the states of interest, performing the calculation bidirectionally, stratifying the reaction pathway and choosing the most appropriate paradigms and algorithms for transforming between states offer significant gains in both accuracy and precision. In thermodynamic integration and probability distribution (histogramming) methods, properly designed adaptive techniques yield nearly uniform sampling of the relevant degrees of freedom and, by doing so, could markedly improve efficiency and accuracy of free energy calculations without incurring any additional computational expense.
Rainer, D.; Serene, J.W.
1976-01-01
A systematic scheme is presented for calculating the free energy of superfluid Fermi liquids by an asymptotic expansion in the small parameter T/subc//T/subF/. This scheme is used to evaluate the strong-coupling corrections to the free energy of superfluid 3 He. It is shown that the leading corrections can be expressed in terms of the normal-state quasiparticle scattering amplitude, and the strong-coupling results are discussed using the s-p approximation for the scattering amplitude
Granata, Daniele; Baftizadeh, Fahimeh; Habchi, Johnny; Galvagnion, Celine; De Simone, Alfonso; Camilloni, Carlo; Laio, Alessandro; Vendruscolo, Michele
2015-10-26
The free energy landscape theory has been very successful in rationalizing the folding behaviour of globular proteins, as this representation provides intuitive information on the number of states involved in the folding process, their populations and pathways of interconversion. We extend here this formalism to the case of the Aβ40 peptide, a 40-residue intrinsically disordered protein fragment associated with Alzheimer's disease. By using an advanced sampling technique that enables free energy calculations to reach convergence also in the case of highly disordered states of proteins, we provide a precise structural characterization of the free energy landscape of this peptide. We find that such landscape has inverted features with respect to those typical of folded proteins. While the global free energy minimum consists of highly disordered structures, higher free energy regions correspond to a large variety of transiently structured conformations with secondary structure elements arranged in several different manners, and are not separated from each other by sizeable free energy barriers. From this peculiar structure of the free energy landscape we predict that this peptide should become more structured and not only more compact, with increasing temperatures, and we show that this is the case through a series of biophysical measurements.
Calculating Free Energies Using Average Force
Darve, Eric; Pohorille, Andrew; DeVincenzi, Donald L. (Technical Monitor)
2001-01-01
A new, general formula that connects the derivatives of the free energy along the selected, generalized coordinates of the system with the instantaneous force acting on these coordinates is derived. The instantaneous force is defined as the force acting on the coordinate of interest so that when it is subtracted from the equations of motion the acceleration along this coordinate is zero. The formula applies to simulations in which the selected coordinates are either unconstrained or constrained to fixed values. It is shown that in the latter case the formula reduces to the expression previously derived by den Otter and Briels. If simulations are carried out without constraining the coordinates of interest, the formula leads to a new method for calculating the free energy changes along these coordinates. This method is tested in two examples - rotation around the C-C bond of 1,2-dichloroethane immersed in water and transfer of fluoromethane across the water-hexane interface. The calculated free energies are compared with those obtained by two commonly used methods. One of them relies on determining the probability density function of finding the system at different values of the selected coordinate and the other requires calculating the average force at discrete locations along this coordinate in a series of constrained simulations. The free energies calculated by these three methods are in excellent agreement. The relative advantages of each method are discussed.
Analysis of the Bogoliubov free energy functional
Reuvers, Robin
In this thesis, we analyse a variational reformulation of the Bogoliubov approximation that is used to describe weakly-interacting translationally-invariant Bose gases. For the resulting model, the `Bogoliubov free energy functional', we demonstrate existence of minimizers as well as the presence...
The new view of hydrophobic free energy.
Baldwin, Robert L
2013-04-17
In the new view, hydrophobic free energy is measured by the work of solute transfer of hydrocarbon gases from vapor to aqueous solution. Reasons are given for believing that older values, measured by solute transfer from a reference solvent to water, are not quantitatively correct. The hydrophobic free energy from gas-liquid transfer is the sum of two opposing quantities, the cavity work (unfavorable) and the solute-solvent interaction energy (favorable). Values of the interaction energy have been found by simulation for linear alkanes and are used here to find the cavity work, which scales linearly with molar volume, not accessible surface area. The hydrophobic free energy is the dominant factor driving folding as judged by the heat capacity change for transfer, which agrees with values for solvating hydrocarbon gases. There is an apparent conflict with earlier values of hydrophobic free energy from studies of large-to-small mutations and an explanation is given. Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.
Ferromagnetic bulk glassy alloys
Inoue, Akihisa; Makino, Akihiro; Mizushima, Takao
2000-01-01
This paper deals with the review on the formation, thermal stability and magnetic properties of the Fe-based bulk glassy alloys in as-cast bulk and melt-spun ribbon forms. A large supercooled liquid region over 50 K before crystallization was obtained in Fe-(Al, Ga)-(P, C, B, Si), Fe-(Cr, Mo, Nb)-(Al, Ga)-(P, C, B) and (Fe, Co, Ni)-Zr-M-B (M=Ti, Hf, V, Nb, Ta, Cr, Mo and W) systems and bulk glassy alloys were produced in a thickness range below 2 mm for the Fe-(Al, Ga)-(P, C, B, Si) system and 6 mm for the Fe-Co-(Zr, Nb, Ta)-(Mo, W)-B system by copper-mold casting. The ring-shaped glassy Fe-(Al, Ga)-(P, C, B, Si) alloys exhibit much better soft magnetic properties as compared with the ring-shaped alloy made from the melt-spun ribbon because of the formation of the unique domain structure. The good combination of high glass-forming ability and good soft magnetic properties indicates the possibility of future development as a new bulk glassy magnetic material
Free energy of formation of lanthanum nickelate
Sreedharan, O.M.; Chandrasekharaiah, M.S.; Karkhanavala, M.D.
1976-01-01
The ΔG 0 /sub f/ of La 2 NiO 4 (s) was determined from the measured emf in the range 1123 to 1373 0 K of the solid oxide electrolyte galvanic cell. The emf data were fitted to a linear equation by the method of least squares. From these data, the standard free-energy change, ΔG 0 , for the reaction NiO(s) + La 2 O 3 (s) = La 2 NiO 4 (s) was calculated. Combining these emf data with the best available free energy of formation data for NiO(s) and La 2 O 3 (s), the following expression for ΔG 0 /sub f/(La 2 NiO 4 (s)) was derived as ΔG 0 /sub f/(La 2 NiO 4 (s)/kJ mole -1 = -2057.0 + 322.8 x 10 -3 T +- 17.30
The Bogoliubov free energy functional II
Napiórkowski, Marcin; Reuvers, Robin; Solovej, Jan Philip
2018-01-01
We analyse the canonical Bogoliubov free energy functional at low temperatures in the dilute limit. We prove existence of a first order phase transition and, in the limit $a_0\\to a$, we determine the critical temperature to be $T_{\\rm{c}}=T_{\\rm{fc}}(1+1.49(\\rho^{1/3}a))$ to leading order. Here, $T......_{\\rm{fc}}$ is the critical temperature of the free Bose gas, $\\rho$ is the density of the gas, $a$ is the scattering length of the pair-interaction potential $V$, and $a_0=(8\\pi)^{-1}\\widehat{V}(0)$ its first order approximation. We also prove asymptotic expansions for the free energy. In particular, we recover the Lee...
Holographic free energy and thermodynamic geometry
Ghorai, Debabrata; Gangopadhyay, Sunandan
2016-12-01
We obtain the free energy and thermodynamic geometry of holographic superconductors in 2+1 dimensions. The gravitational theory in the bulk dual to this 2+1-dimensional strongly coupled theory lives in the 3+1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method.
Holographic free energy and thermodynamic geometry
Ghorai, Debabrata; Gangopadhyay, Sunandan
2016-01-01
We obtain the free energy and thermodynamic geometry of holographic superconductors in 2 + 1 dimensions. The gravitational theory in the bulk dual to this 2 + 1-dimensional strongly coupled theory lives in the 3 + 1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method. (orig.)
Holographic free energy and thermodynamic geometry
Ghorai, Debabrata [S.N. Bose National Centre for Basic Sciences, Kolkata (India); Gangopadhyay, Sunandan [Indian Institute of Science Education and Research, Kolkata, Nadia (India); West Bengal State University, Department of Physics, Barasat (India); Inter University Centre for Astronomy and Astrophysics, Pune (India)
2016-12-15
We obtain the free energy and thermodynamic geometry of holographic superconductors in 2 + 1 dimensions. The gravitational theory in the bulk dual to this 2 + 1-dimensional strongly coupled theory lives in the 3 + 1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method. (orig.)
Exploring the free energy surfaces of clusters using reconnaissance metadynamics
Tribello, Gareth A.; Cuny, Jérôme; Eshet, Hagai; Parrinello, Michele
2011-09-01
A new approach is proposed for exploring the low-energy structures of small to medium-sized aggregates of atoms and molecules. This approach uses the recently proposed reconnaissance metadynamics method [G. A. Tribello, M. Ceriotti, and M. Parrinello. Proc. Natl. Acad. Sci. U.S.A. 107(41), 17509 (2010), 10.1073/pnas.1011511107] in tandem with collective variables that describe the average structure of the coordination sphere around the atoms/molecules. We demonstrate this method on both Lennard-Jones and water clusters and show how it is able to quickly find the global minimum in the potential energy surface, while exploring the finite temperature free energy surface.
Free energy calculations, enhanced by a Gaussian ansatz, for the "chemical work" distribution.
Boulougouris, Georgios C
2014-05-15
The evaluation of the free energy is essential in molecular simulation because it is intimately related with the existence of multiphase equilibrium. Recently, it was demonstrated that it is possible to evaluate the Helmholtz free energy using a single statistical ensemble along an entire isotherm by accounting for the "chemical work" of transforming each molecule, from an interacting one, to an ideal gas. In this work, we show that it is possible to perform such a free energy perturbation over a liquid vapor phase transition. Furthermore, we investigate the link between a general free energy perturbation scheme and the novel nonequilibrium theories of Crook's and Jarzinsky. We find that for finite systems away from the thermodynamic limit the second law of thermodynamics will always be an inequality for isothermal free energy perturbations, resulting always to a dissipated work that may tend to zero only in the thermodynamic limit. The work, the heat, and the entropy produced during a thermodynamic free energy perturbation can be viewed in the context of the Crooks and Jarzinsky formalism, revealing that for a given value of the ensemble average of the "irreversible" work, the minimum entropy production corresponded to a Gaussian distribution for the histogram of the work. We propose the evaluation of the free energy difference in any free energy perturbation based scheme on the average irreversible "chemical work" minus the dissipated work that can be calculated from the variance of the distribution of the logarithm of the work histogram, within the Gaussian approximation. As a consequence, using the Gaussian ansatz for the distribution of the "chemical work," accurate estimates for the chemical potential and the free energy of the system can be performed using much shorter simulations and avoiding the necessity of sampling the computational costly tails of the "chemical work." For a more general free energy perturbation scheme that the Gaussian ansatz may not be
Exploration, Novelty, Surprise and Free Energy Minimisation
Philipp eSchwartenbeck
2013-10-01
Full Text Available This paper reviews recent developments under the free energy principle that introduce a normative perspective on classical economic (utilitarian decision-making based on (active Bayesian inference. It has been suggested that the free energy principle precludes novelty and complexity, because it assumes that biological systems – like ourselves - try to minimise the long-term average of surprise to maintain their homeostasis. However, recent formulations show that minimising surprise leads naturally to concepts such as exploration and novelty bonuses. In this approach, agents infer a policy that minimises surprise by minimising the difference (or relative entropy between likely and desired outcomes, which involves both pursuing the goal-state that has the highest expected utility (often termed ‘exploitation’ and visiting a number of different goal-states (‘exploration’. Crucially, the opportunity to visit new states increases the value of the current state. Casting decision-making problems within a variational framework, therefore, predicts that our behaviour is governed by both the entropy and expected utility of future states. This dissolves any dialectic between minimising surprise and exploration or novelty seeking.
Sakane, Shinichi; Yezdimer, Eric M.; Liu, Wenbin; Barriocanal, Jose A.; Doren, Douglas J.; Wood, Robert H.
2000-01-01
The ab initio/classical free energy perturbation (ABC-FEP) method proposed previously by Wood et al. [J. Chem. Phys. 110, 1329 (1999)] uses classical simulations to calculate solvation free energies within an empirical potential model, then applies free energy perturbation theory to determine the effect of changing the empirical solute-solvent interactions to corresponding interactions calculated from ab initio methods. This approach allows accurate calculation of solvation free energies using an atomistic description of the solvent and solute, with interactions calculated from first principles. Results can be obtained at a feasible computational cost without making use of approximations such as a continuum solvent or an empirical cavity formation energy. As such, the method can be used far from ambient conditions, where the empirical parameters needed for approximate theories of solvation may not be available. The sources of error in the ABC-FEP method are the approximations in the ab initio method, the finite sample of configurations, and the classical solvent model. This article explores the accuracy of various approximations used in the ABC-FEP method by comparing to the experimentally well-known free energy of hydration of water at two state points (ambient conditions, and 973.15 K and 600 kg/m3). The TIP4P-FQ model [J. Chem. Phys. 101, 6141 (1994)] is found to be a reliable solvent model for use with this method, even at supercritical conditions. Results depend strongly on the ab initio method used: a gradient-corrected density functional theory is not adequate, but a localized MP2 method yields excellent agreement with experiment. Computational costs are reduced by using a cluster approximation, in which ab initio pair interaction energies are calculated between the solute and up to 60 solvent molecules, while multi-body interactions are calculated with only a small cluster (5 to 12 solvent molecules). Sampling errors for the ab initio contribution to
On the number of free energy extremums of a solid solution with two long-range order parameters
Dateshidze, N.A.; Ratishvili, I.G.
1977-01-01
The free energy of ordering f.c.c. lattice solid solution is investigated. The ordering is regarded as homogeneous in the whole bulk of the crystal (i.e. resistant towards formation of antiphase domains). It is described by one of the appropriate distribution functions which contains two long-range order parameters. The calculations have revealed the extrema of the free energy function, and their shape and behaviour upon variations of temperature are analyzed. It is shown that under certain circumstances the system can display more than one minimum of free energy within the ordered phase
The Magnetic Free Energy in Active Regions
Metcalf, Thomas R.; Mickey, Donald L.; LaBonte, Barry J.
2001-01-01
The magnetic field permeating the solar atmosphere governs much of the structure, morphology, brightness, and dynamics observed on the Sun. The magnetic field, especially in active regions, is thought to provide the power for energetic events in the solar corona, such as solar flares and Coronal Mass Ejections (CME) and is believed to energize the hot coronal plasma seen in extreme ultraviolet or X-rays. The question remains what specific aspect of the magnetic flux governs the observed variability. To directly understand the role of the magnetic field in energizing the solar corona, it is necessary to measure the free magnetic energy available in active regions. The grant now expiring has demonstrated a new and valuable technique for observing the magnetic free energy in active regions as a function of time.
Generalized formulation of free energy and application to photosynthesis
Zhang, Hwe Ik; Choi, M. Y.
2018-03-01
The origin of free energy on the earth is solar radiation. However, the amount of free energy it contains has seldom been investigated, because the free energy concept was believed to be inappropriate for a system of photons. Instead, the origin of free energy has been sought in the process of photosynthesis, imposing a limit of conversion given by the Carnot efficiency. Here we present a general formulation, capable of not only assessing accurately the available amount of free energy in the photon gas but also explaining the primary photosynthetic process more succinctly. In this formulation, the problem of "photosynthetic conversion of the internal energy of photons into the free energy of chlorophyll" is replaced by simple "free energy transduction" between the photons and chlorophyll. An analytic expression for the photosynthetic efficiency is derived and shown to deviate from the Carnot efficiency. Some predictions verifiable possibly by observation are also suggested.
Calculating Free Energies Using Scaled-Force Molecular Dynamics Algorithm
Darve, Eric; Wilson, Micahel A.; Pohorille, Andrew
2000-01-01
One common objective of molecular simulations in chemistry and biology is to calculate the free energy difference between different states of the system of interest. Examples of problems that have such an objective are calculations of receptor-ligand or protein-drug interactions, associations of molecules in response to hydrophobic, and electrostatic interactions or partition of molecules between immiscible liquids. Another common objective is to describe evolution of the system towards a low energy (possibly the global minimum energy), 'native' state. Perhaps the best example of such a problem is folding of proteins or short RNA molecules. Both types of problems share the same difficulty. Often, different states of the system are separated by high energy barriers, which implies that transitions between these states are rare events. This, in turn, can greatly impede exploration of phase space. In some instances this can lead to 'quasi non-ergodicity', whereby a part of phase space is inaccessible on timescales of the simulation. A host of strategies has been developed to improve efficiency of sampling the phase space. For example, some Monte Carlo techniques involve large steps which move the system between low-energy regions in phase space without the need for sampling the configurations corresponding to energy barriers (J-walking). Most strategies, however, rely on modifying probabilities of sampling low and high-energy regions in phase space such that transitions between states of interest are encouraged. Perhaps the simplest implementation of this strategy is to increase the temperature of the system. This approach was successfully used to identify denaturation pathways in several proteins, but it is clearly not applicable to protein folding. It is also not a successful method for determining free energy differences. Finally, the approach is likely to fail for systems with co-existing phases, such as water-membrane systems, because it may lead to spontaneous
Temperature dependence of grain boundary free energy and elastic constants
Foiles, Stephen M.
2010-01-01
This work explores the suggestion that the temperature dependence of the grain boundary free energy can be estimated from the temperature dependence of the elastic constants. The temperature-dependent elastic constants and free energy of a symmetric Σ79 tilt boundary are computed for an embedded atom method model of Ni. The grain boundary free energy scales with the product of the shear modulus times the lattice constant for temperatures up to about 0.75 the melting temperature.
A Free Energy Model for Hysteresis Ferroelectric Materials
Smith, Ralph C; Ounaies, Zoubeida; Seelecke, Stefan; Smith, Joshua
2003-01-01
This paper provides a theory for quantifying the hysteresis and constitutive nonlinearities inherent to piezoceramic compounds through a combination of free energy analysis and stochastic homogenization techniques...
Free-Energy Calculations. A Mathematical Perspective
Pohorille, Andrzej
2015-01-01
conductance, defined as the ratio of ionic current through the channel to applied voltage, can be calculated in MD simulations by way of applying an external electric field to the system and counting the number of ions that traverse the channel per unit time. If the current is small, a voltage significantly higher than the experimental one needs to be applied to collect sufficient statistics of ion crossing events. Then, the calculated conductance has to be extrapolated to the experimental voltage using procedures of unknown accuracy. Instead, we propose an alternative approach that applies if ion transport through channels can be described with sufficient accuracy by the one-dimensional diffusion equation in the potential given by the free energy profile and applied voltage. Then, it is possible to test the assumptions of the equation, recover the full voltage/current dependence, determine the reliability of the calculated conductance and reconstruct the underlying (equilibrium) free energy profile, all from MD simulations at a single voltage. We will present the underlying theory, model calculations that test this theory and simulations on ion conductance through a channel that has been extensively studied experimentally. To our knowledge this is the first case in which the complete, experimentally measured dependence of the current on applied voltage has been reconstructed from MD simulations.
From quantum chemical formation free energies to evaporation rates
I. K. Ortega
2012-01-01
Full Text Available Atmospheric new particle formation is an important source of atmospheric aerosols. Large efforts have been made during the past few years to identify which molecules are behind this phenomenon, but the actual birth mechanism of the particles is not yet well known. Quantum chemical calculations have proven to be a powerful tool to gain new insights into the very first steps of particle formation. In the present study we use formation free energies calculated by quantum chemical methods to estimate the evaporation rates of species from sulfuric acid clusters containing ammonia or dimethylamine. We have found that dimethylamine forms much more stable clusters with sulphuric acid than ammonia does. On the other hand, the existence of a very deep local minimum for clusters with two sulfuric acid molecules and two dimethylamine molecules hinders their growth to larger clusters. These results indicate that other compounds may be needed to make clusters grow to larger sizes (containing more than three sulfuric acid molecules.
Mapping the conformational free energy of aspartic acid in the gas phase and in aqueous solution.
Comitani, Federico; Rossi, Kevin; Ceriotti, Michele; Sanz, M Eugenia; Molteni, Carla
2017-04-14
The conformational free energy landscape of aspartic acid, a proteogenic amino acid involved in a wide variety of biological functions, was investigated as an example of the complexity that multiple rotatable bonds produce even in relatively simple molecules. To efficiently explore such a landscape, this molecule was studied in the neutral and zwitterionic forms, in the gas phase and in water solution, by means of molecular dynamics and the enhanced sampling method metadynamics with classical force-fields. Multi-dimensional free energy landscapes were reduced to bi-dimensional maps through the non-linear dimensionality reduction algorithm sketch-map to identify the energetically stable conformers and their interconnection paths. Quantum chemical calculations were then performed on the minimum free energy structures. Our procedure returned the low energy conformations observed experimentally in the gas phase with rotational spectroscopy [M. E. Sanz et al., Phys. Chem. Chem. Phys. 12, 3573 (2010)]. Moreover, it provided information on higher energy conformers not accessible to experiments and on the conformers in water. The comparison between different force-fields and quantum chemical data highlighted the importance of the underlying potential energy surface to accurately capture energy rankings. The combination of force-field based metadynamics, sketch-map analysis, and quantum chemical calculations was able to produce an exhaustive conformational exploration in a range of significant free energies that complements the experimental data. Similar protocols can be applied to larger peptides with complex conformational landscapes and would greatly benefit from the next generation of accurate force-fields.
Mapping the conformational free energy of aspartic acid in the gas phase and in aqueous solution
Comitani, Federico; Rossi, Kevin; Ceriotti, Michele; Sanz, M. Eugenia; Molteni, Carla
2017-04-01
The conformational free energy landscape of aspartic acid, a proteogenic amino acid involved in a wide variety of biological functions, was investigated as an example of the complexity that multiple rotatable bonds produce even in relatively simple molecules. To efficiently explore such a landscape, this molecule was studied in the neutral and zwitterionic forms, in the gas phase and in water solution, by means of molecular dynamics and the enhanced sampling method metadynamics with classical force-fields. Multi-dimensional free energy landscapes were reduced to bi-dimensional maps through the non-linear dimensionality reduction algorithm sketch-map to identify the energetically stable conformers and their interconnection paths. Quantum chemical calculations were then performed on the minimum free energy structures. Our procedure returned the low energy conformations observed experimentally in the gas phase with rotational spectroscopy [M. E. Sanz et al., Phys. Chem. Chem. Phys. 12, 3573 (2010)]. Moreover, it provided information on higher energy conformers not accessible to experiments and on the conformers in water. The comparison between different force-fields and quantum chemical data highlighted the importance of the underlying potential energy surface to accurately capture energy rankings. The combination of force-field based metadynamics, sketch-map analysis, and quantum chemical calculations was able to produce an exhaustive conformational exploration in a range of significant free energies that complements the experimental data. Similar protocols can be applied to larger peptides with complex conformational landscapes and would greatly benefit from the next generation of accurate force-fields.
Free-energy coarse-grained potential for C60
Edmunds, D. M.; Tangney, P.; Vvedensky, D. D.; Foulkes, W. M. C.
2015-01-01
We propose a new deformable free energy method for generating a free-energy coarse-graining potential for C 60 . Potentials generated from this approach exhibit a strong temperature dependence and produce excellent agreement with benchmark fully atomistic molecular dynamics simulations. Parameter sets for analytical fits to this potential are provided at four different temperatures
A Short Essay on the Uses of Free Energy
Koutandos, Spyridon
2013-01-01
In this article we examine cases of more classical and less classical nature compared to results found by quantum mechanics and attribute a form of Free Energy discontinuity for each case within a boundary layer. The concept of a boundary layer is broadened as to include areas of first or second variations of the Gibbs free energy. It is…
Cosmological constant versus free energy for heterotic strings
Alvarez, E.; Osorio, M.A.R.
1988-01-01
A detailed analysis is made of the modular-invariant formulation of the free energy of heterotic strings. Several instances are pointed out in which a duality formula can be obtained, and its physical implications are discussed. The interplay between the free energy of a given heterotic string and the cosmological constant of the toroidal compactification of another heterotic string is emphasized. (orig.)
Calculation of molecular free energies in classical potentials
Farhi, Asaf; Singh, Bipin
2016-01-01
Free energies of molecules can be calculated by quantum chemistry computations or by normal mode classical calculations. However, the first can be computationally impractical for large molecules and the second is based on the assumption of harmonic dynamics. We present a novel, accurate and complete calculation of molecular free energies in standard classical potentials. In this method we transform the molecule by relaxing potential terms which depend on the coordinates of a group of atoms in that molecule and calculate the free energy difference associated with the transformation. Then, since the transformed molecule can be treated as non-interacting systems, the free energy associated with these atoms is analytically or numerically calculated. This two-step calculation can be applied to calculate free energies of molecules or free energy difference between (possibly large) molecules in a general environment. We demonstrate the method in free energy calculations for methanethiol and butane molecules in vacuum and solvent. We suggest the potential application of free energy calculation of chemical reactions in classical molecular simulations. (paper)
Free energy from molecular dynamics with multiple constraints
den Otter, Wouter K.; Briels, Willem J.
2000-01-01
In molecular dynamics simulations of reacting systems, the key step to determining the equilibrium constant and the reaction rate is the calculation of the free energy as a function of the reaction coordinate. Intuitively the derivative of the free energy is equal to the average force needed to
Calculation of the surface free energy of fcc copper nanoparticles
Jia Ming; Lai Yanqing; Tian Zhongliang; Liu Yexiang
2009-01-01
Using molecular dynamics simulations with the modified analytic embedded-atom method we calculate the Gibbs free energy and surface free energy for fcc Cu bulk, and further obtain the Gibbs free energy of nanoparticles. Based on the Gibbs free energy of nanoparticles, we have investigated the heat capacity of copper nanoparticles. Calculation results indicate that the Gibbs free energy and the heat capacity of nanoparticles can be divided into two parts: bulk quantity and surface quantity. The molar heat capacity of the bulk sample is lower compared with the molar heat capacity of nanoparticles, and this difference increases with the decrease in the particle size. It is also observed that the size effect on the thermodynamic properties of Cu nanoparticles is not really significant until the particle is less than about 20 nm. It is the surface atoms that decide the size effect on the thermodynamic properties of nanoparticles
Diabat Interpolation for Polymorph Free-Energy Differences.
Kamat, Kartik; Peters, Baron
2017-02-02
Existing methods to compute free-energy differences between polymorphs use harmonic approximations, advanced non-Boltzmann bias sampling techniques, and/or multistage free-energy perturbations. This work demonstrates how Bennett's diabat interpolation method ( J. Comput. Phys. 1976, 22, 245 ) can be combined with energy gaps from lattice-switch Monte Carlo techniques ( Phys. Rev. E 2000, 61, 906 ) to swiftly estimate polymorph free-energy differences. The new method requires only two unbiased molecular dynamics simulations, one for each polymorph. To illustrate the new method, we compute the free-energy difference between face-centered cubic and body-centered cubic polymorphs for a Gaussian core solid. We discuss the justification for parabolic models of the free-energy diabats and similarities to methods that have been used in studies of electron transfer.
Free energy profiles from single-molecule pulling experiments.
Hummer, Gerhard; Szabo, Attila
2010-12-14
Nonequilibrium pulling experiments provide detailed information about the thermodynamic and kinetic properties of molecules. We show that unperturbed free energy profiles as a function of molecular extension can be obtained rigorously from such experiments without using work-weighted position histograms. An inverse Weierstrass transform is used to relate the system free energy obtained from the Jarzynski equality directly to the underlying molecular free energy surface. An accurate approximation for the free energy surface is obtained by using the method of steepest descent to evaluate the inverse transform. The formalism is applied to simulated data obtained from a kinetic model of RNA folding, in which the dynamics consists of jumping between linker-dominated folded and unfolded free energy surfaces.
Guidelines for the analysis of free energy calculations.
Klimovich, Pavel V; Shirts, Michael R; Mobley, David L
2015-05-01
Free energy calculations based on molecular dynamics simulations show considerable promise for applications ranging from drug discovery to prediction of physical properties and structure-function studies. But these calculations are still difficult and tedious to analyze, and best practices for analysis are not well defined or propagated. Essentially, each group analyzing these calculations needs to decide how to conduct the analysis and, usually, develop its own analysis tools. Here, we review and recommend best practices for analysis yielding reliable free energies from molecular simulations. Additionally, we provide a Python tool, alchemical-analysis.py, freely available on GitHub as part of the pymbar package (located at http://github.com/choderalab/pymbar), that implements the analysis practices reviewed here for several reference simulation packages, which can be adapted to handle data from other packages. Both this review and the tool covers analysis of alchemical calculations generally, including free energy estimates via both thermodynamic integration and free energy perturbation-based estimators. Our Python tool also handles output from multiple types of free energy calculations, including expanded ensemble and Hamiltonian replica exchange, as well as standard fixed ensemble calculations. We also survey a range of statistical and graphical ways of assessing the quality of the data and free energy estimates, and provide prototypes of these in our tool. We hope this tool and discussion will serve as a foundation for more standardization of and agreement on best practices for analysis of free energy calculations.
Cugliandolo, Leticia F.
2003-09-01
These lecture notes can be read in two ways. The first two Sections contain a review of the phenomenology of several physical systems with slow nonequilibrium dynamics. In the Conclusions we summarize the scenario for this temporal evolution derived from the solution to some solvable models (p spin and the like) that are intimately connected to the mode coupling approach (and similar ones) to super-cooled liquids. At the end we list a number of open problems of great relevance in this context. These Sections can be read independently of the body of the paper where we present some of the basic analytic techniques used to study the out of equilibrium dynamics of classical and quantum models with and without disorder. We start the technical part by briefly discussing the role played by the environment and by introducing and comparing its representation in the equilibrium and dynamic treatment of classical and quantum systems. We next explain the role played by explicit quenched disorder in both approaches. Later on we focus on analytical techniques; we expand on the dynamic functional methods, and the diagrammatic expansions and resummations used to derive macroscopic equations from the microscopic dynamics. We show why the macroscopic dynamic equations for disordered models and those resulting from self-consistent approximations to non-disordered ones coincide. We review some generic properties of dynamic systems evolving out of equilibrium like the modifications of the fluctuation-dissipation theorem, generic scaling forms of the correlation functions, etc. Finally we solve a family of mean-field models. The connection between the dynamic treatment and the analysis of the free-energy landscape of these models is also presented. We use pedagogical examples all along these lectures to illustrate the properties and results. (author)
Bespoke Bias for Obtaining Free Energy Differences within Variationally Enhanced Sampling.
McCarty, James; Valsson, Omar; Parrinello, Michele
2016-05-10
Obtaining efficient sampling of multiple metastable states through molecular dynamics and hence determining free energy differences is central for understanding many important phenomena. Here we present a new biasing strategy, which employs the recent variationally enhanced sampling approach (Valsson and Parrinello Phys. Rev. Lett. 2014, 113, 090601). The bias is constructed from an intuitive model of the local free energy surface describing fluctuations around metastable minima and depends on only a few parameters which are determined variationally such that efficient sampling between states is obtained. The bias constructed in this manner largely reduces the need of finding a set of collective variables that completely spans the conformational space of interest, as they only need to be a locally valid descriptor of the system about its local minimum. We introduce the method and demonstrate its power on two representative examples.
Free energy evaluation in polymer translocation via Jarzynski equality
Mondaini, Felipe, E-mail: fmondaini@if.ufrj.br [Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Petrópolis, 25.620-003, RJ (Brazil); Moriconi, L., E-mail: moriconi@if.ufrj.br [Instituto de Física, Universidade Federal do Rio de Janeiro, C.P. 68528, 21945-970, Rio de Janeiro, RJ (Brazil)
2014-05-01
We perform, with the help of cloud computing resources, extensive Langevin simulations, which provide free energy estimates for unbiased three-dimensional polymer translocation. We employ the Jarzynski equality in its rigorous setting, to compute the variation of the free energy in single monomer translocation events. In our three-dimensional Langevin simulations, the excluded-volume and van der Waals interactions between beads (monomers and membrane atoms) are modeled through a repulsive Lennard-Jones (LJ) potential and consecutive monomers are subject to the Finite-Extension Nonlinear Elastic (FENE) potential. Analysing data for polymers with different lengths, the free energy profile is noted to have interesting finite-size scaling properties.
Free energy evaluation in polymer translocation via Jarzynski equality
Mondaini, Felipe; Moriconi, L.
2014-01-01
We perform, with the help of cloud computing resources, extensive Langevin simulations, which provide free energy estimates for unbiased three-dimensional polymer translocation. We employ the Jarzynski equality in its rigorous setting, to compute the variation of the free energy in single monomer translocation events. In our three-dimensional Langevin simulations, the excluded-volume and van der Waals interactions between beads (monomers and membrane atoms) are modeled through a repulsive Lennard-Jones (LJ) potential and consecutive monomers are subject to the Finite-Extension Nonlinear Elastic (FENE) potential. Analysing data for polymers with different lengths, the free energy profile is noted to have interesting finite-size scaling properties.
Surface free energy for systems with integrable boundary conditions
Goehmann, Frank; Bortz, Michael; Frahm, Holger
2005-01-01
The surface free energy is the difference between the free energies for a system with open boundary conditions and the same system with periodic boundary conditions. We use the quantum transfer matrix formalism to express the surface free energy in the thermodynamic limit of systems with integrable boundary conditions as a matrix element of certain projection operators. Specializing to the XXZ spin-1/2 chain we introduce a novel 'finite temperature boundary operator' which characterizes the thermodynamical properties of surfaces related to integrable boundary conditions
Information-to-free-energy conversion: Utilizing thermal fluctuations.
Toyabe, Shoichi; Muneyuki, Eiro
2013-01-01
Maxwell's demon is a hypothetical creature that can convert information to free energy. A debate that has lasted for more than 100 years has revealed that the demon's operation does not contradict the laws of thermodynamics; hence, the demon can be realized physically. We briefly review the first experimental demonstration of Maxwell's demon of Szilard's engine type that converts information to free energy. We pump heat from an isothermal environment by using the information about the thermal fluctuations of a Brownian particle and increase the particle's free energy.
Regeneralized London free energy for high-Tc vortex lattices
M. A. Shahzamanian
2006-09-01
Full Text Available The London free-energy is regeneralized by the Ginsburg-Landau free-energy density in the presence of both d and s order parameters. We have shown that the strength of the s-d coupling, makes an important rule to determine the form of the lattice vortex. Appearance of the ratios of the coherence length to penetration depth in the higher order corrections of the free-energy density will truncate these corrections for even large values of .
Implicit ligand theory for relative binding free energies
Nguyen, Trung Hai; Minh, David D. L.
2018-03-01
Implicit ligand theory enables noncovalent binding free energies to be calculated based on an exponential average of the binding potential of mean force (BPMF)—the binding free energy between a flexible ligand and rigid receptor—over a precomputed ensemble of receptor configurations. In the original formalism, receptor configurations were drawn from or reweighted to the apo ensemble. Here we show that BPMFs averaged over a holo ensemble yield binding free energies relative to the reference ligand that specifies the ensemble. When using receptor snapshots from an alchemical simulation with a single ligand, the new statistical estimator outperforms the original.
Esque, Jeremy; Cecchini, Marco
2015-04-23
The calculation of the free energy of conformation is key to understanding the function of biomolecules and has attracted significant interest in recent years. Here, we present an improvement of the confinement method that was designed for use in the context of explicit solvent MD simulations. The development involves an additional step in which the solvation free energy of the harmonically restrained conformers is accurately determined by multistage free energy perturbation simulations. As a test-case application, the newly introduced confinement/solvation free energy (CSF) approach was used to compute differences in free energy between conformers of the alanine dipeptide in explicit water. The results are in excellent agreement with reference calculations based on both converged molecular dynamics and umbrella sampling. To illustrate the general applicability of the method, conformational equilibria of met-enkephalin (5 aa) and deca-alanine (10 aa) in solution were also analyzed. In both cases, smoothly converged free-energy results were obtained in agreement with equilibrium sampling or literature calculations. These results demonstrate that the CSF method may provide conformational free-energy differences of biomolecules with small statistical errors (below 0.5 kcal/mol) and at a moderate computational cost even with a full representation of the solvent.
Free energy distribution function of a random Ising ferromagnet
Dotsenko, Victor; Klumov, Boris
2012-01-01
We study the free energy distribution function of a weakly disordered Ising ferromagnet in terms of the D-dimensional random temperature Ginzburg–Landau Hamiltonian. It is shown that besides the usual Gaussian 'body' this distribution function exhibits non-Gaussian tails both in the paramagnetic and in the ferromagnetic phases. Explicit asymptotic expressions for these tails are derived. It is demonstrated that the tails are strongly asymmetric: the left tail (for large negative values of the free energy) is much slower than the right one (for large positive values of the free energy). It is argued that at the critical point the free energy of the random Ising ferromagnet in dimensions D < 4 is described by a non-trivial universal distribution function which is non-self-averaging
Probing Free-Energy Surfaces with Differential Scanning Calorimetry
Sanchez-Ruiz, Jose M.
2011-05-01
Many aspects of protein folding can be understood in terms of projections of the highly dimensional energy landscape onto a few (or even only one) particularly relevant coordinates. These free-energy surfaces can be probed conveniently from experimental differential scanning calorimetry (DSC) thermograms, as DSC provides a direct relation with the protein partition function. Free-energy surfaces thus obtained are consistent with two fundamental scenarios predicted by the energy-landscape perspective: (a) well-defined macrostates separated by significant free-energy barriers, in some cases, and, in many other cases, (b) marginal or even vanishingly small barriers, which furthermore show a good correlation with kinetics for fast- and ultrafast-folding proteins. Overall, the potential of DSC to assess free-energy surfaces for a wide variety of proteins makes it possible to address fundamental issues, such as the molecular basis of the barrier modulations produced by natural selection in response to functional requirements or to ensure kinetic stability.
The free-energy principle: a unified brain theory?
Friston, Karl
2010-02-01
A free-energy principle has been proposed recently that accounts for action, perception and learning. This Review looks at some key brain theories in the biological (for example, neural Darwinism) and physical (for example, information theory and optimal control theory) sciences from the free-energy perspective. Crucially, one key theme runs through each of these theories - optimization. Furthermore, if we look closely at what is optimized, the same quantity keeps emerging, namely value (expected reward, expected utility) or its complement, surprise (prediction error, expected cost). This is the quantity that is optimized under the free-energy principle, which suggests that several global brain theories might be unified within a free-energy framework.
Free energy surfaces in the superconducting mixed state
Finnemore, D. K.; Fang, M. M.; Bansal, N. P.; Farrell, D. E.
1989-01-01
The free energy surface for Tl2Ba2Ca2Cu3O1O has been measured as a function of temperature and magnetic field to determine the fundamental thermodynamic properties of the mixed state. The change in free energy, G(H)-G(O), is found to be linear in temperature over a wide range indicating that the specific heat is independent of field.
Plotnikov, Nikolay V
2014-08-12
Proposed in this contribution is a protocol for calculating fine-physics (e.g., ab initio QM/MM) free-energy surfaces at a high level of accuracy locally (e.g., only at reactants and at the transition state for computing the activation barrier) from targeted fine-physics sampling and extensive exploratory coarse-physics sampling. The full free-energy surface is still computed but at a lower level of accuracy from coarse-physics sampling. The method is analytically derived in terms of the umbrella sampling and the free-energy perturbation methods which are combined with the thermodynamic cycle and the targeted sampling strategy of the paradynamics approach. The algorithm starts by computing low-accuracy fine-physics free-energy surfaces from the coarse-physics sampling in order to identify the reaction path and to select regions for targeted sampling. Thus, the algorithm does not rely on the coarse-physics minimum free-energy reaction path. Next, segments of high-accuracy free-energy surface are computed locally at selected regions from the targeted fine-physics sampling and are positioned relative to the coarse-physics free-energy shifts. The positioning is done by averaging the free-energy perturbations computed with multistep linear response approximation method. This method is analytically shown to provide results of the thermodynamic integration and the free-energy interpolation methods, while being extremely simple in implementation. Incorporating the metadynamics sampling to the algorithm is also briefly outlined. The application is demonstrated by calculating the B3LYP//6-31G*/MM free-energy barrier for an enzymatic reaction using a semiempirical PM6/MM reference potential. These modifications allow computing the activation free energies at a significantly reduced computational cost but at the same level of accuracy compared to computing full potential of mean force.
QM/MM free energy simulations: recent progress and challenges
Lu, Xiya; Fang, Dong; Ito, Shingo; Okamoto, Yuko; Ovchinnikov, Victor
2016-01-01
Due to the higher computational cost relative to pure molecular mechanical (MM) simulations, hybrid quantum mechanical/molecular mechanical (QM/MM) free energy simulations particularly require a careful consideration of balancing computational cost and accuracy. Here we review several recent developments in free energy methods most relevant to QM/MM simulations and discuss several topics motivated by these developments using simple but informative examples that involve processes in water. For chemical reactions, we highlight the value of invoking enhanced sampling technique (e.g., replica-exchange) in umbrella sampling calculations and the value of including collective environmental variables (e.g., hydration level) in metadynamics simulations; we also illustrate the sensitivity of string calculations, especially free energy along the path, to various parameters in the computation. Alchemical free energy simulations with a specific thermodynamic cycle are used to probe the effect of including the first solvation shell into the QM region when computing solvation free energies. For cases where high-level QM/MM potential functions are needed, we analyze two different approaches: the QM/MM-MFEP method of Yang and co-workers and perturbative correction to low-level QM/MM free energy results. For the examples analyzed here, both approaches seem productive although care needs to be exercised when analyzing the perturbative corrections. PMID:27563170
The free-energy cost of interaction between DNA loops.
Huang, Lifang; Liu, Peijiang; Yuan, Zhanjiang; Zhou, Tianshou; Yu, Jianshe
2017-10-03
From the viewpoint of thermodynamics, the formation of DNA loops and the interaction between them, which are all non-equilibrium processes, result in the change of free energy, affecting gene expression and further cell-to-cell variability as observed experimentally. However, how these processes dissipate free energy remains largely unclear. Here, by analyzing a mechanic model that maps three fundamental topologies of two interacting DNA loops into a 4-state model of gene transcription, we first show that a longer DNA loop needs more mean free energy consumption. Then, independent of the type of interacting two DNA loops (nested, side-by-side or alternating), the promotion between them always consumes less mean free energy whereas the suppression dissipates more mean free energy. More interestingly, we find that in contrast to the mechanism of direct looping between promoter and enhancer, the facilitated-tracking mechanism dissipates less mean free energy but enhances the mean mRNA expression, justifying the facilitated-tracking hypothesis, a long-standing debate in biology. Based on minimal energy principle, we thus speculate that organisms would utilize the mechanisms of loop-loop promotion and facilitated tracking to survive in complex environments. Our studies provide insights into the understanding of gene expression regulation mechanism from the view of energy consumption.
Learning free energy landscapes using artificial neural networks.
Sidky, Hythem; Whitmer, Jonathan K
2018-03-14
Existing adaptive bias techniques, which seek to estimate free energies and physical properties from molecular simulations, are limited by their reliance on fixed kernels or basis sets which hinder their ability to efficiently conform to varied free energy landscapes. Further, user-specified parameters are in general non-intuitive yet significantly affect the convergence rate and accuracy of the free energy estimate. Here we propose a novel method, wherein artificial neural networks (ANNs) are used to develop an adaptive biasing potential which learns free energy landscapes. We demonstrate that this method is capable of rapidly adapting to complex free energy landscapes and is not prone to boundary or oscillation problems. The method is made robust to hyperparameters and overfitting through Bayesian regularization which penalizes network weights and auto-regulates the number of effective parameters in the network. ANN sampling represents a promising innovative approach which can resolve complex free energy landscapes in less time than conventional approaches while requiring minimal user input.
Hierarchical Protein Free Energy Landscapes from Variationally Enhanced Sampling.
Shaffer, Patrick; Valsson, Omar; Parrinello, Michele
2016-12-13
In recent work, we demonstrated that it is possible to obtain approximate representations of high-dimensional free energy surfaces with variationally enhanced sampling ( Shaffer, P.; Valsson, O.; Parrinello, M. Proc. Natl. Acad. Sci. , 2016 , 113 , 17 ). The high-dimensional spaces considered in that work were the set of backbone dihedral angles of a small peptide, Chignolin, and the high-dimensional free energy surface was approximated as the sum of many two-dimensional terms plus an additional term which represents an initial estimate. In this paper, we build on that work and demonstrate that we can calculate high-dimensional free energy surfaces of very high accuracy by incorporating additional terms. The additional terms apply to a set of collective variables which are more coarse than the base set of collective variables. In this way, it is possible to build hierarchical free energy surfaces, which are composed of terms that act on different length scales. We test the accuracy of these free energy landscapes for the proteins Chignolin and Trp-cage by constructing simple coarse-grained models and comparing results from the coarse-grained model to results from atomistic simulations. The approach described in this paper is ideally suited for problems in which the free energy surface has important features on different length scales or in which there is some natural hierarchy.
Learning free energy landscapes using artificial neural networks
Sidky, Hythem; Whitmer, Jonathan K.
2018-03-01
Existing adaptive bias techniques, which seek to estimate free energies and physical properties from molecular simulations, are limited by their reliance on fixed kernels or basis sets which hinder their ability to efficiently conform to varied free energy landscapes. Further, user-specified parameters are in general non-intuitive yet significantly affect the convergence rate and accuracy of the free energy estimate. Here we propose a novel method, wherein artificial neural networks (ANNs) are used to develop an adaptive biasing potential which learns free energy landscapes. We demonstrate that this method is capable of rapidly adapting to complex free energy landscapes and is not prone to boundary or oscillation problems. The method is made robust to hyperparameters and overfitting through Bayesian regularization which penalizes network weights and auto-regulates the number of effective parameters in the network. ANN sampling represents a promising innovative approach which can resolve complex free energy landscapes in less time than conventional approaches while requiring minimal user input.
Accelerated weight histogram method for exploring free energy landscapes
Lindahl, V.; Lidmar, J.; Hess, B. [Department of Theoretical Physics and Swedish e-Science Research Center, KTH Royal Institute of Technology, 10691 Stockholm (Sweden)
2014-07-28
Calculating free energies is an important and notoriously difficult task for molecular simulations. The rapid increase in computational power has made it possible to probe increasingly complex systems, yet extracting accurate free energies from these simulations remains a major challenge. Fully exploring the free energy landscape of, say, a biological macromolecule typically requires sampling large conformational changes and slow transitions. Often, the only feasible way to study such a system is to simulate it using an enhanced sampling method. The accelerated weight histogram (AWH) method is a new, efficient extended ensemble sampling technique which adaptively biases the simulation to promote exploration of the free energy landscape. The AWH method uses a probability weight histogram which allows for efficient free energy updates and results in an easy discretization procedure. A major advantage of the method is its general formulation, making it a powerful platform for developing further extensions and analyzing its relation to already existing methods. Here, we demonstrate its efficiency and general applicability by calculating the potential of mean force along a reaction coordinate for both a single dimension and multiple dimensions. We make use of a non-uniform, free energy dependent target distribution in reaction coordinate space so that computational efforts are not wasted on physically irrelevant regions. We present numerical results for molecular dynamics simulations of lithium acetate in solution and chignolin, a 10-residue long peptide that folds into a β-hairpin. We further present practical guidelines for setting up and running an AWH simulation.
Deng, Nanjie; Zhang, Bin W; Levy, Ronald M
2015-06-09
The ability to accurately model solvent effects on free energy surfaces is important for understanding many biophysical processes including protein folding and misfolding, allosteric transitions, and protein–ligand binding. Although all-atom simulations in explicit solvent can provide an accurate model for biomolecules in solution, explicit solvent simulations are hampered by the slow equilibration on rugged landscapes containing multiple basins separated by barriers. In many cases, implicit solvent models can be used to significantly speed up the conformational sampling; however, implicit solvent simulations do not fully capture the effects of a molecular solvent, and this can lead to loss of accuracy in the estimated free energies. Here we introduce a new approach to compute free energy changes in which the molecular details of explicit solvent simulations are retained while also taking advantage of the speed of the implicit solvent simulations. In this approach, the slow equilibration in explicit solvent, due to the long waiting times before barrier crossing, is avoided by using a thermodynamic cycle which connects the free energy basins in implicit solvent and explicit solvent using a localized decoupling scheme. We test this method by computing conformational free energy differences and solvation free energies of the model system alanine dipeptide in water. The free energy changes between basins in explicit solvent calculated using fully explicit solvent paths agree with the corresponding free energy differences obtained using the implicit/explicit thermodynamic cycle to within 0.3 kcal/mol out of ∼3 kcal/mol at only ∼8% of the computational cost. We note that WHAM methods can be used to further improve the efficiency and accuracy of the implicit/explicit thermodynamic cycle.
Measuring excess free energies of self-assembled membrane structures.
Norizoe, Yuki; Daoulas, Kostas Ch; Müller, Marcus
2010-01-01
Using computer simulation of a solvent-free, coarse-grained model for amphiphilic membranes, we study the excess free energy of hourglass-shaped connections (i.e., stalks) between two apposed bilayer membranes. In order to calculate the free energy by simulation in the canonical ensemble, we reversibly transfer two apposed bilayers into a configuration with a stalk in three steps. First, we gradually replace the intermolecular interactions by an external, ordering field. The latter is chosen such that the structure of the non-interacting system in this field closely resembles the structure of the original, interacting system in the absence of the external field. The absence of structural changes along this path suggests that it is reversible; a fact which is confirmed by expanded-ensemble simulations. Second, the external, ordering field is changed as to transform the non-interacting system from the apposed bilayer structure to two-bilayers connected by a stalk. The final external field is chosen such that the structure of the non-interacting system resembles the structure of the stalk in the interacting system without a field. On the third branch of the transformation path, we reversibly replace the external, ordering field by non-bonded interactions. Using expanded-ensemble techniques, the free energy change along this reversible path can be obtained with an accuracy of 10(-3)k(B)T per molecule in the n VT-ensemble. Calculating the chemical potential, we obtain the free energy of a stalk in the grandcanonical ensemble, and employing semi-grandcanonical techniques, we calculate the change of the excess free energy upon altering the molecular architecture. This computational strategy can be applied to compute the free energy of self-assembled phases in lipid and copolymer systems, and the excess free energy of defects or interfaces.
Analysis of the free-energy surface of proteins from reversible folding simulations.
Lucy R Allen
2009-07-01
Full Text Available Computer generated trajectories can, in principle, reveal the folding pathways of a protein at atomic resolution and possibly suggest general and simple rules for predicting the folded structure of a given sequence. While such reversible folding trajectories can only be determined ab initio using all-atom transferable force-fields for a few small proteins, they can be determined for a large number of proteins using coarse-grained and structure-based force-fields, in which a known folded structure is by construction the absolute energy and free-energy minimum. Here we use a model of the fast folding helical lambda-repressor protein to generate trajectories in which native and non-native states are in equilibrium and transitions are accurately sampled. Yet, representation of the free-energy surface, which underlies the thermodynamic and dynamic properties of the protein model, from such a trajectory remains a challenge. Projections over one or a small number of arbitrarily chosen progress variables often hide the most important features of such surfaces. The results unequivocally show that an unprojected representation of the free-energy surface provides important and unbiased information and allows a simple and meaningful description of many-dimensional, heterogeneous trajectories, providing new insight into the possible mechanisms of fast-folding proteins.
Using the fast fourier transform in binding free energy calculations.
Nguyen, Trung Hai; Zhou, Huan-Xiang; Minh, David D L
2018-04-30
According to implicit ligand theory, the standard binding free energy is an exponential average of the binding potential of mean force (BPMF), an exponential average of the interaction energy between the unbound ligand ensemble and a rigid receptor. Here, we use the fast Fourier transform (FFT) to efficiently evaluate BPMFs by calculating interaction energies when rigid ligand configurations from the unbound ensemble are discretely translated across rigid receptor conformations. Results for standard binding free energies between T4 lysozyme and 141 small organic molecules are in good agreement with previous alchemical calculations based on (1) a flexible complex ( R≈0.9 for 24 systems) and (2) flexible ligand with multiple rigid receptor configurations ( R≈0.8 for 141 systems). While the FFT is routinely used for molecular docking, to our knowledge this is the first time that the algorithm has been used for rigorous binding free energy calculations. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Computation of Hemagglutinin Free Energy Difference by the Confinement Method
2017-01-01
Hemagglutinin (HA) mediates membrane fusion, a crucial step during influenza virus cell entry. How many HAs are needed for this process is still subject to debate. To aid in this discussion, the confinement free energy method was used to calculate the conformational free energy difference between the extended intermediate and postfusion state of HA. Special care was taken to comply with the general guidelines for free energy calculations, thereby obtaining convergence and demonstrating reliability of the results. The energy that one HA trimer contributes to fusion was found to be 34.2 ± 3.4kBT, similar to the known contributions from other fusion proteins. Although computationally expensive, the technique used is a promising tool for the further energetic characterization of fusion protein mechanisms. Knowledge of the energetic contributions per protein, and of conserved residues that are crucial for fusion, aids in the development of fusion inhibitors for antiviral drugs. PMID:29151344
Standard free energy of formation of iron iodide
Khandkar, A.; Tare, V. B.; Wagner, J. B., Jr.
1983-01-01
An experiment is reported where silver iodide is used to determine the standard free energy of formation of iron iodide. By using silver iodide as a solid electrolyte, a galvanic cell, Ag/AgI/Fe-FeI2, is formulated. The standard free energy of formation of AgI is known, and hence it is possible to estimate the standard free energy of formation of FeI2 by measuring the open-circuit emf of the above cell as a function of temperature. The free standard energy of formation of FeI2 determined by this method is -38784 + 24.165T cal/mol. It is estimated that the maximum error associated with this method is plus or minus 2500 cal/mol.
A Variational Approach to Enhanced Sampling and Free Energy Calculations
Parrinello, Michele
2015-03-01
The presence of kinetic bottlenecks severely hampers the ability of widely used sampling methods like molecular dynamics or Monte Carlo to explore complex free energy landscapes. One of the most popular methods for addressing this problem is umbrella sampling which is based on the addition of an external bias which helps overcoming the kinetic barriers. The bias potential is usually taken to be a function of a restricted number of collective variables. However constructing the bias is not simple, especially when the number of collective variables increases. Here we introduce a functional of the bias which, when minimized, allows us to recover the free energy. We demonstrate the usefulness and the flexibility of this approach on a number of examples which include the determination of a six dimensional free energy surface. Besides the practical advantages, the existence of such a variational principle allows us to look at the enhanced sampling problem from a rather convenient vantage point.
Variational Approach to Enhanced Sampling and Free Energy Calculations
Valsson, Omar; Parrinello, Michele
2014-08-01
The ability of widely used sampling methods, such as molecular dynamics or Monte Carlo simulations, to explore complex free energy landscapes is severely hampered by the presence of kinetic bottlenecks. A large number of solutions have been proposed to alleviate this problem. Many are based on the introduction of a bias potential which is a function of a small number of collective variables. However constructing such a bias is not simple. Here we introduce a functional of the bias potential and an associated variational principle. The bias that minimizes the functional relates in a simple way to the free energy surface. This variational principle can be turned into a practical, efficient, and flexible sampling method. A number of numerical examples are presented which include the determination of a three-dimensional free energy surface. We argue that, beside being numerically advantageous, our variational approach provides a convenient and novel standpoint for looking at the sampling problem.
Unsupervised Calculation of Free Energy Barriers in Large Crystalline Systems
Swinburne, Thomas D.; Marinica, Mihai-Cosmin
2018-03-01
The calculation of free energy differences for thermally activated mechanisms in the solid state are routinely hindered by the inability to define a set of collective variable functions that accurately describe the mechanism under study. Even when possible, the requirement of descriptors for each mechanism under study prevents implementation of free energy calculations in the growing range of automated material simulation schemes. We provide a solution, deriving a path-based, exact expression for free energy differences in the solid state which does not require a converged reaction pathway, collective variable functions, Gram matrix evaluations, or probability flux-based estimators. The generality and efficiency of our method is demonstrated on a complex transformation of C 15 interstitial defects in iron and double kink nucleation on a screw dislocation in tungsten, the latter system consisting of more than 120 000 atoms. Both cases exhibit significant anharmonicity under experimentally relevant temperatures.
Virtual substitution scan via single-step free energy perturbation.
Chiang, Ying-Chih; Wang, Yi
2016-02-05
With the rapid expansion of our computing power, molecular dynamics (MD) simulations ranging from hundreds of nanoseconds to microseconds or even milliseconds have become increasingly common. The majority of these long trajectories are obtained from plain (vanilla) MD simulations, where no enhanced sampling or free energy calculation method is employed. To promote the 'recycling' of these trajectories, we developed the Virtual Substitution Scan (VSS) toolkit as a plugin of the open-source visualization and analysis software VMD. Based on the single-step free energy perturbation (sFEP) method, VSS enables the user to post-process a vanilla MD trajectory for a fast free energy scan of substituting aryl hydrogens by small functional groups. Dihedrals of the functional groups are sampled explicitly in VSS, which improves the performance of the calculation and is found particularly important for certain groups. As a proof-of-concept demonstration, we employ VSS to compute the solvation free energy change upon substituting the hydrogen of a benzene molecule by 12 small functional groups frequently considered in lead optimization. Additionally, VSS is used to compute the relative binding free energy of four selected ligands of the T4 lysozyme. Overall, the computational cost of VSS is only a fraction of the corresponding multi-step FEP (mFEP) calculation, while its results agree reasonably well with those of mFEP, indicating that VSS offers a promising tool for rapid free energy scan of small functional group substitutions. This article is protected by copyright. All rights reserved. © 2016 Wiley Periodicals, Inc.
Surface free energy of alkali and transition metal nanoparticles
Aqra, Fathi; Ayyad, Ahmed
2014-01-01
Graphical abstract: Size dependent surface free energy of spherical, cubic and disk Au nanoparticles. - Highlights: • A model to account for the surface free energy of metallic nanoparticles is described. • The model requires only the cohesive energy of the nanoparticle. • The surface free energy of a number of metallic nanoparticles has been calculated, and the obtained values agree well with existing data. • Surface energy falls down very fast when the number of atoms is less than hundred. • The model is applicable to any metallic nanoparticle. - Abstract: This paper addresses an interesting issue on the surface free energy of metallic nanoparticles as compared to the bulk material. Starting from a previously reported equation, a theoretical model, that involves a specific term for calculating the cohesive energy of nanoparticle, is established in a view to describe the behavior of surface free energy of metallic nanoparticles (using different shapes of particle: sphere, cube and disc). The results indicate that the behavior of surface energy is very appropriate for spherical nanoparticle, and thus, it is the most realistic shape of a nanoparticle. The surface energy of copper, silver, gold, platinum, tungsten, molybdenum, tantalum, paladium and alkali metallic nanoparticles is only prominent in the nanoscale size, and it decreases with the decrease of nanoparticle size. Thus, the surface free energy plays a more important role in determining the properties of nanoparticles than in bulk materials. It differs from shape to another, and falls down as the number of atoms (nanoparticle size) decreases. In the case of spherical nanoparticles, the onset of the sharp decrease in surface energy is observed at about 110 atom. A decrease of 16% and 45% in surface energy is found by moving from bulk to 110 atom and from bulk to 5 atom, respectively. The predictions are consistent with the reported data
Conformational Transitions and Convergence of Absolute Binding Free Energy Calculations
Lapelosa, Mauro; Gallicchio, Emilio; Levy, Ronald M.
2011-01-01
The Binding Energy Distribution Analysis Method (BEDAM) is employed to compute the standard binding free energies of a series of ligands to a FK506 binding protein (FKBP12) with implicit solvation. Binding free energy estimates are in reasonably good agreement with experimental affinities. The conformations of the complexes identified by the simulations are in good agreement with crystallographic data, which was not used to restrain ligand orientations. The BEDAM method is based on λ -hopping Hamiltonian parallel Replica Exchange (HREM) molecular dynamics conformational sampling, the OPLS-AA/AGBNP2 effective potential, and multi-state free energy estimators (MBAR). Achieving converged and accurate results depends on all of these elements of the calculation. Convergence of the binding free energy is tied to the level of convergence of binding energy distributions at critical intermediate states where bound and unbound states are at equilibrium, and where the rate of binding/unbinding conformational transitions is maximal. This finding mirrors similar observations in the context of order/disorder transitions as for example in protein folding. Insights concerning the physical mechanism of ligand binding and unbinding are obtained. Convergence for the largest FK506 ligand is achieved only after imposing strict conformational restraints, which however require accurate prior structural knowledge of the structure of the complex. The analytical AGBNP2 model is found to underestimate the magnitude of the hydrophobic driving force towards binding in these systems characterized by loosely packed protein-ligand binding interfaces. Rescoring of the binding energies using a numerical surface area model corrects this deficiency. This study illustrates the complex interplay between energy models, exploration of conformational space, and free energy estimators needed to obtain robust estimates from binding free energy calculations. PMID:22368530
Glassy carbon based supercapacitor stacks
Baertsch, M; Braun, A; Koetz, R; Haas, O [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1997-06-01
Considerable effort is being made to develop electrochemical double layer capacitors (EDLC) that store relatively large quantities of electrical energy and possess at the same time a high power density. Our previous work has shown that glassy carbon is suitable as a material for capacitor electrodes concerning low resistance and high capacity requirements. We present the development of bipolar electrochemical glassy carbon capacitor stacks of up to 3 V. Bipolar stacks are an efficient way to meet the high voltage and high power density requirements for traction applications. Impedance and cyclic voltammogram measurements are reported here and show the frequency response of a 1, 2, and 3 V stack. (author) 3 figs., 1 ref..
Olsson, Martin A; Söderhjelm, Pär; Ryde, Ulf
2016-06-30
In this article, the convergence of quantum mechanical (QM) free-energy simulations based on molecular dynamics simulations at the molecular mechanics (MM) level has been investigated. We have estimated relative free energies for the binding of nine cyclic carboxylate ligands to the octa-acid deep-cavity host, including the host, the ligand, and all water molecules within 4.5 Å of the ligand in the QM calculations (158-224 atoms). We use single-step exponential averaging (ssEA) and the non-Boltzmann Bennett acceptance ratio (NBB) methods to estimate QM/MM free energy with the semi-empirical PM6-DH2X method, both based on interaction energies. We show that ssEA with cumulant expansion gives a better convergence and uses half as many QM calculations as NBB, although the two methods give consistent results. With 720,000 QM calculations per transformation, QM/MM free-energy estimates with a precision of 1 kJ/mol can be obtained for all eight relative energies with ssEA, showing that this approach can be used to calculate converged QM/MM binding free energies for realistic systems and large QM partitions. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.
A Short Essay on the Uses of Free Energy
Koutandos, Spyridon
2013-01-01
In this article we examine cases of more classical and less classical nature compared to results found by quantum mechanics and attribute a form of Free Energy discontinuity for each case within a boundary layer. The concept of a boundary layer is broadened as to include areas of first or second variations of the Gibbs free energy. It is constructive to think not only of implosions like boundary layers but also of explosion like ones. Situations such as boiling and the passage of electric cur...
Free energy surfaces from nonequilibrium processes without work measurement
Adib, Artur B.
2006-04-01
Recent developments in statistical mechanics have allowed the estimation of equilibrium free energies from the statistics of work measurements during processes that drive the system out of equilibrium. Here a different class of processes is considered, wherein the system is prepared and released from a nonequilibrium state, and no external work is involved during its observation. For such "clamp-and-release" processes, a simple strategy for the estimation of equilibrium free energies is offered. The method is illustrated with numerical simulations and analyzed in the context of tethered single-molecule experiments.
Schmid, L. A.
1977-01-01
The first and second variations are calculated for the irreducible form of Hamilton's Principle that involves the minimum number of dependent variables necessary to describe the kinetmatics and thermodynamics of inviscid, compressible, baroclinic flow in a specified gravitational field. The form of the second variation shows that, in the neighborhood of a stationary point that corresponds to physically stable flow, the action integral is a complex saddle surface in parameter space. There exists a form of Hamilton's Principle for which a direct solution of a flow problem is possible. This second form is related to the first by a Friedrichs transformation of the thermodynamic variables. This introduces an extra dependent variable, but the first and second variations are shown to have direct physical significance, namely they are equal to the free energy of fluctuations about the equilibrium flow that satisfies the equations of motion. If this equilibrium flow is physically stable, and if a very weak second order integral constraint on the correlation between the fluctuations of otherwise independent variables is satisfied, then the second variation of the action integral for this free energy form of Hamilton's Principle is positive-definite, so the action integral is a minimum, and can serve as the basis for a direct trail and error solution. The second order integral constraint states that the unavailable energy must be maximum at equilibrium, i.e. the fluctuations must be so correlated as to produce a second order decrease in the total unavailable energy.
Free energy of the Lennard-Jones solid
Hoef, van der M.A.
2000-01-01
We have determined a simple expression for the absolute Helmholtz free energy of the fcc Lennard-Jones solid from molecular dynamics simulations. The pressure and energy data from these simulations have been fitted to a simple functional form (18 parameters) for densities ranging from around
Free energy barriers to evaporation of water in hydrophobic confinement.
Sharma, Sumit; Debenedetti, Pablo G
2012-11-08
We use umbrella sampling Monte Carlo and forward and reverse forward flux sampling (FFS) simulation techniques to compute the free energy barriers to evaporation of water confined between two hydrophobic surfaces separated by nanoscopic gaps, as a function of the gap width, at 1 bar and 298 K. The evaporation mechanism for small (1 × 1 nm(2)) surfaces is found to be fundamentally different from that for large (3 × 3 nm(2)) surfaces. In the latter case, the evaporation proceeds via the formation of a gap-spanning tubular cavity. The 1 × 1 nm(2) surfaces, in contrast, are too small to accommodate a stable vapor cavity. Accordingly, the associated free energy barriers correspond to the formation of a critical-sized cavity for sufficiently large confining surfaces, and to complete emptying of the gap region for small confining surfaces. The free energy barriers to evaporation were found to be of O(20kT) for 14 Å gaps, and to increase by approximately ~5kT with every 1 Å increase in the gap width. The entropy contribution to the free energy of evaporation was found to be independent of the gap width.
Funnel metadynamics as accurate binding free-energy method
Limongelli, Vittorio; Bonomi, Massimiliano; Parrinello, Michele
2013-01-01
A detailed description of the events ruling ligand/protein interaction and an accurate estimation of the drug affinity to its target is of great help in speeding drug discovery strategies. We have developed a metadynamics-based approach, named funnel metadynamics, that allows the ligand to enhance the sampling of the target binding sites and its solvated states. This method leads to an efficient characterization of the binding free-energy surface and an accurate calculation of the absolute protein–ligand binding free energy. We illustrate our protocol in two systems, benzamidine/trypsin and SC-558/cyclooxygenase 2. In both cases, the X-ray conformation has been found as the lowest free-energy pose, and the computed protein–ligand binding free energy in good agreement with experiments. Furthermore, funnel metadynamics unveils important information about the binding process, such as the presence of alternative binding modes and the role of waters. The results achieved at an affordable computational cost make funnel metadynamics a valuable method for drug discovery and for dealing with a variety of problems in chemistry, physics, and material science. PMID:23553839
The Free Energy in the Derrida-Retaux Recursive Model
Hu, Yueyun; Shi, Zhan
2018-05-01
We are interested in a simple max-type recursive model studied by Derrida and Retaux (J Stat Phys 156:268-290, 2014) in the context of a physics problem, and find a wide range for the exponent in the free energy in the nearly supercritical regime.
Calculating zeros: Non-equilibrium free energy calculations
Oostenbrink, Chris; Gunsteren, Wilfred F. van
2006-01-01
Free energy calculations on three model processes with theoretically known free energy changes have been performed using short simulation times. A comparison between equilibrium (thermodynamic integration) and non-equilibrium (fast growth) methods has been made in order to assess the accuracy and precision of these methods. The three processes have been chosen to represent processes often observed in biomolecular free energy calculations. They involve a redistribution of charges, the creation and annihilation of neutral particles and conformational changes. At very short overall simulation times, the thermodynamic integration approach using discrete steps is most accurate. More importantly, reasonable accuracy can be obtained using this method which seems independent of the overall simulation time. In cases where slow conformational changes play a role, fast growth simulations might have an advantage over discrete thermodynamic integration where sufficient sampling needs to be obtained at every λ-point, but only if the initial conformations do properly represent an equilibrium ensemble. From these three test cases practical lessons can be learned that will be applicable to biomolecular free energy calculations
Molecular dynamics simulations and free energy profile of ...
aDepartment of Chemical Engineering, bDepartment of Chemistry, Amirkabir University of Technology,. 15875-4413 ... Lipid bilayers; Paracetamol; free energy; molecular dynamics simulation; membrane. 1. ..... bilayer is less favourable due to the hydrophobic nature .... Orsi M and Essex J W 2010 Soft Matter 6 3797. 54.
Free energy functionals for polarization fluctuations: Pekar factor revisited.
Dinpajooh, Mohammadhasan; Newton, Marshall D; Matyushov, Dmitry V
2017-02-14
The separation of slow nuclear and fast electronic polarization in problems related to electron mobility in polarizable media was considered by Pekar 70 years ago. Within dielectric continuum models, this separation leads to the Pekar factor in the free energy of solvation by the nuclear degrees of freedom. The main qualitative prediction of Pekar's perspective is a significant, by about a factor of two, drop of the nuclear solvation free energy compared to the total (electronic plus nuclear) free energy of solvation. The Pekar factor enters the solvent reorganization energy of electron transfer reactions and is a significant mechanistic parameter accounting for the solvent effect on electron transfer. Here, we study the separation of the fast and slow polarization modes in polar molecular liquids (polarizable dipolar liquids and polarizable water force fields) without relying on the continuum approximation. We derive the nonlocal free energy functional and use atomistic numerical simulations to obtain nonlocal, reciprocal space electronic and nuclear susceptibilities. A consistent transition to the continuum limit is introduced by extrapolating the results of finite-size numerical simulation to zero wavevector. The continuum nuclear susceptibility extracted from the simulations is numerically close to the Pekar factor. However, we derive a new functionality involving the static and high-frequency dielectric constants. The main distinction of our approach from the traditional theories is found in the solvation free energy due to the nuclear polarization: the anticipated significant drop of its magnitude with increasing liquid polarizability does not occur. The reorganization energy of electron transfer is either nearly constant with increasing the solvent polarizability and the corresponding high-frequency dielectric constant (polarizable dipolar liquids) or actually noticeably increases (polarizable force fields of water).
Free energy functionals for polarization fluctuations: Pekar factor revisited
Dinpajooh, Mohammadhasan; Newton, Marshall D.; Matyushov, Dmitry V.
2017-01-01
The separation of slow nuclear and fast electronic polarization in problems related to electron mobility in polarizable media was considered by Pekar 70 years ago. This separation leads to the Pekar factor in the free energy of solvation by the nuclear degrees of freedom, within dielectric continuum models. The main qualitative prediction of Pekar’s perspective is a significant, by about a factor of two, drop of the nuclear solvation free energy compared to the total (electronic plus nuclear) free energy of solvation. The Pekar factor enters the solvent reorganization energy of electron transfer reactions and is a significant mechanistic parameter accounting for the solvent effect on electron transfer. We study the separation of the fast and slow polarization modes in polar molecular liquids (polarizable dipolar liquids and polarizable water force fields) without relying on the continuum approximation. We derive the nonlocal free energy functional and use atomistic numerical simulations to obtain nonlocal, reciprocal space electronic and nuclear susceptibilities. A consistent transition to the continuum limit is introduced by extrapolating the results of finite-size numerical simulation to zero wavevector. The continuum nuclear susceptibility extracted from the simulations is numerically close to the Pekar factor. But, we derive a new functionality involving the static and high-frequency dielectric constants. The main distinction of our approach from the traditional theories is found in the solvation free energy due to the nuclear polarization: the anticipated significant drop of its magnitude with increasing liquid polarizability does not occur. The reorganization energy of electron transfer is either nearly constant with increasing the solvent polarizability and the corresponding high-frequency dielectric constant (polarizable dipolar liquids) or actually noticeably increases (polarizable force fields of water).
Lv, Chao; Aitchison, Erick W; Wu, Dongsheng; Zheng, Lianqing; Cheng, Xiaolin; Yang, Wei
2016-03-05
Hydrogen sulfide (H2 S), a commonly known toxic gas compound, possesses unique chemical features that allow this small solute molecule to quickly diffuse through cell membranes. Taking advantage of the recent orthogonal space tempering (OST) method, we comparatively mapped the transmembrane free energy landscapes of H2 S and its structural analogue, water (H2 O), seeking to decipher the molecular determinants that govern their drastically different permeabilities. As revealed by our OST sampling results, in contrast to the highly polar water solute, hydrogen sulfide is evidently amphipathic, and thus inside membrane is favorably localized at the interfacial region, that is, the interface between the polar head-group and nonpolar acyl chain regions. Because the membrane binding affinity of H2 S is mainly governed by its small hydrophobic moiety and the barrier height inbetween the interfacial region and the membrane center is largely determined by its moderate polarity, the transmembrane free energy barriers to encounter by this toxic molecule are very small. Moreover when H2 S diffuses from the bulk solution to the membrane center, the above two effects nearly cancel each other, so as to lead to a negligible free energy difference. This study not only explains why H2 S can quickly pass through cell membranes but also provides a practical illustration on how to use the OST free energy sampling method to conveniently analyze complex molecular processes. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.
Nonlocal Free Energy of a Spatially Inhomogeneous Superconductor
Grigorishin, K.V.; Lev, B.I.
2012-01-01
The microscopic approach is developed for obtaining of the free energy of a superconductor based on direct calculation of the vacuum amplitude. The free energy functional of the spatially inhomogeneous superconductor in a magnetic field is obtained with help of the developed approach. The obtained functional is generalization of Ginzburg-Landau functionals for any temperature, for arbitrary spatial variations of the order parameter and for the nonlocality of a magnetic response and the order parameter. Moreover, the nonlocality of the magnetic response is the consequence of order parameter's nonlocality. The extremals of this functional are considered in the explicit form in the low- and high-temperature limit at the condition of slowness of spatial variations of the order parameter. (condensed matter: electronic structure, electrical, magnetic, and optical properties)
Solid/liquid interfacial free energies in binary systems
Nason, D.; Tiller, W. A.
1973-01-01
Description of a semiquantitative technique for predicting the segregation characteristics of smooth interfaces between binary solid and liquid solutions in terms of readily available thermodynamic parameters of the bulk solutions. A lattice-liquid interfacial model and a pair-bonded regular solution model are employed in the treatment with an accommodation for liquid interfacial entropy. The method is used to calculate the interfacial segregation and the free energy of segregation for solid-liquid interfaces between binary solutions for the (111) boundary of fcc crystals. The zone of compositional transition across the interface is shown to be on the order of a few atomic layers in width, being moderately narrower for ideal solutions. The free energy of the segregated interface depends primarily upon the solid composition and the heats of fusion of the component atoms, the composition difference of the solutions, and the difference of the heats of mixing of the solutions.
FESetup: Automating Setup for Alchemical Free Energy Simulations.
Loeffler, Hannes H; Michel, Julien; Woods, Christopher
2015-12-28
FESetup is a new pipeline tool which can be used flexibly within larger workflows. The tool aims to support fast and easy setup of alchemical free energy simulations for molecular simulation packages such as AMBER, GROMACS, Sire, or NAMD. Post-processing methods like MM-PBSA and LIE can be set up as well. Ligands are automatically parametrized with AM1-BCC, and atom mappings for a single topology description are computed with a maximum common substructure search (MCSS) algorithm. An abstract molecular dynamics (MD) engine can be used for equilibration prior to free energy setup or standalone. Currently, all modern AMBER force fields are supported. Ease of use, robustness of the code, and automation where it is feasible are the main development goals. The project follows an open development model, and we welcome contributions.
Tarr, Lucas; Longcope, Dana; Millhouse, Margaret [Department of Physics, Montana State University, Bozeman, MT 59717 (United States)
2013-06-10
It is well known that photospheric flux emergence is an important process for stressing coronal fields and storing magnetic free energy, which may then be released during a flare. The Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) captured the entire emergence of NOAA AR 11158. This region emerged as two distinct bipoles, possibly connected underneath the photosphere, yet characterized by different photospheric field evolutions and fluxes. The combined active region complex produced 15 GOES C-class, two M-class, and the X2.2 Valentine's Day Flare during the four days after initial emergence on 2011 February 12. The M and X class flares are of particular interest because they are nonhomologous, involving different subregions of the active region. We use a Magnetic Charge Topology together with the Minimum Current Corona model of the coronal field to model field evolution of the complex. Combining this with observations of flare ribbons in the 1600 A channel of the Atmospheric Imaging Assembly on board SDO, we propose a minimization algorithm for estimating the amount of reconnected flux and resulting drop in magnetic free energy during a flare. For the M6.6, M2.2, and X2.2 flares, we find a flux exchange of 4.2 Multiplication-Sign 10{sup 20} Mx, 2.0 Multiplication-Sign 10{sup 20} Mx, and 21.0 Multiplication-Sign 10{sup 20} Mx, respectively, resulting in free energy drops of 3.89 Multiplication-Sign 10{sup 30} erg, 2.62 Multiplication-Sign 10{sup 30} erg, and 1.68 Multiplication-Sign 10{sup 32} erg.
Thermodynamic picture of the glassy state
Nieuwenhuizen, T.M.
2000-01-01
A picture for the thermodynamics of the glassy state is introduced. It assumes that one extra parameter, the effective temperature, is needed to describe the glassy state. This explains the classical paradoxes concerning the Ehrenfest relations and the Prigogine-Defay ratio. As a second feature, the
Low temperature thermal conductivities of glassy carbons
Anderson, A.C.
1979-01-01
The thermal conductivity of glassy carbon in the temperature range 0.1 to 100 0 K appears to depend only on the temperature at which the material was pyrolyzed. The thermal conductivity can be related to the microscopic structure of glassy carbon. The reticulated structure is especially useful for thermal isolation at cryogenic temperatures
Peptide Free Energy Landscapes Calibrated by Molecular Orbital Calculations
Ono, S.; Kuroda, M.; Higo, J.; Kamiya, N.; Nakajima, N.; Nakamura, H.
2002-01-01
Free energy landscapes of peptide conformations werecalibrated by ab initiomolecular orbital calculations, after enhancedconformational sampling using the multicanonical molecular dynamicssimulations. Three different potentials of mean force for an isolateddipeptide were individually obtained using the conventional force fields,AMBER parm94, AMBER parm96, and CHARMm22. Each potential ofmean force was calibrated based on the umbrella sampling algorithm fromthe adiabatic energy map that was cal...
Free energy landscape and molecular pathways of gas hydrate nucleation
Bi, Yuanfei; Porras, Anna; Li, Tianshu
2016-01-01
Despite the significance of gas hydrates in diverse areas, a quantitative knowledge of hydrate formation at a molecular level is missing. The impediment to acquiring this understanding is primarily attributed to the stochastic nature and ultra-fine scales of nucleation events, posing a great challenge for both experiment and simulation to explore hydrate nucleation. Here we employ advanced molecular simulation methods, including forward flux sampling (FFS), p B histogram analysis, and backward flux sampling, to overcome the limit of direct molecular simulation for exploring both the free energy landscape and molecular pathways of hydrate nucleation. First we test the half-cage order parameter (H-COP) which we developed for driving FFS, through conducting the p B histogram analysis. Our results indeed show that H-COP describes well the reaction coordinates of hydrate nucleation. Through the verified order parameter, we then directly compute the free energy landscape for hydrate nucleation by combining both forward and backward flux sampling. The calculated stationary distribution density, which is obtained independently of nucleation theory, is found to fit well against the classical nucleation theory (CNT). Subsequent analysis of the obtained large ensemble of hydrate nucleation trajectories show that although on average, hydrate formation is facilitated by a two-step like mechanism involving a gradual transition from an amorphous to a crystalline structure, there also exist nucleation pathways where hydrate crystallizes directly, without going through the amorphous stage. The CNT-like free energy profile and the structural diversity suggest the existence of multiple active transition pathways for hydrate nucleation, and possibly also imply the near degeneracy in their free energy profiles among different pathways. Our results thus bring a new perspective to the long standing question of how hydrates crystallize.
Free energy landscape and molecular pathways of gas hydrate nucleation.
Bi, Yuanfei; Porras, Anna; Li, Tianshu
2016-12-07
Despite the significance of gas hydrates in diverse areas, a quantitative knowledge of hydrate formation at a molecular level is missing. The impediment to acquiring this understanding is primarily attributed to the stochastic nature and ultra-fine scales of nucleation events, posing a great challenge for both experiment and simulation to explore hydrate nucleation. Here we employ advanced molecular simulation methods, including forward flux sampling (FFS), p B histogram analysis, and backward flux sampling, to overcome the limit of direct molecular simulation for exploring both the free energy landscape and molecular pathways of hydrate nucleation. First we test the half-cage order parameter (H-COP) which we developed for driving FFS, through conducting the p B histogram analysis. Our results indeed show that H-COP describes well the reaction coordinates of hydrate nucleation. Through the verified order parameter, we then directly compute the free energy landscape for hydrate nucleation by combining both forward and backward flux sampling. The calculated stationary distribution density, which is obtained independently of nucleation theory, is found to fit well against the classical nucleation theory (CNT). Subsequent analysis of the obtained large ensemble of hydrate nucleation trajectories show that although on average, hydrate formation is facilitated by a two-step like mechanism involving a gradual transition from an amorphous to a crystalline structure, there also exist nucleation pathways where hydrate crystallizes directly, without going through the amorphous stage. The CNT-like free energy profile and the structural diversity suggest the existence of multiple active transition pathways for hydrate nucleation, and possibly also imply the near degeneracy in their free energy profiles among different pathways. Our results thus bring a new perspective to the long standing question of how hydrates crystallize.
Interfacial free energy and stiffness of aluminum during rapid solidification
Brown, Nicholas T.; Martinez, Enrique; Qu, Jianmin
2017-01-01
Using molecular dynamics simulations and the capillary fluctuation method, we have calculated the anisotropic crystal-melt interfacial free energy and stiffness of aluminum in a rapid solidification system where a temperature gradient is applied to enforce thermal non-equilibrium. To calculate these material properties, the standard capillary fluctuation method typically used for systems in equilibrium has been modified to incorporate a second-order Taylor expansion of the interfacial free energy term. The result is a robust method for calculating interfacial energy, stiffness and anisotropy as a function of temperature gradient using the fluctuations in the defined interface height. This work includes the calculation of interface characteristics for temperature gradients ranging from 11 to 34 K/nm. The captured results are compared to a thermal equilibrium case using the same model and simulation technique with a zero gradient definition. We define the temperature gradient as the change in temperature over height perpendicular to the crystal-melt interface. The gradients are applied in MD simulations using defined thermostat regions on a stable solid-liquid interface initially in thermal equilibrium. The results of this work show that the interfacial stiffness and free energy for aluminum are dependent on the magnitude of the temperature gradient, however the anisotropic parameters remain independent of the non-equilibrium conditions applied in this analysis. As a result, the relationships of the interfacial free energy/stiffness are determined to be linearly related to the thermal gradient, and can be interpolated to find material characteristics at additional temperature gradients.
Surface free energy analysis of adsorbents used for radioiodine adsorption
González-García, C.M.; Román, S.; González, J.F.; Sabio, E.; Ledesma, B.
2013-01-01
In this work, the surface free energy of biomass-based activated carbons, both fresh and impregnated with triethylenediamine, has been evaluated. The contribution of Lifshitz van der Waals components was determined by the model proposed by van Oss et al. The results obtained allowed predicting the most probable configurations of the impregnant onto the carbon surface and its influence on the subsequent adsorption of radioactive methyl iodide.
Free energy landscape and molecular pathways of gas hydrate nucleation
Bi, Yuanfei; Porras, Anna; Li, Tianshu, E-mail: tsli@gwu.edu [Department of Civil and Environmental Engineering, George Washington University, Washington DC 20052 (United States)
2016-12-07
Despite the significance of gas hydrates in diverse areas, a quantitative knowledge of hydrate formation at a molecular level is missing. The impediment to acquiring this understanding is primarily attributed to the stochastic nature and ultra-fine scales of nucleation events, posing a great challenge for both experiment and simulation to explore hydrate nucleation. Here we employ advanced molecular simulation methods, including forward flux sampling (FFS), p{sub B} histogram analysis, and backward flux sampling, to overcome the limit of direct molecular simulation for exploring both the free energy landscape and molecular pathways of hydrate nucleation. First we test the half-cage order parameter (H-COP) which we developed for driving FFS, through conducting the p{sub B} histogram analysis. Our results indeed show that H-COP describes well the reaction coordinates of hydrate nucleation. Through the verified order parameter, we then directly compute the free energy landscape for hydrate nucleation by combining both forward and backward flux sampling. The calculated stationary distribution density, which is obtained independently of nucleation theory, is found to fit well against the classical nucleation theory (CNT). Subsequent analysis of the obtained large ensemble of hydrate nucleation trajectories show that although on average, hydrate formation is facilitated by a two-step like mechanism involving a gradual transition from an amorphous to a crystalline structure, there also exist nucleation pathways where hydrate crystallizes directly, without going through the amorphous stage. The CNT-like free energy profile and the structural diversity suggest the existence of multiple active transition pathways for hydrate nucleation, and possibly also imply the near degeneracy in their free energy profiles among different pathways. Our results thus bring a new perspective to the long standing question of how hydrates crystallize.
Optimized Free Energies from Bidirectional Single-Molecule Force Spectroscopy
Minh, David D. L.; Adib, Artur B.
2008-05-01
An optimized method for estimating path-ensemble averages using data from processes driven in opposite directions is presented. Based on this estimator, bidirectional expressions for reconstructing free energies and potentials of mean force from single-molecule force spectroscopy—valid for biasing potentials of arbitrary stiffness—are developed. Numerical simulations on a model potential indicate that these methods perform better than unidirectional strategies.
Characterizing structural transitions using localized free energy landscape analysis.
Nilesh K Banavali
Full Text Available Structural changes in molecules are frequently observed during biological processes like replication, transcription and translation. These structural changes can usually be traced to specific distortions in the backbones of the macromolecules involved. Quantitative energetic characterization of such distortions can greatly advance the atomic-level understanding of the dynamic character of these biological processes.Molecular dynamics simulations combined with a variation of the Weighted Histogram Analysis Method for potential of mean force determination are applied to characterize localized structural changes for the test case of cytosine (underlined base flipping in a GTCAGCGCATGG DNA duplex. Free energy landscapes for backbone torsion and sugar pucker degrees of freedom in the DNA are used to understand their behavior in response to the base flipping perturbation. By simplifying the base flipping structural change into a two-state model, a free energy difference of upto 14 kcal/mol can be attributed to the flipped state relative to the stacked Watson-Crick base paired state. This two-state classification allows precise evaluation of the effect of base flipping on local backbone degrees of freedom.The calculated free energy landscapes of individual backbone and sugar degrees of freedom expectedly show the greatest change in the vicinity of the flipping base itself, but specific delocalized effects can be discerned upto four nucleotide positions away in both 5' and 3' directions. Free energy landscape analysis thus provides a quantitative method to pinpoint the determinants of structural change on the atomic scale and also delineate the extent of propagation of the perturbation along the molecule. In addition to nucleic acids, this methodology is anticipated to be useful for studying conformational changes in all macromolecules, including carbohydrates, lipids, and proteins.
Levine, R.D.
1979-01-01
The reaction rate constant is expressed as Z exp(-G/sub a//RT). Z is the binary collision frequency. G/sub a/, the free energy of activation, is shown to be the difference between the free energy of the reactive reactants and the free energy of all reactants. The results are derived from both a statistical mechanical and a collision theoretic point of view. While the later is more suitable for an ab-initio computation of the reaction rate, it is the former that lends itself to the search of systematics and of correlations and to compaction of data. Different thermodynamic-like routes to the characterization of G/sub a/ are thus explored. The two most promising ones appear to be the use of thermodynamic type cycles and the changes of dependent variables using the Legendre transform technique. The dependence of G/sub a/ on ΔG 0 , the standard free energy change in the reaction, is examined from the later point of view. It is shown that one can rigorously express this dependence as G/sub a/ = αΔG 0 + G/sub a/ 0 M(α). Here α is the Bronsted slope, α = -par. delta ln k(T)/par. delta(ΔG 0 /RT), G/sub a/ 0 is independent of ΔG 0 and M(α), the Legendre transform of G/sub a/, is a function only of α. For small changes in ΔG 0 , the general result reduces to the familiar ''linear'' free energy relation delta G/sub a/ = α delta ΔG 0 . It is concluded from general considerations that M(α) is a symmetric, convex function of α and hence that α is a monotonically increasing function of ΔG 0 . Experimental data appear to conform well to the form α = 1/[1 + exp(-ΔG 0 /G/sub s/ 0 )]. A simple interpretation of the ΔG 0 dependence of G/sub a/, based on an interpolation of the free energy from that of the reagents to that of the products, is offered. 4 figures, 69 references
Determination of partial molar volumes from free energy perturbation theory.
Vilseck, Jonah Z; Tirado-Rives, Julian; Jorgensen, William L
2015-04-07
Partial molar volume is an important thermodynamic property that gives insights into molecular size and intermolecular interactions in solution. Theoretical frameworks for determining the partial molar volume (V°) of a solvated molecule generally apply Scaled Particle Theory or Kirkwood-Buff theory. With the current abilities to perform long molecular dynamics and Monte Carlo simulations, more direct methods are gaining popularity, such as computing V° directly as the difference in computed volume from two simulations, one with a solute present and another without. Thermodynamically, V° can also be determined as the pressure derivative of the free energy of solvation in the limit of infinite dilution. Both approaches are considered herein with the use of free energy perturbation (FEP) calculations to compute the necessary free energies of solvation at elevated pressures. Absolute and relative partial molar volumes are computed for benzene and benzene derivatives using the OPLS-AA force field. The mean unsigned error for all molecules is 2.8 cm(3) mol(-1). The present methodology should find use in many contexts such as the development and testing of force fields for use in computer simulations of organic and biomolecular systems, as a complement to related experimental studies, and to develop a deeper understanding of solute-solvent interactions.
Determination of partial molar volumes from free energy perturbation theory†
Vilseck, Jonah Z.; Tirado-Rives, Julian
2016-01-01
Partial molar volume is an important thermodynamic property that gives insights into molecular size and intermolecular interactions in solution. Theoretical frameworks for determining the partial molar volume (V°) of a solvated molecule generally apply Scaled Particle Theory or Kirkwood–Buff theory. With the current abilities to perform long molecular dynamics and Monte Carlo simulations, more direct methods are gaining popularity, such as computing V° directly as the difference in computed volume from two simulations, one with a solute present and another without. Thermodynamically, V° can also be determined as the pressure derivative of the free energy of solvation in the limit of infinite dilution. Both approaches are considered herein with the use of free energy perturbation (FEP) calculations to compute the necessary free energies of solvation at elevated pressures. Absolute and relative partial molar volumes are computed for benzene and benzene derivatives using the OPLS-AA force field. The mean unsigned error for all molecules is 2.8 cm3 mol−1. The present methodology should find use in many contexts such as the development and testing of force fields for use in computer simulations of organic and biomolecular systems, as a complement to related experimental studies, and to develop a deeper understanding of solute–solvent interactions. PMID:25589343
Emotional valence and the free-energy principle.
Joffily, Mateus; Coricelli, Giorgio
2013-01-01
The free-energy principle has recently been proposed as a unified Bayesian account of perception, learning and action. Despite the inextricable link between emotion and cognition, emotion has not yet been formulated under this framework. A core concept that permeates many perspectives on emotion is valence, which broadly refers to the positive and negative character of emotion or some of its aspects. In the present paper, we propose a definition of emotional valence in terms of the negative rate of change of free-energy over time. If the second time-derivative of free-energy is taken into account, the dynamics of basic forms of emotion such as happiness, unhappiness, hope, fear, disappointment and relief can be explained. In this formulation, an important function of emotional valence turns out to regulate the learning rate of the causes of sensory inputs. When sensations increasingly violate the agent's expectations, valence is negative and increases the learning rate. Conversely, when sensations increasingly fulfil the agent's expectations, valence is positive and decreases the learning rate. This dynamic interaction between emotional valence and learning rate highlights the crucial role played by emotions in biological agents' adaptation to unexpected changes in their world.
Emotional valence and the free-energy principle.
Mateus Joffily
Full Text Available The free-energy principle has recently been proposed as a unified Bayesian account of perception, learning and action. Despite the inextricable link between emotion and cognition, emotion has not yet been formulated under this framework. A core concept that permeates many perspectives on emotion is valence, which broadly refers to the positive and negative character of emotion or some of its aspects. In the present paper, we propose a definition of emotional valence in terms of the negative rate of change of free-energy over time. If the second time-derivative of free-energy is taken into account, the dynamics of basic forms of emotion such as happiness, unhappiness, hope, fear, disappointment and relief can be explained. In this formulation, an important function of emotional valence turns out to regulate the learning rate of the causes of sensory inputs. When sensations increasingly violate the agent's expectations, valence is negative and increases the learning rate. Conversely, when sensations increasingly fulfil the agent's expectations, valence is positive and decreases the learning rate. This dynamic interaction between emotional valence and learning rate highlights the crucial role played by emotions in biological agents' adaptation to unexpected changes in their world.
Harris, Robert C; Deng, Nanjie; Levy, Ronald M; Ishizuka, Ryosuke; Matubayasi, Nobuyuki
2017-06-05
Many biomolecules undergo conformational changes associated with allostery or ligand binding. Observing these changes in computer simulations is difficult if their timescales are long. These calculations can be accelerated by observing the transition on an auxiliary free energy surface with a simpler Hamiltonian and connecting this free energy surface to the target free energy surface with free energy calculations. Here, we show that the free energy legs of the cycle can be replaced with energy representation (ER) density functional approximations. We compute: (1) The conformational free energy changes for alanine dipeptide transitioning from the right-handed free energy basin to the left-handed basin and (2) the free energy difference between the open and closed conformations of β-cyclodextrin, a "host" molecule that serves as a model for molecular recognition in host-guest binding. β-cyclodextrin contains 147 atoms compared to 22 atoms for alanine dipeptide, making β-cyclodextrin a large molecule for which to compute solvation free energies by free energy perturbation or integration methods and the largest system for which the ER method has been compared to exact free energy methods. The ER method replaced the 28 simulations to compute each coupling free energy with two endpoint simulations, reducing the computational time for the alanine dipeptide calculation by about 70% and for the β-cyclodextrin by > 95%. The method works even when the distribution of conformations on the auxiliary free energy surface differs substantially from that on the target free energy surface, although some degree of overlap between the two surfaces is required. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
Minakata, Daisuke; Crittenden, John
2011-04-15
The hydroxyl radical (HO(•)) is a strong oxidant that reacts with electron-rich sites on organic compounds and initiates complex radical chain reactions in aqueous phase advanced oxidation processes (AOPs). Computer based kinetic modeling requires a reaction pathway generator and predictions of associated reaction rate constants. Previously, we reported a reaction pathway generator that can enumerate the most important elementary reactions for aliphatic compounds. For the reaction rate constant predictor, we develop linear free energy relationships (LFERs) between aqueous phase literature-reported HO(•) reaction rate constants and theoretically calculated free energies of activation for H-atom abstraction from a C-H bond and HO(•) addition to alkenes. The theoretical method uses ab initio quantum mechanical calculations, Gaussian 1-3, for gas phase reactions and a solvation method, COSMO-RS theory, to estimate the impact of water. Theoretically calculated free energies of activation are found to be within approximately ±3 kcal/mol of experimental values. Considering errors that arise from quantum mechanical calculations and experiments, this should be within the acceptable errors. The established LFERs are used to predict the HO(•) reaction rate constants within a factor of 5 from the experimental values. This approach may be applied to other reaction mechanisms to establish a library of rate constant predictions for kinetic modeling of AOPs.
Cooperative strings and glassy interfaces.
Salez, Thomas; Salez, Justin; Dalnoki-Veress, Kari; Raphaël, Elie; Forrest, James A
2015-07-07
We introduce a minimal theory of glass formation based on the ideas of molecular crowding and resultant string-like cooperative rearrangement, and address the effects of free interfaces. In the bulk case, we obtain a scaling expression for the number of particles taking part in cooperative strings, and we recover the Adam-Gibbs description of glassy dynamics. Then, by including thermal dilatation, the Vogel-Fulcher-Tammann relation is derived. Moreover, the random and string-like characters of the cooperative rearrangement allow us to predict a temperature-dependent expression for the cooperative length ξ of bulk relaxation. Finally, we explore the influence of sample boundaries when the system size becomes comparable to ξ. The theory is in agreement with measurements of the glass-transition temperature of thin polymer films, and allows quantification of the temperature-dependent thickness hm of the interfacial mobile layer.
Trp-cage: Folding free energy landscape in explicit water
Zhou, Ruhong
2003-11-01
Trp-cage is a 20-residue miniprotein, which is believed to be the fastest folder known so far. In this study, the folding free energy landscape of Trp-cage has been explored in explicit solvent by using an OPLSAA force field with periodic boundary condition. A highly parallel replica exchange molecular dynamics method is used for the conformation space sampling, with the help of a recently developed efficient molecular dynamics algorithm P3ME/RESPA (particle-particle particle-mesh Ewald/reference system propagator algorithm). A two-step folding mechanism is proposed that involves an intermediate state where two correctly formed partial hydrophobic cores are separated by an essential salt-bridge between residues Asp-9 and Arg-16 near the center of the peptide. This metastable intermediate state provides an explanation for the superfast folding process. The free energy landscape is found to be rugged at low temperatures, and then becomes smooth and funnel-like above 340 K. The lowest free energy structure at 300 K is only 1.50 Å C-RMSD (C-rms deviation) from the NMR structures. The simulated nuclear Overhauser effect pair distances are in excellent agreement with the raw NMR data. The temperature dependence of the Trp-cage population, however, is found to be significantly different from experiment, with a much higher melting transition temperature above 400 K (experimental 315 K), indicating that the current force fields, parameterized at room temperature, need to be improved to correctly predict the temperature dependence.
Minimal Self-Models and the Free Energy Principle
Jakub eLimanowski
2013-09-01
Full Text Available The term "minimal phenomenal selfhood" describes the basic, pre-reflective experience of being a self (Blanke & Metzinger, 2009. Theoretical accounts of the minimal self have long recognized the importance and the ambivalence of the body as both part of the physical world, and the enabling condition for being in this world (Gallagher, 2005; Grafton, 2009. A recent account of minimal phenomenal selfhood (MPS, Metzinger, 2004a centers on the consideration that minimal selfhood emerges as the result of basic self-modeling mechanisms, thereby being founded on pre-reflective bodily processes. The free energy principle (FEP, Friston, 2010 is a novel unified theory of cortical function that builds upon the imperative that self-organizing systems entail hierarchical generative models of the causes of their sensory input, which are optimized by minimizing free energy as an approximation of the log-likelihood of the model. The implementation of the FEP via predictive coding mechanisms and in particular the active inference principle emphasizes the role of embodiment for predictive self-modeling, which has been appreciated in recent publications. In this review, we provide an overview of these conceptions and illustrate thereby the potential power of the FEP in explaining the mechanisms underlying minimal selfhood and its key constituents, multisensory integration, interoception, agency, perspective, and the experience of mineness. We conclude that the conceptualization of MPS can be well mapped onto a hierarchical generative model furnished by the free energy principle and may constitute the basis for higher-level, cognitive forms of self-referral, as well as the understanding of other minds.
Towards a fossil free energy future. The next energy transition
Lazarus, M.; Greber, L.; Hall, J.; Bartels, C.; Bernow, S.; Hansen, E.; Raskin, P.; Von Hippel, D. (Stockholm Environment Institute, Boston, MA (United States))
1993-04-01
The report provides technical analysis and documentation as input to the Greenpeace project 'Towards a fossil free energy future'. It presents a main scenario and several variants for reducing greenhouse gas emissions, and the technical methods and assumptions used to develop them. The goal is to investigate the technical, economic and policy feasibility to phasing out fossil fuels over the next century as part of a strategy to avert unacceptably high levels or rates of global warming. 209 refs., 42 figs., 27 tabs.
Wettability and surface free energy of polarised ceramic biomaterials
Nakamura, Miho; Hori, Naoko; Namba, Saki; Yamashita, Kimihiro; Toyama, Takeshi; Nishimiya, Nobuyuki
2015-01-01
The surface modification of ceramic biomaterials used for medical devices is expected to improve osteoconductivity through control of the interfaces between the materials and living tissues. Polarisation treatment induced surface charges on hydroxyapatite, β-tricalcium phosphate, carbonate-substituted hydroxyapatite and yttria-stabilized zirconia regardless of the differences in the carrier ions participating in the polarisation. Characterization of the surfaces revealed that the wettability of the polarised ceramic biomaterials was improved through the increase in the surface free energies compared with conventional ceramic surfaces. (note)
Coarse-grained versus atomistic simulations : realistic interaction free energies for real proteins
May, Ali; Pool, René; van Dijk, Erik; Bijlard, Jochem; Abeln, Sanne; Heringa, Jaap; Feenstra, K Anton
2014-01-01
MOTIVATION: To assess whether two proteins will interact under physiological conditions, information on the interaction free energy is needed. Statistical learning techniques and docking methods for predicting protein-protein interactions cannot quantitatively estimate binding free energies. Full
Free energy minimization and information gain: The devil is in the details
Kwisthout, J.H.P.; Rooij, I.J.E.I. van
2015-01-01
Contrary to Friston's previous work, this paper describes free energy minimization using categorical probability distributions over discrete states. This alternative mathematical framework exposes a fundamental, yet unnoticed challenge for the free energy principle. When considering discrete state
Coarse-grained versus atomistic simulations: realistic interaction free energies for real proteins
May, A.; Pool, R.; van Dijk, E.; Bijlard, J.; Abeln, S.; Heringa, J.; Feenstra, K.A.
2014-01-01
MOTIVATION: To assess whether two proteins will interact under physiological conditions, information on the interaction free energy is needed. Statistical learning techniques and docking methods for predicting protein-protein interactions cannot quantitatively estimate binding free energies. Full
Non-Equilibrium Properties from Equilibrium Free Energy Calculations
Pohorille, Andrew; Wilson, Michael A.
2012-01-01
Calculating free energy in computer simulations is of central importance in statistical mechanics of condensed media and its applications to chemistry and biology not only because it is the most comprehensive and informative quantity that characterizes the eqUilibrium state, but also because it often provides an efficient route to access dynamic and kinetic properties of a system. Most of applications of equilibrium free energy calculations to non-equilibrium processes rely on a description in which a molecule or an ion diffuses in the potential of mean force. In general case this description is a simplification, but it might be satisfactorily accurate in many instances of practical interest. This hypothesis has been tested in the example of the electrodiffusion equation . Conductance of model ion channels has been calculated directly through counting the number of ion crossing events observed during long molecular dynamics simulations and has been compared with the conductance obtained from solving the generalized Nernst-Plank equation. It has been shown that under relatively modest conditions the agreement between these two approaches is excellent, thus demonstrating the assumptions underlying the diffusion equation are fulfilled. Under these conditions the electrodiffusion equation provides an efficient approach to calculating the full voltage-current dependence routinely measured in electrophysiological experiments.
Diffusion in multicomponent systems: a free energy approach
Emmanuel, Simon; Cortis, Andrea; Berkowitz, Brian
2004-01-01
This work examines diffusion in ternary non-ideal systems and derives coupled non-linear equations based on a non-equilibrium thermodynamic approach in which an explicit expression for the free energy is substituted into standard diffusion equations. For ideal solutions, the equations employ four mobility parameters (M aa , M ab , M ba , and M bb ), and uphill diffusion is predicted for certain initial conditions and combinations of mobilities. For the more complex case of ternary Simple Mixtures, two non-ideality parameters (χ ac and χ bc ) that are directly related to the excess free energy of mixing are introduced. The solution of the equations is carried out by means of two different numerical schemes: (1) spectral collocation and (2) finite element. An error minimization technique is coupled with the spectral collocation method and applied to diffusional profiles to extract the M and χ parameters. The model satisfactorily reproduces diffusional profiles from published data for silicate melts. Further improvements in numerical and experimental techniques are then suggested
Free energy landscape of a minimalist salt bridge model.
Li, Xubin; Lv, Chao; Corbett, Karen M; Zheng, Lianqing; Wu, Dongsheng; Yang, Wei
2016-01-01
Salt bridges are essential to protein stability and dynamics. Despite the importance, there has been scarce of detailed discussion on how salt bridge partners interact with each other in distinct solvent exposed environments. In this study, employing a recent generalized orthogonal space tempering (gOST) method, we enabled efficient molecular dynamics simulation of repetitive breaking and reforming of salt bridge structures within a minimalist salt-bridge model, the Asp-Arg dipeptide and thereby were able to map its detailed free energy landscape in aqueous solution. Free energy surface analysis shows that although individually-solvated states are more favorable, salt-bridge states still occupy a noticeable portion of the overall population. Notably, the competing forces, e.g. intercharge attractions that drive the formation of salt bridges and solvation forces that pull the charged groups away from each other, are energetically comparable. As the result, the salt bridge stability is highly tunable by local environments; for instance when local water molecules are perturbed to interact more strongly with each other, the population of the salt-bridge states is likely to increase. Our results reveal the critical role of local solvent structures in modulating salt-bridge partner interactions and imply the importance of water fluctuations on conformational dynamics that involves solvent accessible salt bridge formations. © 2015 The Protein Society.
Variationally Optimized Free-Energy Flooding for Rate Calculation
McCarty, James; Valsson, Omar; Tiwary, Pratyush; Parrinello, Michele
2015-08-01
We propose a new method to obtain kinetic properties of infrequent events from molecular dynamics simulation. The procedure employs a recently introduced variational approach [Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] to construct a bias potential as a function of several collective variables that is designed to flood the associated free energy surface up to a predefined level. The resulting bias potential effectively accelerates transitions between metastable free energy minima while ensuring bias-free transition states, thus allowing accurate kinetic rates to be obtained. We test the method on a few illustrative systems for which we obtain an order of magnitude improvement in efficiency relative to previous approaches and several orders of magnitude relative to unbiased molecular dynamics. We expect an even larger improvement in more complex systems. This and the ability of the variational approach to deal efficiently with a large number of collective variables will greatly enhance the scope of these calculations. This work is a vindication of the potential that the variational principle has if applied in innovative ways.
Flavour fields in steady state: stress tensor and free energy
Banerjee, Avik; Kundu, Arnab; Kundu, Sandipan
2016-01-01
The dynamics of a probe brane in a given gravitational background is governed by the Dirac-Born-Infeld action. The corresponding open string metric arises naturally in studying the fluctuations on the probe. In Gauge-String duality, it is known that in the presence of a constant electric field on the worldvolume of the probe, the open string metric acquires an event horizon and therefore the fluctuation modes on the probe experience an effective temperature. In this article, we bring together various properties of such a system to a formal definition and a subsequent narration of the effective thermodynamics and the stress tensor of the corresponding flavour fields, also including a non-vanishing chemical potential. In doing so, we point out a potentially infinitely-degenerate scheme-dependence of regularizing the free energy, which nevertheless yields a universal contribution in certain cases. This universal piece appears as the coefficient of a log-divergence in free energy when a space-filling probe brane is embedded in AdS d+1 -background, for d=2,4, and is related to conformal anomaly. For the special case of d=2, the universal factor has a striking resemblance to the well-known heat current formula in (1+1)-dimensional conformal field theory in steady-state, which endows a plausible physical interpretation to it. Interestingly, we observe a vanishing conformal anomaly in d=6.
Inference with minimal Gibbs free energy in information field theory
Ensslin, Torsten A.; Weig, Cornelius
2010-01-01
Non-linear and non-Gaussian signal inference problems are difficult to tackle. Renormalization techniques permit us to construct good estimators for the posterior signal mean within information field theory (IFT), but the approximations and assumptions made are not very obvious. Here we introduce the simple concept of minimal Gibbs free energy to IFT, and show that previous renormalization results emerge naturally. They can be understood as being the Gaussian approximation to the full posterior probability, which has maximal cross information with it. We derive optimized estimators for three applications, to illustrate the usage of the framework: (i) reconstruction of a log-normal signal from Poissonian data with background counts and point spread function, as it is needed for gamma ray astronomy and for cosmography using photometric galaxy redshifts, (ii) inference of a Gaussian signal with unknown spectrum, and (iii) inference of a Poissonian log-normal signal with unknown spectrum, the combination of (i) and (ii). Finally we explain how Gaussian knowledge states constructed by the minimal Gibbs free energy principle at different temperatures can be combined into a more accurate surrogate of the non-Gaussian posterior.
Iterative free-energy optimization for recurrent neural networks (INFERNO)
2017-01-01
The intra-parietal lobe coupled with the Basal Ganglia forms a working memory that demonstrates strong planning capabilities for generating robust yet flexible neuronal sequences. Neurocomputational models however, often fails to control long range neural synchrony in recurrent spiking networks due to spontaneous activity. As a novel framework based on the free-energy principle, we propose to see the problem of spikes’ synchrony as an optimization problem of the neurons sub-threshold activity for the generation of long neuronal chains. Using a stochastic gradient descent, a reinforcement signal (presumably dopaminergic) evaluates the quality of one input vector to move the recurrent neural network to a desired activity; depending on the error made, this input vector is strengthened to hill-climb the gradient or elicited to search for another solution. This vector can be learned then by one associative memory as a model of the basal-ganglia to control the recurrent neural network. Experiments on habit learning and on sequence retrieving demonstrate the capabilities of the dual system to generate very long and precise spatio-temporal sequences, above two hundred iterations. Its features are applied then to the sequential planning of arm movements. In line with neurobiological theories, we discuss its relevance for modeling the cortico-basal working memory to initiate flexible goal-directed neuronal chains of causation and its relation to novel architectures such as Deep Networks, Neural Turing Machines and the Free-Energy Principle. PMID:28282439
Free-energy landscape of a hyperstable RNA tetraloop.
Miner, Jacob C; Chen, Alan A; García, Angel E
2016-06-14
We report the characterization of the energy landscape and the folding/unfolding thermodynamics of a hyperstable RNA tetraloop obtained through high-performance molecular dynamics simulations at microsecond timescales. Sampling of the configurational landscape is conducted using temperature replica exchange molecular dynamics over three isochores at high, ambient, and negative pressures to determine the thermodynamic stability and the free-energy landscape of the tetraloop. The simulations reveal reversible folding/unfolding transitions of the tetraloop into the canonical A-RNA conformation and the presence of two alternative configurations, including a left-handed Z-RNA conformation and a compact purine Triplet. Increasing hydrostatic pressure shows a stabilizing effect on the A-RNA conformation and a destabilization of the left-handed Z-RNA. Our results provide a comprehensive description of the folded free-energy landscape of a hyperstable RNA tetraloop and highlight the significant advances of all-atom molecular dynamics in describing the unbiased folding of a simple RNA secondary structure motif.
Advancing Drug Discovery through Enhanced Free Energy Calculations.
Abel, Robert; Wang, Lingle; Harder, Edward D; Berne, B J; Friesner, Richard A
2017-07-18
A principal goal of drug discovery project is to design molecules that can tightly and selectively bind to the target protein receptor. Accurate prediction of protein-ligand binding free energies is therefore of central importance in computational chemistry and computer aided drug design. Multiple recent improvements in computing power, classical force field accuracy, enhanced sampling methods, and simulation setup have enabled accurate and reliable calculations of protein-ligands binding free energies, and position free energy calculations to play a guiding role in small molecule drug discovery. In this Account, we outline the relevant methodological advances, including the REST2 (Replica Exchange with Solute Temperting) enhanced sampling, the incorporation of REST2 sampling with convential FEP (Free Energy Perturbation) through FEP/REST, the OPLS3 force field, and the advanced simulation setup that constitute our FEP+ approach, followed by the presentation of extensive comparisons with experiment, demonstrating sufficient accuracy in potency prediction (better than 1 kcal/mol) to substantially impact lead optimization campaigns. The limitations of the current FEP+ implementation and best practices in drug discovery applications are also discussed followed by the future methodology development plans to address those limitations. We then report results from a recent drug discovery project, in which several thousand FEP+ calculations were successfully deployed to simultaneously optimize potency, selectivity, and solubility, illustrating the power of the approach to solve challenging drug design problems. The capabilities of free energy calculations to accurately predict potency and selectivity have led to the advance of ongoing drug discovery projects, in challenging situations where alternative approaches would have great difficulties. The ability to effectively carry out projects evaluating tens of thousands, or hundreds of thousands, of proposed drug candidates
Glassy carbon coated graphite for nuclear applications
Delpeux S; Cacciaguerra T; Duclaux L
2005-01-01
Taking into account the problems caused by the treatment of nuclear wastes, the molten salts breeder reactors are expected to a great development. They use a molten fluorinated salt (mixture of LiF, BeF 2 , ThF 4 , and UF 4 ) as fuel and coolant. The reactor core, made of graphite, is used as a neutrons moderator. Despite of its compatibility with nuclear environment, it appears crucial to improve the stability and inertness of graphite against the diffusion of chemicals species leading to its corrosion. One way is to cover the graphite surface by a protective impermeable deposit made of glassy carbon obtained by the pyrolysis of phenolic resin or polyvinyl chloride precursors. The main difficulty in the synthesis of glassy carbon is to create exclusively, in the primary pyrolysis product, a micro-porosity of about twenty Angstroms which closes later at higher temperature. Therefore, the evacuation of the volatile products occurring mainly between 330 and 600 C, must progress slowly to avoid the material to crack. In this study, the optimal parameters for the synthesis of glassy carbon as well as glassy carbon deposits on nuclear-type graphite pieces are discussed. Both thermal treatment of phenolic and PVC resins have been performed. The structure and micro-texture of glassy carbon have been investigated by X-ray diffraction, scanning and transmission electron microscopies and helium pycno-metry. Glassy carbon samples (obtained at 1200 C) show densities ranging from 1.3 to 1.55 g/cm 3 and closed pores with nano-metric size (∼ 5 to 10 nm) appear clearly on the TEM micrographs. Then, a thermal treatment to 2700 C leads to the shrinkage of the entangled graphene ribbons, in good agreement with the proposed texture model for glassy carbon. Glassy carbon deposits on nuclear graphite have been developed by an impregnation method. The uniformity of the deposit depends clearly on the surface texture and the chemistry of the graphite substrate. The deposit regions where
Glassy carbon coated graphite for nuclear applications
Delpeux, S.; Cacciaguerra, T.; Duclaux, L. [Orleans Univ., CRMD, CNRS, 45 (France)
2005-07-01
Taking into account the problems caused by the treatment of nuclear wastes, the molten salts breeder reactors are expected to a great development. They use a molten fluorinated salt (mixture of LiF, BeF{sub 2}, ThF{sub 4}, and UF{sub 4}) as fuel and coolant. The reactor core, made of graphite, is used as a neutrons moderator. Despite of its compatibility with nuclear environment, it appears crucial to improve the stability and inertness of graphite against the diffusion of chemicals species leading to its corrosion. One way is to cover the graphite surface by a protective impermeable deposit made of glassy carbon obtained by the pyrolysis of phenolic resin [1,2] or polyvinyl chloride [3] precursors. The main difficulty in the synthesis of glassy carbon is to create exclusively, in the primary pyrolysis product, a micro-porosity of about twenty Angstroms which closes later at higher temperature. Therefore, the evacuation of the volatile products occurring mainly between 330 and 600 C, must progress slowly to avoid the material to crack. In this study, the optimal parameters for the synthesis of glassy carbon as well as glassy carbon deposits on nuclear-type graphite pieces are discussed. Both thermal treatment of phenolic and PVC resins have been performed. The structure and micro-texture of glassy carbon have been investigated by X-ray diffraction, scanning and transmission electron microscopies and helium pycno-metry. Glassy carbon samples (obtained at 1200 C) show densities ranging from 1.3 to 1.55 g/cm{sup 3} and closed pores with nano-metric size ({approx} 5 to 10 nm) appear clearly on the TEM micrographs. Then, a thermal treatment to 2700 C leads to the shrinkage of the entangled graphene ribbons (Fig 1), in good agreement with the proposed texture model for glassy carbon (Fig 2) [4]. Glassy carbon deposits on nuclear graphite have been developed by an impregnation method. The uniformity of the deposit depends clearly on the surface texture and the chemistry
Gibbs free energy of formation of UPb(s) compound
Samui, Pradeep; Agarwal, Renu; Mishra, Ratikanta
2012-01-01
Liquid lead and lead-bismuth eutectic (LBE) are being explored as primary candidates for coolants in accelerator driven systems and in advanced nuclear reactors due to their favorable thermo-physical and chemical properties. They are also proposed to be used as spallation neutron source in ADS Reactor Systems. However, corrosion of structural materials (i.e. steel) presents a critical challenge for the use of liquid lead or LBE in advanced nuclear reactors. The interactions of liquid lead or LBE with clad and fuel is of great scientific and technological importance in the development of advanced nuclear reactors. Clad failure/breach can lead to reaction of coolant elements with fuel components. Thus the study of fuel-coolant interaction of U with Pb/Bi is important. The paper deals with the determination of Gibbs free energy of formation of U-rich phase i.e. UPb in Pb-U system, employing Knudsen effusion mass loss technique
Approximate scaling properties of RNA free energy landscapes
Baskaran, S.; Stadler, P. F.; Schuster, P.
1996-01-01
RNA free energy landscapes are analysed by means of "time-series" that are obtained from random walks restricted to excursion sets. The power spectra, the scaling of the jump size distribution, and the scaling of the curve length measured with different yard stick lengths are used to describe the structure of these "time series". Although they are stationary by construction, we find that their local behavior is consistent with both AR(1) and self-affine processes. Random walks confined to excursion sets (i.e., with the restriction that the fitness value exceeds a certain threshold at each step) exhibit essentially the same statistics as free random walks. We find that an AR(1) time series is in general approximately self-affine on timescales up to approximately the correlation length. We present an empirical relation between the correlation parameter rho of the AR(1) model and the exponents characterizing self-affinity.
Hydrogen role in a carbon-free energy mix
2014-02-01
Among the energy storage technologies under development today, there is today an increasing interest towards the hydrogen-based ones. Hydrogen generation allows to store electricity, while its combustion can supply electrical, mechanical or heat energy. The French Atomic Energy Commission (CEA) started to work on hydrogen technologies at the end of the 1990's in order to reinforce its economical interest. The development of these technologies is one of the 34 French industrial programs presented in September 2013 by the French Minister of productive recovery. This paper aims at identifying the hydrogen stakes in a carbon-free energy mix and at highlighting the remaining technological challenges to be met before reaching an industrial development level
Ising model on tangled chain - 1: Free energy and entropy
Mejdani, R.
1993-04-01
In this paper we have considered an Ising model defined on tangled chain, in which more bonds have been added to those of pure Ising chain. to understand their competition, particularly between ferromagnetic and antiferromagnetic bonds, we have studied, using the transfer matrix method, some simple analytical calculations and an iterative algorithm, the behaviour of the free energy and entropy, particularly in the zero-field and zero temperature limit, for different configurations of the ferromagnetic tangled chain and different types of addition interaction (ferromagnetic or antiferromagnetic). We found that the condition J=J' between the ferromagnetic interaction J along the chain and the antiferromagnetic interaction J' across the chain is somewhat as a ''transition-region'' condition for this behaviour. Our results indicate also the existence of non-zero entropy at zero temperature. (author). 17 refs, 8 figs
The puckering free-energy surface of proline
Di Wu
2013-03-01
Full Text Available Proline has two preferred puckering states, which are often characterized by the pseudorotation phase angle and amplitude. Although proline's five endocyclic torsion angles can be utilized to calculate the phase angle and amplitude, it is not clear if there is any direct correlation between each torsion angle and the proline-puckering pathway. Here we have designed five proline puckering pathways utilizing each torsion angle χj (j = 1∼5 as the reaction coordinate. By examining the free-energy surfaces of the five puckering pathways, we find they can be categorized into two groups. The χ2 pathway (χ2 is about the Cβ—Cγ bond is especially meaningful in describing proline puckering: it changes linearly with the puckering amplitude and symmetrically with the phase angle. Our results show that this conclusion applies to both trans and cis proline conformations. We have also analyzed the correlations of proline puckering and its backbone torsion angles ϕ and ψ. We show proline has preferred puckering states at the specific regions of ϕ, ψ angles. Interestingly, the shapes of ψ-χ2 free-energy surfaces are similar among the trans proline in water, cis proline in water and cis proline in the gas phase, but they differ substantially from that of the trans proline in the gas phase. Our calculations are conducted using molecular simulations; we also verify our results using the proline conformations selected from the Protein Data Bank. In addition, we have compared our results with those calculated by the quantum mechanical methods.
Exploration, Sampling, And Reconstruction of Free Energy Surfaces with Gaussian Process Regression.
Mones, Letif; Bernstein, Noam; Csányi, Gábor
2016-10-11
Practical free energy reconstruction algorithms involve three separate tasks: biasing, measuring some observable, and finally reconstructing the free energy surface from those measurements. In more than one dimension, adaptive schemes make it possible to explore only relatively low lying regions of the landscape by progressively building up the bias toward the negative of the free energy surface so that free energy barriers are eliminated. Most schemes use the final bias as their best estimate of the free energy surface. We show that large gains in computational efficiency, as measured by the reduction of time to solution, can be obtained by separating the bias used for dynamics from the final free energy reconstruction itself. We find that biasing with metadynamics, measuring a free energy gradient estimator, and reconstructing using Gaussian process regression can give an order of magnitude reduction in computational cost.
Comment on "Inference with minimal Gibbs free energy in information field theory".
Iatsenko, D; Stefanovska, A; McClintock, P V E
2012-03-01
Enßlin and Weig [Phys. Rev. E 82, 051112 (2010)] have introduced a "minimum Gibbs free energy" (MGFE) approach for estimation of the mean signal and signal uncertainty in Bayesian inference problems: it aims to combine the maximum a posteriori (MAP) and maximum entropy (ME) principles. We point out, however, that there are some important questions to be clarified before the new approach can be considered fully justified, and therefore able to be used with confidence. In particular, after obtaining a Gaussian approximation to the posterior in terms of the MGFE at some temperature T, this approximation should always be raised to the power of T to yield a reliable estimate. In addition, we show explicitly that MGFE indeed incorporates the MAP principle, as well as the MDI (minimum discrimination information) approach, but not the well-known ME principle of Jaynes [E.T. Jaynes, Phys. Rev. 106, 620 (1957)]. We also illuminate some related issues and resolve apparent discrepancies. Finally, we investigate the performance of MGFE estimation for different values of T, and we discuss the advantages and shortcomings of the approach.
Tanaka, Shigenori
2016-03-07
, we observe a nonequilibrium behavior that the system entropy first increases with the broadening of the initially localized walker distribution and then it begins to decrease along with the trapping at the global minimum of the potential, thus leading to the minimization of the free energy.
Development and application of a free energy force field for all atom protein folding
Verma, A.
2007-11-01
Proteins are the workhorses of all cellular life. They constitute the building blocks and the machinery of all cells and typically function in specific three-dimensional conformations into which each protein folds. Currently over one million protein sequences are known, compared to about 40,000 structures deposited in the Protein Data Bank (the world-wide database of protein structures). Reliable theoretical methods for protein structure prediction could help to reduce the gap between sequence and structural databases and elucidate the biological information in structurally unresolved sequences. In this thesis we explore an approach for protein structure prediction and folding that is based on the Anfinsen's hypothesis that most proteins in their native state are in thermodynamic equilibrium with their environment. We have developed a free energy forcefield (PFF02) that locates the native conformation of many proteins from all structural classes at the global minimum of the free-energy model. We have validated the forcefield against a large decoy set (Rosetta). The average root mean square deviation (RMSD) for the lowest energy structure for the 32 proteins of the decoy set was only 2.14 Aa from the experimental conformation. We have successfully implemented and used stochastic optimization methods, such as the basin hopping technique and evolutionary algorithms for all atom protein structure prediction. The evolutionary algorithm performs exceptionally well on large supercomputational architectures, such as BlueGene and MareNostrum. Using the PFF02 forcefield, we were able to fold 13 proteins (12-56 amino acids), which include helix, sheet and mixed secondary structure. On average the predicted structure of these proteins deviated from their experimental conformation by only 2.89 Aa RMSD. (orig.)
Examining ion channel properties using free-energy methods.
Domene, Carmen; Furini, Simone
2009-01-01
Recent advances in structural biology have revealed the architecture of a number of transmembrane channels, allowing for these complex biological systems to be understood in atomistic detail. Computational simulations are a powerful tool by which the dynamic and energetic properties, and thereby the function of these protein architectures, can be investigated. The experimentally observable properties of a system are often determined more by energetic than dynamics, and therefore understanding the underlying free energy (FE) of biophysical processes is of crucial importance. Critical to the accurate evaluation of FE values are the problems of obtaining accurate sampling of complex biological energy landscapes, and of obtaining accurate representations of the potential energy of a system, this latter problem having been addressed through the development of molecular force fields. While these challenges are common to all FE methods, depending on the system under study, and the questions being asked of it, one technique for FE calculation may be preferable to another, the choice of method and simulation protocol being crucial to achieve efficiency. Applied in a correct manner, FE calculations represent a predictive and affordable computational tool with which to make relevant contact with experiments. This chapter, therefore, aims to give an overview of the most widely implemented computational methods used to calculate the FE associated with particular biochemical or biophysical events, and to highlight their recent applications to ion channels. Copyright © 2009 Elsevier Inc. All rights reserved.
Multivariable extrapolation of grand canonical free energy landscapes
Mahynski, Nathan A.; Errington, Jeffrey R.; Shen, Vincent K.
2017-12-01
We derive an approach for extrapolating the free energy landscape of multicomponent systems in the grand canonical ensemble, obtained from flat-histogram Monte Carlo simulations, from one set of temperature and chemical potentials to another. This is accomplished by expanding the landscape in a Taylor series at each value of the order parameter which defines its macrostate phase space. The coefficients in each Taylor polynomial are known exactly from fluctuation formulas, which may be computed by measuring the appropriate moments of extensive variables that fluctuate in this ensemble. Here we derive the expressions necessary to define these coefficients up to arbitrary order. In principle, this enables a single flat-histogram simulation to provide complete thermodynamic information over a broad range of temperatures and chemical potentials. Using this, we also show how to combine a small number of simulations, each performed at different conditions, in a thermodynamically consistent fashion to accurately compute properties at arbitrary temperatures and chemical potentials. This method may significantly increase the computational efficiency of biased grand canonical Monte Carlo simulations, especially for multicomponent mixtures. Although approximate, this approach is amenable to high-throughput and data-intensive investigations where it is preferable to have a large quantity of reasonably accurate simulation data, rather than a smaller amount with a higher accuracy.
Free-energy minimization and the dark-room problem.
Friston, Karl; Thornton, Christopher; Clark, Andy
2012-01-01
Recent years have seen the emergence of an important new fundamental theory of brain function. This theory brings information-theoretic, Bayesian, neuroscientific, and machine learning approaches into a single framework whose overarching principle is the minimization of surprise (or, equivalently, the maximization of expectation). The most comprehensive such treatment is the "free-energy minimization" formulation due to Karl Friston (see e.g., Friston and Stephan, 2007; Friston, 2010a,b - see also Fiorillo, 2010; Thornton, 2010). A recurrent puzzle raised by critics of these models is that biological systems do not seem to avoid surprises. We do not simply seek a dark, unchanging chamber, and stay there. This is the "Dark-Room Problem." Here, we describe the problem and further unpack the issues to which it speaks. Using the same format as the prolog of Eddington's Space, Time, and Gravitation (Eddington, 1920) we present our discussion as a conversation between: an information theorist (Thornton), a physicist (Friston), and a philosopher (Clark).
On the TAP Free Energy in the Mixed p-Spin Models
Chen, Wei-Kuo; Panchenko, Dmitry
2018-05-01
Thouless et al. (Phys Mag 35(3):593-601, 1977), derived a representation for the free energy of the Sherrington-Kirkpatrick model, called the TAP free energy, written as the difference of the energy and entropy on the extended configuration space of local magnetizations with an Onsager correction term. In the setting of mixed p-spin models with Ising spins, we prove that the free energy can indeed be written as the supremum of the TAP free energy over the space of local magnetizations whose Edwards-Anderson order parameter (self-overlap) is to the right of the support of the Parisi measure. Furthermore, for generic mixed p-spin models, we prove that the free energy is equal to the TAP free energy evaluated on the local magnetization of any pure state.
Direct measurement of the free energy of aging hard sphere colloidal glasses.
Zargar, Rojman; Nienhuis, Bernard; Schall, Peter; Bonn, Daniel
2013-06-21
The nature of the glass transition is one of the most important unsolved problems in condensed matter physics. The difference between glasses and liquids is believed to be caused by very large free energy barriers for particle rearrangements; however, so far it has not been possible to confirm this experimentally. We provide the first quantitative determination of the free energy for an aging hard sphere colloidal glass. The determination of the free energy allows for a number of new insights in the glass transition, notably the quantification of the strong spatial and temporal heterogeneity in the free energy. A study of the local minima of the free energy reveals that the observed variations are directly related to the rearrangements of the particles. Our main finding is that the probability of particle rearrangements shows a power law dependence on the free energy changes associated with the rearrangements similar to the Gutenberg-Richter law in seismology.
An ab initio approach to free-energy reconstruction using logarithmic mean force dynamics
Nakamura, Makoto; Obata, Masao; Morishita, Tetsuya; Oda, Tatsuki
2014-01-01
We present an ab initio approach for evaluating a free energy profile along a reaction coordinate by combining logarithmic mean force dynamics (LogMFD) and first-principles molecular dynamics. The mean force, which is the derivative of the free energy with respect to the reaction coordinate, is estimated using density functional theory (DFT) in the present approach, which is expected to provide an accurate free energy profile along the reaction coordinate. We apply this new method, first-principles LogMFD (FP-LogMFD), to a glycine dipeptide molecule and reconstruct one- and two-dimensional free energy profiles in the framework of DFT. The resultant free energy profile is compared with that obtained by the thermodynamic integration method and by the previous LogMFD calculation using an empirical force-field, showing that FP-LogMFD is a promising method to calculate free energy without empirical force-fields
Estimating Atomic Contributions to Hydration and Binding Using Free Energy Perturbation.
Irwin, Benedict W J; Huggins, David J
2018-05-08
We present a general method called atom-wise free energy perturbation (AFEP), which extends a conventional molecular dynamics free energy perturbation (FEP) simulation to give the contribution to a free energy change from each atom. AFEP is derived from an expansion of the Zwanzig equation used in the exponential averaging method by defining that the system total energy can be partitioned into contributions from each atom. A partitioning method is assumed and used to group terms in the expansion to correspond to individual atoms. AFEP is applied to six example free energy changes to demonstrate the method. Firstly, the hydration free energies of methane, methanol, methylamine, methanethiol, and caffeine in water. AFEP highlights the atoms in the molecules that interact favorably or unfavorably with water. Finally AFEP is applied to the binding free energy of human immunodeficiency virus type 1 protease to lopinavir, and AFEP reveals the contribution of each atom to the binding free energy, indicating candidate areas of the molecule to improve to produce a more strongly binding inhibitor. FEP gives a single value for the free energy change and is already a very useful method. AFEP gives a free energy change for each "part" of the system being simulated, where part can mean individual atoms, chemical groups, amino acids, or larger partitions depending on what the user is trying to measure. This method should have various applications in molecular dynamics studies of physical, chemical, or biochemical phenomena, specifically in the field of computational drug discovery.
Chemical Disequilibria and Sources of Gibbs Free Energy Inside Enceladus
Zolotov, M. Y.
2010-12-01
Non-photosynthetic organisms use chemical disequilibria in the environment to gain metabolic energy from enzyme catalyzed oxidation-reduction (redox) reactions. The presence of carbon dioxide, ammonia, formaldehyde, methanol, methane and other hydrocarbons in the eruptive plume of Enceladus [1] implies diverse redox disequilibria in the interior. In the history of the moon, redox disequilibria could have been activated through melting of a volatile-rich ice and following water-rock-organic interactions. Previous and/or present aqueous processes are consistent with the detection of NaCl and Na2CO3/NaHCO3-bearing grains emitted from Enceladus [2]. A low K/Na ratio in the grains [2] and a low upper limit for N2 in the plume [3] indicate low temperature (possibly enzymes if organisms were (are) present. The redox conditions in aqueous systems and amounts of available Gibbs free energy should have been affected by the production, consumption and escape of hydrogen. Aqueous oxidation of minerals (Fe-Ni metal, Fe-Ni phosphides, etc.) accreted on Enceladus should have led to H2 production, which is consistent with H2 detection in the plume [1]. Numerical evaluations based on concentrations of plume gases [1] reveal sufficient energy sources available to support metabolically diverse life at a wide range of activities (a) of dissolved H2 (log aH2 from 0 to -10). Formaldehyde, carbon dioxide [c.f. 4], HCN (if it is present), methanol, acetylene and other hydrocarbons have the potential to react with H2 to form methane. Aqueous hydrogenations of acetylene, HCN and formaldehyde to produce methanol are energetically favorable as well. Both favorable hydrogenation and hydration of HCN lead to formation of ammonia. Condensed organic species could also participate in redox reactions. Methane and ammonia are the final products of these putative redox transformations. Sulfates may have not formed in cold and/or short-term aqueous environments with a limited H2 escape. In contrast to
The Emissions-Free Energy (EFE) Working Group
Humphries, R., E-mail: Roger.Humphries@amec.com [AMEC NSS, Toronto, Ontario (Canada)
2014-07-01
There has been a growing international interest in smaller, simpler reactors for generating electricity and process heat. They incorporate modern technological advances in reactor design, reactor safety, modular construction, proliferation resistance, and risk reduction. The interest in these reactors has been driven by many factors, including the need to reduce greenhouse gas emissions and provide reliable power in 'off-grid' or 'edge-of-grid' locations. Licensing these new small reactors, particularly in Canada's resource rich remote northern regions, will raises issues in a wide variety of technical, institutional, socio-economic and regulatory policy areas. The first small reactor vendor to file a license application or to engage the CNSC in its pre-licensing vendor design review process is going to have to deal with these issues. However these issues affect the entire small reactor industry and it is essential that the industry as a whole address them. Accordingly, a small reactor industry-wide Working Group has been established to identify and prioritize the issues that need to be addressed and work with the CNSC and other interested stakeholders to agree on a resolution acceptable to all parties. The objective of the small reactor industry is to introduce an economical, emissions-free source of electrical and thermal energy. It is the opinion of the WG that our emphasis ought to be on the product rather than the technology, hence the name Emissions-Free Energy Working Group. The EFE WG has initiated contact with the CNSC and has started its review of CNSC draft regulatory and guidance documents. (author)
The free energy landscape of small molecule unbinding.
Danzhi Huang
2011-02-01
Full Text Available The spontaneous dissociation of six small ligands from the active site of FKBP (the FK506 binding protein is investigated by explicit water molecular dynamics simulations and network analysis. The ligands have between four (dimethylsulphoxide and eleven (5-diethylamino-2-pentanone non-hydrogen atoms, and an affinity for FKBP ranging from 20 to 0.2 mM. The conformations of the FKBP/ligand complex saved along multiple trajectories (50 runs at 310 K for each ligand are grouped according to a set of intermolecular distances into nodes of a network, and the direct transitions between them are the links. The network analysis reveals that the bound state consists of several subbasins, i.e., binding modes characterized by distinct intermolecular hydrogen bonds and hydrophobic contacts. The dissociation kinetics show a simple (i.e., single-exponential time dependence because the unbinding barrier is much higher than the barriers between subbasins in the bound state. The unbinding transition state is made up of heterogeneous positions and orientations of the ligand in the FKBP active site, which correspond to multiple pathways of dissociation. For the six small ligands of FKBP, the weaker the binding affinity the closer to the bound state (along the intermolecular distance are the transition state structures, which is a new manifestation of Hammond behavior. Experimental approaches to the study of fragment binding to proteins have limitations in temporal and spatial resolution. Our network analysis of the unbinding simulations of small inhibitors from an enzyme paints a clear picture of the free energy landscape (both thermodynamics and kinetics of ligand unbinding.
mwnts composite film modified glassy carbon electrode
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ABSTRACT: A poly p-aminosalicylic acid (Poly(p-ASA)) and multiwall carbon nanotubes. (MWCNTs) composite modified glassy carbon (GC) electrode was constructed by casting the MWNTs on the GC electrode surface followed by electropolymerization of the p-ASA on the MWCNTs/GCE. The electrochemical behaviours ...
Correcting for the free energy costs of bond or angle constraints in molecular dynamics simulations.
König, Gerhard; Brooks, Bernard R
2015-05-01
Free energy simulations are an important tool in the arsenal of computational biophysics, allowing the calculation of thermodynamic properties of binding or enzymatic reactions. This paper introduces methods to increase the accuracy and precision of free energy calculations by calculating the free energy costs of constraints during post-processing. The primary purpose of employing constraints for these free energy methods is to increase the phase space overlap between ensembles, which is required for accuracy and convergence. The free energy costs of applying or removing constraints are calculated as additional explicit steps in the free energy cycle. The new techniques focus on hard degrees of freedom and use both gradients and Hessian estimation. Enthalpy, vibrational entropy, and Jacobian free energy terms are considered. We demonstrate the utility of this method with simple classical systems involving harmonic and anharmonic oscillators, four-atomic benchmark systems, an alchemical mutation of ethane to methanol, and free energy simulations between alanine and serine. The errors for the analytical test cases are all below 0.0007kcal/mol, and the accuracy of the free energy results of ethane to methanol is improved from 0.15 to 0.04kcal/mol. For the alanine to serine case, the phase space overlaps of the unconstrained simulations range between 0.15 and 0.9%. The introduction of constraints increases the overlap up to 2.05%. On average, the overlap increases by 94% relative to the unconstrained value and precision is doubled. The approach reduces errors arising from constraints by about an order of magnitude. Free energy simulations benefit from the use of constraints through enhanced convergence and higher precision. The primary utility of this approach is to calculate free energies for systems with disparate energy surfaces and bonded terms, especially in multi-scale molecular mechanics/quantum mechanics simulations. This article is part of a Special Issue
Catchment organisation, free energy dynamics and network control on critical zone water flows
Zehe, E.; Ehret, U.; Kleidon, A.; Jackisch, C.; Scherer, U.; Blume, T.
2012-04-01
processes using the behavioural system architecture and small perturbations and compare them with respect to their efficiency to dissipate free energy which is equivalent to produce entropy. The study will present the underlying theory and discuss simulation results with respect to the following core hypotheses: H1: A macro scale configuration of a hydro-geo-ecosystem, is in stationary non equilibrium closer to a functional optimum as other possible configurations, if it "dissipates" more of the available free energy to maintain the stationary cycles that redistribute and export mass and energy within/from the system. This implies (I1) that the system approaches faster a dynamic equilibrium state characterised by a minimum in free energy, and less free energy from persistent gradients is available to perform work in the system. H2: Macroscopically connected flow networks enhance redistribution of mass against macroscale gradients and thus dissipation of free energy, because they minimise local energy dissipation per unit mass flow along the flow path. This implies (I2) mechanic stability of the flow network, of the textural storage elements and thus of the entire system against frequent disturbances under stationary conditions.
Free energy change of off-eutectic binary alloys on solidification
Ohsaka, K.; Trinh, E. H.; Lin, J.-C.; Perepezko, J. H.
1991-01-01
A formula for the free energy difference between the undercooled liquid phase and the stable solid phase is derived for off-eutectic binary alloys in which the equilibrium solid/liquid transition takes place over a certain temperature range. The free energy change is then evaluated numerically for a Bi-25 at. pct Cd alloy modeled as a sub-subregular solution.
A simple free energy for the isotropic-nematic phase transition of rods
Tuinier, R.
2016-01-01
A free energy expression is proposed that describes the isotropic-nematic binodal concentrations of hard rods. A simple analytical form for this free energy was yet only available using a Gaussian trial function for the orientation distribution function (ODF), leading, however, to a significant
Constructing a multidimensional free energy surface like a spider weaving a web.
Chen, Changjun
2017-10-15
Complete free energy surface in the collective variable space provides important information of the reaction mechanisms of the molecules. But, sufficient sampling in the collective variable space is not easy. The space expands quickly with the number of the collective variables. To solve the problem, many methods utilize artificial biasing potentials to flatten out the original free energy surface of the molecule in the simulation. Their performances are sensitive to the definitions of the biasing potentials. Fast-growing biasing potential accelerates the sampling speed but decreases the accuracy of the free energy result. Slow-growing biasing potential gives an optimized result but needs more simulation time. In this article, we propose an alternative method. It adds the biasing potential to a representative point of the molecule in the collective variable space to improve the conformational sampling. And the free energy surface is calculated from the free energy gradient in the constrained simulation, not given by the negative of the biasing potential as previous methods. So the presented method does not require the biasing potential to remove all the barriers and basins on the free energy surface exactly. Practical applications show that the method in this work is able to produce the accurate free energy surfaces for different molecules in a short time period. The free energy errors are small in the cases of various biasing potentials. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Finite-size corrections to the free energies of crystalline solids
Polson, J.M.; Trizac, E.; Pronk, S.; Frenkel, D.
2000-01-01
We analyze the finite-size corrections to the free energy of crystals with a fixed center of mass. When we explicitly correct for the leading (ln N/N) corrections, the remaining free energy is found to depend linearly on 1/N. Extrapolating to the thermodynamic limit (N → ∞), we estimate the free
Free energy on a cycle graph and trigonometric deformation of heat kernel traces on odd spheres
Kan, Nahomi; Shiraishi, Kiyoshi
2018-01-01
We consider a possible ‘deformation’ of the trace of the heat kernel on odd dimensional spheres, motivated by the calculation of the free energy of a scalar field on a discretized circle. By using an expansion in terms of the modified Bessel functions, we obtain the values of the free energies after a suitable regularization.
Designed azurins show lower reorganization free energies for intraprotein electron transfer
Farver, Ole; Marshall, Nicholas M; Wherland, Scot
2013-01-01
Low reorganization free energies are necessary for fast electron transfer (ET) reactions. Hence, rational design of redox proteins with lower reorganization free energies has been a long-standing challenge, promising to yield a deeper understanding of the underlying principles of ET reactivity...
Incorporating the effect of ionic strength in free energy calculations using explicit ions
Donnini, S; Mark, AE; Juffer, AH; Villa, Alessandra
2005-01-01
The incorporation of explicit ions to mimic the effect of ionic strength or to neutralize the overall charge on a system in free energy calculations using molecular dynamics simulations is investigated. The difference in the free energy of hydration between two triosephosphate isomerase inhibitors
CAN THE STABILITY OF PROTEIN MUTANTS BE PREDICTED BY FREE-ENERGY CALCULATIONS
YUNYU, S; MARK, AE; WANG, CX; HUANG, FH; BERENDSEN, HJC; VANGUNSTEREN, WF
The use of free energy simulation techniques in the study of protein stability is critically evaluated. Results from two simulations of the thermostability mutation Asn218 to Ser218 in Subtilisin are presented. It is shown that components of the free energy change can be highly sensitive to the
Direct evaluation of free energy for large system through structure integration approach.
Takeuchi, Kazuhito; Tanaka, Ryohei; Yuge, Koretaka
2015-09-30
We propose a new approach, 'structure integration', enabling direct evaluation of configurational free energy for large systems. The present approach is based on the statistical information of lattice. Through first-principles-based simulation, we find that the present method evaluates configurational free energy accurately in disorder states above critical temperature.
Free energy simulations with the AMOEBA polarizable force field and metadynamics on GPU platform.
Peng, Xiangda; Zhang, Yuebin; Chu, Huiying; Li, Guohui
2016-03-05
The free energy calculation library PLUMED has been incorporated into the OpenMM simulation toolkit, with the purpose to perform enhanced sampling MD simulations using the AMOEBA polarizable force field on GPU platform. Two examples, (I) the free energy profile of water pair separation (II) alanine dipeptide dihedral angle free energy surface in explicit solvent, are provided here to demonstrate the accuracy and efficiency of our implementation. The converged free energy profiles could be obtained within an affordable MD simulation time when the AMOEBA polarizable force field is employed. Moreover, the free energy surfaces estimated using the AMOEBA polarizable force field are in agreement with those calculated from experimental data and ab initio methods. Hence, the implementation in this work is reliable and would be utilized to study more complicated biological phenomena in both an accurate and efficient way. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.
Reply to Comment on 'On the importance of the free energy for elasticity under pressure'
Marcus, P M; Qiu, S L
2004-01-01
All criticisms by Steinle-Neumann and Cohen of the correctness of our calculations of equilibrium structure and elastic constants under pressure from the Gibbs free energy are answered and the criticisms are rejected. The difference between the free energy and the internal energy as functions of structure is described to clarify the use of the free energy. The meaning of elastic constants in a system under pressure is discussed in order to derive the basic quadratic expansion of the free energy in the strains. The coefficients in the expansion are the elastic constants under pressure and are in agreement with well-known work. We give reasons why calculations based on the Gibbs free energy are simpler and more accurate than the usual calculations based on minima of the energy at constant volume. (reply)
Heavy quark free energies for three quark systems at finite temperature
Huebner, Kay; Karsch, Frithjof; Kaczmarek, Olaf; Vogt, Oliver
2008-01-01
We study the free energy of static three quark systems in singlet, octet, decuplet, and average color channels in the quenched approximation and in 2-flavor QCD at finite temperature. We show that in the high temperature phase singlet and decuplet free energies of three quark systems are well described by the sum of the free energies of three diquark systems plus self-energy contributions of the three quarks. In the confining low temperature phase we find evidence for a Y-shaped flux tube in SU(3) pure gauge theory, which is less evident in 2-flavor QCD due to the onset of string breaking. We also compare the short distance behavior of octet and decuplet free energies to the free energies of single static quarks in the corresponding color representations.
Computing the Free Energy along a Reaction Coordinate Using Rigid Body Dynamics.
Tao, Peng; Sodt, Alexander J; Shao, Yihan; König, Gerhard; Brooks, Bernard R
2014-10-14
The calculations of potential of mean force along complex chemical reactions or rare events pathways are of great interest because of their importance for many areas in chemistry, molecular biology, and material science. The major difficulty for free energy calculations comes from the great computational cost for adequate sampling of the system in high-energy regions, especially close to the reaction transition state. Here, we present a method, called FEG-RBD, in which the free energy gradients were obtained from rigid body dynamics simulations. Then the free energy gradients were integrated along a reference reaction pathway to calculate free energy profiles. In a given system, the reaction coordinates defining a subset of atoms (e.g., a solute, or the quantum mechanics (QM) region of a quantum mechanics/molecular mechanics simulation) are selected to form a rigid body during the simulation. The first-order derivatives (gradients) of the free energy with respect to the reaction coordinates are obtained through the integration of constraint forces within the rigid body. Each structure along the reference reaction path is separately subjected to such a rigid body simulation. The individual free energy gradients are integrated along the reference pathway to obtain the free energy profile. Test cases provided demonstrate both the strengths and weaknesses of the FEG-RBD method. The most significant benefit of this method comes from the fast convergence rate of the free energy gradient using rigid-body constraints instead of restraints. A correction to the free energy due to approximate relaxation of the rigid-body constraint is estimated and discussed. A comparison with umbrella sampling using a simple test case revealed the improved sampling efficiency of FEG-RBD by a factor of 4 on average. The enhanced efficiency makes this method effective for calculating the free energy of complex chemical reactions when the reaction coordinate can be unambiguously defined by a
Structural and mechanical properties of glassy water in nanoscale confinement.
Lombardo, Thomas G; Giovambattista, Nicolás; Debenedetti, Pablo G
2009-01-01
We investigate the structure and mechanical properties of glassy water confined between silica-based surfaces with continuously tunable hydrophobicity and hydrophilicity by computing and analyzing minimum energy, mechanically stable configurations (inherent structures). The structured silica substrate imposes long-range order on the first layer of water molecules under hydrophobic confinement at high density (p > or = 1.0 g cm(-3)). This proximal layer is also structured in hydrophilic confinement at very low density (p approximately 0.4 g cm(-3)). The ordering of water next to the hydrophobic surface greatly enhances the mechanical strength of thin films (0.8 nm). This leads to a substantial stress anisotropy; the transverse strength of the film exceeds the normal strength by 500 MPa. The large transverse strength results in a minimum in the equation of state of the energy landscape that does not correspond to a mechanical instability, but represents disruption of the ordered layer of water next to the wall. In addition, we find that the mode of mechanical failure is dependent on the type of confinement. Under large lateral strain, water confined by hydrophilic surfaces preferentially forms voids in the middle of the film and fails cohesively. In contrast, water under hydrophobic confinement tends to form voids near the walls and fails by loss of adhesion.
Daily, Michael D. [Fundamental and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352 (United States); Chun, Jaehun [Energy and Environment Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352 (United States); Heredia-Langner, Alejandro [National Security Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352 (United States); Wei, Guowei [Department of Mathematics, Michigan State University, East Lansing, Michigan 48824 (United States); Baker, Nathan A. [Computational and Statistical Analytics Division, Pacific Northwest National Laboratory, Richland, Washington 99352 (United States)
2013-11-28
Implicit solvent models are important tools for calculating solvation free energies for chemical and biophysical studies since they require fewer computational resources but can achieve accuracy comparable to that of explicit-solvent models. In past papers, geometric flow-based solvation models have been established for solvation analysis of small and large compounds. In the present work, the use of realistic experiment-based parameter choices for the geometric flow models is studied. We find that the experimental parameters of solvent internal pressure p = 172 MPa and surface tension γ = 72 mN/m produce solvation free energies within 1 RT of the global minimum root-mean-squared deviation from experimental data over the expanded set. Our results demonstrate that experimental values can be used for geometric flow solvent model parameters, thus eliminating the need for additional parameterization. We also examine the correlations between optimal values of p and γ which are strongly anti-correlated. Geometric analysis of the small molecule test set shows that these results are inter-connected with an approximately linear relationship between area and volume in the range of molecular sizes spanned by the data set. In spite of this considerable degeneracy between the surface tension and pressure terms in the model, both terms are important for the broader applicability of the model.
Thermonuclear reactor materials composed of glassy carbons
Kazumata, Yukio.
1979-01-01
Purpose: To improve the durability to plasma radiation by the use of glassy carbon as the structural materials for the first wall and the blanket in thermonuclear devices. Constitution: The glassy carbon (glass-like carbon) is obtained by forming specific organic substances into a predetermined configuration and carbonizing them by heat decomposition under special conditions. They are impermeable carbon material of 1.40 - 1.70 specific gravity, less graphitizable and being almost in isotropic crystal forms in which isotropic structure such as in graphite is scarcely observed. They have an extremely high hardness, are less likely to be damaged when exposed to radiation and have great strength and corrosion resistance. Accordingly, the service life of the reactor walls and the likes can remarkably be increased by using the materials. (Horiuchi, T.)
Solvated electron structure in glassy matrices
Kevan, L.
1981-01-01
Current knowledge of the detailed geometrical structure of solvated electrons in aqueous and organic media is summarized. The geometry of solvated electrons in glassy methanol, ethanol, and 2-methyltetrahydrofuran is discussed. Advanced electron magnetic resonance methods and development of new methods of analysis of electron spin echo modulation patterns, second moment line shapes, and forbidden photon spin-flip transitions for paramagnetic species in these disordered systems are discussed. 66 references are cited
Xu, H.; Wang, Y.
1999-01-01
In this letter, a linear free energy relationship is used to predict the Gibbs free energies of formation of crystalline phases of pyrochlore and zirconolite families with stoichiometry of MCaTi 2 O 7 (or, CaMTi 2 O 7 ,) from the known thermodynamic properties of aqueous tetravalent cations (M 4+ ). The linear free energy relationship for tetravalent cations is expressed as ΔG f,M v X 0 =a M v X ΔG n,M 4+ 0 +b M v X +β M v X r M 4+ , where the coefficients a M v X , b M v X , and β M v X characterize a particular structural family of M v X, r M 4+ is the ionic radius of M 4+ cation, ΔG f,M v X 0 is the standard Gibbs free energy of formation of M v X, and ΔG n,M 4+ 0 is the standard non-solvation energy of cation M 4+ . The coefficients for the structural family of zirconolite with the stoichiometry of M 4+ CaTi 2 O 7 are estimated to be: a M v X =0.5717, b M v X =-4284.67 (kJ/mol), and β M v X =27.2 (kJ/mol nm). The coefficients for the structural family of pyrochlore with the stoichiometry of M 4+ CaTi 2 O 7 are estimated to be: a M v X =0.5717, b M v X =-4174.25 (kJ/mol), and β M v X =13.4 (kJ/mol nm). Using the linear free energy relationship, the Gibbs free energies of formation of various zirconolite and pyrochlore phases are calculated. (orig.)
Computational Approach to Explore the B/A Junction Free Energy in DNA.
Kulkarni, Mandar; Mukherjee, Arnab
2016-01-04
Protein-DNA interactions induce conformational changes in DNA such as B- to A-form transitions at a local level. Such transitions are associated with a junction free energy cost at the boundary of two different conformations in a DNA molecule. In this study, we performed umbrella sampling simulations to find the free energy values of the B-A transition at the dinucleotide and trinucleotide level of DNA. Using a combination of dinucleotide and trinucleotide free energy costs obtained from simulations, we calculated the B/A junction free energy. Our study shows that the B/A junction free energy is 0.52 kcal mol(-1) for the A-philic GG step and 1.59 kcal mol(-1) for the B-philic AA step. This observation is in agreement with experimentally derived values. After excluding junction effects, we obtained an absolute free energy cost for the B- to A-form conversion for all the dinucleotide steps. These absolute free energies may be used for predicting the propensity of structural transitions in DNA. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Free-energy analysis of spin models on hyperbolic lattice geometries.
Serina, Marcel; Genzor, Jozef; Lee, Yoju; Gendiar, Andrej
2016-04-01
We investigate relations between spatial properties of the free energy and the radius of Gaussian curvature of the underlying curved lattice geometries. For this purpose we derive recurrence relations for the analysis of the free energy normalized per lattice site of various multistate spin models in the thermal equilibrium on distinct non-Euclidean surface lattices of the infinite sizes. Whereas the free energy is calculated numerically by means of the corner transfer matrix renormalization group algorithm, the radius of curvature has an analytic expression. Two tasks are considered in this work. First, we search for such a lattice geometry, which minimizes the free energy per site. We conjecture that the only Euclidean flat geometry results in the minimal free energy per site regardless of the spin model. Second, the relations among the free energy, the radius of curvature, and the phase transition temperatures are analyzed. We found out that both the free energy and the phase transition temperature inherit the structure of the lattice geometry and asymptotically approach the profile of the Gaussian radius of curvature. This achievement opens new perspectives in the AdS-CFT correspondence theories.
The elastic free energy of a tandem modular protein under force.
Valle-Orero, Jessica; Eckels, Edward C; Stirnemann, Guillaume; Popa, Ionel; Berkovich, Ronen; Fernandez, Julio M
2015-05-01
Recent studies have provided a theoretical framework for including entropic elasticity in the free energy landscape of proteins under mechanical force. Accounting for entropic elasticity using polymer physics models has helped explain the hopping behavior seen in single molecule experiments in the low force regime. Here, we expand on the construction of the free energy of a single protein domain under force proposed by Berkovich et al. to provide a free energy landscape for N tandem domains along a continuous polypeptide. Calculation of the free energy of individual domains followed by their concatenation provides a continuous free energy landscape whose curvature is dominated by the worm-like chain at forces below 20 pN. We have validated our free energy model using Brownian dynamics and reproduce key features of protein folding. This free energy model can predict the effects of changes in the elastic properties of a multidomain protein as a consequence of biological modifications such as phosphorylation or the formation of disulfide bonds. This work lays the foundations for the modeling of tissue elasticity, which is largely determined by the properties of tandem polyproteins. Copyright © 2015. Published by Elsevier Inc.
Calculation of free-energy differences from computer simulations of initial and final states
Hummer, G.; Szabo, A.
1996-01-01
A class of simple expressions of increasing accuracy for the free-energy difference between two states is derived based on numerical thermodynamic integration. The implementation of these formulas requires simulations of the initial and final (and possibly a few intermediate) states. They involve higher free-energy derivatives at these states which are related to the moments of the probability distribution of the perturbation. Given a specified number of such derivatives, these integration formulas are optimal in the sense that they are exact to the highest possible order of free-energy perturbation theory. The utility of this approach is illustrated for the hydration free energy of water. This problem provides a quite stringent test because the free energy is a highly nonlinear function of the charge so that even fourth order perturbation theory gives a very poor estimate of the free-energy change. Our results should prove most useful for complex, computationally demanding problems where free-energy differences arise primarily from changes in the electrostatic interactions (e.g., electron transfer, charging of ions, protonation of amino acids in proteins). copyright 1996 American Institute of Physics
Iwamatsu, Masao
2016-09-20
The free-energy barrier of filling a spherical cavity having an inner wall of various wettabilities is studied. The morphology and free energy of a lens-shaped droplet are determined from the minimum of the free energy. The effect of line tension on the free energy is also studied. Then, the equilibrium contact angle of the droplet is determined from the generalized Young's equation. By increasing the droplet volume within the spherical cavity, the droplet morphology changes from spherical with an equilibrium contact angle of 180° to a lens with a convex meniscus, where the morphological complete drying transition occurs. By further increasing the droplet volume, the meniscus changes from convex to concave. Then, the lens-shaped droplet with concave meniscus spreads over the whole inner wall, resulting in an equilibrium contact angle of 0° to leave a spherical bubble, where the morphological complete wetting transition occurs. Finally, the whole cavity is filled with liquid. The free energy shows a barrier from complete drying to complete wetting as a function of droplet volume, which corresponds to the energy barrier between the Cassie and Wenzel states of the superhydrophobic surface with spherical cavities. The free-energy maximum occurs when the meniscus of the droplet becomes flat, and it is given by an analytic formula. The effect of line tension is expressed by the scaled line tension, and this effect is largest at the free-energy maximum. The positive line tension increases the free-energy maximum, which thus increases the stability of the Cassie superhydrophobic state, whereas the negative line tension destabilizes the superhydrophobic state.
Inequalities for magnetic-flux free energies and confinement in lattice gauge theories
Yoneya, T.
1982-01-01
Rigorous inequalities among magnetic-flux free energies of tori with varying diameters are derived in lattice gauge theories. From the inequalities, it follows that if the magnetic-flux free energy vanishes in the limit of large uniform dilatation of a torus, the free energy must always decrease exponentially with the area of the cross section of the torus. The latter property is known to be sufficient for permanent confinement of static quarks. As a consequence of this property, a lower bound V(R) >= const x R for the static quark-antiquark potential is obtained in three-dimensional U(n) lattice gauge theory for sufficiently large R. (orig.)
Gibbs free energy of formation of liquid lanthanide-bismuth alloys
Sheng Jiawei; Yamana, Hajimu; Moriyama, Hirotake
2001-01-01
The linear free energy relationship developed by Sverjensky and Molling provides a way to predict Gibbs free energies of liquid Ln-Bi alloys formation from the known thermodynamic properties of aqueous trivalent lanthanides (Ln 3(5(6+ ). The Ln-Bi alloys are divided into two isostructural families named as the LnBi 2 (Ln=La, Ce, Pr, Nd and Pm) and LnBi (Ln=Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm and Yb). The calculated Gibbs free energy values are well agreed with experimental data
Yavari, M., E-mail: yavari@iaukashan.ac.ir [Islamic Azad University, Kashan Branch (Iran, Islamic Republic of)
2016-06-15
We generalize the results of Nesterenko [13, 14] and Gogilidze and Surovtsev [15] for DNA structures. Using the generalized Hamiltonian formalism, we investigate solutions of the equilibrium shape equations for the linear free energy model.
Knot soliton in DNA and geometric structure of its free-energy density.
Wang, Ying; Shi, Xuguang
2018-03-01
In general, the geometric structure of DNA is characterized using an elastic rod model. The Landau model provides us a new theory to study the geometric structure of DNA. By using the decomposition of the arc unit in the helical axis of DNA, we find that the free-energy density of DNA is similar to the free-energy density of a two-condensate superconductor. By using the φ-mapping topological current theory, the torus knot soliton hidden in DNA is demonstrated. We show the relation between the geometric structure and free-energy density of DNA and the Frenet equations in differential geometry theory are considered. Therefore, the free-energy density of DNA can be expressed by the curvature and torsion of the helical axis.
Olson, Mark
2004-01-01
... screening of charge-charge interactions. This paper compares different solvent models applied to the problem of estimating the free-energy difference between two loop conformations in acetylcholinesterase...
Relationship between wave energy and free energy from pickup ions in the Comet Halley environment
Huddleston, D. E.; Johnstone, A. D.
1992-01-01
The free energy available from the implanted heavy ion population at Comet Halley is calculated by assuming that the initial unstable velocity space ring distribution of the ions evolves toward a bispherical shell. Ultimately this free energy adds to the turbulence in the solar wind. Upstream and downstream free energies are obtained separately for the conditions observed along the Giotto spacecraft trajectory. The results indicate that the waves are mostly upstream propagating in the solar wind frame. The total free energy density always exceeds the measured wave energy density because, as expected in the nonlinear process of ion scattering, the available energy is not all immediately released. An estimate of the amount which has been released can be obtained from the measured oxygen ion distributions and again it exceeds that observed. The theoretical analysis is extended to calculate the k spectrum of the cometary-ion-generated turbulence.
Free Energy, Enthalpy and Entropy from Implicit Solvent End-Point Simulations.
Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro
2018-01-01
Free energy is the key quantity to describe the thermodynamics of biological systems. In this perspective we consider the calculation of free energy, enthalpy and entropy from end-point molecular dynamics simulations. Since the enthalpy may be calculated as the ensemble average over equilibrated simulation snapshots the difficulties related to free energy calculation are ultimately related to the calculation of the entropy of the system and in particular of the solvent entropy. In the last two decades implicit solvent models have been used to circumvent the problem and to take into account solvent entropy implicitly in the solvation terms. More recently outstanding advancement in both implicit solvent models and in entropy calculations are making the goal of free energy estimation from end-point simulations more feasible than ever before. We review briefly the basic theory and discuss the advancements in light of practical applications.
The free energy of locking a ring: Changing a deoxyribonucleoside to a locked nucleic acid.
Xu, You; Villa, Alessandra; Nilsson, Lennart
2017-06-05
Locked nucleic acid (LNA), a modified nucleoside which contains a bridging group across the ribose ring, improves the stability of DNA/RNA duplexes significantly, and therefore is of interest in biotechnology and gene therapy applications. In this study, we investigate the free energy change between LNA and DNA nucleosides. The transformation requires the breaking of the bridging group across the ribose ring, a problematic transformation in free energy calculations. To address this, we have developed a 3-step (easy to implement) and a 1-step protocol (more efficient, but more complicated to setup), for single and dual topologies in classical molecular dynamics simulations, using the Bennett Acceptance Ratio method to calculate the free energy. We validate the approach on the solvation free energy difference for the nucleosides thymidine, cytosine, and 5-methyl-cytosine. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.
Free energy change of a dislocation due to a Cottrell atmosphere
Sills, R. B.; Cai, W.
2018-06-01
The free energy reduction of a dislocation due to a Cottrell atmosphere of solutes is computed using a continuum model. We show that the free energy change is composed of near-core and far-field components. The far-field component can be computed analytically using the linearized theory of solid solutions. Near the core the linearized theory is inaccurate, and the near-core component must be computed numerically. The influence of interactions between solutes in neighbouring lattice sites is also examined using the continuum model. We show that this model is able to reproduce atomistic calculations of the nickel-hydrogen system, predicting hydride formation on dislocations. The formation of these hydrides leads to dramatic reductions in the free energy. Finally, the influence of the free energy change on a dislocation's line tension is examined by computing the equilibrium shape of a dislocation shear loop and the activation stress for a Frank-Read source using discrete dislocation dynamics.
The calculation of surface free energy based on embedded atom method for solid nickel
Luo Wenhua; Hu Wangyu; Su Kalin; Liu Fusheng
2013-01-01
Highlights: ► A new solution for accurate prediction of surface free energy based on embedded atom method was proposed. ► The temperature dependent anisotropic surface energy of solid nickel was obtained. ► In isotropic environment, the approach does not change most predictions of bulk material properties. - Abstract: Accurate prediction of surface free energy of crystalline metals is a challenging task. The theory calculations based on embedded atom method potentials often underestimate surface free energy of metals. With an analytical charge density correction to the argument of the embedding energy of embedded atom method, an approach to improve the prediction for surface free energy is presented. This approach is applied to calculate the temperature dependent anisotropic surface energy of bulk nickel and surface energies of nickel nanoparticles, and the obtained results are in good agreement with available experimental data.
Free Energy, Enthalpy and Entropy from Implicit Solvent End-Point Simulations
Federico Fogolari
2018-02-01
Full Text Available Free energy is the key quantity to describe the thermodynamics of biological systems. In this perspective we consider the calculation of free energy, enthalpy and entropy from end-point molecular dynamics simulations. Since the enthalpy may be calculated as the ensemble average over equilibrated simulation snapshots the difficulties related to free energy calculation are ultimately related to the calculation of the entropy of the system and in particular of the solvent entropy. In the last two decades implicit solvent models have been used to circumvent the problem and to take into account solvent entropy implicitly in the solvation terms. More recently outstanding advancement in both implicit solvent models and in entropy calculations are making the goal of free energy estimation from end-point simulations more feasible than ever before. We review briefly the basic theory and discuss the advancements in light of practical applications.
An asymptotic formula for the free energy density of ideal quantum gases
Mackowiak, J.
1988-01-01
It is shown that the expressions for the free energy density of ideal quantum gases in the canonical and grand canonical ensembles, are identical up to additive terms which vanish in the thermodynamic limit. (orig.)
Hritz, J.; Oostenbrink, C.
2009-01-01
Compounds with high intramolecular energy barriers represent challenging targets for free energy calculations because of the difficulty to obtain sufficient conformational sampling. Existing approaches are therefore computationally very demanding, thus preventing practical applications for such
A free energy study of the liquid-liquid phase transition of the Jagla ...
Appendix” preliminary free energy surface calculations for select parameterizations of the generalized family of Jagla potentials spanning from the original (anomalous,water-like) Jagla model to the Lennard-Jones model. These calculations ...
Wai, C. M.; Hutchinson, S. G.
1989-01-01
Discusses the calculation of free energy in reactions between silicon dioxide and carbon. Describes several computer programs for calculating the free energy minimization and their uses in chemistry classrooms. Lists 16 references. (YP)
Frimurer, Thomas M.; Günther, Peter H.; Sørensen, Morten Dahl
1999-01-01
adiabatic mapping, conformational change, essentialdynamics, free energy simulations, Kunitz type inhibitor *ga3(VI)......adiabatic mapping, conformational change, essentialdynamics, free energy simulations, Kunitz type inhibitor *ga3(VI)...
2015-01-01
The reliability of free energy simulations (FES) is limited by two factors: (a) the need for correct sampling and (b) the accuracy of the computational method employed. Classical methods (e.g., force fields) are typically used for FES and present a myriad of challenges, with parametrization being a principle one. On the other hand, parameter-free quantum mechanical (QM) methods tend to be too computationally expensive for adequate sampling. One widely used approach is a combination of methods, where the free energy difference between the two end states is computed by, e.g., molecular mechanics (MM), and the end states are corrected by more accurate methods, such as QM or hybrid QM/MM techniques. Here we report two new approaches that significantly improve the aforementioned scheme; with a focus on how to compute corrections between, e.g., the MM and the more accurate QM calculations. First, a molecular dynamics trajectory that properly samples relevant conformational degrees of freedom is generated. Next, potential energies of each trajectory frame are generated with a QM or QM/MM Hamiltonian. Free energy differences are then calculated based on the QM or QM/MM energies using either a non-Boltzmann Bennett approach (QM-NBB) or non-Boltzmann free energy perturbation (NB-FEP). Both approaches are applied to calculate relative and absolute solvation free energies in explicit and implicit solvent environments. Solvation free energy differences (relative and absolute) between ethane and methanol in explicit solvent are used as the initial test case for QM-NBB. Next, implicit solvent methods are employed in conjunction with both QM-NBB and NB-FEP to compute absolute solvation free energies for 21 compounds. These compounds range from small molecules such as ethane and methanol to fairly large, flexible solutes, such as triacetyl glycerol. Several technical aspects were investigated. Ultimately some best practices are suggested for improving methods that seek to connect
Free energy diagram for the heterogeneous enzymatic hydrolysis of glycosidic bonds in cellulose
Westh, Peter; Cruys-Bagger, Nicolaj; Sørensen, Trine Holst
2015-01-01
for all stable and activated complexes defined by the reaction scheme, and hence propose a free energy diagram for the full heterogeneous process. For other Cel7A enzymes, including variants with and without carbohydrate binding module (CBM), we obtained activation parameters for the association...... no influence on the transition state for association, but increased the free energy barrier for dissociation. Hence, the CBM appeared to promote the stability of the complex by delaying dissociation rather than accelerating association....
A Python tool to set up relative free energy calculations in GROMACS.
Klimovich, Pavel V; Mobley, David L
2015-11-01
Free energy calculations based on molecular dynamics (MD) simulations have seen a tremendous growth in the last decade. However, it is still difficult and tedious to set them up in an automated manner, as the majority of the present-day MD simulation packages lack that functionality. Relative free energy calculations are a particular challenge for several reasons, including the problem of finding a common substructure and mapping the transformation to be applied. Here we present a tool, alchemical-setup.py, that automatically generates all the input files needed to perform relative solvation and binding free energy calculations with the MD package GROMACS. When combined with Lead Optimization Mapper (LOMAP; Liu et al. in J Comput Aided Mol Des 27(9):755-770, 2013), recently developed in our group, alchemical-setup.py allows fully automated setup of relative free energy calculations in GROMACS. Taking a graph of the planned calculations and a mapping, both computed by LOMAP, our tool generates the topology and coordinate files needed to perform relative free energy calculations for a given set of molecules, and provides a set of simulation input parameters. The tool was validated by performing relative hydration free energy calculations for a handful of molecules from the SAMPL4 challenge (Mobley et al. in J Comput Aided Mol Des 28(4):135-150, 2014). Good agreement with previously published results and the straightforward way in which free energy calculations can be conducted make alchemical-setup.py a promising tool for automated setup of relative solvation and binding free energy calculations.
Roy, Arijit; Gururajan, M P
2017-01-01
A wide variety of morphologies arise due to the tetragonal anisotropy in interfacial free energy. In this paper, we report on a family of Extended Cahn-Hilliard (ECH) models for incorporating tetragonal anisotropy in interfacial free energy. We list the non-zero and independent parameters that are introduced in our model and list the constraints on them. For appropriate choice of these parameters, our model can produce a many of the morphologies seen in tetragonal systems such as di-pyramids,...
Chen, Changjun
2016-03-31
The free energy landscape is the most important information in the study of the reaction mechanisms of the molecules. However, it is difficult to calculate. In a large collective variable space, a molecule must take a long time to obtain the sufficient sampling during the simulation. To save the calculation quantity, decreasing the sampling region and constructing the local free energy landscape is required in practice. However, the restricted region in the collective variable space may have an irregular shape. Simply restricting one or more collective variables of the molecule cannot satisfy the requirement. In this paper, we propose a modified tomographic method to perform the simulation. First, it divides the restricted region by some hyperplanes and connects the centers of hyperplanes together by a curve. Second, it forces the molecule to sample on the curve and the hyperplanes in the simulation and calculates the free energy data on them. Finally, all the free energy data are combined together to form the local free energy landscape. Without consideration of the area outside the restricted region, this free energy calculation can be more efficient. By this method, one can further optimize the path quickly in the collective variable space.
Chemical Denaturants Smoothen Ruggedness on the Free Energy Landscape of Protein Folding.
Malhotra, Pooja; Jethva, Prashant N; Udgaonkar, Jayant B
2017-08-08
To characterize experimentally the ruggedness of the free energy landscape of protein folding is challenging, because the distributed small free energy barriers are usually dominated by one, or a few, large activation free energy barriers. This study delineates changes in the roughness of the free energy landscape by making use of the observation that a decrease in ruggedness is accompanied invariably by an increase in folding cooperativity. Hydrogen exchange (HX) coupled to mass spectrometry was used to detect transient sampling of local energy minima and the global unfolded state on the free energy landscape of the small protein single-chain monellin. Under native conditions, local noncooperative openings result in interconversions between Boltzmann-distributed intermediate states, populated on an extremely rugged "uphill" energy landscape. The cooperativity of these interconversions was increased by selectively destabilizing the native state via mutations, and further by the addition of a chemical denaturant. The perturbation of stability alone resulted in seven backbone amide sites exchanging cooperatively. The size of the cooperatively exchanging and/or unfolding unit did not depend on the extent of protein destabilization. Only upon the addition of a denaturant to a destabilized mutant variant did seven additional backbone amide sites exchange cooperatively. Segmentwise analysis of the HX kinetics of the mutant variants further confirmed that the observed increase in cooperativity was due to the smoothing of the ruggedness of the free energy landscape of folding of the protein by the chemical denaturant.
Binding free energy analysis of protein-protein docking model structures by evERdock.
Takemura, Kazuhiro; Matubayasi, Nobuyuki; Kitao, Akio
2018-03-14
To aid the evaluation of protein-protein complex model structures generated by protein docking prediction (decoys), we previously developed a method to calculate the binding free energies for complexes. The method combines a short (2 ns) all-atom molecular dynamics simulation with explicit solvent and solution theory in the energy representation (ER). We showed that this method successfully selected structures similar to the native complex structure (near-native decoys) as the lowest binding free energy structures. In our current work, we applied this method (evERdock) to 100 or 300 model structures of four protein-protein complexes. The crystal structures and the near-native decoys showed the lowest binding free energy of all the examined structures, indicating that evERdock can successfully evaluate decoys. Several decoys that show low interface root-mean-square distance but relatively high binding free energy were also identified. Analysis of the fraction of native contacts, hydrogen bonds, and salt bridges at the protein-protein interface indicated that these decoys were insufficiently optimized at the interface. After optimizing the interactions around the interface by including interfacial water molecules, the binding free energies of these decoys were improved. We also investigated the effect of solute entropy on binding free energy and found that consideration of the entropy term does not necessarily improve the evaluations of decoys using the normal model analysis for entropy calculation.
Interfacial free energy governs single polystyrene chain collapse in water and aqueous solutions.
Li, Isaac T S; Walker, Gilbert C
2010-05-12
The hydrophobic interaction is significantly responsible for driving protein folding and self-assembly. To understand it, the thermodynamics, the role of water structure, the dewetting process surrounding hydrophobes, and related aspects have undergone extensive investigations. Here, we examine the hypothesis that polymer-solvent interfacial free energy is adequate to describe the energetics of the collapse of a hydrophobic homopolymer chain at fixed temperature, which serves as a much simplified model for studying the hydrophobic collapse of a protein. This implies that changes in polymer-solvent interfacial free energy should be directly proportional to the force to extend a collapsed polymer into a bad solvent. To test this hypothesis, we undertook single-molecule force spectroscopy on a collapsed, single, polystyrene chain in water-ethanol and water-salt mixtures where we measured the monomer solvation free energy from an ensemble average conformations. Different proportions within the binary mixture were used to create solvents with different interfacial free energies with polystyrene. In these mixed solvents, we observed a linear correlation between the interfacial free energy and the force required to extend the chain into solution, which is a direct measure of the solvation free energy per monomer on a single chain at room temperature. A simple analytical model compares favorably with the experimental results. This knowledge supports a common assumption that explicit water solvent may not be necessary for cases whose primary concerns are hydrophobic interactions and hydrophobic hydration.
Metadyn View: Fast web-based viewer of free energy surfaces calculated by metadynamics
Hošek, Petr; Spiwok, Vojtěch
2016-01-01
Metadynamics is a highly successful enhanced sampling technique for simulation of molecular processes and prediction of their free energy surfaces. An in-depth analysis of data obtained by this method is as important as the simulation itself. Although there are several tools to compute free energy surfaces from metadynamics data, they usually lack user friendliness and a build-in visualization part. Here we introduce Metadyn View as a fast and user friendly viewer of bias potential/free energy surfaces calculated by metadynamics in Plumed package. It is based on modern web technologies including HTML5, JavaScript and Cascade Style Sheets (CSS). It can be used by visiting the web site and uploading a HILLS file. It calculates the bias potential/free energy surface on the client-side, so it can run online or offline without necessity to install additional web engines. Moreover, it includes tools for measurement of free energies and free energy differences and data/image export.
Duignan, Timothy T.; Baer, Marcel D.; Schenter, Gregory K.; Mundy, Chistopher J.
2017-10-01
Determining the solvation free energies of single ions in water is one of the most fundamental problems in physical chemistry and yet many unresolved questions remain. In particular, the ability to decompose the solvation free energy into simple and intuitive contributions will have important implications for models of electrolyte solution. Here, we provide definitions of the various types of single ion solvation free energies based on different simulation protocols. We calculate solvation free energies of charged hard spheres using density functional theory interaction potentials with molecular dynamics simulation and isolate the effects of charge and cavitation, comparing to the Born (linear response) model. We show that using uncorrected Ewald summation leads to unphysical values for the single ion solvation free energy and that charging free energies for cations are approximately linear as a function of charge but that there is a small non-linearity for small anions. The charge hydration asymmetry for hard spheres, determined with quantum mechanics, is much larger than for the analogous real ions. This suggests that real ions, particularly anions, are significantly more complex than simple charged hard spheres, a commonly employed representation.
Workman, Christopher; Krogh, Anders Stærmose
1999-01-01
This work investigates whether mRNA has a lower estimated folding free energy than random sequences. The free energy estimates are calculated by the mfold program for prediction of RNA secondary structures. For a set of 46 mRNAs it is shown that the predicted free energy is not significantly diff...
Spatially heterogeneous ages in glassy dynamics
Castillo, Horacio E.; Chamon, Claudio Chamon; Cugliandolo, Leticia F.; Iguain, Jose Luis; Kennett, Malcolm P.
2003-09-01
We construct a framework for the study of fluctuations in the nonequilibrium relaxation of glassy systems with and without quenched disorder. We study two types of two-time local correlators with the aim of characterizing the heterogeneous evolution in these systems: in one case we average the local correlators over histories of the thermal noise, in the other case we simply coarse-grain the local correlators obtained for a given noise realization. We explain why the noise-averaged correlators describe the fingerprint of quenched disorder when it exists, while the coarse-grained correlators are linked to noise-induced mesoscopic fluctuations. We predict constraints on the distribution of the fluctuations of the coarse-grained quantities. In particular, we show that locally defined correlations and responses are connected by a generalized local out-of-equilibrium fluctuation-dissipation relation. We argue that large size heterogeneities in the age of the system survive in the long-time limit. A symmetry of the underlying theory, namely invariance under reparametrizations of the time coordinates, underlies these results. We establish a connection between the probabilities of spatial distributions of local coarse-grained quantities and the theory of dynamic random manifolds. We define, and discuss the behavior of, a two-time dependent correlation length from the spatial decay of the fluctuations in the two-time local functions. We characterize the fluctuations in the system in terms of their fractal properties. For concreteness, we present numerical tests performed on disordered spin models in finite and infinite dimensions. Finally, we explain how these ideas can be applied to the analysis of the dynamics of other glassy systems that can be either spin models without disorder or atomic and molecular glassy systems. (author)
Martyushev, Leonid M.
2018-03-01
processes occurring at constant temperatures and volumes. In physics, the minimum free energy corresponds to an equilibrium state to which an isochoric-isothermal system relaxes [4,5]. It is obvious that the biological systems considered by the authors are fundamentally non-equilibrium, do not seek equilibrium, and, in most cases, do not retain their volumes as they develop. For a biological system, the equilibrium means death, decay. Therefore, to base the idea of life on FEP is the same as to state that the pursuit of death is the purpose and meaning of life. In order to consider processes addressed by the authors, one needs functionals employed in non-equilibrium rather than equilibrium thermodynamics [6-8]. Specifically, I would like to draw their attention to the rate of change of the Gibbs energy with time, or entropy production (the maximum entropy production principle can be useful here [7,9-12]).
Glassy slags as novel waste forms for remediating mixed wastes with high metal contents
Feng, X.; Wronkiewicz, D.J.; Bates, J.K.; Brown, N.R.; Buck, E.C.; Gong, M.; Ebert, W.L.
1994-01-01
Argonne National Laboratory (ANL) is developing a glassy slag final waste form for the remediation of low-level radioactive and mixed wastes with high metal contents. This waste form is composed of various crystalline and metal oxide phases embedded in a silicate glass phase. This work indicates that glassy slag shows promise as final waste form because (1) it has similar or better chemical durability than high-level nuclear waste (HLW) glasses, (2) it can incorporate large amounts of metal wastes, (3) it can incorporate waste streams having low contents of flux components (boron and alkalis), (4) it has less stringent processing requirements (e.g., viscosity and electric conductivity) than glass waste forms, (5) its production can require little or no purchased additives, which can result in greater reduction in waste volume and overall treatment costs. By using glassy slag waste forms, minimum additive waste stabilization approach can be applied to a much wider range of waste streams than those amenable only to glass waste forms
Computational scheme for pH-dependent binding free energy calculation with explicit solvent.
Lee, Juyong; Miller, Benjamin T; Brooks, Bernard R
2016-01-01
We present a computational scheme to compute the pH-dependence of binding free energy with explicit solvent. Despite the importance of pH, the effect of pH has been generally neglected in binding free energy calculations because of a lack of accurate methods to model it. To address this limitation, we use a constant-pH methodology to obtain a true ensemble of multiple protonation states of a titratable system at a given pH and analyze the ensemble using the Bennett acceptance ratio (BAR) method. The constant pH method is based on the combination of enveloping distribution sampling (EDS) with the Hamiltonian replica exchange method (HREM), which yields an accurate semi-grand canonical ensemble of a titratable system. By considering the free energy change of constraining multiple protonation states to a single state or releasing a single protonation state to multiple states, the pH dependent binding free energy profile can be obtained. We perform benchmark simulations of a host-guest system: cucurbit[7]uril (CB[7]) and benzimidazole (BZ). BZ experiences a large pKa shift upon complex formation. The pH-dependent binding free energy profiles of the benchmark system are obtained with three different long-range interaction calculation schemes: a cutoff, the particle mesh Ewald (PME), and the isotropic periodic sum (IPS) method. Our scheme captures the pH-dependent behavior of binding free energy successfully. Absolute binding free energy values obtained with the PME and IPS methods are consistent, while cutoff method results are off by 2 kcal mol(-1) . We also discuss the characteristics of three long-range interaction calculation methods for constant-pH simulations. © 2015 The Protein Society.
Heenan, Patrick R; Yu, Hao; Siewny, Matthew G W; Perkins, Thomas T
2018-03-28
Precisely quantifying the energetics that drive the folding of membrane proteins into a lipid bilayer remains challenging. More than 15 years ago, atomic force microscopy (AFM) emerged as a powerful tool to mechanically extract individual membrane proteins from a lipid bilayer. Concurrently, fluctuation theorems, such as the Jarzynski equality, were applied to deduce equilibrium free energies (ΔG 0 ) from non-equilibrium single-molecule force spectroscopy records. The combination of these two advances in single-molecule studies deduced the free-energy of the model membrane protein bacteriorhodopsin in its native lipid bilayer. To elucidate this free-energy landscape at a higher resolution, we applied two recent developments. First, as an input to the reconstruction, we used force-extension curves acquired with a 100-fold higher time resolution and 10-fold higher force precision than traditional AFM studies of membrane proteins. Next, by using an inverse Weierstrass transform and the Jarzynski equality, we removed the free energy associated with the force probe and determined the molecular free-energy landscape of the molecule under study, bacteriorhodopsin. The resulting landscape yielded an average unfolding free energy per amino acid (aa) of 1.0 ± 0.1 kcal/mol, in agreement with past single-molecule studies. Moreover, on a smaller spatial scale, this high-resolution landscape also agreed with an equilibrium measurement of a particular three-aa transition in bacteriorhodopsin that yielded 2.7 kcal/mol/aa, an unexpectedly high value. Hence, while average unfolding ΔG 0 per aa is a useful metric, the derived high-resolution landscape details significant local variation from the mean. More generally, we demonstrated that, as anticipated, the inverse Weierstrass transform is an efficient means to reconstruct free-energy landscapes from AFM data.
How Glassy States Affect Brown Carbon Production?
Liu, P.; Li, Y.; Wang, Y.; Bateman, A. P.; Zhang, Y.; Gong, Z.; Gilles, M. K.; Martin, S. T.
2015-12-01
Secondary organic material (SOM) can become light-absorbing (i.e. brown carbon) via multiphase reactions with nitrogen-containing species such as ammonia and amines. The physical states of SOM, however, potentially slow the diffusion of reactant molecules in organic matrix under conditions that semisolids or solids prevail, thus inhibiting the browning reaction pathways. In this study, the physical states and the in-particle diffusivity were investigated by measuring the evaporation kinetics of both water and organics from aromatic-derived SOMs using a quartz-crystal-microbalance (QCM). The results indicate that the SOMs derived from aromatic precursors toluene and m-xylene became solid (glassy) and the in particle diffusion was significantly impeded for sufficiently low relative humidity ( toluene-derived SOM after ammonia exposure at varied RHs. The results suggest that the production of light-absorbing nitrogen-containing compounds from multiphase reactions with ammonia was kinetically limited in the glassy organic matrix, which otherwise produce brown carbon. The results of this study have significant implications for production and optical properties of brown carbon in urban atmospheres that ultimately influence the climate and tropospheric photochemistry.
The sorption induced glass transition in amorphous glassy polymers
van der Vegt, N.F.A.; Wessling, Matthias; Strathmann, H.; Briels, Willem J.
1999-01-01
Sorption of CO2 in both the glassy and the rubbery state of an amorphous polyethylenelike polymer was investigated using molecular dynamics simulations. The temperature was chosen such that the system was in its glassy state at low solute concentrations and its rubbery state at large solute
Atmospheric pressure plasma treatment of glassy carbon for adhesion improvement
Kusano, Yukihiro; Mortensen, Henrik Junge; Stenum, Bjarne
2007-01-01
density increased with the plasma treatments. Adhesion test of the treated glassy carbon covered with cured epoxy showed cohesive failure, indicating strong bonding after the treatments. This is in contrast to the adhesion tests of untreated samples where the epoxy readily peeled off the glassy carbon....
Tozzi, Arturo; Peters, James F.
2018-03-01
The paper by Ramstead et al. [1] [in this issue] reminds us the efforts of eminent scientists such as Whitehead and Godel. After having produced influential manuscripts, they turned to more philosophical issues, understanding the need for a larger formalization of their bounteous scientific results [2,3]. In a similar way, the successful free-energy principle has been generalized, in order to encompass not only the brain activity of the original formulation, but also the whole spectrum of life [1]. The final result is of prominent importance, because, in touch with Quine's naturalized epistemology [4] and Badiou's account of set theory [5], provides philosophical significance to otherwise purely scientific matters. The free energy principle becomes a novel paradigm that attempts to explain general physical/biological mechanisms in the light of a novel scientific ontology, the "variational neuroethology". The latter, seemingly grounded in a recursive multilevel reductionistic/emergentistic approach à la Bechtel [6], has also its roots in a rationalistic top-down approach that, starting from mathematical/physical general concepts (von Helmholtz's free energy), formulates experimentally testable (and falsifiable) theories.
Bishop, Kevin P; Roy, Pierre-Nicholas
2018-03-14
Free energy calculations are a crucial part of understanding chemical systems but are often computationally expensive for all but the simplest of systems. Various enhanced sampling techniques have been developed to improve the efficiency of these calculations in numerical simulations. However, the majority of these approaches have been applied using classical molecular dynamics. There are many situations where nuclear quantum effects impact the system of interest and a classical description fails to capture these details. In this work, path integral molecular dynamics has been used in conjunction with umbrella sampling, and it has been observed that correct results are only obtained when the umbrella sampling potential is applied to a single path integral bead post quantization. This method has been validated against a Lennard-Jones benchmark system before being applied to the more complicated water dimer system over a broad range of temperatures. Free energy profiles are obtained, and these are utilized in the calculation of the second virial coefficient as well as the change in free energy from the separated water monomers to the dimer. Comparisons to experimental and ground state calculation values from the literature are made for the second virial coefficient at higher temperature and the dissociation energy of the dimer in the ground state.
Lee, Geun Woo; Jeon, Sangho; Park, Cheolmin; Kang, Dong-Hee
2013-01-01
Highlights: • Thermophysical properties of liquid Ti are obtained by electrostatic levitation. • How to measure the thermophysical properties is shown with non-contact method. • Hypercooling limit of liquid Ti guarantying homogeneous nucleation is 341 K. • Accurate ratio C p /ε T of the liquid Ti is obtained with weak temperature dependence. • Interfacial free energy of Ti is estimated with the thermophysical parameters. -- Abstract: Thermophysical properties of liquid Ti are measured by a newly developed electrostatic levitation. In this study, we measure a hypercooling limit (ΔT hyp ), specific heat (C p ), total hemispherical emissivity (ε T ), and density (ρ) of liquid Ti. The ΔT hyp of the liquid Ti is 341 K. The C p of the liquid Ti shows very weak temperature dependence during supercooling. The ε T and ρ of the liquid Ti are given by 0.329 and ρ(T) (g/cm 3 ) = (4.16 − 2.36) · 10 −4 (T − T m ). Finally, the interfacial free energy is estimated with the measured thermophysical parameters. The interfacial free energy is 0.164 J/m 2 , and Turnbull’s coefficient is 0.48
The Gibbs free energy of homogeneous nucleation: From atomistic nuclei to the planar limit.
Cheng, Bingqing; Tribello, Gareth A; Ceriotti, Michele
2017-09-14
In this paper we discuss how the information contained in atomistic simulations of homogeneous nucleation should be used when fitting the parameters in macroscopic nucleation models. We show how the number of solid and liquid atoms in such simulations can be determined unambiguously by using a Gibbs dividing surface and how the free energy as a function of the number of solid atoms in the nucleus can thus be extracted. We then show that the parameters (the chemical potential, the interfacial free energy, and a Tolman correction) of a model based on classical nucleation theory can be fitted using the information contained in these free-energy profiles but that the parameters in such models are highly correlated. This correlation is unfortunate as it ensures that small errors in the computed free energy surface can give rise to large errors in the extrapolated properties of the fitted model. To resolve this problem we thus propose a method for fitting macroscopic nucleation models that uses simulations of planar interfaces and simulations of three-dimensional nuclei in tandem. We show that when the chemical potentials and the interface energy are pinned to their planar-interface values, more precise estimates for the Tolman length are obtained. Extrapolating the free energy profile obtained from small simulation boxes to larger nuclei is thus more reliable.
Nagura, Yuko; Tsujimoto, Akimasa; Barkmeier, Wayne W; Watanabe, Hidehiko; Johnson, William W; Takamizawa, Toshiki; Latta, Mark A; Miyazaki, Masashi
2018-04-01
The relationship between enamel bond fatigue durability and surface free-energy characteristics with universal adhesives was investigated. The initial shear bond strengths and shear fatigue strengths of five universal adhesives to enamel were determined with and without phosphoric acid pre-etching. The surface free-energy characteristics of adhesive-treated enamel with and without pre-etching were also determined. The initial shear bond strength and shear fatigue strength of universal adhesive to pre-etched enamel were higher than those to ground enamel. The initial shear bond strength and shear fatigue strength of universal adhesive to pre-etched enamel were material dependent, unlike those to ground enamel. The surface free-energy of the solid (γ S ) and the hydrogen-bonding force (γSh) of universal adhesive-treated enamel were different depending on the adhesive, regardless of the presence or absence of pre-etching. The bond fatigue durability of universal adhesives was higher to pre-etched enamel than to ground enamel. In addition, the bond fatigue durability to pre-etched enamel was material dependent, unlike that to ground enamel. The surface free-energy characteristics of universal adhesive-treated enamel were influenced by the adhesive type, regardless of the presence or absence of pre-etching. The surface free-energy characteristics of universal adhesive-treated enamel were related to the results of the bond fatigue durability. © 2018 Eur J Oral Sci.
SAAMBE: Webserver to Predict the Charge of Binding Free Energy Caused by Amino Acids Mutations.
Petukh, Marharyta; Dai, Luogeng; Alexov, Emil
2016-04-12
Predicting the effect of amino acid substitutions on protein-protein affinity (typically evaluated via the change of protein binding free energy) is important for both understanding the disease-causing mechanism of missense mutations and guiding protein engineering. In addition, researchers are also interested in understanding which energy components are mostly affected by the mutation and how the mutation affects the overall structure of the corresponding protein. Here we report a webserver, the Single Amino Acid Mutation based change in Binding free Energy (SAAMBE) webserver, which addresses the demand for tools for predicting the change of protein binding free energy. SAAMBE is an easy to use webserver, which only requires that a coordinate file be inputted and the user is provided with various, but easy to navigate, options. The user specifies the mutation position, wild type residue and type of mutation to be made. The server predicts the binding free energy change, the changes of the corresponding energy components and provides the energy minimized 3D structure of the wild type and mutant proteins for download. The SAAMBE protocol performance was tested by benchmarking the predictions against over 1300 experimentally determined changes of binding free energy and a Pearson correlation coefficient of 0.62 was obtained. How the predictions can be used for discriminating disease-causing from harmless mutations is discussed. The webserver can be accessed via http://compbio.clemson.edu/saambe_webserver/.
Tinker-OpenMM: Absolute and relative alchemical free energies using AMOEBA on GPUs.
Harger, Matthew; Li, Daniel; Wang, Zhi; Dalby, Kevin; Lagardère, Louis; Piquemal, Jean-Philip; Ponder, Jay; Ren, Pengyu
2017-09-05
The capabilities of the polarizable force fields for alchemical free energy calculations have been limited by the high computational cost and complexity of the underlying potential energy functions. In this work, we present a GPU-based general alchemical free energy simulation platform for polarizable potential AMOEBA. Tinker-OpenMM, the OpenMM implementation of the AMOEBA simulation engine has been modified to enable both absolute and relative alchemical simulations on GPUs, which leads to a ∼200-fold improvement in simulation speed over a single CPU core. We show that free energy values calculated using this platform agree with the results of Tinker simulations for the hydration of organic compounds and binding of host-guest systems within the statistical errors. In addition to absolute binding, we designed a relative alchemical approach for computing relative binding affinities of ligands to the same host, where a special path was applied to avoid numerical instability due to polarization between the different ligands that bind to the same site. This scheme is general and does not require ligands to have similar scaffolds. We show that relative hydration and binding free energy calculated using this approach match those computed from the absolute free energy approach. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Koji Ogata
2018-02-01
Full Text Available The octanol–water partition coefficient (logPow is an important index for measuring solubility, membrane permeability, and bioavailability in the drug discovery field. In this paper, the logPow values of 58 compounds were predicted by alchemical free energy calculation using molecular dynamics simulation. In free energy calculations, the atomic charges of the compounds are always fixed. However, they must be recalculated for each solvent. Therefore, three different sets of atomic charges were tested using quantum chemical calculations, taking into account vacuum, octanol, and water environments. The calculated atomic charges in the different environments do not necessarily influence the correlation between calculated and experimentally measured ∆Gwater values. The largest correlation coefficient values of the solvation free energy in water and octanol were 0.93 and 0.90, respectively. On the other hand, the correlation coefficient of logPow values calculated from free energies, the largest of which was 0.92, was sensitive to the combination of the solvation free energies calculated from the calculated atomic charges. These results reveal that the solvent assumed in the atomic charge calculation is an important factor determining the accuracy of predicted logPow values.
Kearns, F L; Hudson, P S; Boresch, S; Woodcock, H L
2016-01-01
Enzyme activity is inherently linked to free energies of transition states, ligand binding, protonation/deprotonation, etc.; these free energies, and thus enzyme function, can be affected by residue mutations, allosterically induced conformational changes, and much more. Therefore, being able to predict free energies associated with enzymatic processes is critical to understanding and predicting their function. Free energy simulation (FES) has historically been a computational challenge as it requires both the accurate description of inter- and intramolecular interactions and adequate sampling of all relevant conformational degrees of freedom. The hybrid quantum mechanical molecular mechanical (QM/MM) framework is the current tool of choice when accurate computations of macromolecular systems are essential. Unfortunately, robust and efficient approaches that employ the high levels of computational theory needed to accurately describe many reactive processes (ie, ab initio, DFT), while also including explicit solvation effects and accounting for extensive conformational sampling are essentially nonexistent. In this chapter, we will give a brief overview of two recently developed methods that mitigate several major challenges associated with QM/MM FES: the QM non-Boltzmann Bennett's acceptance ratio method and the QM nonequilibrium work method. We will also describe usage of these methods to calculate free energies associated with (1) relative properties and (2) along reaction paths, using simple test cases with relevance to enzymes examples. © 2016 Elsevier Inc. All rights reserved.
AlaScan: A Graphical User Interface for Alanine Scanning Free-Energy Calculations.
Ramadoss, Vijayaraj; Dehez, François; Chipot, Christophe
2016-06-27
Computation of the free-energy changes that underlie molecular recognition and association has gained significant importance due to its considerable potential in drug discovery. The massive increase of computational power in recent years substantiates the application of more accurate theoretical methods for the calculation of binding free energies. The impact of such advances is the application of parent approaches, like computational alanine scanning, to investigate in silico the effect of amino-acid replacement in protein-ligand and protein-protein complexes, or probe the thermostability of individual proteins. Because human effort represents a significant cost that precludes the routine use of this form of free-energy calculations, minimizing manual intervention constitutes a stringent prerequisite for any such systematic computation. With this objective in mind, we propose a new plug-in, referred to as AlaScan, developed within the popular visualization program VMD to automate the major steps in alanine-scanning calculations, employing free-energy perturbation as implemented in the widely used molecular dynamics code NAMD. The AlaScan plug-in can be utilized upstream, to prepare input files for selected alanine mutations. It can also be utilized downstream to perform the analysis of different alanine-scanning calculations and to report the free-energy estimates in a user-friendly graphical user interface, allowing favorable mutations to be identified at a glance. The plug-in also assists the end-user in assessing the reliability of the calculation through rapid visual inspection.
BFEE: A User-Friendly Graphical Interface Facilitating Absolute Binding Free-Energy Calculations.
Fu, Haohao; Gumbart, James C; Chen, Haochuan; Shao, Xueguang; Cai, Wensheng; Chipot, Christophe
2018-03-26
Quantifying protein-ligand binding has attracted the attention of both theorists and experimentalists for decades. Many methods for estimating binding free energies in silico have been reported in recent years. Proper use of the proposed strategies requires, however, adequate knowledge of the protein-ligand complex, the mathematical background for deriving the underlying theory, and time for setting up the simulations, bookkeeping, and postprocessing. Here, to minimize human intervention, we propose a toolkit aimed at facilitating the accurate estimation of standard binding free energies using a geometrical route, coined the binding free-energy estimator (BFEE), and introduced it as a plug-in of the popular visualization program VMD. Benefitting from recent developments in new collective variables, BFEE can be used to generate the simulation input files, based solely on the structure of the complex. Once the simulations are completed, BFEE can also be utilized to perform the post-treatment of the free-energy calculations, allowing the absolute binding free energy to be estimated directly from the one-dimensional potentials of mean force in simulation outputs. The minimal amount of human intervention required during the whole process combined with the ergonomic graphical interface makes BFEE a very effective and practical tool for the end-user.
Feng, X.; Wronkiewicz, D.J.; Brown, N.R.; Gong, M.; Whitworth, C.; Filius, K.; Battleson, D.
1994-01-01
Vitrification is currently the best demonstrated available technology for the disposal of high-level radioactive wastes. An innovative vitrification approach known as minimum additive waste stabilization (MAWS) is being developed. Both homogeneous glass and glassy slags have been used in implementing MAWS. Glassy slags (vitro-ceramics) are glass-crystal composites, and they are composed of various metal oxide crystalline phases embedded in an aluminosilicate glass matrix. Glassy slags with compositions developed in crucible melts at Argonne National Laboratory (ANL) were successfully produced in a bench-scale Retech plasma centrifugal furnace (PCF) by MSE, Inc. Detailed examinations of these materials showed that the crucible melts and the PCF produced similar glass and crystalline phases. The two sets of glassy slags exhibited similar chemical durability in terms of normalized releases of their major components. The slags produced in the PCF furnace using metals were usually less oxidized, although this had no effect on the corrosion behavior of the major components of the slags. However, the normalized release rate of cerium was initially lower for the PCF slags. This difference diminished with time as the redox sates of the metal oxides in slags began to be controlled by exposure to air in the tests. Thus, the deference in cerium release due to the differences in slag redox state may be transitory. The cerium solubility is a complex function of redox state and solution pH and Eh
Free energy and plaquette expectation value for gluons on the lattice, in three dimensions
Panagopoulos, H.; Skouroupathis, A.; Tsapalis, A.
2006-01-01
We calculate the perturbative value of the free energy in lattice QCD in three dimensions, up to three loops. Our calculation is performed using the Wilson formulation for gluons in SU(N) gauge theories. The free energy is directly related to the average plaquette. To carry out the calculation, we compute the coefficients involved in the perturbative expansion of the Free Energy up to three loops, using an automated set of procedures developed by us in Mathematica. The dependence on N is shown explicitly in our results. For purposes of comparison, we also present the individual contributions from every diagram. These have been obtained by means of two independent calculations, in order to cross check our results
Absolute Hydration Free Energy of Proton from First Principles Electronic Structure Calculations
Zhan, Chang-Guo; Dixon, David A.
2001-01-01
The absolute hydration free energy of the proton, DGhyd298(H+), is one of the fundamental quantities for the thermodynamics of aqueous systems. Its exact value remains unknown despite extensive experimental and computational efforts. We report a first-principles determination of DGhyd298(H+) by using the latest developments in electronic structure theory and massively parallel computers. DGhyd298(H+) is accurately predicted to be -262.4 kcal/mol based on high-level, first-principles solvation-included electronic structure calculations. The absolute hydration free energies of other cations can be obtained by using appropriate available thermodynamic data in combination with this value. The high accuracy of the predicted absolute hydration free energy of proton is confirmed by applying the same protocol to predict DGhyd298(Li+)
The vortex free energy in the screening phase of the Z(2) Higgs model
Meyer, H.
1983-06-01
The vortex free energy was proposed to distinguish between the confinement - and the Higgs phase (in the sense of 't Hooft) in lattice gauge theory, when matter fields are present that transform according to an arbitrary representation of the gauge group. In this paper I consider the Z(2) Higgs model and calculate the vortex free energy in the screening part of the confining/screening phase of Fradkin and Shenker. The result does not agree with the expected behavior that corresponds to the structure of the phase diagram. Therefore the vortex free energy is no longer a good indicator for confinement when matter fields transform nontrivially under the center of the gauge group (such as Z(2) Higgs scalars). (orig.)
Free energies of stable and metastable pores in lipid membranes under tension.
den Otter, Wouter K
2009-11-28
The free energy profile of pore formation in a lipid membrane, covering the entire range from a density fluctuation in an intact bilayer to a large tension-stabilized pore, has been calculated by molecular dynamics simulations with a coarse-grained lipid model. Several fixed elongations are used to obtain the Helmholtz free energy as a function of pore size for thermodynamically stable, metastable, and unstable pores, and the system-size dependence of these elongations is discussed. A link to the Gibbs free energy at constant tension, commonly known as the Litster model, is established by a Legendre transformation. The change of genus upon pore formation is exploited to estimate the saddle-splay modulus or Gaussian curvature modulus of the membrane leaflets. Details are provided of the simulation approach, which combines the potential of mean constraint force method with a reaction coordinate based on the local lipid density.
Free energy calculations along entropic pathways. III. Nucleation of capillary bridges and bubbles
Desgranges, Caroline; Delhommelle, Jerome
2017-05-01
Using molecular simulation, we analyze the capillary condensation and evaporation processes for argon confined in a cylindrical nanopore. For this purpose, we define the entropy of the adsorbed fluid as a reaction coordinate and determine the free energy associated with both processes along entropic pathways. For capillary condensation, we identify a complex free energy profile resulting from the multi-stage nature of this phenomenon. We find capillary condensation to proceed through the nucleation of a liquid bridge across the nanopore, followed by its expansion throughout the pore to give rise to the stable phase of high density. In the case of capillary evaporation, the free energy profile along the entropy pathway also exhibits different regimes, corresponding to the initial destabilization of the layered structure of the fluid followed by the formation, and subsequent expansion, of a bubble across the nanopore.
Tremaine, P.R.
1979-01-01
Methods for calculating high-temprature Gibbs free energies of mononuclear cations and anions from room-temperature data are reviewed. Emphasis is given to species required for oxide solubility calculations relevant to mass transport situations in the nuclear industry. Free energies predicted by each method are compared to selected values calculated from recently reported solubility studies and other literature data. Values for monatomic ions estimated using the assumption anti C 0 p(T) = anti C 0 p(298) agree best with experiment to 423 K. From 423 K to 523 K, free energies from an electrostatic model for ion hydration are more accurate. Extrapolations for hydrolyzed species are limited by a lack of room-temperature entropy data and expressions for estimating these entropies are discussed. (orig.) [de
Grain-boundary free energy in an assembly of elastic disks.
Lusk, Mark T; Beale, Paul D
2004-02-01
Grain-boundary free energy is estimated as a function of misoriention for symmetric tilt boundaries in an assembly of nearly hard disks. Fluctuating cell theory is used to accomplish this since the most common techniques for calculating interfacial free energy cannot be applied to such assemblies. The results are analogous to those obtained using a Leonard-Jones potential, but in this case the interfacial energy is dominated by an entropic contribution. Disk assemblies colorized with free and specific volume elucidate differences between these two characteristics of boundary structure. Profiles are also provided of the Helmholtz and Gibbs free energies as a function of distance from the grain boundaries. Low angle grain boundaries are shown to follow the classical relationship between dislocation orientation/spacing and misorientation angle.
Control of the Effective Free-Energy Landscape in a Frustrated Magnet by a Field Pulse
Wan, Yuan; Moessner, Roderich
2017-10-01
Thermal fluctuations can lift the degeneracy of a ground state manifold, producing a free-energy landscape without accidentally degenerate minima. In a process known as order by disorder, a subset of states incorporating symmetry breaking may be selected. Here, we show that such a free-energy landscape can be controlled in a nonequilibrium setting as the slow motion within the ground state manifold is governed by the fast modes out of it. For the paradigmatic case of the classical pyrochlore X Y antiferromagnet, we show that a uniform magnetic field pulse can excite these fast modes to generate a tunable effective free-energy landscape with minima at thermodynamically unstable portions of the ground state manifold.
Modeling free energy availability from Hadean hydrothermal systems to the first metabolism.
Simoncini, E; Russell, M J; Kleidon, A
2011-12-01
Off-axis Hydrothermal Systems (HSs) are seen as the possible setting for the emergence of life. As the availability of free energy is a general requirement to drive any form of metabolism, we ask here under which conditions free energy generation by geologic processes is greatest and relate these to the conditions found at off-axis HSs. To do so, we present a conceptual model in which we explicitly capture the energetics of fluid motion and its interaction with exothermic reactions to maintain a state of chemical disequilibrium. Central to the interaction is the temperature at which the exothermic reactions take place. This temperature not only sets the equilibrium constant of the chemical reactions and thereby the distance of the actual state to chemical equilibrium, but these reactions also shape the temperature gradient that drives convection and thereby the advection of reactants to the reaction sites and the removal of the products that relate to geochemical free energy generation. What this conceptual model shows is that the positive feedback between convection and the chemical kinetics that is found at HSs favors a greater rate of free energy generation than in the absence of convection. Because of the lower temperatures and because the temperature of reactions is determined more strongly by these dynamics rather than an external heat flux, the conditions found at off-axis HSs should result in the greatest rates of geochemical free energy generation. Hence, we hypothesize from these thermodynamic considerations that off-axis HSs seem most conducive for the emergence of protometabolic pathways as these provide the greatest, abiotic generation rates of chemical free energy.
Morishita, Tetsuya; Yonezawa, Yasushige; Ito, Atsushi M
2017-07-11
Efficient and reliable estimation of the mean force (MF), the derivatives of the free energy with respect to a set of collective variables (CVs), has been a challenging problem because free energy differences are often computed by integrating the MF. Among various methods for computing free energy differences, logarithmic mean-force dynamics (LogMFD) [ Morishita et al., Phys. Rev. E 2012 , 85 , 066702 ] invokes the conservation law in classical mechanics to integrate the MF, which allows us to estimate the free energy profile along the CVs on-the-fly. Here, we present a method called parallel dynamics, which improves the estimation of the MF by employing multiple replicas of the system and is straightforwardly incorporated in LogMFD or a related method. In the parallel dynamics, the MF is evaluated by a nonequilibrium path-ensemble using the multiple replicas based on the Crooks-Jarzynski nonequilibrium work relation. Thanks to the Crooks relation, realizing full-equilibrium states is no longer mandatory for estimating the MF. Additionally, sampling in the hidden subspace orthogonal to the CV space is highly improved with appropriate weights for each metastable state (if any), which is hardly achievable by typical free energy computational methods. We illustrate how to implement parallel dynamics by combining it with LogMFD, which we call logarithmic parallel dynamics (LogPD). Biosystems of alanine dipeptide and adenylate kinase in explicit water are employed as benchmark systems to which LogPD is applied to demonstrate the effect of multiple replicas on the accuracy and efficiency in estimating the free energy profiles using parallel dynamics.
Water droplet excess free energy determined by cluster mitosis using guided molecular dynamics
Lau, Gabriel V.; Hunt, Patricia A.; Müller, Erich A.; Jackson, George; Ford, Ian J.
2015-12-01
Atmospheric aerosols play a vital role in affecting climate by influencing the properties and lifetimes of clouds and precipitation. Understanding the underlying microscopic mechanisms involved in the nucleation of aerosol droplets from the vapour phase is therefore of great interest. One key thermodynamic quantity in nucleation is the excess free energy of cluster formation relative to that of the saturated vapour. In our current study, the excess free energy is extracted for clusters of pure water modelled with the TIP4P/2005 intermolecular potential using a method based on nonequilibrium molecular dynamics and the Jarzynski relation. The change in free energy associated with the "mitosis" or division of a cluster of N water molecules into two N/2 sub-clusters is evaluated. This methodology is an extension of the disassembly procedure used recently to calculate the excess free energy of argon clusters [H. Y. Tang and I. J. Ford, Phys. Rev. E 91, 023308 (2015)]. Our findings are compared to the corresponding excess free energies obtained from classical nucleation theory (CNT) as well as internally consistent classical theory (ICCT). The values of the excess free energy that we obtain with the mitosis method are consistent with CNT for large cluster sizes but for the smallest clusters, the results tend towards ICCT; for intermediate sized clusters, we obtain values between the ICCT and CNT predictions. Furthermore, the curvature-dependent surface tension which can be obtained by regarding the clusters as spherical droplets of bulk density is found to be a monotonically increasing function of cluster size for the studied range. The data are compared to other values reported in the literature, agreeing qualitatively with some but disagreeing with the values determined by Joswiak et al. [J. Phys. Chem. Lett. 4, 4267 (2013)] using a biased mitosis approach; an assessment of the differences is the main motivation for our current study.
Water droplet excess free energy determined by cluster mitosis using guided molecular dynamics
Lau, Gabriel V.; Müller, Erich A.; Jackson, George [Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ (United Kingdom); Hunt, Patricia A. [Department of Chemistry, Imperial College London, South Kensington Campus, London SW7 2AZ (United Kingdom); Ford, Ian J. [Department of Physics and Astronomy and London Centre for Nanotechnology, University College London, Gower Street, London WC1E 6BT (United Kingdom)
2015-12-28
Atmospheric aerosols play a vital role in affecting climate by influencing the properties and lifetimes of clouds and precipitation. Understanding the underlying microscopic mechanisms involved in the nucleation of aerosol droplets from the vapour phase is therefore of great interest. One key thermodynamic quantity in nucleation is the excess free energy of cluster formation relative to that of the saturated vapour. In our current study, the excess free energy is extracted for clusters of pure water modelled with the TIP4P/2005 intermolecular potential using a method based on nonequilibrium molecular dynamics and the Jarzynski relation. The change in free energy associated with the “mitosis” or division of a cluster of N water molecules into two N/2 sub-clusters is evaluated. This methodology is an extension of the disassembly procedure used recently to calculate the excess free energy of argon clusters [H. Y. Tang and I. J. Ford, Phys. Rev. E 91, 023308 (2015)]. Our findings are compared to the corresponding excess free energies obtained from classical nucleation theory (CNT) as well as internally consistent classical theory (ICCT). The values of the excess free energy that we obtain with the mitosis method are consistent with CNT for large cluster sizes but for the smallest clusters, the results tend towards ICCT; for intermediate sized clusters, we obtain values between the ICCT and CNT predictions. Furthermore, the curvature-dependent surface tension which can be obtained by regarding the clusters as spherical droplets of bulk density is found to be a monotonically increasing function of cluster size for the studied range. The data are compared to other values reported in the literature, agreeing qualitatively with some but disagreeing with the values determined by Joswiak et al. [J. Phys. Chem. Lett. 4, 4267 (2013)] using a biased mitosis approach; an assessment of the differences is the main motivation for our current study.
Glassy slag from rotary hearth vitrification
Eschenbach, R.C.; Simpson, M.D.; Paulson, W.S.; Whitworth, C.G.
1995-01-01
Use of a Plasma Arc Centrifugal Treatment (PACT) system for treating mixed wastes containing significant quantities of soil results in formation of a glassy slag which melts at significantly higher temperatures than the borosilicate glasses. The slag typically contains mostly crystalline material, frequently in an amorphous matrix, thus the appellation open-quotes glassy slag.close quotes Details of the PACT process are given. The process will be used for treating buried wastes from Pit 9 at the Idaho National Engineering Laboratory and low-level mixed wastes from nuclear power plants in Switzerland. Properties of the slag after cooling to room temperature are reported, in particular the Product Consistency Test, for a number of different feedstocks. In almost all cases, the results compare favorably with conventional borosilicate glasses. In the PACT system, a transferred arc carries current from the plasma torch to a rotating molten bed of slag, which is the material being heated. Thus this transferred arc adds energy where it is needed - at and near the surface of the molten bath. Material is fed into the furnace through a sealed feeder, and falls into a rotating tub which is heated by the arc. Any organic material is quickly vaporized into the space above the slag bed and burned by the oxygen in the furnace. Metal oxides in the charge are melted into the slag. Metal in the feed tends to melt and collect as a separate phase underneath the slag, but can be oxidized if desired. When oxidized, it unites with other constituents forming a homogeneous slag
Free Energy Self-Averaging in Protein-Sized Random Heteropolymers
Chuang, Jeffrey; Grosberg, Alexander Yu.; Kardar, Mehran
2001-01-01
Current theories of heteropolymers are inherently macroscopic, but are applied to mesoscopic proteins. To compute the free energy over sequences, one assumes self-averaging -- a property established only in the macroscopic limit. By enumerating the states and energies of compact 18, 27, and 36mers on a lattice with an ensemble of random sequences, we test the self-averaging approximation. We find that fluctuations in the free energy between sequences are weak, and that self-averaging is valid at the scale of real proteins. The results validate sequence design methods which exponentially speed up computational design and simplify experimental realizations
Interaction Free Energies of Eight Sodium Salts and a Phosphatidylcholine Membrane
Wang, C. H.; Ge, Y.; Mortensen, J.
2011-01-01
Many recent reports have discussed specific effects of anions on the properties of lipid membranes and possible roles of such effects within biochemistry. One key parameter in both theoretical and experimental treatments of membrane-salt interactions is the net affinity, that is, the free energy...... salts by dialysis equilibrium measurements. This method provides model free thermodynamic data and allows investigations in the dilute concentration range where solution nonideality and perturbation of membrane structure is limited. The transfer free energy of DMPC from water to salt solutions, Delta mu...
Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach
Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro
2013-01-01
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message passing fixed-point equations obtained with this combination...... correspond to stationary points of a constrained region-based free energy approximation. Moreover, we present a convergent implementation of these message passing fixed-point equations provided that the underlying factor graph fulfills certain technical conditions. In addition, we show how to include hard...
Efficiency of free-energy calculations of spin lattices by spectral quantum algorithms
Master, Cyrus P.; Yamaguchi, Fumiko; Yamamoto, Yoshihisa
2003-01-01
Ensemble quantum algorithms are well suited to calculate estimates of the energy spectra for spin-lattice systems. Based on the phase estimation algorithm, these algorithms efficiently estimate discrete Fourier coefficients of the density of states. Their efficiency in calculating the free energy per spin of general spin lattices to bounded error is examined. We find that the number of Fourier components required to bound the error in the free energy due to the broadening of the density of states scales polynomially with the number of spins in the lattice. However, the precision with which the Fourier components must be calculated is found to be an exponential function of the system size
Xiong Shiyun; Qi Weihong; Huang Baiyun; Wang Mingpu; Li Yejun
2010-01-01
The Debye model of Helmholtz free energy for bulk material is generalized to Gibbs free energy (GFE) model for nanomaterial, while a shape factor is introduced to characterize the shape effect on GFE. The structural transitions of Ti and Zr nanoparticles are predicted based on GFE. It is further found that GFE decreases with the shape factor and increases with decreasing of the particle size. The critical size of structural transformation for nanoparticles goes up as temperature increases in the absence of change in shape factor. For specified temperature, the critical size climbs up with the increase of shape factor. The present predictions agree well with experiment values.
Polymer in a pore: Effect of confinement on the free energy barrier
Kumar, Sanjiv; Kumar, Sanjay
2018-06-01
We investigate the transfer of a polymer chain from cis- side to trans- side through two types of pores: cone-shaped channel and flat-channel. Using the exact enumeration technique, we obtain the free energy landscapes of a polymer chain for such systems. We have also calculated the free-energy barrier of a polymer chain attached to the edge of the pore. The model system allows us to calculate the force required to pull polymer from the pore and stall-force to confine polymer within the pore.
Holm, Oeystein B.
2006-01-01
Norway has fallen behind in the development of district heating and use of solar energy compared to Sweden and Denmark. It is a myth that Norway has less hours of sun than its neighbours; southern and eastern Norway has equally good conditions as areas in Sweden and Denmark that have large solar collector installations used for district heating. Benefits of the solar energy technology are highlighted, especially environmental aspects (ml)
New model system in radiation cryochemistry:. hyperquenched glassy water
Bednarek, Janusz; Plonka, Andrzej; Hallbrucker, Andreas; Mayer, Erwin
1999-08-01
Radicals generated by high-energy irradiation of liquid water, short-lived at ambient temperature, can be studied at cryogenic temperatures after irradiating water and dilute aqueous solutions in their glassy states which can be obtained by so-called hyperquenching of the liquids at cooling rates of ˜10 6-10 7 K s -1. In the glassy states of hyperquenched dilute aqueous solutions there is no problem with phase separation and radiolysis of glassy water is quite distinct from radiolysis of polycrystalline ice obtained from liquid water on slow-cooling in liquid nitrogen.
Formation of a glassy phase in ceramic-like coatings
Sazonova, M.V.; Gorbatova, G.N.
1986-01-01
The authors investigate the synthesis directly in coatings of a borosilicate melt that could fill the role of glassy matrix, thereby avoiding fusion and processing of the glassy material. The effect of added boron on the formation of coatings based on molybdenum disilicide and tungsten disilicide in air at 900 degrees C is presented. Without an additive no coating forms; there is no adhesion to the graphite and a continuous film does not form. As a result of boron oxidation an easily fused glassy matrix forms, which bonds the molybdenum disilicide or tungsten disilicide particles together and ensures adhesion to the graphite
Chung, Jun Young; Douglas, Jack F; Stafford, Christopher M
2017-10-21
We investigate the relaxation dynamics of thin polymer films at temperatures below the bulk glass transition T g by first compressing polystyrene films supported on a polydimethylsiloxane substrate to create wrinkling patterns and then observing the slow relaxation of the wrinkled films back to their final equilibrium flat state by small angle light scattering. As with recent relaxation measurements on thin glassy films reported by Fakhraai and co-workers, we find the relaxation time of our wrinkled films to be strongly dependent on film thickness below an onset thickness on the order of 100 nm. By varying the temperature between room temperature and T g (≈100 °C), we find that the relaxation time follows an Arrhenius-type temperature dependence to a good approximation at all film thicknesses investigated, where both the activation energy and the relaxation time pre-factor depend appreciably on film thickness. The wrinkling relaxation curves tend to cross at a common temperature somewhat below T g , indicating an entropy-enthalpy compensation relation between the activation free energy parameters. This compensation effect has also been observed recently in simulated supported polymer films in the high temperature Arrhenius relaxation regime rather than the glassy state. In addition, we find that the film stress relaxation function, as well as the height of the wrinkle ridges, follows a stretched exponential time dependence and the short-time effective Young's modulus derived from our modeling decreases sigmoidally with increasing temperature-both characteristic features of glassy materials. The relatively facile nature of the wrinkling-based measurements in comparison to other film relaxation measurements makes our method attractive for practical materials development, as well as fundamental studies of glass formation.
Diagrams of the variations in the free energy of formation of metallic compounds (1960)
Darras, R.; Loriers, H.
1960-01-01
The variations in the standard free energy ΔG produced during the formation of the principal simple metallic compounds have been calculated as a function of the temperature from recently published data, and are presented in convenient diagram form. Their usefulness in metallurgy is illustrated by some possible applications. (author) [fr
Enhanced conformational sampling to visualize a free-energy landscape of protein complex formation.
Iida, Shinji; Nakamura, Haruki; Higo, Junichi
2016-06-15
We introduce various, recently developed, generalized ensemble methods, which are useful to sample various molecular configurations emerging in the process of protein-protein or protein-ligand binding. The methods introduced here are those that have been or will be applied to biomolecular binding, where the biomolecules are treated as flexible molecules expressed by an all-atom model in an explicit solvent. Sampling produces an ensemble of conformations (snapshots) that are thermodynamically probable at room temperature. Then, projection of those conformations to an abstract low-dimensional space generates a free-energy landscape. As an example, we show a landscape of homo-dimer formation of an endothelin-1-like molecule computed using a generalized ensemble method. The lowest free-energy cluster at room temperature coincided precisely with the experimentally determined complex structure. Two minor clusters were also found in the landscape, which were largely different from the native complex form. Although those clusters were isolated at room temperature, with rising temperature a pathway emerged linking the lowest and second-lowest free-energy clusters, and a further temperature increment connected all the clusters. This exemplifies that the generalized ensemble method is a powerful tool for computing the free-energy landscape, by which one can discuss the thermodynamic stability of clusters and the temperature dependence of the cluster networks. © 2016 The Author(s).
Competition Experiments as a Means of Evaluating Linear Free Energy Relationships
Mullins, Richard J.; Vedernikov, Andrei; Viswanathan, Rajesh
2004-01-01
The use of competition experiments as a means of evaluating linear free energy relationship in the undergraduate teaching laboratory is reported. The use of competition experiments proved to be a reliable method for the construction of Hammett plots with good correlation providing great flexibility with regard to the compounds and reactions that…
Lee, M.W.; Meuwly, M.
2013-01-01
The evaluation of hydration free energies is a sensitive test to assess force fields used in atomistic simulations. We showed recently that the vibrational relaxation times, 1D- and 2D-infrared spectroscopies for CN(-) in water can be quantitatively described from molecular dynamics (MD) simulations with multipolar force fields and slightly enlarged van der Waals radii for the C- and N-atoms. To validate such an approach, the present work investigates the solvation free energy of cyanide in water using MD simulations with accurate multipolar electrostatics. It is found that larger van der Waals radii are indeed necessary to obtain results close to the experimental values when a multipolar force field is used. For CN(-), the van der Waals ranges refined in our previous work yield hydration free energy between -72.0 and -77.2 kcal mol(-1), which is in excellent agreement with the experimental data. In addition to the cyanide ion, we also study the hydroxide ion to show that the method used here is readily applicable to similar systems. Hydration free energies are found to sensitively depend on the intermolecular interactions, while bonded interactions are less important, as expected. We also investigate in the present work the possibility of applying the multipolar force field in scoring trajectories generated using computationally inexpensive methods, which should be useful in broader parametrization studies with reduced computational resources, as scoring is much faster than the generation of the trajectories.
Experimental Determination of Third Derivative of the Gibbs Free Energy, G II
Koga, Yoshikata; Westh, Peter; Inaba, Akira
2010-01-01
We have been evaluating third derivative quantities of the Gibbs free energy, G, by graphically differentiating the second derivatives that are accessible experimentally, and demonstrated their power in elucidating the mixing schemes in aqueous solutions. Here we determine directly one of the third...
Elfwing, Stefan; Uchibe, Eiji; Doya, Kenji
2016-12-01
Free-energy based reinforcement learning (FERL) was proposed for learning in high-dimensional state and action spaces. However, the FERL method does only really work well with binary, or close to binary, state input, where the number of active states is fewer than the number of non-active states. In the FERL method, the value function is approximated by the negative free energy of a restricted Boltzmann machine (RBM). In our earlier study, we demonstrated that the performance and the robustness of the FERL method can be improved by scaling the free energy by a constant that is related to the size of network. In this study, we propose that RBM function approximation can be further improved by approximating the value function by the negative expected energy (EERL), instead of the negative free energy, as well as being able to handle continuous state input. We validate our proposed method by demonstrating that EERL: (1) outperforms FERL, as well as standard neural network and linear function approximation, for three versions of a gridworld task with high-dimensional image state input; (2) achieves new state-of-the-art results in stochastic SZ-Tetris in both model-free and model-based learning settings; and (3) significantly outperforms FERL and standard neural network function approximation for a robot navigation task with raw and noisy RGB images as state input and a large number of actions. Copyright © 2016 The Author(s). Published by Elsevier Ltd.. All rights reserved.
Gamma-point lattice free energy estimates from O(1) force calculations
Voss, Johannes; Vegge, Tejs
2008-01-01
We present a new method for estimating the vibrational free energy of crystal (and molecular) structures employing only a single force calculation, for a particularly displaced configuration, in addition to the calculation of the ground state configuration. This displacement vector is the sum...
Ragavan, Anpalaki J.
2006-01-01
Linear free energy relationships for trivalent cations with crystalline M 2 O 3 and, M(OH) 3 phases of lanthanides and actinides were developed from known thermodynamic properties of the aqueous trivalent cations, modifying the Sverjensky and Molling equation. The linear free energy relationship for trivalent cations is as ΔG f,MvX 0 =a MvX ΔG n,M 3+ 0 +b MvX +β MvX r M 3+ , where the coefficients a MvX , b MvX , and β MvX characterize a particular structural family of MvX, r M 3+ is the ionic radius of M 3+ cation, ΔG f,MvX 0 is the standard Gibbs free energy of formation of MvX and ΔG n,M 3+ 0 is the standard non-solvation free energy of the cation. The coefficients for the oxide family are: a MvX =0.2705, b MvX =-1984.75 (kJ/mol), and β MvX =197.24 (kJ/molnm). The coefficients for the hydroxide family are: a MvX =0.1587, b MvX =-1474.09 (kJ/mol), and β MvX =791.70 (kJ/molnm).
Fast exploration of an optimal path on the multidimensional free energy surface
Chen, Changjun
2017-01-01
In a reaction, determination of an optimal path with a high reaction rate (or a low free energy barrier) is important for the study of the reaction mechanism. This is a complicated problem that involves lots of degrees of freedom. For simple models, one can build an initial path in the collective variable space by the interpolation method first and then update the whole path constantly in the optimization. However, such interpolation method could be risky in the high dimensional space for large molecules. On the path, steric clashes between neighboring atoms could cause extremely high energy barriers and thus fail the optimization. Moreover, performing simulations for all the snapshots on the path is also time-consuming. In this paper, we build and optimize the path by a growing method on the free energy surface. The method grows a path from the reactant and extends its length in the collective variable space step by step. The growing direction is determined by both the free energy gradient at the end of the path and the direction vector pointing at the product. With fewer snapshots on the path, this strategy can let the path avoid the high energy states in the growing process and save the precious simulation time at each iteration step. Applications show that the presented method is efficient enough to produce optimal paths on either the two-dimensional or the twelve-dimensional free energy surfaces of different small molecules. PMID:28542475
Free energy minimization to predict RNA secondary structures and computational RNA design.
Churkin, Alexander; Weinbrand, Lina; Barash, Danny
2015-01-01
Determining the RNA secondary structure from sequence data by computational predictions is a long-standing problem. Its solution has been approached in two distinctive ways. If a multiple sequence alignment of a collection of homologous sequences is available, the comparative method uses phylogeny to determine conserved base pairs that are more likely to form as a result of billions of years of evolution than by chance. In the case of single sequences, recursive algorithms that compute free energy structures by using empirically derived energy parameters have been developed. This latter approach of RNA folding prediction by energy minimization is widely used to predict RNA secondary structure from sequence. For a significant number of RNA molecules, the secondary structure of the RNA molecule is indicative of its function and its computational prediction by minimizing its free energy is important for its functional analysis. A general method for free energy minimization to predict RNA secondary structures is dynamic programming, although other optimization methods have been developed as well along with empirically derived energy parameters. In this chapter, we introduce and illustrate by examples the approach of free energy minimization to predict RNA secondary structures.
Kaliakin, Danil S.; Zaari, Ryan R.; Varganov, Sergey A.
2015-01-01
Teaching fundamental physical chemistry concepts such as the potential energy surface, transition state, and reaction path is a challenging task. The traditionally used oversimplified 2D representation of potential and free energy surfaces makes this task even more difficult and often confuses students. We show how this 2D representation can be…
Free energies of stable and metastable pores in lipid membranes under tension
den Otter, Wouter K.
2009-01-01
The free energy profile of pore formation in a lipid membrane, covering the entire range from a density fluctuation in an intact bilayer to a large tension-stabilized pore, has been calculated by molecular dynamics simulations with a coarse-grained lipid model. Several fixed elongations are used to
Spontaneous symmetry breaking and self-consistent equations for the free-energy
Lovesey, S.W.
1980-03-01
A variational procedure for the free-energy is used to derive self-consistent equations that allow for spontaneous symmetry breaking. For an N-component phi 4 -model the equations are identical to those obtained by summing all loops to order 1/N. (author)
Interfacial free energy of the NaCl crystal-melt interface from capillary wave fluctuations.
Benet, Jorge; MacDowell, Luis G; Sanz, Eduardo
2015-04-07
In this work we study, by means of molecular dynamics simulations, the solid-liquid interface of NaCl under coexistence conditions. By analysing capillary waves, we obtain the stiffness for different orientations of the solid and calculate the interfacial free energy by expanding the dependency of the interfacial free energy with the solid orientation in terms of cubic harmonics. We obtain an average value for the solid-fluid interfacial free energy of 89 ± 6 mN m(-1) that is consistent with previous results based on the measure of nucleation free energy barriers [Valeriani et al., J. Chem. Phys. 122, 194501 (2005)]. We analyse the influence of the simulation setup on interfacial properties and find that facets prepared as an elongated rectangular stripe give the same results as those prepared as squares for all cases but the 111 face. For some crystal orientations, we observe at small wave-vectors a behaviour not consistent with capillary wave theory and show that this behavior does not depend on the simulation setup.
Statistical mechanical perturbation theory of solid-vapor interfacial free energy
Kalikmanov, Vitalij Iosifovitsj; Hagmeijer, Rob; Venner, Cornelis H.
2017-01-01
The solid–vapor interfacial free energy γsv plays an important role in a number of physical phenomena, such as adsorption, wetting, and adhesion. We propose a closed form expression for the orientation averaged value of this quantity using a statistical mechanical perturbation approach developed in
Statistical Mechanical Perturbation Theory of Solid−Vapor Interfacial Free Energy
Kalikmanov, V.I.; Hagmeijer, R.; Venner, C.H.
2017-01-01
The solid–vapor interfacial free energy γsv plays an important role in a number of physical phenomena, such as adsorption, wetting, and adhesion. We propose a closed form expression for the orientation averaged value of this quantity using a statistical mechanical perturbation approach developed in
Using reweighting and free energy surface interpolation to predict solid-solid phase diagrams
Schieber, Natalie P.; Dybeck, Eric C.; Shirts, Michael R.
2018-04-01
Many physical properties of small organic molecules are dependent on the current crystal packing, or polymorph, of the material, including bioavailability of pharmaceuticals, optical properties of dyes, and charge transport properties of semiconductors. Predicting the most stable crystalline form at a given temperature and pressure requires determining the crystalline form with the lowest relative Gibbs free energy. Effective computational prediction of the most stable polymorph could save significant time and effort in the design of novel molecular crystalline solids or predict their behavior under new conditions. In this study, we introduce a new approach using multistate reweighting to address the problem of determining solid-solid phase diagrams and apply this approach to the phase diagram of solid benzene. For this approach, we perform sampling at a selection of temperature and pressure states in the region of interest. We use multistate reweighting methods to determine the reduced free energy differences between T and P states within a given polymorph and validate this phase diagram using several measures. The relative stability of the polymorphs at the sampled states can be successively interpolated from these points to create the phase diagram by combining these reduced free energy differences with a reference Gibbs free energy difference between polymorphs. The method also allows for straightforward estimation of uncertainties in the phase boundary. We also find that when properly implemented, multistate reweighting for phase diagram determination scales better with the size of the system than previously estimated.
Rigorous bounds on the free energy of electron-phonon models
Raedt, Hans De; Michielsen, Kristel
1997-01-01
We present a collection of rigorous upper and lower bounds to the free energy of electron-phonon models with linear electron-phonon interaction. These bounds are used to compare different variational approaches. It is shown rigorously that the ground states corresponding to the sharpest bounds do
Probing the Free Energy Landscape of the FBP28 WW Domain Using Multiple Techniques
Periole, Xavier; Allen, Lucy R.; Tamiola, Kamil; Mark, Alan E.; Paci, Emanuele
The free-energy landscape of a small protein, the FBP 28 WW domain, has been explored using molecular dynamics (MD) simulations with alternative descriptions of the molecule. The molecular models used range from coarse-grained to all-atom with either an implicit or explicit treatment of the solvent.
Kroonblawd, Matthew P; Pietrucci, Fabio; Saitta, Antonino Marco; Goldman, Nir
2018-04-10
We demonstrate the capability of creating robust density functional tight binding (DFTB) models for chemical reactivity in prebiotic mixtures through force matching to short time scale quantum free energy estimates. Molecular dynamics using density functional theory (DFT) is a highly accurate approach to generate free energy surfaces for chemical reactions, but the extreme computational cost often limits the time scales and range of thermodynamic states that can feasibly be studied. In contrast, DFTB is a semiempirical quantum method that affords up to a thousandfold reduction in cost and can recover DFT-level accuracy. Here, we show that a force-matched DFTB model for aqueous glycine condensation reactions yields free energy surfaces that are consistent with experimental observations of reaction energetics. Convergence analysis reveals that multiple nanoseconds of combined trajectory are needed to reach a steady-fluctuating free energy estimate for glycine condensation. Predictive accuracy of force-matched DFTB is demonstrated by direct comparison to DFT, with the two approaches yielding surfaces with large regions that differ by only a few kcal mol -1 .
Estimates of Gibbs free energies of formation of chlorinated aliphatic compounds
Dolfing, Jan; Janssen, Dick B.
1994-01-01
The Gibbs free energy of formation of chlorinated aliphatic compounds was estimated with Mavrovouniotis' group contribution method. The group contribution of chlorine was estimated from the scarce data available on chlorinated aliphatics in the literature, and found to vary somewhat according to the
Free-energy calculations for semi-flexible macromolecules: Applications to DNA knotting and looping
Giovan, Stefan M.; Scharein, Robert G.; Hanke, Andreas; Levene, Stephen D.
2014-01-01
We present a method to obtain numerically accurate values of configurational free energies of semiflexible macromolecular systems, based on the technique of thermodynamic integration combined with normal-mode analysis of a reference system subject to harmonic constraints. Compared with previous free-energy calculations that depend on a reference state, our approach introduces two innovations, namely, the use of internal coordinates to constrain the reference states and the ability to freely select these reference states. As a consequence, it is possible to explore systems that undergo substantially larger fluctuations than those considered in previous calculations, including semiflexible biopolymers having arbitrary ratios of contour length L to persistence length P. To validate the method, high accuracy is demonstrated for free energies of prime DNA knots with L/P = 20 and L/P = 40, corresponding to DNA lengths of 3000 and 6000 base pairs, respectively. We then apply the method to study the free-energy landscape for a model of a synaptic nucleoprotein complex containing a pair of looped domains, revealing a bifurcation in the location of optimal synapse (crossover) sites. This transition is relevant to target-site selection by DNA-binding proteins that occupy multiple DNA sites separated by large linear distances along the genome, a problem that arises naturally in gene regulation, DNA recombination, and the action of type-II topoisomerases
Free-energy calculations for semi-flexible macromolecules: Applications to DNA knotting and looping
Giovan, Stefan M. [Department of Molecular and Cell Biology, University of Texas at Dallas, Richardson, Texas 75083 (United States); Scharein, Robert G. [Hypnagogic Software, Vancouver, British Columbia V6K 1V6 (Canada); Hanke, Andreas [Department of Physics and Astronomy, University of Texas at Brownsville, Brownsville, Texas 78520 (United States); Levene, Stephen D., E-mail: sdlevene@utdallas.edu [Department of Molecular and Cell Biology, University of Texas at Dallas, Richardson, Texas 75083 (United States); Department of Bioengineering, University of Texas at Dallas, Richardson, Texas 75083 (United States); Department of Physics, University of Texas at Dallas, Richardson, Texas 75083 (United States)
2014-11-07
We present a method to obtain numerically accurate values of configurational free energies of semiflexible macromolecular systems, based on the technique of thermodynamic integration combined with normal-mode analysis of a reference system subject to harmonic constraints. Compared with previous free-energy calculations that depend on a reference state, our approach introduces two innovations, namely, the use of internal coordinates to constrain the reference states and the ability to freely select these reference states. As a consequence, it is possible to explore systems that undergo substantially larger fluctuations than those considered in previous calculations, including semiflexible biopolymers having arbitrary ratios of contour length L to persistence length P. To validate the method, high accuracy is demonstrated for free energies of prime DNA knots with L/P = 20 and L/P = 40, corresponding to DNA lengths of 3000 and 6000 base pairs, respectively. We then apply the method to study the free-energy landscape for a model of a synaptic nucleoprotein complex containing a pair of looped domains, revealing a bifurcation in the location of optimal synapse (crossover) sites. This transition is relevant to target-site selection by DNA-binding proteins that occupy multiple DNA sites separated by large linear distances along the genome, a problem that arises naturally in gene regulation, DNA recombination, and the action of type-II topoisomerases.
Free energy and structure of dislocation cores in two-dimensional crystals
Bladon, P.B.; Frenkel, D.
2004-01-01
The nature of the melting transition in two dimensions is critically dependent on the core energy of dislocations. In this paper, we report calculations of the core free energy and the core size of dislocations in two-dimensional solids of systems interacting via square well, hard disk, and r-12
Minimizing the Free Energy: A Computer Method for Teaching Chemical Equilibrium Concepts.
Heald, Emerson F.
1978-01-01
Presents a computer method for teaching chemical equilibrium concepts using material balance conditions and the minimization of the free energy. Method for the calculation of chemical equilibrium, the computer program used to solve equilibrium problems and applications of the method are also included. (HM)
Shi, Frank G.
1994-01-01
A method is introduced to measure the free-energy barrier W(sup *), the activation energy, and activation entropy to nucleation of crystallites in amorphous solids, independent of the energy barrier to growth. The method allows one to determine the temperature dependence of W(sup *), and the effect of the preparation conditions of the initial amorphous phase, the dopants, and the crystallization methds on W(sup *). The method is applied to determine the free-energy barrier to nucleation of crystallites in amorphous silicon (a-Si) thin films. For thermally induced nucleation in a-Si thin films with annealing temperatures in the range of from 824 to 983 K, the free-energy barrier W(sup *) to nucleation of silicon crystals is about 2.0 - 2.1 eV regardless of the preparation conditions of the films. The observation supports the idea that a-Si transforms into an intermediate amorphous state through the structural relaxation prior to the onset of nucleation of crystallites in a-Si. The observation also indicates that the activation entropy may be an insignificant part of the free-energy barrier for the nucleation of crystallites in a-Si. Compared with the free-energy barrier to nucleation of crystallites in undoped a-Si films, a significant reduction is observed in the free-energy barrier to nucleation in Cu-doped a-Si films. For a-Si under irradiation of Xe(2+) at 10(exp 5) eV, the free-energy barrier to ion-induced nucleation of crystallites is shown to be about half of the value associated with thermal-induced nucleation of crystallites in a-Si under the otherwise same conditions, which is much more significant than previously expected. The present method has a general kinetic basis; it thus should be equally applicable to nucleation of crystallites in any amorphous elemental semiconductors and semiconductor alloys, metallic and polymeric glasses, and to nucleation of crystallites in melts and solutions.
Inquiries into the Nature of Free Energy and Entropy in Respect to Biochemical Thermodynamics
Clinton D. Stoner
2000-08-01
Full Text Available Free energy and entropy are examined in detail from the standpoint of classical thermodynamics. The approach is logically based on the fact that thermodynamic work is mediated by thermal energy through the tendency for nonthermal energy to convert spontaneously into thermal energy and for thermal energy to distribute spontaneously and uniformly within the accessible space. The fact that free energy is a Second-Law, expendable energy that makes it possible for thermodynamic work to be done at finite rates is emphasized. Entropy, as originally defined, is pointed out to be the capacity factor for thermal energy that is hidden with respect to temperature; it serves to evaluate the practical quality of thermal energy and to account for changes in the amounts of latent thermal energies in systems maintained at constant temperature. With entropy thus operationally defined, it is possible to see that TDSÃ‚Â° of the Gibbs standard free energy relation DGÃ‚Â°= DHÃ‚Â°-TDSÃ‚Â° serves to account for differences or changes in nonthermal energies that do not contribute to DGÃ‚Â° and that, since DHÃ‚Â° serves to account for differences or changes in total energy, complete enthalpy-entropy (DHÃ‚Â° - TDSÃ‚Â° compensation must invariably occur in isothermal processes for which TDSÃ‚Â° is finite. A major objective was to clarify the means by which free energy is transferred and conserved in sequences of biological reactions coupled by freely diffusible intermediates. In achieving this objective it was found necessary to distinguish between a 'characteristic free energy' possessed by all First-Law energies in amounts equivalent to the amounts of the energies themselves and a 'free energy of concentration' that is intrinsically mechanical and relatively elusive in that it can appear to be free of First-Law energy. The findings in this regard serve to clarify the fact that the transfer of chemical potential energy from one
EDTA modified glassy carbon electrode: Preparation and characterization
Ustuendag, Zafer; Solak, Ali Osman
2009-01-01
EDTA-phenoxyamide modified glassy carbon electrode (EDTA-GC) was prepared at a glassy carbon electrode by surface synthesis. In the first step, nitrophenyl was grafted to the glassy carbon (GC) surface via the electrochemical reduction of its tetraflouroborate diazonium salt. In the second step, nitrophenyl-modified electrode (NP-GC) was subjected to the cathodic potential scan to reduce the nitro to amine group. p-Aminophenyl modified glassy carbon electrode (AP-GC) was dipped into a EDTA solution containing 1-ethyl-3(3-(dimethlyamino)propyl)-carbodiimide (EDC) as an activating agent. Thus formed ((2-anilino-2-oxoethyl){2-[bis(carboxymethyl)amino]-ethyl}amino)acetic acid modified GC electrode was denoted as EDTA-GC and characterized by cyclic voltammetry (CV), electrochemical impedance spectroscopy (EIS), ellipsometry and X-ray photoelectron spectroscopy (XPS). Complexation of the EDTA-GC surface with Pb 2+ ions was investigated if this electrode could be used as a metal sensor.
Feng, X.; Ordaz, G.; Krumrine, P.
1994-01-01
Glassy slag waste forms are being developed to complement glass waste forms in implementing the Minimum Additive Waste Stabilization (MAWS) Program for supporting DOE's environmental restoration efforts. These glassy slags are composed of various metal oxide crystalline phases embedded in an alumino-silicate glass phase. The slags are appropriate final waste forms for waste streams that contain large amounts of scrap metals and elements with low solubilities in glass, and that have low-flux contents. Homogeneous glass waste forms are appropriate for wastes with sufficient fluxes and low metal contents. Therefore, utilization of both glass and glassy slag waste forms will make vitrification technology applicable to the treatment of a much larger range of radioactive and mixed wastes. The MAWS approach was a plied to glassy slags by blending multiple waste streams to produce the final waste form, minimizing overall waste form volume and reducing costs. The crystalline oxide phases formed in the glassy slags can be specially formulated so that they are very durable and contain hazardous and radioactive elements in their lattice structures. The Structural Bond Strength (SBS) Model was used to predict the chemical durability of the product from the slag composition so that optimized slag compositions could be obtain with a limited number of crucible melts and testing
Towards accurate free energy calculations in ligand protein-binding studies.
Steinbrecher, Thomas; Labahn, Andreas
2010-01-01
Cells contain a multitude of different chemical reaction paths running simultaneously and quite independently next to each other. This amazing feat is enabled by molecular recognition, the ability of biomolecules to form stable and specific complexes with each other and with their substrates. A better understanding of this process, i.e. of the kinetics, structures and thermodynamic properties of biomolecule binding, would be invaluable in the study of biological systems. In addition, as the mode of action of many pharmaceuticals is based upon their inhibition or activation of biomolecule targets, predictive models of small molecule receptor binding are very helpful tools in rational drug design. Since the goal here is normally to design a new compound with a high inhibition strength, one of the most important thermodynamic properties is the binding free energy DeltaG(0). The prediction of binding constants has always been one of the major goals in the field of computational chemistry, because the ability to reliably assess a hypothetical compound's binding properties without having to synthesize it first would save a tremendous amount of work. The different approaches to this question range from fast and simple empirical descriptor methods to elaborate simulation protocols aimed at putting the computation of free energies onto a solid foundation of statistical thermodynamics. While the later methods are still not suited for the screenings of thousands of compounds that are routinely performed in computational drug design studies, they are increasingly put to use for the detailed study of protein ligand interactions. This review will focus on molecular mechanics force field based free energy calculations and their application to the study of protein ligand interactions. After a brief overview of other popular methods for the calculation of free energies, we will describe recent advances in methodology and a variety of exemplary studies of molecular dynamics
Mrugalla, Florian; Kast, Stefan M
2016-01-01
Complex formation between molecules in solution is the key process by which molecular interactions are translated into functional systems. These processes are governed by the binding or free energy of association which depends on both direct molecular interactions and the solvation contribution. A design goal frequently addressed in pharmaceutical sciences is the optimization of chemical properties of the complex partners in the sense of minimizing their binding free energy with respect to a change in chemical structure. Here, we demonstrate that liquid-state theory in the form of the solute–solute equation of the reference interaction site model provides all necessary information for such a task with high efficiency. In particular, computing derivatives of the potential of mean force (PMF), which defines the free-energy surface of complex formation, with respect to potential parameters can be viewed as a means to define a direction in chemical space toward better binders. We illustrate the methodology in the benchmark case of alkali ion binding to the crown ether 18-crown-6 in aqueous solution. In order to examine the validity of the underlying solute–solute theory, we first compare PMFs computed by different approaches, including explicit free-energy molecular dynamics simulations as a reference. Predictions of an optimally binding ion radius based on free-energy derivatives are then shown to yield consistent results for different ion parameter sets and to compare well with earlier, orders-of-magnitude more costly explicit simulation results. This proof-of-principle study, therefore, demonstrates the potential of liquid-state theory for molecular design problems. (paper)
Sampling free energy surfaces as slices by combining umbrella sampling and metadynamics.
Awasthi, Shalini; Kapil, Venkat; Nair, Nisanth N
2016-06-15
Metadynamics (MTD) is a very powerful technique to sample high-dimensional free energy landscapes, and due to its self-guiding property, the method has been successful in studying complex reactions and conformational changes. MTD sampling is based on filling the free energy basins by biasing potentials and thus for cases with flat, broad, and unbound free energy wells, the computational time to sample them becomes very large. To alleviate this problem, we combine the standard Umbrella Sampling (US) technique with MTD to sample orthogonal collective variables (CVs) in a simultaneous way. Within this scheme, we construct the equilibrium distribution of CVs from biased distributions obtained from independent MTD simulations with umbrella potentials. Reweighting is carried out by a procedure that combines US reweighting and Tiwary-Parrinello MTD reweighting within the Weighted Histogram Analysis Method (WHAM). The approach is ideal for a controlled sampling of a CV in a MTD simulation, making it computationally efficient in sampling flat, broad, and unbound free energy surfaces. This technique also allows for a distributed sampling of a high-dimensional free energy surface, further increasing the computational efficiency in sampling. We demonstrate the application of this technique in sampling high-dimensional surface for various chemical reactions using ab initio and QM/MM hybrid molecular dynamics simulations. Further, to carry out MTD bias reweighting for computing forward reaction barriers in ab initio or QM/MM simulations, we propose a computationally affordable approach that does not require recrossing trajectories. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
Thermodynamic free energy methods to investigate shape transitions in bilayer membranes.
Ramakrishnan, N; Tourdot, Richard W; Radhakrishnan, Ravi
2016-06-01
The conformational free energy landscape of a system is a fundamental thermodynamic quantity of importance particularly in the study of soft matter and biological systems, in which the entropic contributions play a dominant role. While computational methods to delineate the free energy landscape are routinely used to analyze the relative stability of conformational states, to determine phase boundaries, and to compute ligand-receptor binding energies its use in problems involving the cell membrane is limited. Here, we present an overview of four different free energy methods to study morphological transitions in bilayer membranes, induced either by the action of curvature remodeling proteins or due to the application of external forces. Using a triangulated surface as a model for the cell membrane and using the framework of dynamical triangulation Monte Carlo, we have focused on the methods of Widom insertion, thermodynamic integration, Bennett acceptance scheme, and umbrella sampling and weighted histogram analysis. We have demonstrated how these methods can be employed in a variety of problems involving the cell membrane. Specifically, we have shown that the chemical potential, computed using Widom insertion, and the relative free energies, computed using thermodynamic integration and Bennett acceptance method, are excellent measures to study the transition from curvature sensing to curvature inducing behavior of membrane associated proteins. The umbrella sampling and WHAM analysis has been used to study the thermodynamics of tether formation in cell membranes and the quantitative predictions of the computational model are in excellent agreement with experimental measurements. Furthermore, we also present a method based on WHAM and thermodynamic integration to handle problems related to end-point-catastrophe that are common in most free energy methods.
Protein Folding Free Energy Landscape along the Committor - the Optimal Folding Coordinate.
Krivov, Sergei V
2018-06-06
Recent advances in simulation and experiment have led to dramatic increases in the quantity and complexity of produced data, which makes the development of automated analysis tools very important. A powerful approach to analyze dynamics contained in such data sets is to describe/approximate it by diffusion on a free energy landscape - free energy as a function of reaction coordinates (RC). For the description to be quantitatively accurate, RCs should be chosen in an optimal way. Recent theoretical results show that such an optimal RC exists; however, determining it for practical systems is a very difficult unsolved problem. Here we describe a solution to this problem. We describe an adaptive nonparametric approach to accurately determine the optimal RC (the committor) for an equilibrium trajectory of a realistic system. In contrast to alternative approaches, which require a functional form with many parameters to approximate an RC and thus extensive expertise with the system, the suggested approach is nonparametric and can approximate any RC with high accuracy without system specific information. To avoid overfitting for a realistically sampled system, the approach performs RC optimization in an adaptive manner by focusing optimization on less optimized spatiotemporal regions of the RC. The power of the approach is illustrated on a long equilibrium atomistic folding simulation of HP35 protein. We have determined the optimal folding RC - the committor, which was confirmed by passing a stringent committor validation test. It allowed us to determine a first quantitatively accurate protein folding free energy landscape. We have confirmed the recent theoretical results that diffusion on such a free energy profile can be used to compute exactly the equilibrium flux, the mean first passage times, and the mean transition path times between any two points on the profile. We have shown that the mean squared displacement along the optimal RC grows linear with time as for
Casimir free energy of dielectric films: classical limit, low-temperature behavior and control.
Klimchitskaya, G L; Mostepanenko, V M
2017-07-12
The Casimir free energy of dielectric films, both free-standing in vacuum and deposited on metallic or dielectric plates, is investigated. It is shown that the values of the free energy depend considerably on whether the calculation approach used neglects or takes into account the dc conductivity of film material. We demonstrate that there are material-dependent and universal classical limits in the former and latter cases, respectively. The analytic behavior of the Casimir free energy and entropy for a free-standing dielectric film at low temperature is found. According to our results, the Casimir entropy goes to zero when the temperature vanishes if the calculation approach with neglected dc conductivity of a film is employed. If the dc conductivity is taken into account, the Casimir entropy takes the positive value at zero temperature, depending on the parameters of a film, i.e. the Nernst heat theorem is violated. By considering the Casimir free energy of SiO 2 and Al 2 O 3 films deposited on a Au plate in the framework of two calculation approaches, we argue that physically correct values are obtained by disregarding the role of dc conductivity. A comparison with the well known results for the configuration of two parallel plates is made. Finally, we compute the Casimir free energy of SiO 2 , Al 2 O 3 and Ge films deposited on high-resistivity Si plates of different thicknesses and demonstrate that it can be positive, negative and equal to zero. The effect of illumination of a Si plate with laser light is considered. Possible applications of the obtained results to thin films used in microelectronics are discussed.
Evaluation of the accuracy of the free-energy-minimization method
Najafabadi, R.; Srolovitz, D.J.
1995-01-01
We have made a detailed comparison between three competing methods for determining the free energies of solids and their defects: the thermodynamic integration of Monte Carlo (TIMC) data, the quasiharmonic (QH) model, and the free-energy-minimization (FEM) method. The accuracy of these methods decreases from the TIMC to QH to FEM method, while the computational efficiency improves in that order. All three methods yield perfect crystal lattice parameters and free energies at finite temperatures which are in good agreement for three different Cu interatomic potentials [embedded atom method (EAM), Morse and Lennard-Jones]. The FEM error (relative to the TIMC) in the (001) surface free energy and in the vacancy formation energy were found to be much larger for the EAM potential than for the other two potentials. Part of the errors in the FEM determination of the free energies are associated with anharmonicities in the interatomic potentials, with the remainder attributed to decoupling of the atomic vibrations. The anharmonicity of the EAM potential was found to be unphysically large compared with experimental vacancy formation entropy determinations. Based upon these results, we show that the FEM method provides a reasonable compromise between accuracy and computational demands. However, the accuracy of this approach is sensitive to the choice of interatomic potential and the nature of the defect to which it is being applied. The accuracy of the FEM is best in high-symmetry environments (perfect crystal, high-symmetry defects, etc.) and when used to describe materials where the anharmonicity is not too large
Casimir free energy of dielectric films: classical limit, low-temperature behavior and control
Klimchitskaya, G. L.; Mostepanenko, V. M.
2017-07-01
The Casimir free energy of dielectric films, both free-standing in vacuum and deposited on metallic or dielectric plates, is investigated. It is shown that the values of the free energy depend considerably on whether the calculation approach used neglects or takes into account the dc conductivity of film material. We demonstrate that there are material-dependent and universal classical limits in the former and latter cases, respectively. The analytic behavior of the Casimir free energy and entropy for a free-standing dielectric film at low temperature is found. According to our results, the Casimir entropy goes to zero when the temperature vanishes if the calculation approach with neglected dc conductivity of a film is employed. If the dc conductivity is taken into account, the Casimir entropy takes the positive value at zero temperature, depending on the parameters of a film, i.e. the Nernst heat theorem is violated. By considering the Casimir free energy of SiO2 and Al2O3 films deposited on a Au plate in the framework of two calculation approaches, we argue that physically correct values are obtained by disregarding the role of dc conductivity. A comparison with the well known results for the configuration of two parallel plates is made. Finally, we compute the Casimir free energy of SiO2, Al2O3 and Ge films deposited on high-resistivity Si plates of different thicknesses and demonstrate that it can be positive, negative and equal to zero. The effect of illumination of a Si plate with laser light is considered. Possible applications of the obtained results to thin films used in microelectronics are discussed.
Accuracy of free energies of hydration using CM1 and CM3 atomic charges.
Udier-Blagović, Marina; Morales De Tirado, Patricia; Pearlman, Shoshannah A; Jorgensen, William L
2004-08-01
Absolute free energies of hydration (DeltaGhyd) have been computed for 25 diverse organic molecules using partial atomic charges derived from AM1 and PM3 wave functions via the CM1 and CM3 procedures of Cramer, Truhlar, and coworkers. Comparisons are made with results using charges fit to the electrostatic potential surface (EPS) from ab initio 6-31G* wave functions and from the OPLS-AA force field. OPLS Lennard-Jones parameters for the organic molecules were used together with the TIP4P water model in Monte Carlo simulations with free energy perturbation theory. Absolute free energies of hydration were computed for OPLS united-atom and all-atom methane by annihilating the solutes in water and in the gas phase, and absolute DeltaGhyd values for all other molecules were computed via transformation to one of these references. Optimal charge scaling factors were determined by minimizing the unsigned average error between experimental and calculated hydration free energies. The PM3-based charge models do not lead to lower average errors than obtained with the EPS charges for the subset of 13 molecules in the original study. However, improvement is obtained by scaling the CM1A partial charges by 1.14 and the CM3A charges by 1.15, which leads to average errors of 1.0 and 1.1 kcal/mol for the full set of 25 molecules. The scaled CM1A charges also yield the best results for the hydration of amides including the E/Z free-energy difference for N-methylacetamide in water. Copyright 2004 Wiley Periodicals, Inc.
Free Energy Landscapes of Alanine Oligopeptides in Rigid-Body and Hybrid Water Models.
Nayar, Divya; Chakravarty, Charusita
2015-08-27
Replica exchange molecular dynamics is used to study the effect of different rigid-body (mTIP3P, TIP4P, SPC/E) and hybrid (H1.56, H3.00) water models on the conformational free energy landscape of the alanine oligopeptides (acAnme and acA5nme), in conjunction with the CHARMM22 force field. The free energy landscape is mapped out as a function of the Ramachandran angles. In addition, various secondary structure metrics, solvation shell properties, and the number of peptide-solvent hydrogen bonds are monitored. Alanine dipeptide is found to have similar free energy landscapes in different solvent models, an insensitivity which may be due to the absence of possibilities for forming i-(i + 4) or i-(i + 3) intrapeptide hydrogen bonds. The pentapeptide, acA5nme, where there are three intrapeptide backbone hydrogen bonds, shows a conformational free energy landscape with a much greater degree of sensitivity to the choice of solvent model, though the three rigid-body water models differ only quantitatively. The pentapeptide prefers nonhelical, non-native PPII and β-sheet populations as the solvent is changed from SPC/E to the less tetrahedral liquid (H1.56) to an LJ-like liquid (H3.00). The pentapeptide conformational order metrics indicate a preference for open, solvent-exposed, non-native structures in hybrid solvent models at all temperatures of study. The possible correlations between the properties of solvent models and secondary structure preferences of alanine oligopeptides are discussed, and the competition between intrapeptide, peptide-solvent, and solvent-solvent hydrogen bonding is shown to be crucial in the relative free energies of different conformers.
Breaking the polar-nonpolar division in solvation free energy prediction.
Wang, Bao; Wang, Chengzhang; Wu, Kedi; Wei, Guo-Wei
2018-02-05
Implicit solvent models divide solvation free energies into polar and nonpolar additive contributions, whereas polar and nonpolar interactions are inseparable and nonadditive. We present a feature functional theory (FFT) framework to break this ad hoc division. The essential ideas of FFT are as follows: (i) representability assumption: there exists a microscopic feature vector that can uniquely characterize and distinguish one molecule from another; (ii) feature-function relationship assumption: the macroscopic features, including solvation free energy, of a molecule is a functional of microscopic feature vectors; and (iii) similarity assumption: molecules with similar microscopic features have similar macroscopic properties, such as solvation free energies. Based on these assumptions, solvation free energy prediction is carried out in the following protocol. First, we construct a molecular microscopic feature vector that is efficient in characterizing the solvation process using quantum mechanics and Poisson-Boltzmann theory. Microscopic feature vectors are combined with macroscopic features, that is, physical observable, to form extended feature vectors. Additionally, we partition a solvation dataset into queries according to molecular compositions. Moreover, for each target molecule, we adopt a machine learning algorithm for its nearest neighbor search, based on the selected microscopic feature vectors. Finally, from the extended feature vectors of obtained nearest neighbors, we construct a functional of solvation free energy, which is employed to predict the solvation free energy of the target molecule. The proposed FFT model has been extensively validated via a large dataset of 668 molecules. The leave-one-out test gives an optimal root-mean-square error (RMSE) of 1.05 kcal/mol. FFT predictions of SAMPL0, SAMPL1, SAMPL2, SAMPL3, and SAMPL4 challenge sets deliver the RMSEs of 0.61, 1.86, 1.64, 0.86, and 1.14 kcal/mol, respectively. Using a test set of 94
Ma, Songling; Hwang, Sungbo; Lee, Sehan; Acree, William E; No, Kyoung Tai
2018-04-23
To describe the physically realistic solvation free energy surface of a molecule in a solvent, a generalized version of the solvation free energy density (G-SFED) calculation method has been developed. In the G-SFED model, the contribution from the hydrogen bond (HB) between a solute and a solvent to the solvation free energy was calculated as the product of the acidity of the donor and the basicity of the acceptor of an HB pair. The acidity and basicity parameters of a solute were derived using the summation of acidities and basicities of the respective acidic and basic functional groups of the solute, and that of the solvent was experimentally determined. Although the contribution of HBs to the solvation free energy could be evenly distributed to grid points on the surface of a molecule, the G-SFED model was still inadequate to describe the angle dependency of the HB of a solute with a polarizable continuum solvent. To overcome this shortcoming of the G-SFED model, the contribution of HBs was formulated using the geometric parameters of the grid points described in the HB coordinate system of the solute. We propose an HB angle dependency incorporated into the G-SFED model, i.e., the G-SFED-HB model, where the angular-dependent acidity and basicity densities are defined and parametrized with experimental data. The G-SFED-HB model was then applied to calculate the solvation free energies of organic molecules in water, various alcohols and ethers, and the log P values of diverse organic molecules, including peptides and a protein. Both the G-SFED model and the G-SFED-HB model reproduced the experimental solvation free energies with similar accuracy, whereas the distributions of the SFED on the molecular surface calculated by the G-SFED and G-SFED-HB models were quite different, especially for molecules having HB donors or acceptors. Since the angle dependency of HBs was included in the G-SFED-HB model, the SFED distribution of the G-SFED-HB model is well described
Thermodynamic free-energy minimization for unsupervised fusion of dual-color infrared breast images
Szu, Harold; Miao, Lidan; Qi, Hairong
2006-04-01
function [A] may vary from the point tumor to its neighborhood, we could not rely on neighborhood statistics as did in a popular unsupervised independent component analysis (ICA) mathematical statistical method, we instead impose the physics equilibrium condition of the minimum of Helmholtz free-energy, H = E - T °S. In case of the point breast cancer, we can assume the constant ground state energy E ° to be normalized by those benign neighborhood tissue, and then the excited state can be computed by means of Taylor series expansion in terms of the pixel I/O data. We can augment the X-ray mammogram technique with passive IR imaging to reduce the unwanted X-rays during the chemotherapy recovery. When the sequence is animated into a movie, and the recovery dynamics is played backward in time, the movie simulates the cameras' potential for early detection without suffering the PD=0.1 search uncertainty. In summary, we applied two satellite-grade dual-color IR imaging cameras and advanced military (automatic target recognition) ATR spectrum fusion algorithm at the middle wavelength IR (3 - 5μm) and long wavelength IR (8 - 12μm), which are capable to screen malignant tumors proved by the time-reverse fashion of the animated movie experiments. On the contrary, the traditional thermal breast scanning/imaging, known as thermograms over decades, was IR spectrum-blind, and limited to a single night-vision camera and the necessary waiting for the cool down period for taking a second look for change detection suffers too many environmental and personnel variabilities.
Yamashita, Kazuo; Kitamura, Mitsutaka; Imai, Hideo
1976-01-01
The modified Born equation was tentatively applied to estimate the electrostatic free energies of solvation of the electron in various polar solvents. The related data of halide ions and a datum of the hydration free energy of the electron obtained by radiation chemical studies were used for the numerical calculations. (auth.)
Okano, Yasushi
1999-08-01
In order to analyze the reaction heat and compounds due to sodium combustion, the multiphase chemical equilibrium calculation program for chemical reaction among sodium, oxygen and hydrogen is developed in this study. The developed numerical program is named BISHOP; which denotes Bi-Phase, Sodium - Oxygen - Hydrogen, Chemical Equilibrium Calculation Program'. Gibbs free energy minimization method is used because of the special merits that easily add and change chemical species, and generally deal many thermochemical reaction systems in addition to constant temperature and pressure one. Three new methods are developed for solving multi-phase sodium reaction system in this study. One is to construct equation system by simplifying phase, and the other is to expand the Gibbs free energy minimization method into multi-phase system, and the last is to establish the effective searching method for the minimum value. Chemical compounds by the combustion of sodium in the air are calculated using BISHOP. The Calculated temperature and moisture conditions where sodium-oxide and hydroxide are formed qualitatively agree with the experiments. Deformation of sodium hydride is calculated by the program. The estimated result of the relationship between the deformation temperature and pressure closely agree with the well known experimental equation of Roy and Rodgers. It is concluded that BISHOP can be used for evaluated the combustion and deformation behaviors of sodium and its compounds. Hydrogen formation condition of the dump-tank room at the sodium leak event of FBR is quantitatively evaluated by BISHOP. It can be concluded that to keep the temperature of dump-tank room lower is effective method to suppress the formation of hydrogen. In case of choosing the lower inflammability limit of 4.1 mol% as the hydrogen concentration criterion, formation reaction of sodium hydride from sodium and hydrogen is facilitated below the room temperature of 800 K, and concentration of hydrogen
The role of the concentration scale in the definition of transfer free energies.
Moeser, Beate; Horinek, Dominik
2015-01-01
The Gibbs free energy of transferring a solute at infinite dilution between two solvents quantifies differences in solute-solvent interactions - if the transfer takes place at constant molarity of the solute. Yet, many calculation formulae and measuring instructions that are commonly used to quantify solute-solvent interactions correspond to transfer processes in which not the molarity of the solute but its concentration measured in another concentration scale is constant. Here, we demonstrate that in this case, not only the change in solute-solvent interactions is quantified but also the entropic effect of a volume change during the transfer. Consequently, the "phenomenon" which is known as "concentration-scale dependence" of transfer free energies is simply explained by a volume-entropy effect. Our explanations are of high importance for the study of cosolvent effects on protein stability. Copyright © 2014 Elsevier B.V. All rights reserved.
Gibbs free energy of formation of lanthanum rhodate by quadrupole mass spectrometer
Prasad, R.; Banerjee, Aparna; Venugopal, V.
2003-01-01
The ternary oxide in the system La-Rh-O is of considerable importance because of its application in catalysis. Phase equilibria in the pseudo-binary system La 2 O 3 -Rh 2 O 3 has been investigated by Shevyakov et. al. Gibbs free energy of LaRhO 3 (s) was determined by Jacob et. al. using a solid state Galvanic cell in the temperature range 890 to 1310 K. No other thermodynamic data were available in the literature. Hence it was decided to determine Gibbs free energy of formation of LaRhO 3 (s) by an independent technique, viz. quadrupole mass spectrometer (QMS) coupled with a Knudsen effusion cell and the results are presented
Free energy for protonation reaction in lithium-ion battery cathode materials
Benedek, R.; Thackeray, M. M.; van de Walle, A.
2008-01-01
Calculations are performed of free energies for proton-for-lithium-ion exchange reactions in lithium-ion battery cathode materials. First-principles calculations are employed for the solid phases and tabulated ionization potential and hydration energy data for aqueous ions. Layered structures, spinel LiMn 2 O 4 , and olivine LiFePO 4 are considered. Protonation is most favorable energetically in layered systems, such as Li 2 MnO 3 and LiCoO 2 . Less favorable are ion-exchange in spinel LiMn 2 O 4 and LiV 3 O 8 . Unfavorable is the substitution of protons for Li in olivine LiFePO 4 , because of the large distortion of the Fe and P coordination polyhedra. The reaction free energy scales roughly linearly with the volume change in the reaction
Efficient approach to obtain free energy gradient using QM/MM MD simulation
Asada, Toshio; Koseki, Shiro; Ando, Kanta
2015-01-01
The efficient computational approach denoted as charge and atom dipole response kernel (CDRK) model to consider polarization effects of the quantum mechanical (QM) region is described using the charge response and the atom dipole response kernels for free energy gradient (FEG) calculations in the quantum mechanical/molecular mechanical (QM/MM) method. CDRK model can reasonably reproduce energies and also energy gradients of QM and MM atoms obtained by expensive QM/MM calculations in a drastically reduced computational time. This model is applied on the acylation reaction in hydrated trypsin-BPTI complex to optimize the reaction path on the free energy surface by means of FEG and the nudged elastic band (NEB) method
Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
Lostaglio, Matteo; Jennings, David; Rudolph, Terry
2015-01-01
Recent studies have developed fundamental limitations on nanoscale thermodynamics, in terms of a set of independent free energy relations. Here we show that free energy relations cannot properly describe quantum coherence in thermodynamic processes. By casting time-asymmetry as a quantifiable, fundamental resource of a quantum state, we arrive at an additional, independent set of thermodynamic constraints that naturally extend the existing ones. These asymmetry relations reveal that the traditional Szilárd engine argument does not extend automatically to quantum coherences, but instead only relational coherences in a multipartite scenario can contribute to thermodynamic work. We find that coherence transformations are always irreversible. Our results also reveal additional structural parallels between thermodynamics and the theory of entanglement. PMID:25754774
Structure-based prediction of free energy changes of binding of PTP1B inhibitors
Wang, Jing; Ling Chan, Shek; Ramnarayan, Kal
2003-08-01
The goals were (1) to understand the driving forces in the binding of small molecule inhibitors to the active site of PTP1B and (2) to develop a molecular mechanics-based empirical free energy function for compound potency prediction. A set of compounds with known activities was docked onto the active site. The related energy components and molecular surface areas were calculated. The bridging water molecules were identified and their contributions were considered. Linear relationships were explored between the above terms and the binding free energies of compounds derived based on experimental inhibition constants. We found that minimally three terms are required to give rise to a good correlation (0.86) with predictive power in five-group cross-validation test (q2 = 0.70). The dominant terms are the electrostatic energy and non-electrostatic energy stemming from the intra- and intermolecular interactions of solutes and from those of bridging water molecules in complexes.
Unbiased free energy estimates in fast nonequilibrium transformations using Gaussian mixtures
Procacci, Piero
2015-01-01
In this paper, we present an improved method for obtaining unbiased estimates of the free energy difference between two thermodynamic states using the work distribution measured in nonequilibrium driven experiments connecting these states. The method is based on the assumption that any observed work distribution is given by a mixture of Gaussian distributions, whose normal components are identical in either direction of the nonequilibrium process, with weights regulated by the Crooks theorem. Using the prototypical example for the driven unfolding/folding of deca-alanine, we show that the predicted behavior of the forward and reverse work distributions, assuming a combination of only two Gaussian components with Crooks derived weights, explains surprisingly well the striking asymmetry in the observed distributions at fast pulling speeds. The proposed methodology opens the way for a perfectly parallel implementation of Jarzynski-based free energy calculations in complex systems
QCD inequalities for the nucleon mass and the free energy of baryonic matter.
Cohen, Thomas D
2003-07-18
The positivity of the integrand of certain Euclidean space functional integrals for two flavor QCD with degenerate quark masses implies that the free energy per unit volume for QCD with a baryon chemical potential mu(B) (and zero isospin chemical potential) is greater than the free energy with an isospin chemical potential mu(I)=(2 mu(B)/N(c)) (and zero baryon chemical potential). The same result applies to QCD with any number of heavy flavors in addition to the two light flavors so long as the chemical potential is understood as applying to the light quark contributions to the baryon number. This relation implies a bound on the nucleon mass: there exists a particle X in QCD (presumably the pion) such that M(N)> or =(N(c) m(X)/2 I(X)) where m(X) is the mass of the particle and I(X) is its isospin.
Bardhan, Jaydeep P; Knepley, Matthew G
2014-10-07
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley "bracelet" and "rod" test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, "Charge asymmetries in hydration of polar solutes," J. Phys. Chem. B 112, 2405-2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.
Bardhan, Jaydeep P.; Knepley, Matthew G.
2014-01-01
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys. Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry
Khavrutskii, Ilja V; Wallqvist, Anders
2010-11-09
This paper introduces an efficient single-topology variant of Thermodynamic Integration (TI) for computing relative transformation free energies in a series of molecules with respect to a single reference state. The presented TI variant that we refer to as Single-Reference TI (SR-TI) combines well-established molecular simulation methodologies into a practical computational tool. Augmented with Hamiltonian Replica Exchange (HREX), the SR-TI variant can deliver enhanced sampling in select degrees of freedom. The utility of the SR-TI variant is demonstrated in calculations of relative solvation free energies for a series of benzene derivatives with increasing complexity. Noteworthy, the SR-TI variant with the HREX option provides converged results in a challenging case of an amide molecule with a high (13-15 kcal/mol) barrier for internal cis/trans interconversion using simulation times of only 1 to 4 ns.
Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
Lostaglio, Matteo; Jennings, David; Rudolph, Terry
2015-03-01
Recent studies have developed fundamental limitations on nanoscale thermodynamics, in terms of a set of independent free energy relations. Here we show that free energy relations cannot properly describe quantum coherence in thermodynamic processes. By casting time-asymmetry as a quantifiable, fundamental resource of a quantum state, we arrive at an additional, independent set of thermodynamic constraints that naturally extend the existing ones. These asymmetry relations reveal that the traditional Szilárd engine argument does not extend automatically to quantum coherences, but instead only relational coherences in a multipartite scenario can contribute to thermodynamic work. We find that coherence transformations are always irreversible. Our results also reveal additional structural parallels between thermodynamics and the theory of entanglement.
Bardhan, Jaydeep P.; Knepley, Matthew G.
2014-01-01
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys. Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry. PMID:25296776
Bardhan, Jaydeep P. [Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115 (United States); Knepley, Matthew G. [Computation Institute, The University of Chicago, Chicago, Illinois 60637 (United States)
2014-10-07
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys. Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.
Meisel, D
1975-07-15
Recent experimental data concerning the rate constants for electron transfer reactions of organic systems in aqueous solutions and their equilibrium constants is examined for possible correlation. The data is correlated quite well by the Marcus theory, if a reorganization parameter, lambda, of 18 kcal/mole is used. Assuming that the only contribution to lambda is the free energy of rearrangement of the water molecules, an effective radius of 5 A for the reacting entities is estimated. For the zero free energy change reaction, i.e., electron exchange between a radical ion and its parent molecule, a rate constant of about 5 X 10/sup 7/ M/sup -1/ s/sup -1/ is predicted. (auth)
Quantitative prediction of solvation free energy in octanol of organic compounds.
Delgado, Eduardo J; Jaña, Gonzalo A
2009-03-01
The free energy of solvation, DeltaGS0, in octanol of organic compounds is quantitatively predicted from the molecular structure. The model, involving only three molecular descriptors, is obtained by multiple linear regression analysis from a data set of 147 compounds containing diverse organic functions, namely, halogenated and non-halogenated alkanes, alkenes, alkynes, aromatics, alcohols, aldehydes, ketones, amines, ethers and esters; covering a DeltaGS0 range from about -50 to 0 kJ.mol(-1). The model predicts the free energy of solvation with a squared correlation coefficient of 0.93 and a standard deviation, 2.4 kJ.mol(-1), just marginally larger than the generally accepted value of experimental uncertainty. The involved molecular descriptors have definite physical meaning corresponding to the different intermolecular interactions occurring in the bulk liquid phase. The model is validated with an external set of 36 compounds not included in the training set.
Quantitative Prediction of Solvation Free Energy in Octanol of Organic Compounds
Eduardo J. Delgado
2009-03-01
Full Text Available The free energy of solvation, ΔGS0 , in octanol of organic compunds is quantitatively predicted from the molecular structure. The model, involving only three molecular descriptors, is obtained by multiple linear regression analysis from a data set of 147 compounds containing diverse organic functions, namely, halogenated and non-halogenated alkanes, alkenes, alkynes, aromatics, alcohols, aldehydes, ketones, amines, ethers and esters; covering a ΔGS0 range from about –50 to 0 kJ·mol-1. The model predicts the free energy of solvation with a squared correlation coefficient of 0.93 and a standard deviation, 2.4 kJ·mol-1, just marginally larger than the generally accepted value of experimental uncertainty. The involved molecular descriptors have definite physical meaning corresponding to the different intermolecular interactions occurring in the bulk liquid phase. The model is validated with an external set of 36 compounds not included in the training set.
Tsallis’ non-extensive free energy as a subjective value of an uncertain reward
Takahashi, Taiki
2009-03-01
Recent studies in neuroeconomics and econophysics revealed the importance of reward expectation in decision under uncertainty. Behavioral neuroeconomic studies have proposed that the unpredictability and the probability of an uncertain reward are distinctly encoded as entropy and a distorted probability weight, respectively, in the separate neural systems. However, previous behavioral economic and decision-theoretic models could not quantify reward-seeking and uncertainty aversion in a theoretically consistent manner. In this paper, we have: (i) proposed that generalized Helmholtz free energy in Tsallis’ non-extensive thermostatistics can be utilized to quantify a perceived value of an uncertain reward, and (ii) empirically examined the explanatory powers of the models. Future study directions in neuroeconomics and econophysics by utilizing the Tsallis’ free energy model are discussed.
S. Alexis Paz
2018-03-01
Full Text Available In this work, we study the influence of hidden barriers on the convergence behavior of three free-energy calculation methods: well-tempered metadynamics (WTMD, adaptive-biasing forces (ABF, and on-the-fly parameterization (OTFP. We construct a simple two-dimensional potential-energy surfaces (PES that allows for an exact analytical result for the free-energy in any one-dimensional order parameter. Then we chose different CV definitions and PES parameters to create three different systems with increasing sampling challenges. We find that all three methods are not greatly affected by the hidden-barriers in the simplest case considered. The adaptive sampling methods show faster sampling while the auxiliary high-friction requirement of OTFP makes it slower for this case. However, a slight change in the CV definition has a strong impact in the ABF and WTMD performance, illustrating the importance of choosing suitable collective variables.
Free energy option and its relevance to improve domestic energy demands in southern Nigeria
Moses Eterigho Emetere
2016-11-01
Full Text Available The aim of this paper is to seek an energy option that would benefit the growing energy demands. Domestic energy demands in southern Nigeria had increased greatly due to failing power programs and seasonal migrations. The fossil fuel option is gradually fading away due to environmental pollution and recent dynamic cost. The renewable energy option had been celebrated with little success in the coastal area of southern Nigeria. At the moment, the renewable energy option is very expensive with little guarantee on its efficiency with time. The data set used for this study was obtained from the Davis weather installation in Covenant University. The free energy option was considered. The cost and its environmental implication for domestic use were comparatively discussed alongside other energy options — using the Life cycle cost analysis. It was found out that free energy option is more affordable and efficient for domestic use.
Communication: Theoretical prediction of free-energy landscapes for complex self-assembly
Jacobs, William M.; Reinhardt, Aleks; Frenkel, Daan [Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW (United Kingdom)
2015-01-14
We present a technique for calculating free-energy profiles for the nucleation of multicomponent structures that contain as many species as building blocks. We find that a key factor is the topology of the graph describing the connectivity of the target assembly. By considering the designed interactions separately from weaker, incidental interactions, our approach yields predictions for the equilibrium yield and nucleation barriers. These predictions are in good agreement with corresponding Monte Carlo simulations. We show that a few fundamental properties of the connectivity graph determine the most prominent features of the assembly thermodynamics. Surprisingly, we find that polydispersity in the strengths of the designed interactions stabilizes intermediate structures and can be used to sculpt the free-energy landscape for self-assembly. Finally, we demonstrate that weak incidental interactions can preclude assembly at equilibrium due to the combinatorial possibilities for incorrect association.
The thermodynamic properties of the upper continental crust: Exergy, Gibbs free energy and enthalpy
Valero, Alicia; Valero, Antonio; Vieillard, Philippe
2012-01-01
This paper shows a comprehensive database of the thermodynamic properties of the most abundant minerals of the upper continental crust. For those substances whose thermodynamic properties are not listed in the literature, their enthalpy and Gibbs free energy are calculated with 11 different estimation methods described in this study, with associated errors of up to 10% with respect to values published in the literature. Thanks to this procedure we have been able to make a first estimation of the enthalpy, Gibbs free energy and exergy of the bulk upper continental crust and of each of the nearly 300 most abundant minerals contained in it. Finally, the chemical exergy of the continental crust is compared to the exergy of the concentrated mineral resources. The numbers obtained indicate the huge chemical exergy wealth of the crust: 6 × 10 6 Gtoe. However, this study shows that approximately only 0.01% of that amount can be effectively used by man.
Two-Dimensional Free Energy Surfaces for Electron Transfer Reactions in Solution
Shigeo Murata
2008-01-01
Full Text Available Change in intermolecular distance between electron donor (D and acceptor (A can induce intermolecular electron transfer (ET even in nonpolar solvent, where solvent orientational polarization is absent. This was shown by making simple calculations of the energies of the initial and final states of ET. In the case of polar solvent, the free energies are functions of both D-A distance and solvent orientational polarization. On the basis of 2-dimensional free energy surfaces, the relation of Marcus ET and exciplex formation is discussed. The transient effect in fluorescence quenching was measured for several D-A pairs in a nonpolar solvent. The results were analyzed by assuming a distance dependence of the ET rate that is consistent with the above model.
De Beer, Stephanie B A; Glättli, Alice; Hutzler, Johannes; Vermeulen, Nico P E; Oostenbrink, Chris
2011-07-30
4-Hydroxyphenylpyruvate dioxygenase is a relevant target in both pharmaceutical and agricultural research. We report on molecular dynamics simulations and free energy calculations on this enzyme, in complex with 12 inhibitors for which experimental affinities were determined. We applied the thermodynamic integration approach and the more efficient one-step perturbation. Even though simulations seem well converged and both methods show excellent agreement between them, the correlation with the experimental values remains poor. We investigate the effect of slight modifications on the charge distribution of these highly conjugated systems and find that accurate models can be obtained when using improved force field parameters. This study gives insight into the applicability of free energy methods and current limitations in force field parameterization. Copyright © 2011 Wiley Periodicals, Inc.
Treatment of early glassy cell carcinoma of uterine cervix
Kim, Ok Bae; Kim, Jin Hee; Choi, Tae Jin
2006-01-01
The purpose of this study was to investigate the clinical findings, treatment, and outcome of patients with glassy cell carcinoma of cervix. We reviewed all cases of glassy cell carcinoma of the uterine cervix confirmed and treated at the Dongsan Medical Center, Keimyung University, between January 1993 and December 2005. There were 7 cases with histopathologically confirmed gassy cell carcinoma. A tumor was diagnosed as glassy cell carcinoma if over 50% of the tumor cell type displayed glassy cell features. Six patients with stage IB had radical hysterectomy and bilateral pelvic node dissection, and 2 of them received adjuvant external pelvic irradiation with concurrent chemotherapy. Remaining one patient with stage IIA had curative concurrent chemoradiotherapy with external pelvic irradiation and brachytherapy. There were 7 patients diagnosed as glassy cell carcinoma among the 3,745 (0.2%) patients of carcinoma of uterine cervix. The mean age of 7 patients was 44 years with range of 35 to 53 years of age. The most frequent symptom was vaginal bleeding (86%). By the punch biopsy undertaken before treatment of 7 cases, 2 only cases could diagnose as glassy cell carcinoma of uterine cervix, but remaining of them confirmed by surgical pathological examination. The mean follow up duration was 73 months with range of 13 to 150 months. All 7 patients were alive without disease after treatment. Glassy cell carcinoma of the uterine cervix is a distinct clinicopathologic entity that demonstrates an aggressive biologic behavior. However for early-stage disease, we may have more favorable clinical outcome with radical surgery followed by chemoradiotherapy
Relative Free Energies for Hydration of Monovalent Ions from QM and QM/MM Simulations.
Lev, Bogdan; Roux, Benoît; Noskov, Sergei Yu
2013-09-10
Methods directly evaluating the hydration structure and thermodynamics of physiologically relevant cations (Na(+), K(+), Cl(-), etc.) have wide ranging applications in the fields of inorganic, physical, and biological chemistry. All-atom simulations based on accurate potential energy surfaces appear to offer a viable option for assessing the chemistry of ion solvation. Although MD and free energy simulations of ion solvation with classical force fields have proven their usefulness, a number of challenges still remain. One of them is the difficulty of force field benchmarking and validation against structural and thermodynamic data obtained for a condensed phase. Hybrid quantum mechanical/molecular mechanical (QM/MM) models combined with sampling algorithms have the potential to provide an accurate solvation model and to incorporate the effects from the surrounding, which is often missing in gas-phase ab initio computations. Herein, we report the results from QM/MM free energy simulations of Na(+)/K(+) and Cl(-)/Br(-) hydration where we simultaneously characterized the relative thermodynamics of ion solvation and changes in the solvation structure. The Flexible Inner Region Ensemble Separator (FIRES) method was used to impose a spatial separation between QM region and the outer sphere of solvent molecules treated with the CHARMM27 force field. FEP calculations based on QM/MM simulations utilizing the CHARMM/deMon2k interface were performed with different basis set combinations for K(+)/Na(+) and Cl(-)/Br(-) perturbations to establish the dependence of the computed free energies on the basis set level. The dependence of the computed relative free energies on the size of the QM and MM regions is discussed. The current methodology offers an accurate description of structural and thermodynamic aspects of the hydration of alkali and halide ions in neat solvents and can be used to obtain thermodynamic data on ion solvation in condensed phase along with underlying
Effect of Collagen Matrix Saturation on the Surface Free Energy of Dentin using Different Agents.
de Almeida, Leopoldina de Fátima Dantas; Souza, Samilly Evangelista; Sampaio, Aline Araújo; Cavalcanti, Yuri Wanderley; da Silva, Wander José; Del Bel Cur, Altair A; Hebling, Josimeri
2015-07-01
The surface free energy of conditioned-dentin is one of the factors that interfere with monomeric infiltration of the interfibrillar spaces. Saturation of the tooth matrix with different substances may modulate this energy and, consequently, the wettability of the dentin. To evaluate the influence of different substances used to saturate conditioned-dentin on surface free energy (SFE) of this substrate. Dentin blocks (4 × 7 × 1 mm, n = 6/ group), obtained from the roots of bovine incisors, were etched using phosphoric acid for 15 seconds, rinsed and gently dried. The surfaces were treated for 60 seconds with: ultra-purified water (H20-control); ethanol (EtOH), acetone (ACT), chlorhexidine (CHX), ethylenediaminetetraacetic acid (EDTA); or sodium hypochlorite (NaOCl). The tooth surfaces were once again dried with absorbent paper and prepared for SFE evaluation using three standards: water, formamide and bromonaphthalene. Analysis of variance (ANOVA) and Dunnet's tests (a = 0.05) were applied to the data. Ethylenediaminetetraacetic acid was the only substance that caused a change to the contact angle for the standards water and formamide, while only EtOH influenced the angles formed between formamide and the dentin surface. None of the substances exerted a significant effect for bromonaphtha-lene. In comparison to the control, only EDTA and NaOCl altered both polar components of the SFE. Total SFE was increased by saturation of the collagen matrix by EDTA and reduced when NaOCl was used. Saturation of the collagen matrix by EDTA and EtOH changed the surface free energy of the dentin. In addition, the use of NaOCl negatively interfered with the properties evaluated. The increase of surface free energy and wettability of the dentin surface would allow higher penetration of the the adhesive system, which would be of importance to the clinical success of resin-dentin union.
Direct measurements of the Gibbs free energy of OH using a CW tunable laser
Killinger, D. K.; Wang, C. C.
1979-01-01
The paper describes an absorption measurement for determining the Gibbs free energy of OH generated in a mixture of water and oxygen vapor. These measurements afford a direct verification of the accuracy of thermochemical data of H2O at high temperatures and pressures. The results indicate that values for the heat capacity of H2O obtained through numerical computations are correct within an experimental uncertainty of 0.15 cal/mole K.
Standard Gibbs free energies for transfer of actinyl ions at the aqueous/organic solution interface
Kitatsuji, Yoshihiro; Okugaki, Tomohiko; Kasuno, Megumi; Kubota, Hiroki; Maeda, Kohji; Kimura, Takaumi; Yoshida, Zenko; Kihara, Sorin
2011-01-01
Research highlights: → Standard Gibbs free energies for ion-transfer of tri- to hexavalent actinide ions. → Determination is based on distribution method combined with ion-transfer voltammetry. → Organic solvents examined are nitrobenzene, DCE, benzonitrile, acetophenone and NPOE. → Gibbs free energies of U(VI), Np(VI) and Pu(VI) are similar to each other. → Gibbs free energies of Np(V) is very large, comparing with ordinary monovalent cations. - Abstract: Standard Gibbs free energies for transfer (ΔG tr 0 ) of actinyl ions (AnO 2 z+ ; z = 2 or 1; An: U, Np, or Pu) between an aqueous solution and an organic solution were determined based on distribution method combined with voltammetry for ion transfer at the interface of two immiscible electrolyte solutions. The organic solutions examined were nitrobenzene, 1,2-dichloroethane, benzonitrile, acetophenone, and 2-nitrophenyl octyl ether. Irrespective of the type of organic solutions, ΔG tr 0 of UO 2 2+ ,NpO 2 2+ , and PuO 2 2+ were nearly equal to each other and slightly larger than that of Mg 2+ . The ΔG tr 0 of NpO 2 + was extraordinary large compared with those of ordinary monovalent cations. The dependence of ΔG tr 0 of AnO 2 z+ on the type of organic solutions was similar to that of H + or Mg 2+ . The ΔG tr 0 of An 3+ and An 4+ were also discussed briefly.
Gibbs Free-Energy Gradient along the Path of Glucose Transport through Human Glucose Transporter 3.
Liang, Huiyun; Bourdon, Allen K; Chen, Liao Y; Phelix, Clyde F; Perry, George
2018-06-11
Fourteen glucose transporters (GLUTs) play essential roles in human physiology by facilitating glucose diffusion across the cell membrane. Due to its central role in the energy metabolism of the central nervous system, GLUT3 has been thoroughly investigated. However, the Gibbs free-energy gradient (what drives the facilitated diffusion of glucose) has not been mapped out along the transport path. Some fundamental questions remain. Here we present a molecular dynamics study of GLUT3 embedded in a lipid bilayer to quantify the free-energy profile along the entire transport path of attracting a β-d-glucose from the interstitium to the inside of GLUT3 and, from there, releasing it to the cytoplasm by Arrhenius thermal activation. From the free-energy profile, we elucidate the unique Michaelis-Menten characteristics of GLUT3, low K M and high V MAX , specifically suitable for neurons' high and constant demand of energy from their low-glucose environments. We compute GLUT3's binding free energy for β-d-glucose to be -4.6 kcal/mol in agreement with the experimental value of -4.4 kcal/mol ( K M = 1.4 mM). We also compute the hydration energy of β-d-glucose, -18.0 kcal/mol vs the experimental data, -17.8 kcal/mol. In this, we establish a dynamics-based connection from GLUT3's crystal structure to its cellular thermodynamics with quantitative accuracy. We predict equal Arrhenius barriers for glucose uptake and efflux through GLUT3 to be tested in future experiments.
Free Energy Rate Density and Self-organization in Complex Systems
Georgiev, Georgi Yordanov; Gombos, Erin; Bates, Timothy; Henry, Kaitlin; Casey, Alexander; Daly, Michael
2015-01-01
One of the most important tasks in science is to understand the self-organization's arrow of time. To attempt this we utilize the connection between self-organization and non-equilibrium thermodynamics. Eric Chaisson calculated an exponential increase of Free Energy Rate Density (FERD) in Cosmic Evolution, from the Big Bang until now, paralleling the increase of system's structure. We term these studies "Devology". We connect FERD to the principle of least action for complex systems, driving ...
Surface free energy of CrN x films deposited using closed field unbalanced magnetron sputtering
Sun, C.-C.; Lee, S.-C.; Dai, S.-B.; Fu, Y.-S.; Wang, Y.-C.; Lee, Y.-H.
2006-01-01
CrN x thin films have attracted much attention for semiconductor IC packaging molding dies and forming tools due to their excellent hardness, thermal stability and non-sticking properties (low surface free energy). However, few data has been published on the surface free energy (SFE) of CrN x films at temperatures in the range 20-170 deg. C. In this study CrN x thin films with CrN, Cr(N), Cr 2 N (and mixture of these phases) were prepared using closed field unbalanced magnetron sputtering at a wide range of Cr +2 emission intensity. The contact angles of water, di-iodomethane and ethylene glycol on the coated surfaces were measured at temperatures in the range 20-170 deg. C using a Dataphysics OCA-20 contact angle analyzer. The surface free energy of the CrN x films and their components (e.g., dispersion, polar) were calculated using the Owens-Wendt geometric mean approach. The influences of CrN x film surface roughness and microstructure on the surface free energy were investigated by atomic force microscopy (AFM) and X-ray diffraction (XRD), respectively. The experimental results showed that the lowest total SFE was obtained corresponding to CrN at temperature in 20 deg. C. This is lower than that of Cr(N), Cr 2 N (and mixture of these phases). The total SFE, dispersive SFE and polar SFE of CrN x films decreased with increasing surface temperature. The film roughness has an obvious effect on the SFE and there is tendency for the SFE to increase with increasing film surface roughness
Notman, Rebecca; Anwar, Jamshed; Briels, W. J.; Noro, Massimo G.; den Otter, Wouter K.
2008-01-01
Transmembrane pore formation is central to many biological processes such as ion transport, cell fusion, and viral infection. Furthermore, pore formation in the ceramide bilayers of the stratum corneum may be an important mechanism by which penetration enhancers such as dimethylsulfoxide (DMSO) weaken the barrier function of the skin. We have used the potential of mean constraint force (PMCF) method to calculate the free energy of pore formation in ceramide bilayers in both the innate gel pha...
On the free-energy of three-dimensional CFTs and polylogarithms
Petkou, Anastasios C.
1998-12-01
We discuss the O(N) vector model and the U(N) Gross-Neveu model with fixed total fermion number, for large-N in three dimensions. Using non-trivial polylogarithmic identities, we calculate the renormalized free-energy density of these models at their conformal points in a 'slab' geometry with one finite dimension of length L. We briefly comment on the possible implications of our results. (author)
On the free-energy of three-dimensional CFTs and polylogarithms
Petkou, Anastasios C. [Dortmund Univ. (Germany). Inst. fuer Physik; Silva Neto, Marcello B. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
1998-12-01
We discuss the O(N) vector model and the U(N) Gross-Neveu model with fixed total fermion number, for large-N in three dimensions. Using non-trivial polylogarithmic identities, we calculate the renormalized free-energy density of these models at their conformal points in a 'slab' geometry with one finite dimension of length L. We briefly comment on the possible implications of our results. (author)
Kravchenko-Balasha, Nataly; Shin, Young Shik; Sutherland, Alex; Levine, R D; Heath, James R
2016-05-17
Controlling cell migration is important in tissue engineering and medicine. Cell motility depends on factors such as nutrient concentration gradients and soluble factor signaling. In particular, cell-cell signaling can depend on cell-cell separation distance and can influence cellular arrangements in bulk cultures. Here, we seek a physical-based approach, which identifies a potential governed by cell-cell signaling that induces a directed cell-cell motion. A single-cell barcode chip (SCBC) was used to experimentally interrogate secreted proteins in hundreds of isolated glioblastoma brain cancer cell pairs and to monitor their relative motions over time. We used these trajectories to identify a range of cell-cell separation distances where the signaling was most stable. We then used a thermodynamics-motivated analysis of secreted protein levels to characterize free-energy changes for different cell-cell distances. We show that glioblastoma cell-cell movement can be described as Brownian motion biased by cell-cell potential. To demonstrate that the free-energy potential as determined by the signaling is the driver of motion, we inhibited two proteins most involved in maintaining the free-energy gradient. Following inhibition, cell pairs showed an essentially random Brownian motion, similar to the case for untreated, isolated single cells.
Nascimento, Érica C M; Oliva, Mónica; Andrés, Juan
2018-05-01
In the present study, the binding free energy of a family of huprines with acetylcholinesterase (AChE) is calculated by means of the free energy perturbation method, based on hybrid quantum mechanics and molecular mechanics potentials. Binding free energy calculations and the analysis of the geometrical parameters highlight the importance of the stereochemistry of huprines in AChE inhibition. Binding isotope effects are calculated to unravel the interactions between ligands and the gorge of AChE. New chemical insights are provided to explain and rationalize the experimental results. A good correlation with the experimental data is found for a family of inhibitors with moderate differences in the enzyme affinity. The analysis of the geometrical parameters and interaction energy per residue reveals that Asp72, Glu199, and His440 contribute significantly to the network of interactions between active site residues, which stabilize the inhibitors in the gorge. It seems that a cooperative effect of the residues of the gorge determines the affinity of the enzyme for these inhibitors, where Asp72, Glu199, and His440 make a prominent contribution.
Modifying Poisson equation for near-solute dielectric polarization and solvation free energy
Yang, Pei-Kun, E-mail: peikun@isu.edu.tw
2016-06-15
Highlights: • We modify the Poisson equation. • The dielectric polarization was calculated from the modified Poisson equation. • The solvation free energies of the solutes were calculated from the dielectric polarization. • The calculated solvation free energies were similar to those obtained from MD simulations. - Abstract: The dielectric polarization P is important for calculating the stability of protein conformation and the binding affinity of protein–protein/ligand interactions and for exploring the nonthermal effect of an external electric field on biomolecules. P was decomposed into the product of the electric dipole moment per molecule p; bulk solvent density N{sub bulk}; and relative solvent molecular density g. For a molecular solute, 4πr{sup 2}p(r) oscillates with the distance r to the solute, and g(r) has a large peak in the near-solute region, as observed in molecular dynamics (MD) simulations. Herein, the Poisson equation was modified for computing p based on the modified Gauss’s law of Maxwell’s equations, and the potential of the mean force was used for computing g. For one or two charged atoms in a water cluster, the solvation free energies of the solutes obtained by these equations were similar to those obtained from MD simulations.
Free Energy Calculations using a Swarm-Enhanced Sampling Molecular Dynamics Approach.
Burusco, Kepa K; Bruce, Neil J; Alibay, Irfan; Bryce, Richard A
2015-10-26
Free energy simulations are an established computational tool in modelling chemical change in the condensed phase. However, sampling of kinetically distinct substates remains a challenge to these approaches. As a route to addressing this, we link the methods of thermodynamic integration (TI) and swarm-enhanced sampling molecular dynamics (sesMD), where simulation replicas interact cooperatively to aid transitions over energy barriers. We illustrate the approach by using alchemical alkane transformations in solution, comparing them with the multiple independent trajectory TI (IT-TI) method. Free energy changes for transitions computed by using IT-TI grew increasingly inaccurate as the intramolecular barrier was heightened. By contrast, swarm-enhanced sampling TI (sesTI) calculations showed clear improvements in sampling efficiency, leading to more accurate computed free energy differences, even in the case of the highest barrier height. The sesTI approach, therefore, has potential in addressing chemical change in systems where conformations exist in slow exchange. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Tomcho, Jeremy C; Tillman, Magdalena R; Znosko, Brent M
2015-09-01
Predicting the secondary structure of RNA is an intermediate in predicting RNA three-dimensional structure. Commonly, determining RNA secondary structure from sequence uses free energy minimization and nearest neighbor parameters. Current algorithms utilize a sequence-independent model to predict free energy contributions of dinucleotide bulges. To determine if a sequence-dependent model would be more accurate, short RNA duplexes containing dinucleotide bulges with different sequences and nearest neighbor combinations were optically melted to derive thermodynamic parameters. These data suggested energy contributions of dinucleotide bulges were sequence-dependent, and a sequence-dependent model was derived. This model assigns free energy penalties based on the identity of nucleotides in the bulge (3.06 kcal/mol for two purines, 2.93 kcal/mol for two pyrimidines, 2.71 kcal/mol for 5'-purine-pyrimidine-3', and 2.41 kcal/mol for 5'-pyrimidine-purine-3'). The predictive model also includes a 0.45 kcal/mol penalty for an A-U pair adjacent to the bulge and a -0.28 kcal/mol bonus for a G-U pair adjacent to the bulge. The new sequence-dependent model results in predicted values within, on average, 0.17 kcal/mol of experimental values, a significant improvement over the sequence-independent model. This model and new experimental values can be incorporated into algorithms that predict RNA stability and secondary structure from sequence.
Cultured Cortical Neurons Can Perform Blind Source Separation According to the Free-Energy Principle
Isomura, Takuya; Kotani, Kiyoshi; Jimbo, Yasuhiko
2015-01-01
Blind source separation is the computation underlying the cocktail party effect––a partygoer can distinguish a particular talker’s voice from the ambient noise. Early studies indicated that the brain might use blind source separation as a signal processing strategy for sensory perception and numerous mathematical models have been proposed; however, it remains unclear how the neural networks extract particular sources from a complex mixture of inputs. We discovered that neurons in cultures of dissociated rat cortical cells could learn to represent particular sources while filtering out other signals. Specifically, the distinct classes of neurons in the culture learned to respond to the distinct sources after repeating training stimulation. Moreover, the neural network structures changed to reduce free energy, as predicted by the free-energy principle, a candidate unified theory of learning and memory, and by Jaynes’ principle of maximum entropy. This implicit learning can only be explained by some form of Hebbian plasticity. These results are the first in vitro (as opposed to in silico) demonstration of neural networks performing blind source separation, and the first formal demonstration of neuronal self-organization under the free energy principle. PMID:26690814
Exploring the free energy landscape: from dynamics to networks and back.
Diego Prada-Gracia
2009-06-01
Full Text Available Knowledge of the Free Energy Landscape topology is the essential key to understanding many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers there are, what the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times and rate constants, or hierarchical relationships among basins, completes the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.
Solid-liquid interface free energies of pure bcc metals and B2 phases
Wilson, S. R.; Gunawardana, K. G. S. H.; Mendelev, M. I.
2015-04-01
The solid-liquid interface (SLI) free energy was determined from molecular dynamics (MD) simulation for several body centered cubic (bcc) metals and B2 metallic compounds (space group: P m 3 ¯ m ; prototype: CsCl). In order to include a bcc metal with a low melting temperature in our study, a semi-empirical potential was developed for Na. Two additional synthetic "Na" potentials were also developed to explore the effect of liquid structure and latent heat on the SLI free energy. The obtained MD data were compared with the empirical Turnbull, Laird, and Ewing relations. All three relations are found to predict the general trend observed in the MD data for bcc metals obtained within the present study. However, only the Laird and Ewing relations are able to predict the trend obtained within the sequence of "Na" potentials. The Laird relation provides the best prediction for our MD data and other MD data for bcc metals taken from the literature. Overall, the Laird relation also agrees well with our B2 data but requires a proportionality constant that is substantially different from the bcc case. It also fails to explain a considerable difference between the SLI free energies of some B2 phases which have nearly the same melting temperature. In contrast, this difference is satisfactorily described by the Ewing relation. Moreover, the Ewing relation obtained from the bcc dataset also provides a reasonable description of the B2 data.
Free Energy Adjusted Peak Signal to Noise Ratio (FEA-PSNR) for Image Quality Assessment
Liu, Ning; Zhai, Guangtao
2017-12-01
Peak signal to noise ratio (PSNR), the de facto universal image quality metric has been widely criticized as having poor correlation with human subjective quality ratings. In this paper, it will be illustrated that the low performance of PSNR as an image quality metric is partially due to its inability of differentiating image contents. And it is revealed that the deviation between subjective score and PSNR for each type of distortions can be systematically captured by perceptual complexity of the target image. The free energy modelling technique is then introduced to simulate the human cognitive process and measure perceptual complexity of an image. Then it is shown that performance of PSNR can be effectively improved using a linear score mapping process considering image free energy and distortion type. The proposed free energy adjusted peak signal to noise ratio (FEA-PSNR) does not change computational steps the of ordinary PSNR and therefore it inherits the merits of being simple, derivable and physically meaningful. So FEA-PSNR can be easily integrated into existing PSNR based image processing systems to achieve more visually plausible results. And the proposed analysis approach can be extended to other types of image quality metrics for enhanced performance.
Takuya Isomura
2015-12-01
Full Text Available Blind source separation is the computation underlying the cocktail party effect--a partygoer can distinguish a particular talker's voice from the ambient noise. Early studies indicated that the brain might use blind source separation as a signal processing strategy for sensory perception and numerous mathematical models have been proposed; however, it remains unclear how the neural networks extract particular sources from a complex mixture of inputs. We discovered that neurons in cultures of dissociated rat cortical cells could learn to represent particular sources while filtering out other signals. Specifically, the distinct classes of neurons in the culture learned to respond to the distinct sources after repeating training stimulation. Moreover, the neural network structures changed to reduce free energy, as predicted by the free-energy principle, a candidate unified theory of learning and memory, and by Jaynes' principle of maximum entropy. This implicit learning can only be explained by some form of Hebbian plasticity. These results are the first in vitro (as opposed to in silico demonstration of neural networks performing blind source separation, and the first formal demonstration of neuronal self-organization under the free energy principle.
Nascimento, Érica C. M.; Oliva, Mónica; Andrés, Juan
2018-05-01
In the present study, the binding free energy of a family of huprines with acetylcholinesterase (AChE) is calculated by means of the free energy perturbation method, based on hybrid quantum mechanics and molecular mechanics potentials. Binding free energy calculations and the analysis of the geometrical parameters highlight the importance of the stereochemistry of huprines in AChE inhibition. Binding isotope effects are calculated to unravel the interactions between ligands and the gorge of AChE. New chemical insights are provided to explain and rationalize the experimental results. A good correlation with the experimental data is found for a family of inhibitors with moderate differences in the enzyme affinity. The analysis of the geometrical parameters and interaction energy per residue reveals that Asp72, Glu199, and His440 contribute significantly to the network of interactions between active site residues, which stabilize the inhibitors in the gorge. It seems that a cooperative effect of the residues of the gorge determines the affinity of the enzyme for these inhibitors, where Asp72, Glu199, and His440 make a prominent contribution.
Notman, Rebecca; Anwar, Jamshed; Briels, W J; Noro, Massimo G; den Otter, Wouter K
2008-11-15
Transmembrane pore formation is central to many biological processes such as ion transport, cell fusion, and viral infection. Furthermore, pore formation in the ceramide bilayers of the stratum corneum may be an important mechanism by which penetration enhancers such as dimethylsulfoxide (DMSO) weaken the barrier function of the skin. We have used the potential of mean constraint force (PMCF) method to calculate the free energy of pore formation in ceramide bilayers in both the innate gel phase and in the DMSO-induced fluidized state. Our simulations show that the fluid phase bilayers form archetypal water-filled hydrophilic pores similar to those observed in phospholipid bilayers. In contrast, the rigid gel-phase bilayers develop hydrophobic pores. At the relatively small pore diameters studied here, the hydrophobic pores are empty rather than filled with bulk water, suggesting that they do not compromise the barrier function of ceramide membranes. A phenomenological analysis suggests that these vapor pores are stable, below a critical radius, because the penalty of creating water-vapor and tail-vapor interfaces is lower than that of directly exposing the strongly hydrophobic tails to water. The PMCF free energy profile of the vapor pore supports this analysis. The simulations indicate that high DMSO concentrations drastically impair the barrier function of the skin by strongly reducing the free energy required for pore opening.
Mey, Antonia S. J. S.; Jiménez, Jordi Juárez; Michel, Julien
2018-01-01
The Drug Design Data Resource (D3R) consortium organises blinded challenges to address the latest advances in computational methods for ligand pose prediction, affinity ranking, and free energy calculations. Within the context of the second D3R Grand Challenge several blinded binding free energies predictions were made for two congeneric series of Farsenoid X Receptor (FXR) inhibitors with a semi-automated alchemical free energy calculation workflow featuring FESetup and SOMD software tools. Reasonable performance was observed in retrospective analyses of literature datasets. Nevertheless, blinded predictions on the full D3R datasets were poor due to difficulties encountered with the ranking of compounds that vary in their net-charge. Performance increased for predictions that were restricted to subsets of compounds carrying the same net-charge. Disclosure of X-ray crystallography derived binding modes maintained or improved the correlation with experiment in a subsequent rounds of predictions. The best performing protocols on D3R set1 and set2 were comparable or superior to predictions made on the basis of analysis of literature structure activity relationships (SAR)s only, and comparable or slightly inferior, to the best submissions from other groups.
Husowitz, B; Talanquer, V
2007-02-07
Density functional theory is used to explore the solvation properties of a spherical solute immersed in a supercritical diatomic fluid. The solute is modeled as a hard core Yukawa particle surrounded by a diatomic Lennard-Jones fluid represented by two fused tangent spheres using an interaction site approximation. The authors' approach is particularly suitable for thoroughly exploring the effect of different interaction parameters, such as solute-solvent interaction strength and range, solvent-solvent long-range interactions, and particle size, on the local solvent structure and the solvation free energy under supercritical conditions. Their results indicate that the behavior of the local coordination number in homonuclear diatomic fluids follows trends similar to those reported in previous studies for monatomic fluids. The local density augmentation is particularly sensitive to changes in solute size and is affected to a lesser degree by variations in the solute-solvent interaction strength and range. The associated solvation free energies exhibit a nonmonotonous behavior as a function of density for systems with weak solute-solvent interactions. The authors' results suggest that solute-solvent interaction anisotropies have a major influence on the nature and extent of local solvent density inhomogeneities and on the value of the solvation free energies in supercritical solutions of heteronuclear molecules.
Adhesion Evaluation of Asphalt-Aggregate Interface Using Surface Free Energy Method
Jie Ji
2017-02-01
Full Text Available The influence of organic additives (Sasobit and RH and water on the adhesion of the asphalt-aggregate interface was studied according to the surface free energy theory. Two asphalt binders (SK-70 and SK-90, and two aggregate types (limestone and basalt were used in this study. The sessile drop method was employed to test surface free energy components of asphalt, organic additives and aggregates. The adhesion models of the asphalt-aggregate interface in dry and wet conditions were established, and the adhesion work was calculated subsequently. The energy ratios were built to evaluate the effect of organic additives and water on the adhesiveness of the asphalt-aggregate interface. The results indicate that the addition of organic additives can enhance the adhesion of the asphalt-aggregate interface in dry conditions, because organic additives reduced the surface free energy of asphalt. However, the organic additives have hydrophobic characteristics and are sensitive to water. As a result, the adhesiveness of the asphalt-aggregate interface of the asphalt containing organic additives in wet conditions sharply decreased due to water damage to asphalt and organic additives. Furthermore, the compatibility of asphalt, aggregate with organic additive was noted and discussed.
Chiriki, Siva; Jindal, Shweta; Bulusu, Satya S
2017-10-21
For understanding the structure, dynamics, and thermal stability of (AgAu) 55 nanoalloys, knowledge of the composition-temperature (c-T) phase diagram is essential due to the explicit dependence of properties on composition and temperature. Experimentally, generating the phase diagrams is very challenging, and therefore theoretical insight is necessary. We use an artificial neural network potential for (AgAu) 55 nanoalloys. Predicted global minimum structures for pure gold and gold rich compositions are lower in energy compared to previous reports by density functional theory. The present work based on c-T phase diagram, surface area, surface charge, probability of isomers, and Landau free energies supports the enhancement of catalytic property of Ag-Au nanoalloys by incorporation of Ag up to 24% by composition in Au nanoparticles as found experimentally. The phase diagram shows that there is a coexistence temperature range of 70 K for Ag 28 Au 27 compared to all other compositions. We propose the power spectrum coefficients derived from spherical harmonics as an order parameter to calculate Landau free energies.
Metcalf, Thomas R.
1994-01-01
I present a robust algorithm that resolves the 180-deg ambiguity in measurements of the solar vector magnetic field. The technique simultaneously minimizes both the divergence of the magnetic field and the electric current density using a simulated annealing algorithm. This results in the field orientation with approximately minimum free energy. The technique is well-founded physically and is simple to implement.
Johari, G.P.; Shanker, Ravi M.
2014-01-01
Highlights: • Heat capacity data do not yield the solubility advantage of amorphous and metastable crystal pharmaceuticals. • There is no reversible equilibrium of an amorphous solid with its saturated solution. • Solubility advantage of an amorphous solid depends upon the solvent and other interactions. - Abstract: At equilibrium, the saturation solubility and vapor pressure of a material in a state of high free energy are greater than in its state of low free energy. This knowledge from classical thermodynamics is currently used for increasing the solubility of crystalline pharmaceuticals by producing them in their glassy state, or in other solid states of high free energy. The ratio of the apparent saturation solubility of these solids to that of a crystal, calculated from the thermodynamic data of the pure solute, ϕ cal , is called the solubility advantage, and it is used as a guide for increasing the solubility of a pharmaceutical. We argue that the ϕ cal differs from the measured solubility ratio, ϕ meas , because, (i) ϕ cal is independent of the solvent, but ϕ meas is not so, (ii) ϕ cal would increase with the dissolution time monotonically to a constant value, but ϕ meas would first reach a maximum and then decrease, and (iii) approximations are made in estimating ϕ cal and the effect of thermal history on high free energy solids is ignored. On the other hand, ϕ meas is affected by, (a) another chemical equilibrium in the solution, e.g., hydrogen-bond formation and ionic dissociation, (b) the production method and thermal history of a glass or an amorphous samples, and (c) mutarotation in the solution, isomerization or tautomeric conversion in the solid. We also discuss the effects of structural relaxation and crystallization on ϕ meas . The ϕ meas value of a (crystal) polymorph would be affected by all the three, and further if the polymorph is orientationally disordered. We provide evidence for these effects from analysis of the known
Gibbs Sampler-Based λ-Dynamics and Rao-Blackwell Estimator for Alchemical Free Energy Calculation.
Ding, Xinqiang; Vilseck, Jonah Z; Hayes, Ryan L; Brooks, Charles L
2017-06-13
λ-dynamics is a generalized ensemble method for alchemical free energy calculations. In traditional λ-dynamics, the alchemical switch variable λ is treated as a continuous variable ranging from 0 to 1 and an empirical estimator is utilized to approximate the free energy. In the present article, we describe an alternative formulation of λ-dynamics that utilizes the Gibbs sampler framework, which we call Gibbs sampler-based λ-dynamics (GSLD). GSLD, like traditional λ-dynamics, can be readily extended to calculate free energy differences between multiple ligands in one simulation. We also introduce a new free energy estimator, the Rao-Blackwell estimator (RBE), for use in conjunction with GSLD. Compared with the current empirical estimator, the advantage of RBE is that RBE is an unbiased estimator and its variance is usually smaller than the current empirical estimator. We also show that the multistate Bennett acceptance ratio equation or the unbinned weighted histogram analysis method equation can be derived using the RBE. We illustrate the use and performance of this new free energy computational framework by application to a simple harmonic system as well as relevant calculations of small molecule relative free energies of solvation and binding to a protein receptor. Our findings demonstrate consistent and improved performance compared with conventional alchemical free energy methods.
Zhang, Yuxin; Huang, Xiaoqin; Han, Keli; Zheng, Fang; Zhan, Chang-Guo
2016-11-25
The combined molecular dynamics (MD) and potential of mean force (PMF) simulations have been performed to determine the free energy profile of the CocE)-(+)-cocaine binding process in comparison with that of the corresponding CocE-(-)-cocaine binding process. According to the MD simulations, the equilibrium CocE-(+)-cocaine binding mode is similar to the CocE-(-)-cocaine binding mode. However, based on the simulated free energy profiles, a significant free energy barrier (∼5 kcal/mol) exists in the CocE-(+)-cocaine binding process whereas no obvious free energy barrier exists in the CocE-(-)-cocaine binding process, although the free energy barrier of ∼5 kcal/mol is not high enough to really slow down the CocE-(+)-cocaine binding process. In addition, the obtained free energy profiles also demonstrate that (+)-cocaine and (-)-cocaine have very close binding free energies with CocE, with a negligible difference (∼0.2 kcal/mol), which is qualitatively consistent with the nearly same experimental K M values of the CocE enzyme for (+)-cocaine and (-)-cocaine. The consistency between the computational results and available experimental data suggests that the mechanistic insights obtained from this study are reasonable. Copyright Â© 2016 Elsevier Ireland Ltd. All rights reserved.
Martins, Silvia A; Sousa, Sergio F
2013-06-05
The determination of differences in solvation free energies between related drug molecules remains an important challenge in computational drug optimization, when fast and accurate calculation of differences in binding free energy are required. In this study, we have evaluated the performance of five commonly used polarized continuum model (PCM) methodologies in the determination of solvation free energies for 53 typical alcohol and alkane small molecules. In addition, the performance of these PCM methods, of a thermodynamic integration (TI) protocol and of the Poisson-Boltzmann (PB) and generalized Born (GB) methods, were tested in the determination of solvation free energies changes for 28 common alkane-alcohol transformations, by the substitution of an hydrogen atom for a hydroxyl substituent. The results show that the solvation model D (SMD) performs better among the PCM-based approaches in estimating solvation free energies for alcohol molecules, and solvation free energy changes for alkane-alcohol transformations, with an average error below 1 kcal/mol for both quantities. However, for the determination of solvation free energy changes on alkane-alcohol transformation, PB and TI yielded better results. TI was particularly accurate in the treatment of hydroxyl groups additions to aromatic rings (0.53 kcal/mol), a common transformation when optimizing drug-binding in computer-aided drug design. Copyright © 2013 Wiley Periodicals, Inc.
Koettgen, Julius; Schmidt, Peter C.; Bučko, Tomáš; Martin, Manfred
2018-01-01
We have studied the free energy migration barriers Δ F‡ for oxygen diffusion in pure ceria and Sm-doped ceria for the temperatures 300, 700, and 1000 K. We used the density functional theory in the generalized gradient approximation and an additional Hubbard U parameter for the Ce 4 f electronic states. We compare the results for the free energy deduced from three different methods. First, a static harmonic approach is applied in which the temperature dependent vibrational contributions to energy and entropy are deduced from the phonon frequencies of supercells with a fixed volume. Second, a static quasiharmonic approach is used in which a part of the anharmonicity effect is introduced via an implicit dependence of the harmonic frequencies on the thermally expanding cell volume. Third, the free energy barriers are calculated using metadynamics and molecular dynamics in which anharmonicity effects are naturally taken into account. The three methods examined in this study lead to distinctly different results. According to the harmonic approximation, the migration free energy difference Δ F‡ increases with increasing temperature due to an increasing entropic contribution. According to the quasiharmonic approximation, the migration free energy is independent of temperature. Finally, molecular dynamics predicts a thermally induced increase in the migration free energy. We conclude that temperature dependent experimental lattice constants cancel out the increasing entropic contribution with increasing temperature in the static quasiharmonic approach. The full consideration of anharmonicity effects in the metadynamics method again leads to a temperature dependent migration free energy.
Murata, Shigeo; Tachiya, M
2007-09-27
The mechanism of exciplex formation proposed in a previous paper has been refined to show how exciplex formation and Marcus electron transfer (ET) in fluorescence quenching are related to each other. This was done by making simple calculations of the free energies of the initial (DA*) and final (D+A-) states of ET. First it was shown that the decrease in D-A distance can induce intermolecular ET even in nonpolar solvents where solvent orientational polarization is absent, and that it leads to exciplex formation. This is consistent with experimental results that exciplex is most often observed in nonpolar solvents. The calculation was then extended to ET in polar solvents where the free energies are functions of both D-A distance and solvent orientational polarization. This enabled us to discuss both exciplex formation and Marcus ET in the same D-A pair and solvent on the basis of 2-dimensional free energy surfaces. The surfaces contain more information about the rates of these reactions, the mechanism of fluorescence quenching by ET, etc., than simple reaction schemes. By changing the parameters such as the free energy change of reaction, solvent dielectric constants, etc., one can construct the free energy surfaces for various systems. The effects of free energy change of reaction and of solvent polarity on the mechanism and relative importance of exciplex formation and Marcus ET in fluorescence quenching can be well explained. The free energy surface will also be useful for discussion of other phenomena related to ET reactions.
Thermal Barrier Coatings Resistant to Glassy Deposits
Drexler, Julie Marie
Engineering of alloys has for years allowed aircraft turbine engines to become more efficient and operate at higher temperatures. As advancements in these alloy systems have become more difficult, ceramic thermal barrier coatings (TBCs), often yttria (7 wt %) stabilized zirconia (7YSZ), have been utilized for thermal protection. TBCs have allowed for higher engine operating temperatures and better fuel efficiency but have also created new engineering problems. Specifically, silica based particles such as sand and volcanic ash that enter the engine during operation form glassy deposits on the TBCs. These deposits can cause the current industrial 7YSZ thermal barrier coatings to fail since the glass formed penetrates and chemically interacts with the TBC. When this occurs, coating failure may occur due to a loss of strain tolerance, which can lead to fracture, and phase changes of the TBC material. There have been several approaches used to stop calcium-magnesium aluminio-silcate (CMAS) glasses (molten sand) from destroying the entire TBC, but overall there is still limited knowledge. In this thesis, 7YSZ and new TBC materials will be examined for thermochemical and thermomechanical performance in the presence of molten CMAS and volcanic ash. Two air plasma sprayed TBCs will be shown to be resistant to volcanic ash and CMAS. The first type of coating is a modified 7YSZ coating with 20 mol% Al2O3 and 5 mol% TiO2 in solid solution (YSZ+20Al+5Ti). The second TBC is made of gadolinium zirconate. These novel TBCs impede CMAS and ash penetration by interacting with the molten CMAS or ash and drastically changing the chemistry. The chemically modified CMAS or ash will crystallize into an apatite or anorthite phase, blocking the CMAS or ash from further destroying the coating. A presented mechanism study will show these coatings are effective due to the large amount of solute (Gd, Al) in the zirconia structure, which is the key to creating the crystalline apatite or
Thermodynamics of Supercooled and Glassy Water
Debenedetti, Pablo G.
1998-03-01
The behavior of metastable water at low temperatures is unusual. The isothermal compressibility, the isobaric heat capacity, and the magnitude of the thermal expansion coefficient increase sharply upon supercooling, and structural relaxation becomes extremely sluggish at temperatures far above the glass transition(Angell, C.A., Annu. Rev. Phys. Chem., 34, 593, 1983)(Debenedetti, P.G., Metastable Liquids. Concepts and Principles, Princeton University Press, 1996). Water has two distinct glassy phases, low- and high-density amorphous ice (LDA, HDA). The transition between LDA and HDA is accompanied by sharp volume and enthalpy changes, and appears to be first-order(Mishima, O., L.D.Calvert, and E. Whalley, Nature, 314, 76, 1985)(Mishima, O., J. Chem. Phys., 100, 5910, 1994). The understanding of these observations in terms of an underlying global phase behavior remains incomplete(Speedy, R.J., J. Phys. Chem., 86, 982, 1982)(Poole, P.H., F. Sciortino, U. Essman, and H.E. Stanley, Nature, 360, 324, 1992)(Sastry, S., P.G. Debenedetti, F. Sciortino, and H.E. Stanley, Phys. Rev. E, 53, 6144, 1996)(Tanaka, H., Nature, 380, 328, 1996)(Xie, Y., K.F. Ludwig, G. Morales, D.E. Hare, and C.M. Sorensen, Phys. Rev. Lett., 71, 2050, 1993). Microscopic theories and computer simulations suggest several scenarios that can reproduce some experimental observations. Interesting and novel ideas have resulted from this body of theoretical work, such as the possibility of liquid-liquid immiscibility in a pure substance(Poole, P.H., F.Sciortino, T.Grande, H.E. Stanley, and C.A. Angell, Phys. Rev. Lett., 73, 1632, 1994)(Roberts, C.J., and P.G. Debenedetti, J. Chem. Phys., 105, 658, 1996)(Roberts, C.J., P.G. Debenedetti, and A.Z. Panagiotopoulos, Phys. Rev. Lett., 77, 4386, 1996)(Harrington, S., R. Zhang, P.H. Poole, F. Sciortino, and H.E. Stanley, Phys. Rev. Lett., 78, 2409, 1997). In this talk I will review the experimental facts, discuss their theoretical interpretation, and identify key
Bozym, David J; Uralcan, Betül; Limmer, David T; Pope, Michael A; Szamreta, Nicholas J; Debenedetti, Pablo G; Aksay, Ilhan A
2015-07-02
We use electrochemical impedance spectroscopy to measure the effect of diluting a hydrophobic room temperature ionic liquid with miscible organic solvents on the differential capacitance of the glassy carbon-electrolyte interface. We show that the minimum differential capacitance increases with dilution and reaches a maximum value at ionic liquid contents near 5-10 mol% (i.e., ∼1 M). We provide evidence that mixtures with 1,2-dichloroethane, a low-dielectric constant solvent, yield the largest gains in capacitance near the open circuit potential when compared against two traditional solvents, acetonitrile and propylene carbonate. To provide a fundamental basis for these observations, we use a coarse-grained model to relate structural variations at the double layer to the occurrence of the maximum. Our results reveal the potential for the enhancement of double-layer capacitance through dilution.
Minimum Additive Waste Stabilization (MAWS)
1994-02-01
In the Minimum Additive Waste Stabilization(MAWS) concept, actual waste streams are utilized as additive resources for vitrification, which may contain the basic components (glass formers and fluxes) for making a suitable glass or glassy slag. If too much glass former is present, then the melt viscosity or temperature will be too high for processing; while if there is too much flux, then the durability may suffer. Therefore, there are optimum combinations of these two important classes of constituents depending on the criteria required. The challenge is to combine these resources in such a way that minimizes the use of non-waste additives yet yields a processable and durable final waste form for disposal. The benefit to this approach is that the volume of the final waste form is minimized (waste loading maximized) since little or no additives are used and vitrification itself results in volume reduction through evaporation of water, combustion of organics, and compaction of the solids into a non-porous glass. This implies a significant reduction in disposal costs due to volume reduction alone, and minimizes future risks/costs due to the long term durability and leach resistance of glass. This is accomplished by using integrated systems that are both cost-effective and produce an environmentally sound waste form for disposal. individual component technologies may include: vitrification; thermal destruction; soil washing; gas scrubbing/filtration; and, ion-exchange wastewater treatment. The particular combination of technologies will depend on the waste streams to be treated. At the heart of MAWS is vitrification technology, which incorporates all primary and secondary waste streams into a final, long-term, stabilized glass wasteform. The integrated technology approach, and view of waste streams as resources, is innovative yet practical to cost effectively treat a broad range of DOE mixed and low-level wastes
Grain-boundary, glassy-phase identification and possible artifacts
Simpson, Y.K.; Carter, C.B.; Sklad, P.; Bentley, J.
1985-01-01
Specimen artifacts such as grain boundary grooving, surface damage of the specimen, and Si contamination are shown experimentally to arise from the ion milling used in the preparation of transmission electron microscopy specimens. These artifacts in polycrystalline, ceramic specimens can cause clean grain boundaries to appear to contain a glassy phase when the dark-field diffuse scattering technique, the Fresnel fringe technique, and analytical electron microscopy (energy dispersive spectroscopy) are used to identify glassy phases at a grain boundary. The ambiguity in interpreting each of these techniques due to the ion milling artifacts will be discussed from a theoretical view point and compared to experimental results obtained for alumina
Vivcharuk, Victor; Tomberli, Bruno; Tolokh, Igor S.; Gray, C. G.
2008-03-01
Molecular dynamics (MD) simulations are used to study the interaction of a zwitterionic palmitoyl-oleoyl-phosphatidylcholine (POPC) bilayer with the cationic antimicrobial peptide bovine lactoferricin (LFCinB) in a 100 mM NaCl solution at 310 K. The interaction of LFCinB with POPC is used as a model system for studying the details of membrane-peptide interactions, with the peptide selected because of its antimicrobial nature. Seventy-two 3 ns MD simulations, with six orientations of LFCinB at 12 different distances from a POPC membrane, are carried out to determine the potential of mean force (PMF) or free energy profile for the peptide as a function of the distance between LFCinB and the membrane surface. To calculate the PMF for this relatively large system a new variant of constrained MD and thermodynamic integration is developed. A simplified method for relating the PMF to the LFCinB-membrane binding free energy is described and used to predict a free energy of adsorption (or binding) of -1.05±0.39kcal/mol , and corresponding maximum binding force of about 20 pN, for LFCinB-POPC. The contributions of the ions-LFCinB and the water-LFCinB interactions to the PMF are discussed. The method developed will be a useful starting point for future work simulating peptides interacting with charged membranes and interactions involved in the penetration of membranes, features necessary to understand in order to rationally design peptides as potential alternatives to traditional antibiotics.
Benson, Mark L.; Faver, John C.; Ucisik, Melek N.; Dashti, Danial S.; Zheng, Zheng; Merz, Kenneth M.
2012-05-01
Two families of binding affinity estimation methodologies are described which were utilized in the SAMPL3 trypsin/fragment binding affinity challenge. The first is a free energy decomposition scheme based on a thermodynamic cycle, which included separate contributions from enthalpy and entropy of binding as well as a solvent contribution. Enthalpic contributions were estimated with PM6-DH2 semiempirical quantum mechanical interaction energies, which were modified with a statistical error correction procedure. Entropic contributions were estimated with the rigid-rotor harmonic approximation, and solvent contributions to the free energy were estimated with several different methods. The second general methodology is the empirical score LISA, which contains several physics-based terms trained with the large PDBBind database of protein/ligand complexes. Here we also introduce LISA+, an updated version of LISA which, prior to scoring, classifies systems into one of four classes based on a ligand's hydrophobicity and molecular weight. Each version of the two methodologies (a total of 11 methods) was trained against a compiled set of known trypsin binders available in the Protein Data Bank to yield scaling parameters for linear regression models. Both raw and scaled scores were submitted to SAMPL3. Variants of LISA showed relatively low absolute errors but also low correlation with experiment, while the free energy decomposition methods had modest success when scaling factors were included. Nonetheless, re-scaled LISA yielded the best predictions in the challenge in terms of RMS error, and six of these models placed in the top ten best predictions by RMS error. This work highlights some of the difficulties of predicting binding affinities of small molecular fragments to protein receptors as well as the benefit of using training data.
Dependence of Interaction Free Energy between Solutes on an External Electrostatic Field
Pei-Kun Yang
2013-07-01
Full Text Available To explore the athermal effect of an external electrostatic field on the stabilities of protein conformations and the binding affinities of protein-protein/ligand interactions, the dependences of the polar and hydrophobic interactions on the external electrostatic field, −Eext, were studied using molecular dynamics (MD simulations. By decomposing Eext into, along, and perpendicular to the direction formed by the two solutes, the effect of Eext on the interactions between these two solutes can be estimated based on the effects from these two components. Eext was applied along the direction of the electric dipole formed by two solutes with opposite charges. The attractive interaction free energy between these two solutes decreased for solutes treated as point charges. In contrast, the attractive interaction free energy between these two solutes increased, as observed by MD simulations, for Eext = 40 or 60 MV/cm. Eext was applied perpendicular to the direction of the electric dipole formed by these two solutes. The attractive interaction free energy was increased for Eext = 100 MV/cm as a result of dielectric saturation. The force on the solutes along the direction of Eext computed from MD simulations was greater than that estimated from a continuum solvent in which the solutes were treated as point charges. To explore the hydrophobic interactions, Eext was applied to a water cluster containing two neutral solutes. The repulsive force between these solutes was decreased/increased for Eext along/perpendicular to the direction of the electric dipole formed by these two solutes.
Reddy, M Rami; Erion, Mark D
2009-12-01
Molecular dynamics (MD) simulations in conjunction with thermodynamic perturbation approach was used to calculate relative solvation free energies of five pairs of small molecules, namely; (1) methanol to ethane, (2) acetone to acetamide, (3) phenol to benzene, (4) 1,1,1 trichloroethane to ethane, and (5) phenylalanine to isoleucine. Two studies were performed to evaluate the dependence of the convergence of these calculations on MD simulation length and starting configuration. In the first study, each transformation started from the same well-equilibrated configuration and the simulation length was varied from 230 to 2,540 ps. The results indicated that for transformations involving small structural changes, a simulation length of 860 ps is sufficient to obtain satisfactory convergence. In contrast, transformations involving relatively large structural changes, such as phenylalanine to isoleucine, require a significantly longer simulation length (>2,540 ps) to obtain satisfactory convergence. In the second study, the transformation was completed starting from three different configurations and using in each case 860 ps of MD simulation. The results from this study suggest that performing one long simulation may be better than averaging results from three different simulations using a shorter simulation length and three different starting configurations.
Free energy landscape and cooperatively rearranging region in a hard sphere glass
Yoshidome, Takashi; Yoshimori, Akira; Odagaki, Takashi
2007-08-01
Exploiting the density functional theory, we calculate the free energy landscape (FEL) of the hard sphere glass in three dimensions. From the FEL, we estimate the number of the particles in the cooperatively rearranging region (CRR). We find that the density dependence of the number of the particles in the CRR is expressed as a power law function of the density. Analyzing the relaxation process in the CRR, we also find that the string motion is the elementary process for the structural relaxation, which leads to the natural definition of the simultaneously rearranging region as the particles displaced in the string motion.
Ligand Conformational and Solvation/Desolvation Free Energy in Protein-Ligand Complex Formation
Kolář, Michal; Fanfrlík, Jindřich; Hobza, Pavel
2011-01-01
Roč. 115, č. 16 (2011), s. 4718-4724 ISSN 1520-6106 R&D Projects: GA MŠk LC512; GA ČR GAP208/11/0295 Grant - others:Korea Science and Engineering Foundation(KR) R32-2008-000-10180-0; European Science Fund(XE) CZ.1.05/2.1.00/03.0058 Institutional research plan: CEZ:AV0Z40550506 Keywords : solvation free energy * SMD * HIV protease inhibitors Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.696, year: 2011
Similarity Laws for the Lines of Ideal Free Energy and Chemical Potential in Supercritical Fluids.
Apfelbaum, E M; Vorob'ev, V S
2017-09-21
We have found the curves on the density-temperature plane, along which the values of free energy and chemical potential correspond to ideal gas quantities. At first, we have applied the van der Waals equation to construct them and to derive their equations. Then we have shown that the same lines for real substances (Ar, N 2 , CH 4 , SF 6 , H 2 , H 2 O) and for the model Lennard-Jones system constructed on the basis of the measurements data and calculations are well matched with the derived equations. The validity and deviations from the obtained similarity laws are discussed.
Analytical free energy gradient for the molecular Ornstein-Zernike self-consistent-field method
N.Yoshida
2007-09-01
Full Text Available An analytical free energy gradient for the molecular Ornstein-Zernike self-consistent-field (MOZ-SCF method is presented. MOZ-SCF theory is one of the theories to considering the solvent effects on the solute electronic structure in solution. [Yoshida N. et al., J. Chem. Phys., 2000, 113, 4974] Molecular geometries of water, formaldehyde, acetonitrile and acetone in water are optimized by analytical energy gradient formula. The results are compared with those from the polarizable continuum model (PCM, the reference interaction site model (RISM-SCF and the three dimensional (3D RISM-SCF.
Heavy-quark free energies, internal-energy and entropy contributions
Kaczmarek, O.
2009-01-01
We present lattice QCD results on heavy-quark free energies, extract from its temperature dependence the entropy and internal-energy contributions, and discuss the onset of medium effects that lead to screening of static quark-antiquark sources in a thermal medium. The detailed analysis of the temperature and distance dependence of the different contributions indicate the complex non-perturbative nature of strongly interacting matter. We shall discuss the necessity to include those effects in studies on the behavior of heavy quarks, heavy-quark bound states and their dissociation in the quark-gluon plasma phase. (orig.)
Sørensen, Jesper; Hamelberg, Donald; McCammon, J. Andrew
experimental results have helped to explain this aberrant behavior of TTR, however, structural insights of the amyloidgenic process are still lacking. Therefore, we have used all-atom molecular dynamics simulation and free energy calculations to study the initial phase of this process. We have calculated......Many questions about the nature of aggregation and the proteins that are involved in these events are still left unanswered. One of the proteins that is known to form amyloids is Transthyretine (TTR), the secondary transporter of thyroxine and transporter of retinol-binding-protein. Several...
Cournia, Zoe; Allen, Bryce; Sherman, Woody
2017-12-26
Accurate in silico prediction of protein-ligand binding affinities has been a primary objective of structure-based drug design for decades due to the putative value it would bring to the drug discovery process. However, computational methods have historically failed to deliver value in real-world drug discovery applications due to a variety of scientific, technical, and practical challenges. Recently, a family of approaches commonly referred to as relative binding free energy (RBFE) calculations, which rely on physics-based molecular simulations and statistical mechanics, have shown promise in reliably generating accurate predictions in the context of drug discovery projects. This advance arises from accumulating developments in the underlying scientific methods (decades of research on force fields and sampling algorithms) coupled with vast increases in computational resources (graphics processing units and cloud infrastructures). Mounting evidence from retrospective validation studies, blind challenge predictions, and prospective applications suggests that RBFE simulations can now predict the affinity differences for congeneric ligands with sufficient accuracy and throughput to deliver considerable value in hit-to-lead and lead optimization efforts. Here, we present an overview of current RBFE implementations, highlighting recent advances and remaining challenges, along with examples that emphasize practical considerations for obtaining reliable RBFE results. We focus specifically on relative binding free energies because the calculations are less computationally intensive than absolute binding free energy (ABFE) calculations and map directly onto the hit-to-lead and lead optimization processes, where the prediction of relative binding energies between a reference molecule and new ideas (virtual molecules) can be used to prioritize molecules for synthesis. We describe the critical aspects of running RBFE calculations, from both theoretical and applied perspectives
Ge, Hao; Qian, Hong
2013-06-01
Nonequilibrium thermodynamics of a system situated in a sustained environment with influx and efflux is usually treated as a subsystem in a larger, closed "universe." A question remains with regard to what the minimally required description for the surrounding of such an open driven system is so that its nonequilibrium thermodynamics can be established solely based on the internal stochastic kinetics. We provide a solution to this problem using insights from studies of molecular motors in a chemical nonequilibrium steady state (NESS) with sustained external drive through a regenerating system or in a quasisteady state (QSS) with an excess amount of adenosine triphosphate (ATP), adenosine diphosphate (ADP), and inorganic phosphate (Pi). We introduce the key notion of minimal work that is needed, W(min), for the external regenerating system to sustain a NESS (e.g., maintaining constant concentrations of ATP, ADP and Pi for a molecular motor). Using a Markov (master-equation) description of a motor protein, we illustrate that the NESS and QSS have identical kinetics as well as the second law in terms of the same positive entropy production rate. The heat dissipation of a NESS without mechanical output is exactly the W(min). This provides a justification for introducing an ideal external regenerating system and yields a free-energy balance equation between the net free-energy input F(in) and total dissipation F(dis) in an NESS: F(in) consists of chemical input minus mechanical output; F(dis) consists of dissipative heat, i.e. the amount of useful energy becoming heat, which also equals the NESS entropy production. Furthermore, we show that for nonstationary systems, the F(dis) and F(in) correspond to the entropy production rate and housekeeping heat in stochastic thermodynamics and identify a relative entropy H as a generalized free energy. We reach a new formulation of Markovian nonequilibrium thermodynamics based on only the internal kinetic equation without further
Abel, Robert; Wang, Lingle; Mobley, David L; Friesner, Richard A
2017-01-01
Protein-ligand binding is among the most fundamental phenomena underlying all molecular biology, and a greater ability to more accurately and robustly predict the binding free energy of a small molecule ligand for its cognate protein is expected to have vast consequences for improving the efficiency of pharmaceutical drug discovery. We briefly reviewed a number of scientific and technical advances that have enabled alchemical free energy calculations to recently emerge as a preferred approach, and critically considered proper validation and effective use of these techniques. In particular, we characterized a selection bias effect which may be important in prospective free energy calculations, and introduced a strategy to improve the accuracy of the free energy predictions. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.
Hubbard, W.B.; Dewitt, H.E.
1985-01-01
A model free energy is presented which accurately represents results from 45 high-precision Monte Carlo calculations of the thermodynamics of hydrogen-helium mixtures at pressures of astrophysical and planetophysical interest. The free energy is calculated using free-electron perturbation theory (dielectric function theory), and is an extension of the expression given in an earlier paper in this series. However, it fits the Monte Carlo results more accurately, and is valid for the full range of compositions from pure hydrogen to pure helium. Using the new free energy, the phase diagram of mixtures of liquid metallic hydrogen and helium is calculated and compared with earlier results. Sample results for mixing volumes are also presented, and the new free energy expression is used to compute a theoretical Jovian adiabat and compare the adiabat with results from three-dimensional Thomas-Fermi-Dirac theory. The present theory gives slightly higher densities at pressures of about 10 megabars. 20 references
Hubbard, W. B.; Dewitt, H. E.
1985-01-01
A model free energy is presented which accurately represents results from 45 high-precision Monte Carlo calculations of the thermodynamics of hydrogen-helium mixtures at pressures of astrophysical and planetophysical interest. The free energy is calculated using free-electron perturbation theory (dielectric function theory), and is an extension of the expression given in an earlier paper in this series. However, it fits the Monte Carlo results more accurately, and is valid for the full range of compositions from pure hydrogen to pure helium. Using the new free energy, the phase diagram of mixtures of liquid metallic hydrogen and helium is calculated and compared with earlier results. Sample results for mixing volumes are also presented, and the new free energy expression is used to compute a theoretical Jovian adiabat and compare the adiabat with results from three-dimensional Thomas-Fermi-Dirac theory. The present theory gives slightly higher densities at pressures of about 10 megabars.
Sergiievskyi, Volodymyr P; Jeanmairet, Guillaume; Levesque, Maximilien; Borgis, Daniel
2014-06-05
Molecular density functional theory (MDFT) offers an efficient implicit-solvent method to estimate molecule solvation free-energies, whereas conserving a fully molecular representation of the solvent. Even within a second-order approximation for the free-energy functional, the so-called homogeneous reference fluid approximation, we show that the hydration free-energies computed for a data set of 500 organic compounds are of similar quality as those obtained from molecular dynamics free-energy perturbation simulations, with a computer cost reduced by 2-3 orders of magnitude. This requires to introduce the proper partial volume correction to transform the results from the grand canonical to the isobaric-isotherm ensemble that is pertinent to experiments. We show that this correction can be extended to 3D-RISM calculations, giving a sound theoretical justification to empirical partial molar volume corrections that have been proposed recently.
Pollard, Travis P.; Beck, Thomas L.
2018-06-01
Attempts to establish an absolute single-ion hydration free energy scale have followed multiple strategies. Two central themes consist of (1) employing bulk pair thermodynamic data and an underlying interfacial-potential-free model to partition the hydration free energy into individual contributions [Marcus, Latimer, and tetraphenyl-arsonium/tetraphenyl-borate (TATB) methods] or (2) utilizing bulk thermodynamic and cluster data to estimate the free energy to insert a proton into water, including in principle an interfacial potential contribution [the cluster pair approximation (CPA)]. While the results for the hydration free energy of the proton agree remarkably well between the three approaches in the first category, the value differs from the CPA result by roughly +10 kcal/mol, implying a value for the effective electrochemical surface potential of water of -0.4 V. This paper provides a computational re-analysis of the TATB method for single-ion free energies using quasichemical theory. A previous study indicated a significant discrepancy between the free energies of hydration for the TA cation and the TB anion. We show that the main contribution to this large computed difference is an electrostatic artifact arising from modeling interactions in periodic boundaries. No attempt is made here to develop more accurate models for the local ion/solvent interactions that may lead to further small free energy differences between the TA and TB ions, but the results clarify the primary importance of interfacial potential effects for analysis of the various free energy scales. Results are also presented, related to the TATB assumption in the organic solvents dimethyl sulfoxide and 1,2-dichloroethane.
Stable, metastable and unstable solutions of a spin-1 Ising system based on the free energy surfaces
Keskİin, Mustafa; Özgan, Şükrü
1990-04-01
Stable, metastable and unstable solutions of a spin-1 Ising model with bilinear and biquadratic interactions are found by using the free energy surfaces. The free energy expression is obtained in the lowest approximation of the cluster variation method. All these solutions are shown in the two-dimensional phase space, especially the unstable solutions which in some cases are difficult to illustrate in the two-dimensional phase space, found by Keskin et al. recently.
König, Gerhard; Miller, Benjamin T; Boresch, Stefan; Wu, Xiongwu; Brooks, Bernard R
2012-10-09
One of the key requirements for the accurate calculation of free energy differences is proper sampling of conformational space. Especially in biological applications, molecular dynamics simulations are often confronted with rugged energy surfaces and high energy barriers, leading to insufficient sampling and, in turn, poor convergence of the free energy results. In this work, we address this problem by employing enhanced sampling methods. We explore the possibility of using self-guided Langevin dynamics (SGLD) to speed up the exploration process in free energy simulations. To obtain improved free energy differences from such simulations, it is necessary to account for the effects of the bias due to the guiding forces. We demonstrate how this can be accomplished for the Bennett's acceptance ratio (BAR) and the enveloping distribution sampling (EDS) methods. While BAR is considered among the most efficient methods available for free energy calculations, the EDS method developed by Christ and van Gunsteren is a promising development that reduces the computational costs of free energy calculations by simulating a single reference state. To evaluate the accuracy of both approaches in connection with enhanced sampling, EDS was implemented in CHARMM. For testing, we employ benchmark systems with analytical reference results and the mutation of alanine to serine. We find that SGLD with reweighting can provide accurate results for BAR and EDS where conventional molecular dynamics simulations fail. In addition, we compare the performance of EDS with other free energy methods. We briefly discuss the implications of our results and provide practical guidelines for conducting free energy simulations with SGLD.
Aryl Diazonium Chemistry for the Surface Functionalization of Glassy Biosensors
Wei Zheng
2016-03-01
Full Text Available Nanostring resonator and fiber-optics-based biosensors are of interest as they offer high sensitivity, real-time measurements and the ability to integrate with electronics. However, these devices are somewhat impaired by issues related to surface modification. Both nanostring resonators and photonic sensors employ glassy materials, which are incompatible with electrochemistry. A surface chemistry approach providing strong and stable adhesion to glassy surfaces is thus required. In this work, a diazonium salt induced aryl film grafting process is employed to modify a novel SiCN glassy material. Sandwich rabbit IgG binding assays are performed on the diazonium treated SiCN surfaces. Fluorescently labelled anti-rabbit IgG and anti-rabbit IgG conjugated gold nanoparticles were used as markers to demonstrate the absorption of anti-rabbit IgG and therefore verify the successful grafting of the aryl film. The results of the experiments support the effectiveness of diazonium chemistry for the surface functionalization of SiCN surfaces. This method is applicable to other types of glassy materials and potentially can be expanded to various nanomechanical and optical biosensors.
EDTA modified glassy carbon electrode: Preparation and characterization
Ustuendag, Zafer [Dumlupinar University, Faculty of Arts and Sciences, Department of Chemistry, Kuetahya (Turkey); Solak, Ali Osman [Ankara University, Faculty of Science, Department of Chemistry, Degol Street, Tandogan, 06100 Ankara (Turkey)], E-mail: osolak@science.ankara.edu.tr
2009-11-01
EDTA-phenoxyamide modified glassy carbon electrode (EDTA-GC) was prepared at a glassy carbon electrode by surface synthesis. In the first step, nitrophenyl was grafted to the glassy carbon (GC) surface via the electrochemical reduction of its tetraflouroborate diazonium salt. In the second step, nitrophenyl-modified electrode (NP-GC) was subjected to the cathodic potential scan to reduce the nitro to amine group. p-Aminophenyl modified glassy carbon electrode (AP-GC) was dipped into a EDTA solution containing 1-ethyl-3(3-(dimethlyamino)propyl)-carbodiimide (EDC) as an activating agent. Thus formed ((2-anilino-2-oxoethyl){l_brace}2-[bis(carboxymethyl)amino]-ethyl{r_brace}amino)acetic acid modified GC electrode was denoted as EDTA-GC and characterized by cyclic voltammetry (CV), electrochemical impedance spectroscopy (EIS), ellipsometry and X-ray photoelectron spectroscopy (XPS). Complexation of the EDTA-GC surface with Pb{sup 2+} ions was investigated if this electrode could be used as a metal sensor.
Thermodynamic behavior of glassy state of structurally related compounds.
Kaushal, Aditya Mohan; Bansal, Arvind Kumar
2008-08-01
Thermodynamic properties of amorphous pharmaceutical forms are responsible for enhanced solubility as well as poor physical stability. The present study was designed to investigate the differences in thermodynamic parameters arising out of disparate molecular structures and associations for four structurally related pharmaceutical compounds--celecoxib, valdecoxib, rofecoxib, and etoricoxib. Conventional and modulated temperature differential scanning calorimetry were employed to study glass forming ability and thermodynamic behavior of the glassy state of model compounds. Glass transition temperature of four glassy compounds was in a close range of 327.6-331.8 K, however, other thermodynamic parameters varied considerably. Kauzmann temperature, strength parameter and fragility parameter showed rofecoxib glass to be most fragile of the four compounds. Glass forming ability of the compounds fared similar in the critical cooling rate experiments, suggesting that different factors were determining the glass forming ability and subsequent behavior of the compounds in glassy state. A comprehensive understanding of such thermodynamic facets of amorphous form would help in rationalizing the approaches towards development of stable glassy pharmaceuticals.
Glassy carbon supercapacitor: 100,000 cycles demonstrated
Baertsch, M; Braun, A; Schnyder, B; Koetz, R [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1999-08-01
A 5 V glassy carbon capacitor stack was built consisting of four bipolar and two end-plate electrodes. More than 100,000 charging/discharging cycles were applied to test the stability of the double-layer capacitor. Low and high frequency resistances were measured as a function of the number of cycles. (author) 2 figs., 1 ref.
Playback interference of glassy-winged sharp shooter communication
Animal communication is vital to reproduction, particularly for securing a mate. Insects commonly communicate by exchanging vibrational signals that are transmitted through host plants. The glassy-winged sharpshooter (GWSS), Homalodisca vitripennis, is an important vector of Xylella fastidiosa, a pl...
Aryl Diazonium Chemistry for the Surface Functionalization of Glassy Biosensors.
Zheng, Wei; van den Hurk, Remko; Cao, Yong; Du, Rongbing; Sun, Xuejun; Wang, Yiyu; McDermott, Mark T; Evoy, Stephane
2016-03-14
Nanostring resonator and fiber-optics-based biosensors are of interest as they offer high sensitivity, real-time measurements and the ability to integrate with electronics. However, these devices are somewhat impaired by issues related to surface modification. Both nanostring resonators and photonic sensors employ glassy materials, which are incompatible with electrochemistry. A surface chemistry approach providing strong and stable adhesion to glassy surfaces is thus required. In this work, a diazonium salt induced aryl film grafting process is employed to modify a novel SiCN glassy material. Sandwich rabbit IgG binding assays are performed on the diazonium treated SiCN surfaces. Fluorescently labelled anti-rabbit IgG and anti-rabbit IgG conjugated gold nanoparticles were used as markers to demonstrate the absorption of anti-rabbit IgG and therefore verify the successful grafting of the aryl film. The results of the experiments support the effectiveness of diazonium chemistry for the surface functionalization of SiCN surfaces. This method is applicable to other types of glassy materials and potentially can be expanded to various nanomechanical and optical biosensors.
Electrochemical and microstructural characterization of platinum supported on glassy carbon
Terzić Sanja
2007-01-01
Full Text Available The effect of the electrochemical oxidation of glassy carbon on the deposition of platinum particles and the electrocatalytic activity of platinum supported on oxidized glassy carbon were studied for methanol oxidation in H2SO4 solution. Platinum was potentiostatically deposited from H2SO4 + 6mM H2PtCl6 solution. Glassy carbon was anodically polarized in 1 M NaOH at 1.41 V (SCE for 35 and 95 s and in 0.5 M H2SO4 at 2V (SCE for 35; 95 s and 2.25 V for 35 and 95 s. Electrochemical treatment of the GC support leads to a better distribution of platinum on the substrate and has remarkable effect on the activity. The activity of the Pt/GCox electrode for methanol oxidation is larger than that of polycrystalline Pt and by more than one order of magnitude larger than that of a Pt/GC electrode. This increase in activity indicates the pronounced role of the organic residues of the GC support on the properties of Pt particles deposited on glassy carbon.
A study of nanostructured gold modified glassy carbon electrode for ...
A nanostructured gold modified glassy carbon electrode (Aunano/GCE) was employed for the determination of trace chromium(VI). To prepare Aunano/GCE, the GCE was immersed into KAuCl4 solution and electrodeposition was conducted at the potential of -0.4 V (vs Ag/AgCl) for 600 s. Scanning electron microscopy ...
Electrochemical oxidation of niclosamide at a glassy carbon ...
Cyclic voltammetry, square-wave voltammetry and controlled potential electrolysis have been used to study the electrochemical oxidation behaviour of niclosamide at a glassy carbon electrode. The number of electrons transferred, the wave characteristics, the diffusion coefficient and reversibility of the reactions have been ...
Permeation of Mixed Penetrants through Glassy Polymer Membranes.
1985-03-15
and LOPE. Also, ESCA was used in conjunction with plasma etching to determine the effects of the gas phase fluorine concentration and fluorination...at 35 3C. ARD-AISS5 65 PERMEATION OF MIXED PENETRANTS THROUGH GLASSY POLYMER 213 MENBRANES (U) NORTH CAROLINA STATE UNIV AT RALEIGH R T CHERN ET AL. 15
Equation-free dynamic renormalization in a glassy compaction model
Chen, L.; Kevrekidis, I. G.; Kevrekidis, P. G.
2006-01-01
Combining dynamic renormalization with equation-free computational tools, we study the apparently asymptotically self-similar evolution of void distribution dynamics in the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev. Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches, forward as well as backward in time; these can be used to accelerate simulators of glassy dynamic phenomena
Equation-free dynamic renormalization in a glassy compaction model
Chen, L.; Kevrekidis, I. G.; Kevrekidis, P. G.
2006-07-01
Combining dynamic renormalization with equation-free computational tools, we study the apparently asymptotically self-similar evolution of void distribution dynamics in the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev. Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches, forward as well as backward in time; these can be used to accelerate simulators of glassy dynamic phenomena.
Relook on fitting of viscosity with undercooling of glassy liquids
Department of Materials Science and Engineering, Indian Institute of Technology, Kanpur ... The present approach is on the modification of viscosity fitting of undercooled liquid as a function of ... behaviour of glassy alloys and organic and ionic compounds ...... the present method is applied to calculate the analytical solu-.
Effective Ginzburg–Landau free energy functional for multi-band isotropic superconductors
Grigorishin, Konstantin V.
2016-01-01
Highlights: • The intergradient coupling of order parameters in a two-band superconductor plays important role and cannot be neglected. • A two-band superconductor must be characterized with a single coherence length and a single Ginzburg–Landau parameter. • Type-1.5 superconductors are impossible. • The free energy functional for a multi-band superconductor can be reduced to the effective single-band Ginzburg–Landau functional. - Abstract: It has been shown that interband mixing of gradients of two order parameters (drag effect) in an isotropic bulk two-band superconductor plays important role – such a quantity of the intergradients coupling exists that the two-band superconductor is characterized with a single coherence length and a single Ginzburg–Landau (GL) parameter. Other quantities or neglecting of the drag effect lead to existence of two coherence lengths and dynamical instability due to violation of the phase relations between the order parameters. Thus so-called type-1.5 superconductors are impossible. An approximate method for solving of set of GL equations for a multi-band superconductor has been developed: using the result about the drag effect it has been shown that the free-energy functional for a multi-band superconductor can be reduced to the GL functional for an effective single-band superconductor.
Casimir-Foucault interaction: Free energy and entropy at low temperature
Intravaia, Francesco; Ellingsen, Simen Å.; Henkel, Carsten
2010-09-01
It was recently found that thermodynamic anomalies which arise in the Casimir effect between metals described by the Drude model can be attributed to the interaction of fluctuating Foucault (or eddy) currents [F. Intravaia and C. Henkel, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.103.130405 103, 130405 (2009).] We focus on the transverse electric (TE) polarization, where the anomalies occur, and show explicitly that the two leading terms of the low-temperature correction to the Casimir free energy of interaction between two plates are identical to those pertaining to the Foucault current interaction alone, up to a correction which is very small for good metals. Moreover, a mode density along real frequencies is introduced, showing that the TE contribution to the Casimir free energy, as given by the Lifshitz theory, separates in a natural manner into contributions from eddy currents and propagating cavity modes, respectively. The latter have long been known to be of little importance to the low-temperature Casimir anomalies. This convincingly demonstrates that eddy current modes are responsible for the large temperature correction to the Casimir effect between Drude metals, predicted by the Lifshitz theory, but not observed in experiments.
Huang, Yu-Ming M; McCammon, J Andrew; Miao, Yinglong
2018-04-10
Through adding a harmonic boost potential to smooth the system potential energy surface, Gaussian accelerated molecular dynamics (GaMD) provides enhanced sampling and free energy calculation of biomolecules without the need of predefined reaction coordinates. This work continues to improve the acceleration power and energy reweighting of the GaMD by combining the GaMD with replica exchange algorithms. Two versions of replica exchange GaMD (rex-GaMD) are presented: force constant rex-GaMD and threshold energy rex-GaMD. During simulations of force constant rex-GaMD, the boost potential can be exchanged between replicas of different harmonic force constants with fixed threshold energy. However, the algorithm of threshold energy rex-GaMD tends to switch the threshold energy between lower and upper bounds for generating different levels of boost potential. Testing simulations on three model systems, including the alanine dipeptide, chignolin, and HIV protease, demonstrate that through continuous exchanges of the boost potential, the rex-GaMD simulations not only enhance the conformational transitions of the systems but also narrow down the distribution width of the applied boost potential for accurate energetic reweighting to recover biomolecular free energy profiles.
Apparent Surface Free Energy of Polymer/Paper Composite Material Treated by Air Plasma
Konrad Terpiłowski
2017-01-01
Full Text Available Surface plasma treatment consists in changes of surface properties without changing internal properties. In this paper composite polymer/paper material is used for production of packaging in cosmetic industry. There are problems with bonding this material at the time of packaging production due to its properties. Composite surface was treated by air plasma for 1, 10, 20, and 30 s. The advancing and receding contact angles of water, formamide, and diiodomethane were measured using both treated and untreated samples. Apparent surface free energy was estimated using the hysteresis (CAH and Van Oss, Good, Chaudhury approaches (LWAB. Surface roughness was investigated using optical profilometry and identification of after plasma treatment emerging chemical groups was made by means of the XPS (X-ray photoelectron spectroscopy technique. After plasma treatment the values of contact angles decreased which is particularly evident for polar liquids. Apparent surface free energy increased compared to that of untreated samples. Changes of energy value are due to the electron-donor parameter of energy. This parameter increases as a result of adding polar groups at the time of surface plasma activation. Changes of surface properties are combination of increase of polar chemical functional groups, increase on the surface, and surface roughness increase.
Casimir-Foucault interaction: Free energy and entropy at low temperature
Intravaia, Francesco; Ellingsen, Simen A.; Henkel, Carsten
2010-01-01
It was recently found that thermodynamic anomalies which arise in the Casimir effect between metals described by the Drude model can be attributed to the interaction of fluctuating Foucault (or eddy) currents [F. Intravaia and C. Henkel, Phys. Rev. Lett. 103, 130405 (2009).] We focus on the transverse electric (TE) polarization, where the anomalies occur, and show explicitly that the two leading terms of the low-temperature correction to the Casimir free energy of interaction between two plates are identical to those pertaining to the Foucault current interaction alone, up to a correction which is very small for good metals. Moreover, a mode density along real frequencies is introduced, showing that the TE contribution to the Casimir free energy, as given by the Lifshitz theory, separates in a natural manner into contributions from eddy currents and propagating cavity modes, respectively. The latter have long been known to be of little importance to the low-temperature Casimir anomalies. This convincingly demonstrates that eddy current modes are responsible for the large temperature correction to the Casimir effect between Drude metals, predicted by the Lifshitz theory, but not observed in experiments.
Yan, Yaming; Song, Linze; Shi, Qiang
2018-02-28
By employing several lattice model systems, we investigate the free energy barrier and real-time dynamics of charge separation in organic photovoltaic (OPV) cells. It is found that the combined effects of the external electric field, entropy, and charge delocalization reduce the free energy barrier significantly. The dynamic disorder reduces charge carrier delocalization and results in the increased charge separation barrier, while the effect of static disorder is more complicated. Simulation of the real-time dynamics indicates that the free charge generation process involves multiple time scales, including an ultrafast component within hundreds of femtoseconds, an intermediate component related to the relaxation of the hot charge transfer (CT) state, and a slow component on the time scale of tens of picoseconds from the thermally equilibrated CT state. Effects of hot exciton dissociation as well as its dependence on the energy offset between the Frenkel exciton and the CT state are also analyzed. The current results indicate that only a small energy offset between the band gap and the lowest energy CT state is needed to achieve efficient free charge generation in OPV devices, which agrees with recent experimental findings.
Bryce, Richard A
2011-04-01
The ability to accurately predict the interaction of a ligand with its receptor is a key limitation in computer-aided drug design approaches such as virtual screening and de novo design. In this article, we examine current strategies for a physics-based approach to scoring of protein-ligand affinity, as well as outlining recent developments in force fields and quantum chemical techniques. We also consider advances in the development and application of simulation-based free energy methods to study protein-ligand interactions. Fuelled by recent advances in computational algorithms and hardware, there is the opportunity for increased integration of physics-based scoring approaches at earlier stages in computationally guided drug discovery. Specifically, we envisage increased use of implicit solvent models and simulation-based scoring methods as tools for computing the affinities of large virtual ligand libraries. Approaches based on end point simulations and reference potentials allow the application of more advanced potential energy functions to prediction of protein-ligand binding affinities. Comprehensive evaluation of polarizable force fields and quantum mechanical (QM)/molecular mechanical and QM methods in scoring of protein-ligand interactions is required, particularly in their ability to address challenging targets such as metalloproteins and other proteins that make highly polar interactions. Finally, we anticipate increasingly quantitative free energy perturbation and thermodynamic integration methods that are practical for optimization of hits obtained from screened ligand libraries.
Nucleus-size pinning for determination of nucleation free-energy barriers and nucleus geometry
Sharma, Abhishek K.; Escobedo, Fernando A.
2018-05-01
Classical Nucleation Theory (CNT) has recently been used in conjunction with a seeding approach to simulate nucleation phenomena at small-to-moderate supersaturation conditions when large free-energy barriers ensue. In this study, the conventional seeding approach [J. R. Espinosa et al., J. Chem. Phys. 144, 034501 (2016)] is improved by a novel, more robust method to estimate nucleation barriers. Inspired by the interfacial pinning approach [U. R. Pedersen, J. Chem. Phys. 139, 104102 (2013)] used before to determine conditions where two phases coexist, the seed of the incipient phase is pinned to a preselected size to iteratively drive the system toward the conditions where the seed becomes a critical nucleus. The proposed technique is first validated by estimating the critical nucleation conditions for the disorder-to-order transition in hard spheres and then applied to simulate and characterize the highly non-trivial (prolate) morphology of the critical crystal nucleus in hard gyrobifastigia. A generalization of CNT is used to account for nucleus asphericity and predict nucleation free-energy barriers for gyrobifastigia. These predictions of nuclei shape and barriers are validated by independent umbrella sampling calculations.
An Accurate Estimate of the Free Energy and Phase Diagram of All-DNA Bulk Fluids
Emanuele Locatelli
2018-04-01
Full Text Available We present a numerical study in which large-scale bulk simulations of self-assembled DNA constructs have been carried out with a realistic coarse-grained model. The investigation aims at obtaining a precise, albeit numerically demanding, estimate of the free energy for such systems. We then, in turn, use these accurate results to validate a recently proposed theoretical approach that builds on a liquid-state theory, the Wertheim theory, to compute the phase diagram of all-DNA fluids. This hybrid theoretical/numerical approach, based on the lowest-order virial expansion and on a nearest-neighbor DNA model, can provide, in an undemanding way, a parameter-free thermodynamic description of DNA associating fluids that is in semi-quantitative agreement with experiments. We show that the predictions of the scheme are as accurate as those obtained with more sophisticated methods. We also demonstrate the flexibility of the approach by incorporating non-trivial additional contributions that go beyond the nearest-neighbor model to compute the DNA hybridization free energy.
Yan, Yaming; Song, Linze; Shi, Qiang
2018-02-01
By employing several lattice model systems, we investigate the free energy barrier and real-time dynamics of charge separation in organic photovoltaic (OPV) cells. It is found that the combined effects of the external electric field, entropy, and charge delocalization reduce the free energy barrier significantly. The dynamic disorder reduces charge carrier delocalization and results in the increased charge separation barrier, while the effect of static disorder is more complicated. Simulation of the real-time dynamics indicates that the free charge generation process involves multiple time scales, including an ultrafast component within hundreds of femtoseconds, an intermediate component related to the relaxation of the hot charge transfer (CT) state, and a slow component on the time scale of tens of picoseconds from the thermally equilibrated CT state. Effects of hot exciton dissociation as well as its dependence on the energy offset between the Frenkel exciton and the CT state are also analyzed. The current results indicate that only a small energy offset between the band gap and the lowest energy CT state is needed to achieve efficient free charge generation in OPV devices, which agrees with recent experimental findings.
Calculation of absolute protein-ligand binding free energy using distributed replica sampling.
Rodinger, Tomas; Howell, P Lynne; Pomès, Régis
2008-10-21
Distributed replica sampling [T. Rodinger et al., J. Chem. Theory Comput. 2, 725 (2006)] is a simple and general scheme for Boltzmann sampling of conformational space by computer simulation in which multiple replicas of the system undergo a random walk in reaction coordinate or temperature space. Individual replicas are linked through a generalized Hamiltonian containing an extra potential energy term or bias which depends on the distribution of all replicas, thus enforcing the desired sampling distribution along the coordinate or parameter of interest regardless of free energy barriers. In contrast to replica exchange methods, efficient implementation of the algorithm does not require synchronicity of the individual simulations. The algorithm is inherently suited for large-scale simulations using shared or heterogeneous computing platforms such as a distributed network. In this work, we build on our original algorithm by introducing Boltzmann-weighted jumping, which allows moves of a larger magnitude and thus enhances sampling efficiency along the reaction coordinate. The approach is demonstrated using a realistic and biologically relevant application; we calculate the standard binding free energy of benzene to the L99A mutant of T4 lysozyme. Distributed replica sampling is used in conjunction with thermodynamic integration to compute the potential of mean force for extracting the ligand from protein and solvent along a nonphysical spatial coordinate. Dynamic treatment of the reaction coordinate leads to faster statistical convergence of the potential of mean force than a conventional static coordinate, which suffers from slow transitions on a rugged potential energy surface.
Improving the Efficiency of Free Energy Calculations in the Amber Molecular Dynamics Package.
Kaus, Joseph W; Pierce, Levi T; Walker, Ross C; McCammont, J Andrew
2013-09-10
Alchemical transformations are widely used methods to calculate free energies. Amber has traditionally included support for alchemical transformations as part of the sander molecular dynamics (MD) engine. Here we describe the implementation of a more efficient approach to alchemical transformations in the Amber MD package. Specifically we have implemented this new approach within the more computational efficient and scalable pmemd MD engine that is included with the Amber MD package. The majority of the gain in efficiency comes from the improved design of the calculation, which includes better parallel scaling and reduction in the calculation of redundant terms. This new implementation is able to reproduce results from equivalent simulations run with the existing functionality, but at 2.5 times greater computational efficiency. This new implementation is also able to run softcore simulations at the λ end states making direct calculation of free energies more accurate, compared to the extrapolation required in the existing implementation. The updated alchemical transformation functionality will be included in the next major release of Amber (scheduled for release in Q1 2014) and will be available at http://ambermd.org, under the Amber license.
Binding mode and free energy prediction of fisetin/β-cyclodextrin inclusion complexes
Bodee Nutho
2014-11-01
Full Text Available In the present study, our aim is to investigate the preferential binding mode and encapsulation of the flavonoid fisetin in the nano-pore of β-cyclodextrin (β-CD at the molecular level using various theoretical approaches: molecular docking, molecular dynamics (MD simulations and binding free energy calculations. The molecular docking suggested four possible fisetin orientations in the cavity through its chromone or phenyl ring with two different geometries of fisetin due to the rotatable bond between the two rings. From the multiple MD results, the phenyl ring of fisetin favours its inclusion into the β-CD cavity, whilst less binding or even unbinding preference was observed in the complexes where the larger chromone ring is located in the cavity. All MM- and QM-PBSA/GBSA free energy predictions supported the more stable fisetin/β-CD complex of the bound phenyl ring. Van der Waals interaction is the key force in forming the complexes. In addition, the quantum mechanics calculations with M06-2X/6-31G(d,p clearly showed that both solvation effect and BSSE correction cannot be neglected for the energy determination of the chosen system.
Strategies for the exploration of free energy landscapes: Unity in diversity and challenges ahead
Fabio Pietrucci
2017-11-01
Full Text Available Computer simulations play an important role in the study of transformation processes of condensed matter, including phase transitions, chemical reactions, and conformational changes of biomolecules. In principle, atomic trajectories, such as those generated using the molecular dynamics approach, contain detailed structural, thermodynamic, and kinetic information about activated processes. In practice, due to free energy barriers, there is often a wide gap between the time scale of the transformation and the time scale accessible with simulations. This review offers a practical guide to the ingenious methods aimed to accelerate the exploration and reconstruction of free energy landscapes of complex systems. The focus is on basic unifying concepts, successful strategies, and pitfalls, illustrated with examples of application to scientific problems from different disciplines. The current challenges in the field consist mainly in the cumbersome identification of optimal reaction coordinates and in the extensive recourse to expert human supervision and fine tuning of the algorithms. The full achievement of wide-spectrum formulations and easy reproducibility of results would constitute the breakthrough necessary to enter the era of routine use of enhanced sampling simulations.
Is the climate system an anticipatory system that minimizes free energy?
Rubin, Sergio; Crucifix, Michel
2017-04-01
All systems, whether they are alive or not are structured determined systems, i.e. their present states [x (t)] depends of past states [x (t - α)]. However it has been suggested [Rosen, 1985; Friston, 2013] that systems that contain life are capable of anticipation and active inference. The underlying principle is that state changes in living systems are best modelled as a function of past and future states [ x(t) = f (x (t - α), x(t), x (t + β)) ]. The reason for this is that living systems contain a predictive model of their ambiance on which they are active: they appear to model their ambiance to preserve their integrity and homeorhesis. We therefore formulate the following hypothesis: can the climate system be interpreted as an anticipatory system that minimizes free energy? Can its variability (catastrophe, bifurcation and/or tipping points) be interpreted in terms of active inference and anticipation failure? Here we present a mathematical formulation of the climate system as an anticipatory system that minimizes free energy and its possible implication in the future climate predictability. References Rosen, R. (1985). Anticipatory systems. In Anticipatory systems (pp. 313-370). Springer New York. Friston, K. (2013). Life as we know it. Journal of the Royal Society Interface, 10(86), 20130475.
Pazzona, Federico G.; Pireddu, Giovanni; Gabrieli, Andrea; Pintus, Alberto M.; Demontis, Pierfranco
2018-05-01
We investigate the coarse-graining of host-guest systems under the perspective of the local distribution of pore occupancies, along with the physical meaning and actual computability of the coarse-interaction terms. We show that the widely accepted approach, in which the contributions to the free energy given by the molecules located in two neighboring pores are estimated through Monte Carlo simulations where the two pores are kept separated from the rest of the system, leads to inaccurate results at high sorbate densities. In the coarse-graining strategy that we propose, which is based on the Bethe-Peierls approximation, density-independent interaction terms are instead computed according to local effective potentials that take into account the correlations between the pore pair and its surroundings by means of mean-field correction terms without the need for simulating the pore pair separately. Use of the interaction parameters obtained this way allows the coarse-grained system to reproduce more closely the equilibrium properties of the original one. Results are shown for lattice-gases where the local free energy can be computed exactly and for a system of Lennard-Jones particles under the effect of a static confining field.
Minakata, Daisuke; Mezyk, Stephen P; Jones, Jace W; Daws, Brittany R; Crittenden, John C
2014-12-02
Aqueous phase advanced oxidation processes (AOPs) produce hydroxyl radicals (HO•) which can completely oxidize electron rich organic compounds. The proper design and operation of AOPs require that we predict the formation and fate of the byproducts and their associated toxicity. Accordingly, there is a need to develop a first-principles kinetic model that can predict the dominant reaction pathways that potentially produce toxic byproducts. We have published some of our efforts on predicting the elementary reaction pathways and the HO• rate constants. Here we develop linear free energy relationships (LFERs) that predict the rate constants for aqueous phase radical reactions. The LFERs relate experimentally obtained kinetic rate constants to quantum mechanically calculated aqueous phase free energies of activation. The LFERs have been applied to 101 reactions, including (1) HO• addition to 15 aromatic compounds; (2) addition of molecular oxygen to 65 carbon-centered aliphatic and cyclohexadienyl radicals; (3) disproportionation of 10 peroxyl radicals, and (4) unimolecular decay of nine peroxyl radicals. The LFERs correlations predict the rate constants within a factor of 2 from the experimental values for HO• reactions and molecular oxygen addition, and a factor of 5 for peroxyl radical reactions. The LFERs and the elementary reaction pathways will enable us to predict the formation and initial fate of the byproducts in AOPs. Furthermore, our methodology can be applied to other environmental processes in which aqueous phase radical-involved reactions occur.
Topography and surface free energy of DPPC layers deposited on a glass, mica, or PMMA support.
Jurak, Malgorzata; Chibowski, Emil
2006-08-15
An investigation of energetic properties of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) layers deposited on glass, mica, and PMMA (poly(methyl methacrylate)) surfaces was carried out by means of contact angles measurements (advancing and receding) for three probe liquids (diiodomethane, water, and formamide). DPPC was deposited on the surfaces from water (on glass and mica) or methanol (on PMMA) solutions. The topography of the tested surfaces was determined with a help of scanning electron microscopy (SEM) and atomic force microscopy (AFM). Using the measured contact angles, the total apparent surface free energy and its components of the studied layers were determined from van Oss et al.'s (Lifshitz-van der Waals and acid-base components, LWAB) and contact angle hysteresis (CAH) approaches. It allowed us to learn about changes in the surface free energy of the layers (hydrophobicity/hydrophilicity) depending on their number and kind of support. It was found that the changes in the energy greatly depended on the surface properties of the substrate as well as the statistical number of monolayers of DPPC. However, principal changes took place for first three monolayers.
Unconstrained Enhanced Sampling for Free Energy Calculations of Biomolecules: A Review
Miao, Yinglong; McCammon, J. Andrew
2016-01-01
Free energy calculations are central to understanding the structure, dynamics and function of biomolecules. Yet insufficient sampling of biomolecular configurations is often regarded as one of the main sources of error. Many enhanced sampling techniques have been developed to address this issue. Notably, enhanced sampling methods based on biasing collective variables (CVs), including the widely used umbrella sampling, adaptive biasing force and metadynamics, have been discussed in a recent excellent review (Abrams and Bussi, Entropy, 2014). Here, we aim to review enhanced sampling methods that do not require predefined system-dependent CVs for biomolecular simulations and as such do not suffer from the hidden energy barrier problem as encountered in the CV-biasing methods. These methods include, but are not limited to, replica exchange/parallel tempering, self-guided molecular/Langevin dynamics, essential energy space random walk and accelerated molecular dynamics. While it is overwhelming to describe all details of each method, we provide a summary of the methods along with the applications and offer our perspectives. We conclude with challenges and prospects of the unconstrained enhanced sampling methods for accurate biomolecular free energy calculations. PMID:27453631
Gibbs Free Energy of Formation for Selected Platinum Group Minerals (PGM
Spiros Olivotos
2016-01-01
Full Text Available Thermodynamic data for platinum group (Os, Ir, Ru, Rh, Pd and Pt minerals are very limited. The present study is focused on the calculation of the Gibbs free energy of formation (ΔfG° for selected PGM occurring in layered intrusions and ophiolite complexes worldwide, applying available experimental data on their constituent elements at their standard state (ΔG = G(species − ΔG(elements, using the computer program HSC Chemistry software 6.0. The evaluation of the accuracy of the calculation method was made by the calculation of (ΔGf of rhodium sulfide phases. The calculated values were found to be ingood agreement with those measured in the binary system (Rh + S as a function of temperature by previous authors (Jacob and Gupta (2014. The calculated Gibbs free energy (ΔfG° followed the order RuS2 < (Ir,OsS2 < (Pt, PdS < (Pd, PtTe2, increasing from compatible to incompatible noble metals and from sulfides to tellurides.
The role of chemical free energy and elastic strain in the nucleation of zirconium hydride
Barrow, A.T.W.; Toffolon-Masclet, C.; Almer, J.; Daymond, M.R.
2013-01-01
In this work a combination of synchrotron X-ray diffraction and thermodynamic modelling has been used to study the dissolution and precipitation of zirconium hydride in α-Zr establishing the role of elastic misfit strain and chemical free energy in the α → α + δ phase transformation. The nucleation of zirconium hydride is dominated by the chemical free energy where the chemical driving force for hydride precipitation is proportional to the terminal-solid solubility for precipitation and can be predicted by a function that is analogous to the universal nucleation parameter for the bainite transformation in ferrous alloys. The terminal-solid solubility for precipitation was found to be kinetically limited ⩾287 °C at a cooling rate of 5 °C min −1 or greater. The terminal solubilities were established using an offset method applied to the lattice strain data where a resolution of ∼10 wppm H can be achieved in the 〈c〉-direction. This is aided by the introduction of intra-granular strains in the 〈c〉-direction during cooling as a result of the thermal expansion anisotropy which increases the anisotropy associated with the misfitting H atoms within the α-Zr lattice
CaFE: a tool for binding affinity prediction using end-point free energy methods.
Liu, Hui; Hou, Tingjun
2016-07-15
Accurate prediction of binding free energy is of particular importance to computational biology and structure-based drug design. Among those methods for binding affinity predictions, the end-point approaches, such as MM/PBSA and LIE, have been widely used because they can achieve a good balance between prediction accuracy and computational cost. Here we present an easy-to-use pipeline tool named Calculation of Free Energy (CaFE) to conduct MM/PBSA and LIE calculations. Powered by the VMD and NAMD programs, CaFE is able to handle numerous static coordinate and molecular dynamics trajectory file formats generated by different molecular simulation packages and supports various force field parameters. CaFE source code and documentation are freely available under the GNU General Public License via GitHub at https://github.com/huiliucode/cafe_plugin It is a VMD plugin written in Tcl and the usage is platform-independent. tingjunhou@zju.edu.cn. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
Demuynck, Ruben; Rogge, Sven M J; Vanduyfhuys, Louis; Wieme, Jelle; Waroquier, Michel; Van Speybroeck, Veronique
2017-12-12
In order to reliably predict and understand the breathing behavior of highly flexible metal-organic frameworks from thermodynamic considerations, an accurate estimation of the free energy difference between their different metastable states is a prerequisite. Herein, a variety of free energy estimation methods are thoroughly tested for their ability to construct the free energy profile as a function of the unit cell volume of MIL-53(Al). The methods comprise free energy perturbation, thermodynamic integration, umbrella sampling, metadynamics, and variationally enhanced sampling. A series of molecular dynamics simulations have been performed in the frame of each of the five methods to describe structural transformations in flexible materials with the volume as the collective variable, which offers a unique opportunity to assess their computational efficiency. Subsequently, the most efficient method, umbrella sampling, is used to construct an accurate free energy profile at different temperatures for MIL-53(Al) from first principles at the PBE+D3(BJ) level of theory. This study yields insight into the importance of the different aspects such as entropy contributions and anharmonic contributions on the resulting free energy profile. As such, this thorough study provides unparalleled insight in the thermodynamics of the large structural deformations of flexible materials.
2017-01-01
In order to reliably predict and understand the breathing behavior of highly flexible metal–organic frameworks from thermodynamic considerations, an accurate estimation of the free energy difference between their different metastable states is a prerequisite. Herein, a variety of free energy estimation methods are thoroughly tested for their ability to construct the free energy profile as a function of the unit cell volume of MIL-53(Al). The methods comprise free energy perturbation, thermodynamic integration, umbrella sampling, metadynamics, and variationally enhanced sampling. A series of molecular dynamics simulations have been performed in the frame of each of the five methods to describe structural transformations in flexible materials with the volume as the collective variable, which offers a unique opportunity to assess their computational efficiency. Subsequently, the most efficient method, umbrella sampling, is used to construct an accurate free energy profile at different temperatures for MIL-53(Al) from first principles at the PBE+D3(BJ) level of theory. This study yields insight into the importance of the different aspects such as entropy contributions and anharmonic contributions on the resulting free energy profile. As such, this thorough study provides unparalleled insight in the thermodynamics of the large structural deformations of flexible materials. PMID:29131647
Wei, Qichao; Zhao, Weilong; Yang, Yang; Cui, Beiliang; Xu, Zhijun; Yang, Xiaoning
2018-03-19
Considerable interest in characterizing protein/peptide-surface interactions has prompted extensive computational studies on calculations of adsorption free energy. However, in many cases, each individual study has focused on the application of free energy calculations to a specific system; therefore, it is difficult to combine the results into a general picture for choosing an appropriate strategy for the system of interest. Herein, three well-established computational algorithms are systemically compared and evaluated to compute the adsorption free energy of small molecules on two representative surfaces. The results clearly demonstrate that the characteristics of studied interfacial systems have crucial effects on the accuracy and efficiency of the adsorption free energy calculations. For the hydrophobic surface, steered molecular dynamics exhibits the highest efficiency, which appears to be a favorable method of choice for enhanced sampling simulations. However, for the charged surface, only the umbrella sampling method has the ability to accurately explore the adsorption free energy surface. The affinity of the water layer to the surface significantly affects the performance of free energy calculation methods, especially at the region close to the surface. Therefore, a general principle of how to discriminate between methodological and sampling issues based on the interfacial characteristics of the system under investigation is proposed. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Asada, Toshio; Ando, Kanta; Bandyopadhyay, Pradipta; Koseki, Shiro
2016-09-08
A widely applicable free energy contribution analysis (FECA) method based on the quantum mechanical/molecular mechanical (QM/MM) approximation using response kernel approaches has been proposed to investigate the influences of environmental residues and/or atoms in the QM region on the free energy profile. This method can evaluate atomic contributions to the free energy along the reaction path including polarization effects on the QM region within a dramatically reduced computational time. The rate-limiting step in the deactivation of the β-lactam antibiotic cefalotin (CLS) by β-lactamase was studied using this method. The experimentally observed activation barrier was successfully reproduced by free energy perturbation calculations along the optimized reaction path that involved activation by the carboxylate moiety in CLS. It was found that the free energy profile in the QM region was slightly higher than the isolated energy and that two residues, Lys67 and Lys315, as well as water molecules deeply influenced the QM atoms associated with the bond alternation reaction in the acyl-enzyme intermediate. These facts suggested that the surrounding residues are favorable for the reactant complex and prevent the intermediate from being too stabilized to proceed to the following deacylation reaction. We have demonstrated that the free energy contribution analysis should be a useful method to investigate enzyme catalysis and to facilitate intelligent molecular design.
Zhang, Baofeng; D'Erasmo, Michael P; Murelli, Ryan P; Gallicchio, Emilio
2016-09-30
We report the results of a binding free energy-based virtual screening campaign of a library of 77 α-hydroxytropolone derivatives against the challenging RNase H active site of the reverse transcriptase (RT) enzyme of human immunodeficiency virus-1. Multiple protonation states, rotamer states, and binding modalities of each compound were individually evaluated. The work involved more than 300 individual absolute alchemical binding free energy parallel molecular dynamics calculations and over 1 million CPU hours on national computing clusters and a local campus computational grid. The thermodynamic and structural measures obtained in this work rationalize a series of characteristics of this system useful for guiding future synthetic and biochemical efforts. The free energy model identified key ligand-dependent entropic and conformational reorganization processes difficult to capture using standard docking and scoring approaches. Binding free energy-based optimization of the lead compounds emerging from the virtual screen has yielded four compounds with very favorable binding properties, which will be the subject of further experimental investigations. This work is one of the few reported applications of advanced-binding free energy models to large-scale virtual screening and optimization projects. It further demonstrates that, with suitable algorithms and automation, advanced-binding free energy models can have a useful role in early-stage drug-discovery programs.
Fox, Stephen J; Pittock, Chris; Tautermann, Christofer S; Fox, Thomas; Christ, Clara; Malcolm, N O J; Essex, Jonathan W; Skylaris, Chris-Kriton
2013-08-15
Schemes of increasing sophistication for obtaining free energies of binding have been developed over the years, where configurational sampling is used to include the all-important entropic contributions to the free energies. However, the quality of the results will also depend on the accuracy with which the intermolecular interactions are computed at each molecular configuration. In this context, the energy change associated with the rearrangement of electrons (electronic polarization and charge transfer) upon binding is a very important effect. Classical molecular mechanics force fields do not take this effect into account explicitly, and polarizable force fields and semiempirical quantum or hybrid quantum-classical (QM/MM) calculations are increasingly employed (at higher computational cost) to compute intermolecular interactions in free-energy schemes. In this work, we investigate the use of large-scale quantum mechanical calculations from first-principles as a way of fully taking into account electronic effects in free-energy calculations. We employ a one-step free-energy perturbation (FEP) scheme from a molecular mechanical (MM) potential to a quantum mechanical (QM) potential as a correction to thermodynamic integration calculations within the MM potential. We use this approach to calculate relative free energies of hydration of small aromatic molecules. Our quantum calculations are performed on multiple configurations from classical molecular dynamics simulations. The quantum energy of each configuration is obtained from density functional theory calculations with a near-complete psinc basis set on over 600 atoms using the ONETEP program.
König, Gerhard; Mei, Ye; Pickard, Frank C; Simmonett, Andrew C; Miller, Benjamin T; Herbert, John M; Woodcock, H Lee; Brooks, Bernard R; Shao, Yihan
2016-01-12
A recently developed MESS-E-QM/MM method (multiple-environment single-system quantum mechanical molecular/mechanical calculations with a Roothaan-step extrapolation) is applied to the computation of hydration free energies for the blind SAMPL4 test set and for 12 small molecules. First, free energy simulations are performed with a classical molecular mechanics force field using fixed-geometry solute molecules and explicit TIP3P solvent, and then the non-Boltzmann-Bennett method is employed to compute the QM/MM correction (QM/MM-NBB) to the molecular mechanical hydration free energies. For the SAMPL4 set, MESS-E-QM/MM-NBB corrections to the hydration free energy can be obtained 2 or 3 orders of magnitude faster than fully converged QM/MM-NBB corrections, and, on average, the hydration free energies predicted with MESS-E-QM/MM-NBB fall within 0.10-0.20 kcal/mol of full-converged QM/MM-NBB results. Out of five density functionals (BLYP, B3LYP, PBE0, M06-2X, and ωB97X-D), the BLYP functional is found to be most compatible with the TIP3P solvent model and yields the most accurate hydration free energies against experimental values for solute molecules included in this study.
Pressure-induced transformations in computer simulations of glassy water
Chiu, Janet; Starr, Francis W.; Giovambattista, Nicolas
2013-11-01
Glassy water occurs in at least two broad categories: low-density amorphous (LDA) and high-density amorphous (HDA) solid water. We perform out-of-equilibrium molecular dynamics simulations to study the transformations of glassy water using the ST2 model. Specifically, we study the known (i) compression-induced LDA-to-HDA, (ii) decompression-induced HDA-to-LDA, and (iii) compression-induced hexagonal ice-to-HDA transformations. We study each transformation for a broad range of compression/decompression temperatures, enabling us to construct a "P-T phase diagram" for glassy water. The resulting phase diagram shows the same qualitative features reported from experiments. While many simulations have probed the liquid-state phase behavior, comparatively little work has examined the transitions of glassy water. We examine how the glass transformations relate to the (first-order) liquid-liquid phase transition previously reported for this model. Specifically, our results support the hypothesis that the liquid-liquid spinodal lines, between a low-density and high-density liquid, are extensions of the LDA-HDA transformation lines in the limit of slow compression. Extending decompression runs to negative pressures, we locate the sublimation lines for both LDA and hyperquenched glassy water (HGW), and find that HGW is relatively more stable to the vapor. Additionally, we observe spontaneous crystallization of HDA at high pressure to ice VII. Experiments have also seen crystallization of HDA, but to ice XII. Finally, we contrast the structure of LDA and HDA for the ST2 model with experiments. We find that while the radial distribution functions (RDFs) of LDA are similar to those observed in experiments, considerable differences exist between the HDA RDFs of ST2 water and experiment. The differences in HDA structure, as well as the formation of ice VII (a tetrahedral crystal), are a consequence of ST2 overemphasizing the tetrahedral character of water.
Kaus, Joseph W; Harder, Edward; Lin, Teng; Abel, Robert; McCammon, J Andrew; Wang, Lingle
2015-06-09
Recent advances in improved force fields and sampling methods have made it possible for the accurate calculation of protein–ligand binding free energies. Alchemical free energy perturbation (FEP) using an explicit solvent model is one of the most rigorous methods to calculate relative binding free energies. However, for cases where there are high energy barriers separating the relevant conformations that are important for ligand binding, the calculated free energy may depend on the initial conformation used in the simulation due to the lack of complete sampling of all the important regions in phase space. This is particularly true for ligands with multiple possible binding modes separated by high energy barriers, making it difficult to sample all relevant binding modes even with modern enhanced sampling methods. In this paper, we apply a previously developed method that provides a corrected binding free energy for ligands with multiple binding modes by combining the free energy results from multiple alchemical FEP calculations starting from all enumerated poses, and the results are compared with Glide docking and MM-GBSA calculations. From these calculations, the dominant ligand binding mode can also be predicted. We apply this method to a series of ligands that bind to c-Jun N-terminal kinase-1 (JNK1) and obtain improved free energy results. The dominant ligand binding modes predicted by this method agree with the available crystallography, while both Glide docking and MM-GBSA calculations incorrectly predict the binding modes for some ligands. The method also helps separate the force field error from the ligand sampling error, such that deviations in the predicted binding free energy from the experimental values likely indicate possible inaccuracies in the force field. An error in the force field for a subset of the ligands studied was identified using this method, and improved free energy results were obtained by correcting the partial charges assigned to the
2016-01-01
Recent advances in improved force fields and sampling methods have made it possible for the accurate calculation of protein–ligand binding free energies. Alchemical free energy perturbation (FEP) using an explicit solvent model is one of the most rigorous methods to calculate relative binding free energies. However, for cases where there are high energy barriers separating the relevant conformations that are important for ligand binding, the calculated free energy may depend on the initial conformation used in the simulation due to the lack of complete sampling of all the important regions in phase space. This is particularly true for ligands with multiple possible binding modes separated by high energy barriers, making it difficult to sample all relevant binding modes even with modern enhanced sampling methods. In this paper, we apply a previously developed method that provides a corrected binding free energy for ligands with multiple binding modes by combining the free energy results from multiple alchemical FEP calculations starting from all enumerated poses, and the results are compared with Glide docking and MM-GBSA calculations. From these calculations, the dominant ligand binding mode can also be predicted. We apply this method to a series of ligands that bind to c-Jun N-terminal kinase-1 (JNK1) and obtain improved free energy results. The dominant ligand binding modes predicted by this method agree with the available crystallography, while both Glide docking and MM-GBSA calculations incorrectly predict the binding modes for some ligands. The method also helps separate the force field error from the ligand sampling error, such that deviations in the predicted binding free energy from the experimental values likely indicate possible inaccuracies in the force field. An error in the force field for a subset of the ligands studied was identified using this method, and improved free energy results were obtained by correcting the partial charges assigned to the
Minimum spanning trees and random resistor networks in d dimensions.
Read, N
2005-09-01
We consider minimum-cost spanning trees, both in lattice and Euclidean models, in d dimensions. For the cost of the optimum tree in a box of size L , we show that there is a correction of order L(theta) , where theta or =1 . The arguments all rely on the close relation of Kruskal's greedy algorithm for the minimum spanning tree, percolation, and (for some arguments) random resistor networks. The scaling of the entropy and free energy at small nonzero T , and hence of the number of near-optimal solutions, is also discussed. We suggest that the Steiner tree problem is in the same universality class as the minimum spanning tree in all dimensions, as is the traveling salesman problem in two dimensions. Hence all will have the same value of theta=-3/4 in two dimensions.
Fields, Gary S.; Kanbur, Ravi
2005-01-01
Textbook analysis tells us that in a competitive labor market, the introduction of a minimum wage above the competitive equilibrium wage will cause unemployment. This paper makes two contributions to the basic theory of the minimum wage. First, we analyze the effects of a higher minimum wage in terms of poverty rather than in terms of unemployment. Second, we extend the standard textbook model to allow for incomesharing between the employed and the unemployed. We find that there are situation...
W. L. Silva
2008-09-01
Full Text Available The reduction efficiency is an important variable during the black liquor burning process in the Kraft recovery boiler. This variable value is obtained by slow experimental routines and the delay of this measure disturbs the pulp and paper industry customary control. This paper describes an optimization approach for the reduction efficiency determination in the furnace bottom of the recovery boiler based on the minimization of the Gibbs free energy. The industrial data used in this study were directly obtained from CENIBRA's data acquisition system. The resulting approach is able to predict the steady state behavior of the chemical composition of the furnace recovery boiler, - especially the reduction efficiency when different operational conditions are used. This result confirms the potential of this approach in the analysis of the daily operation of the recovery boiler.
Surface free energy predominates in cell adhesion to hydroxyapatite through wettability.
Nakamura, Miho; Hori, Naoko; Ando, Hiroshi; Namba, Saki; Toyama, Takeshi; Nishimiya, Nobuyuki; Yamashita, Kimihiro
2016-05-01
The initial adhesion of cells to biomaterials is critical in the regulation of subsequent cell behaviors. The purpose of this study was to investigate a mechanism through which the surface wettability of biomaterials can be improved and determine the effects of biomaterial surface characteristics on cellular behaviors. We investigated the surface characteristics of various types of hydroxyapatite after sintering in different atmospheres and examined the effects of various surface characteristics on cell adhesion to study cell-biomaterial interactions. Sintering atmosphere affects the polarization capacity of hydroxyapatite by changing hydroxide ion content and grain size. Compared with hydroxyapatite sintered in air, hydroxyapatite sintered in saturated water vapor had a higher polarization capacity that increased surface free energy and improved wettability, which in turn accelerated cell adhesion. We determined the optimal conditions of hydroxyapatite polarization for the improvement of surface wettability and acceleration of cell adhesion. Copyright © 2016 Elsevier B.V. All rights reserved.
Nucleation theory - Is replacement free energy needed?. [error analysis of capillary approximation
Doremus, R. H.
1982-01-01
It has been suggested that the classical theory of nucleation of liquid from its vapor as developed by Volmer and Weber (1926) needs modification with a factor referred to as the replacement free energy and that the capillary approximation underlying the classical theory is in error. Here, the classical nucleation equation is derived from fluctuation theory, Gibb's result for the reversible work to form a critical nucleus, and the rate of collision of gas molecules with a surface. The capillary approximation is not used in the derivation. The chemical potential of small drops is then considered, and it is shown that the capillary approximation can be derived from thermodynamic equations. The results show that no corrections to Volmer's equation are needed.
Antenna entropy in plant photosystems does not reduce the free energy for primary charge separation.
Jennings, Robert C; Zucchelli, Giuseppe
2014-12-01
We have investigated the concept of the so-called "antenna entropy" of higher plant photosystems. Several interesting points emerge: 1. In the case of a photosystemwhich harbours an excited state, the “antenna entropy” is equivalent to the configurational (mixing) entropy of a thermodynamic canonical ensemble. The energy associated with this parameter has been calculated for a hypothetical isoenergetic photosystem, photosystem I and photosystem II, and comes out in the range of 3.5 - 8% of the photon energy considering 680 nm. 2. The “antenna entropy” seems to be a rather unique thermodynamic phenomenon, in as much as it does not modify the free energy available for primary photochemistry, as has been previously suggested. 3. It is underlined that this configurational (mixing) entropy, unlike heat dispersal in a thermal system, does not involve energy dilution. This points out an important difference between thermal and electronic energy dispersal. Copyright © 2014 Elsevier B.V. All rights reserved.
Answering Schrödinger's question: A free-energy formulation
Ramstead, Maxwell James Désormeau; Badcock, Paul Benjamin; Friston, Karl John
2018-03-01
The free-energy principle (FEP) is a formal model of neuronal processes that is widely recognised in neuroscience as a unifying theory of the brain and biobehaviour. More recently, however, it has been extended beyond the brain to explain the dynamics of living systems, and their unique capacity to avoid decay. The aim of this review is to synthesise these advances with a meta-theoretical ontology of biological systems called variational neuroethology, which integrates the FEP with Tinbergen's four research questions to explain biological systems across spatial and temporal scales. We exemplify this framework by applying it to Homo sapiens, before translating variational neuroethology into a systematic research heuristic that supplies the biological, cognitive, and social sciences with a computationally tractable guide to discovery.
Selwa, Edithe; Elisée, Eddy; Zavala, Agustin; Iorga, Bogdan I.
2018-01-01
Our participation to the D3R Grand Challenge 2 involved a protocol in two steps, with an initial analysis of the available structural data from the PDB allowing the selection of the most appropriate combination of docking software and scoring function. Subsequent docking calculations showed that the pose prediction can be carried out with a certain precision, but this is dependent on the specific nature of the ligands. The correct ranking of docking poses is still a problem and cannot be successful in the absence of good pose predictions. Our free energy calculations on two different subsets provided contrasted results, which might have the origin in non-optimal force field parameters associated with the sulfonamide chemical moiety.
Predicting hydration free energies of amphetamine-type stimulants with a customized molecular model
Li, Jipeng; Lu, Diannan; Fu, Jia; Wu, Jianzhong; Huang, Xing
2016-01-01
Amphetamine-type stimulants (ATS) are a group of incitation and psychedelic drugs affecting the central nervous system. Physicochemical data for these compounds are essential for understanding the stimulating mechanism, for assessing their environmental impacts, and for developing new drug detection methods. However, experimental data are scarce due to tight regulation of such illicit drugs, yet conventional methods to estimate their properties are often unreliable. Here we introduce a tailor-made multiscale procedure for predicting the hydration free energies and the solvation structures of ATS molecules by a combination of first principles calculations and the classical density functional theory. We demonstrate that the multiscale procedure performs well for a training set with similar molecular characteristics and yields good agreement with a testing set not used in the training. The theoretical predictions serve as a benchmark for the missing experimental data and, importantly, provide microscopic insights into manipulating the hydrophobicity of ATS compounds by chemical modifications. (paper)
Free Energy Landscape of the Dissolution of Gibbsite at High pH
Shen, Zhizhang; Kerisit, Sebastien N.; Stack, Andrew G.; Rosso, Kevin M.
2018-03-26
The individual elementary reactions involved in the dissolution of a solid into solution remain mostly speculative due to a lack of suitable, direct experimental probes. In this regard, we have applied atomistic simulations to map the free energy landscape of the dissolution of gibbsite from a step edge, as a model of metal hydroxide dissolution. The overall reaction combines kink site formation and kink site propagation. Two individual reactions were found to be rate-limiting for kink site formation, that is, the displacement of Al from a step site to a ledge adatom site and its detachment from ledge/terrace adatom sites into the solution. As a result, a pool of mobile and labile Al adsorbed species, or adatoms, exists before the release of Al into solution. Because of the quasi-hexagonal symmetry of gibbsite, kink site propagation can occur in multiple directions. Overall, the simulation results will enable the development of microscopic mechanistic models of metal oxide dissolution.
Standard molar Gibbs free energy of formation of URh3(s)
Prasad, Rajendra; Sayi, Y.S.; Radhakrishna, J.; Yadav, C.S.; Shankaran, P.S.; Chhapru, G.C.
1992-01-01
Equilibrium partial pressures of CO(g) over the system (UO 2 (s) + C(s) + Rh(s) + URh 3 (s)) were measured in the temperature range 1327 - 1438 K. Standard Gibbs molar free energy of formation of URh 3 (Δ f G o m ) in the above temperature range can be expressed as Δ f G o m (URh 3 ,s,T)+-3.0(kJ/mol)= -348.165 + 0.03144 T(K). The second and third law enthalpy of formation, ΔfH o m (URh 3 ,s,298.15 K) are (-318.4 +- 3.0) and (298.3 +- 2.5) kJ/mol respectively. (author). 7 refs., 3 tabs
Incremental binding free energies of aluminum (III) vs. magnesium (II) complexes
Mercero, Jose M.; Mujika, Jon I.; Matxain, Jon M.; Lopez, Xabier; Ugalde, Jesus M.
2003-01-01
A sequential ligand addition to the aluminum (III) cation has been studied using the B3LYP functional and a combined all-electron/pseudopotentials basis set. The aluminum complexes are compared with analogous magnesium (II) complexes. Different thermodynamical data, such as incremental binding energies, enthalpies, entropies and free energies, are presented for these addition reactions. While the magnesium (II) cation can only accommodate three negatively charged ligands, aluminum (III) accommodates four even after including bulk solvent effects. The main differences between both cations complexing with the neutral ligands, is that aluminum (III) is not able to form complexes with methanol until the number of methanol ligands is equal to 3. Magnesium (II) prefers to bind methanol and formamide when the number of ligands is small, while aluminum prefers formamide. For the largest complexes both cations prefer to bind water
The free energy of spherical bubbles in lattice SU(3) gauge theory
Kajantie, Keijo; Rummukainen, K; Karkkainen, Leo
1992-01-01
We study the coefficients of the expansion $F(R) = 1/3 c_3 R^3 + 1/2 c_2 R^2 + c_1 R$ of the free energy of spherical bubbles at $T=T_c$ in pure glue QCD using lattice Monte Carlo techniques. The coefficient $c_3$ vanishes at $T=T_c$ and our results suggest that the sign and the order of magnitude of $c_1$ is in agreement with the value $c_1=\\pm 32\\pi T_c^2/9$ (- for hadronic bubbles in quark phase, + for quark bubbles in hadronic phase) computed by Mardor and Svetitsky from the MIT bag model. The parameter $c_2$ is small in agreement with earlier determinations.
Heavy quark free energy in QCD and in gauge theories with gravity duals
Noronha, Jorge
2010-09-01
Recent lattice results in pure glue SU(3) theory at high temperatures have shown that the expectation value of the renormalized Polyakov loop approaches its asymptotic limit at high temperatures from above. We show that this implies that the “heavy quark free energy” obtained from the renormalized loop computed on the lattice does not behave like a true thermodynamic free energy. While this should be expected to occur in asymptotically free gauge theories such as QCD, we use the gauge/string duality to show that in a large class of strongly coupled gauge theories with nontrivial UV fixed points the Polyakov loop reaches its asymptotic value from above only if the dimension of the relevant operator used to deform the conformal field theory is greater than or equal to 3.
Donovan-Maiye, Rory M; Langmead, Christopher J; Zuckerman, Daniel M
2018-01-09
Motivated by the extremely high computing costs associated with estimates of free energies for biological systems using molecular simulations, we further the exploration of existing "belief propagation" (BP) algorithms for fixed-backbone peptide and protein systems. The precalculation of pairwise interactions among discretized libraries of side-chain conformations, along with representation of protein side chains as nodes in a graphical model, enables direct application of the BP approach, which requires only ∼1 s of single-processor run time after the precalculation stage. We use a "loopy BP" algorithm, which can be seen as an approximate generalization of the transfer-matrix approach to highly connected (i.e., loopy) graphs, and it has previously been applied to protein calculations. We examine the application of loopy BP to several peptides as well as the binding site of the T4 lysozyme L99A mutant. The present study reports on (i) the comparison of the approximate BP results with estimates from unbiased estimators based on the Amber99SB force field; (ii) investigation of the effects of varying library size on BP predictions; and (iii) a theoretical discussion of the discretization effects that can arise in BP calculations. The data suggest that, despite their approximate nature, BP free-energy estimates are highly accurate-indeed, they never fall outside confidence intervals from unbiased estimators for the systems where independent results could be obtained. Furthermore, we find that libraries of sufficiently fine discretization (which diminish library-size sensitivity) can be obtained with standard computing resources in most cases. Altogether, the extremely low computing times and accurate results suggest the BP approach warrants further study.
Surface free energy of TiC layers deposited by electrophoretic deposition (EPD)
Gorji, Mohammad Reza; Sanjabi, Sohrab
2018-01-01
In this study porous structure coatings of bare TiC (i.e. 20 nm, 0.7 µm and 5/45 µm) and core-shell structures of TiC/NiP synthesized through electroless plating were deposited by EPD. Room temperature surface free energy (i.e. γs) of TiC and TiC/NiP coatings were determined via measuring contact angles of distilled water and diiodemethane liquids. The effect of Ni-P shell on spreading behavior of pure copper on porous EPD structures was also investigated by high temperature wetting experiments. According to the results existence of a Ni-P layer around the TiC particles has led to roughness (i.e. at least 0.1 µm), and porosity mean length (i.e. at least 1 µm) increase. This might be related to various sizes of TiC agglomerates formed during electroless plating. It has been observed that room temperature γs changed from 44.49 to 54.12 mJ.m-2 as a consequence of particle size enlargement for TiC. The highest and lowest (67.25 and 44.49 mJ.m-2) γs were measured for TiC nanoparticles which showed 1.5 times increase in surface free energy after being plated with Ni-P. It was also observed that plating Ni-P altered non-spreading (θs > 100 o) behavior of TiC to full-spreading ((θs 0o)) which can be useful for preparation of hard coatings by infiltration sintering phenomenon. Zeta potential of EPD suspensions, morphology, phase structure and topography of as-EPD layers were investigated through Zetasizer, field emission scanning electron microscopy (FESEM), X-ray diffraction (XRD) and atomic force microscopy (AFM) instruments respectively.
Paul, Sanjib; Paul, Tanmoy Kumar; Taraphder, Srabani
2018-03-22
The role of structure and dynamics of an enzyme has been investigated at three different stages of its function including the chemical event it catalyzes. A one-pot computational method has been designed for each of these stages on the basis of classical and/or quantum mechanical-molecular mechanical molecular dynamics and transition path sampling simulations. For a pair of initial and final states A and B separated by a high free-energy barrier, using a two-stage selection process, several collective variables (CVs) are identified that can delineate A and B. However, these CVs are found to exhibit strong cross-coupling over the transition paths. A set of mutually orthogonal order parameters is then derived from these CVs and an optimal reaction coordinate, r, determined applying half-trajectory likelihood maximization along with a Bayesian information criterion. The transition paths are also used to project the multidimensional free energy surface and barrier crossing dynamics along r. The proposed scheme has been applied to the rate-determining intramolecular proton transfer reaction of the well-known enzyme human carbonic anhydrase II. The potential of mean force, F( r), in the absence of the chemical step is found to reproduce earlier results on the equilibrium population of two side-chain orientations of key residue His-64. Estimation of rate constants, k, from mean first passage times for the three different stages of catalysis shows that the rate-determining step of intramolecular proton transfer occurs with k ≃ 1.0 × 10 6 s -1 , in close agreement with known experimental results.
Free energy of mixing of acetone and methanol: a computer simulation investigation.
Idrissi, Abdenacer; Polok, Kamil; Barj, Mohammed; Marekha, Bogdan; Kiselev, Mikhail; Jedlovszky, Pál
2013-12-19
The change of the Helmholtz free energy, internal energy, and entropy accompanying the mixing of acetone and methanol is calculated in the entire composition range by the method of thermodynamic integration using three different potential model combinations of the two compounds. In the first system, both molecules are described by the OPLS, and in the second system, both molecules are described by the original TraPPE force field, whereas in the third system a modified version of the TraPPE potential is used for acetone in combination with the original TraPPE model of methanol. The results reveal that, in contrast with the acetone-water system, all of these three model combinations are able to reproduce the full miscibility of acetone and methanol, although the thermodynamic driving force of this mixing is very small. It is also seen, in accordance with the finding of former structural analyses, that the mixing of the two components is driven by the entropy term corresponding to the ideal mixing, which is large enough to overcompensate the effect of the energy increase and entropy loss due to the interaction of the unlike components in the mixtures. Among the three model combinations, the use of the original TraPPE model of methanol and modified TraPPE model of acetone turns out to be clearly the best in this respect, as it is able to reproduce the experimental free energy, internal energy, and entropy of mixing values within 0.15 kJ/mol, 0.2 kJ/mol, and 1 J/(mol K), respectively, in the entire composition range. The success of this model combination originates from the fact that the use of the modified TraPPE model of acetone instead of the original one in these mixtures improves the reproduction of the entropy of mixing, while it retains the ability of the original model of excellently reproducing the internal energy of mixing.
Free-energy relationships in ion channels activated by voltage and ligand
Chowdhury, Sandipan
2013-01-01
Many ion channels are modulated by multiple stimuli, which allow them to integrate a variety of cellular signals and precisely respond to physiological needs. Understanding how these different signaling pathways interact has been a challenge in part because of the complexity of underlying models. In this study, we analyzed the energetic relationships in polymodal ion channels using linkage principles. We first show that in proteins dually modulated by voltage and ligand, the net free-energy change can be obtained by measuring the charge-voltage (Q-V) relationship in zero ligand condition and the ligand binding curve at highly depolarizing membrane voltages. Next, we show that the voltage-dependent changes in ligand occupancy of the protein can be directly obtained by measuring the Q-V curves at multiple ligand concentrations. When a single reference ligand binding curve is available, this relationship allows us to reconstruct ligand binding curves at different voltages. More significantly, we establish that the shift of the Q-V curve between zero and saturating ligand concentration is a direct estimate of the interaction energy between the ligand- and voltage-dependent pathway. These free-energy relationships were tested by numerical simulations of a detailed gating model of the BK channel. Furthermore, as a proof of principle, we estimate the interaction energy between the ligand binding and voltage-dependent pathways for HCN2 channels whose ligand binding curves at various voltages are available. These emerging principles will be useful for high-throughput mutagenesis studies aimed at identifying interaction pathways between various regulatory domains in a polymodal ion channel. PMID:23250866
Procacci, Piero
2016-06-01
In this contribution I critically revise the alchemical reversible approach in the context of the statistical mechanics theory of non-covalent bonding in drug-receptor systems. I show that most of the pitfalls and entanglements for the binding free energy evaluation in computer simulations are rooted in the equilibrium assumption that is implicit in the reversible method. These critical issues can be resolved by using a non-equilibrium variant of the alchemical method in molecular dynamics simulations, relying on the production of many independent trajectories with a continuous dynamical evolution of an externally driven alchemical coordinate, completing the decoupling of the ligand in a matter of a few tens of picoseconds rather than nanoseconds. The absolute binding free energy can be recovered from the annihilation work distributions by applying an unbiased unidirectional free energy estimate, on the assumption that any observed work distribution is given by a mixture of normal distributions, whose components are identical in either direction of the non-equilibrium process, with weights regulated by the Crooks theorem. I finally show that the inherent reliability and accuracy of the unidirectional estimate of the decoupling free energies, based on the production of a few hundreds of non-equilibrium independent sub-nanosecond unrestrained alchemical annihilation processes, is a direct consequence of the funnel-like shape of the free energy surface in molecular recognition. An application of the technique to a real drug-receptor system is presented in the companion paper.
Olariu, Victor; Manesso, Erica; Peterson, Carsten
2017-06-01
Depicting developmental processes as movements in free energy genetic landscapes is an illustrative tool. However, exploring such landscapes to obtain quantitative or even qualitative predictions is hampered by the lack of free energy functions corresponding to the biochemical Michaelis-Menten or Hill rate equations for the dynamics. Being armed with energy landscapes defined by a network and its interactions would open up the possibility of swiftly identifying cell states and computing optimal paths, including those of cell reprogramming, thereby avoiding exhaustive trial-and-error simulations with rate equations for different parameter sets. It turns out that sigmoidal rate equations do have approximate free energy associations. With this replacement of rate equations, we develop a deterministic method for estimating the free energy surfaces of systems of interacting genes at different noise levels or temperatures. Once such free energy landscape estimates have been established, we adapt a shortest path algorithm to determine optimal routes in the landscapes. We explore the method on three circuits for haematopoiesis and embryonic stem cell development for commitment and reprogramming scenarios and illustrate how the method can be used to determine sequential steps for onsets of external factors, essential for efficient reprogramming.
Panel, Nicolas; Sun, Young Joo; Fuentes, Ernesto J; Simonson, Thomas
2017-01-01
PDZ domains generally bind short amino acid sequences at the C-terminus of target proteins, and short peptides can be used as inhibitors or model ligands. Here, we used experimental binding assays and molecular dynamics simulations to characterize 51 complexes involving the Tiam1 PDZ domain and to test the performance of a semi-empirical free energy function. The free energy function combined a Poisson-Boltzmann (PB) continuum electrostatic term, a van der Waals interaction energy, and a surface area term. Each term was empirically weighted, giving a Linear Interaction Energy or "PB/LIE" free energy. The model yielded a mean unsigned deviation of 0.43 kcal/mol and a Pearson correlation of 0.64 between experimental and computed free energies, which was superior to a Null model that assumes all complexes have the same affinity. Analyses of the models support several experimental observations that indicate the orientation of the α 2 helix is a critical determinant for peptide specificity. The models were also used to predict binding free energies for nine new variants, corresponding to point mutants of the Syndecan1 and Caspr4 peptides. The predictions did not reveal improved binding; however, they suggest that an unnatural amino acid could be used to increase protease resistance and peptide lifetimes in vivo . The overall performance of the model should allow its use in the design of new PDZ ligands in the future.
Mirzaeinia, Ali; Feyzi, Farzaneh; Hashemianzadeh, Seyed Majid
2017-12-07
Simple and accurate expressions are presented for the equation of state (EOS) and absolute Helmholtz free energy of a system composed of simple atomic particles interacting through the repulsive Lennard-Jones potential model in the fluid and solid phases. The introduced EOS has 17 and 22 coefficients for fluid and solid phases, respectively, which are regressed to the Monte Carlo (MC) simulation data over the reduced temperature range of 0.6≤T * ≤6.0 and the packing fraction range of 0.1 ≤ η ≤ 0.72. The average absolute relative percent deviation in fitting the EOS parameters to the MC data is 0.06 and 0.14 for the fluid and solid phases, respectively. The thermodynamic integration method is used to calculate the free energy using the MC simulation results. The Helmholtz free energy of the ideal gas is employed as the reference state for the fluid phase. For the solid phase, the values of the free energy at the reduced density equivalent to the close-packed of a hard sphere are used as the reference state. To check the validity of the predicted values of the Helmholtz free energy, the Widom particle insertion method and the Einstein crystal technique of Frenkel and Ladd are employed. The results obtained from the MC simulation approaches are well agreed to the EOS results, which show that the proposed model can reliably be utilized in the framework of thermodynamic theories.
Mikhailova, Valentina A; Malykhin, Roman E; Ivanov, Anatoly I
2018-05-16
To elucidate the regularities inherent in the kinetics of ultrafast charge recombination following photoinduced charge separation in donor-acceptor dyads in solutions, the simulations of the kinetics have been performed within the stochastic multichannel point-transition model. Increasing the solvent relaxation time scales has been shown to strongly vary the dependence of the charge recombination rate constant on the free energy gap. In slow relaxing solvents the non-equilibrium charge recombination occurring in parallel with solvent relaxation is very effective so that the charge recombination terminates at the non-equilibrium stage. This results in a crucial difference between the free energy gap laws for the ultrafast charge recombination and the thermal charge transfer. For the thermal reactions the well-known Marcus bell-shaped dependence of the rate constant on the free energy gap is realized while for the ultrafast charge recombination only a descending branch is predicted in the whole area of the free energy gap exceeding 0.2 eV. From the available experimental data on the population kinetics of the second and first excited states for a series of Zn-porphyrin-imide dyads in toluene and tetrahydrofuran solutions, an effective rate constant of the charge recombination into the first excited state has been calculated. The obtained rate constant being very high is nearly invariable in the area of the charge recombination free energy gap from 0.2 to 0.6 eV that supports the theoretical prediction.
Pliego, Josefredo R; Miguel, Elizabeth L M
2013-05-02
Absolute solvation free energy of the lithium cation in methanol was calculated by the cluster-continuum quasichemical theory of solvation. Clusters with up to five methanol molecules were investigated using X3LYP, MP2, and MP4 methods with DZVP, 6-311+G(2df,2p), TZVPP+diff, and QZVPP+diff basis sets and including the cluster solvation through the PCM and SMD continuum models. Our calculations have determined a value of -118.1 kcal mol(-1) for the solvation free energy of the lithium, in close agreement with a value of -116.6 kcal mol(-1) consistent with the TATB assumption. Using data of solvation and transfer free energy of a pair of ions, electrode potentials and pKa, we have obtained the solvation free energy of 25 ions in methanol. Our analysis leads to a value of -253.6 kcal mol(-1) for the solvation free energy of the proton, which can be compared with the value of -263.5 kcal mol(-1) obtained by Kelly et al. using the cluster pair approximation. Considering that this difference is due to the methanol surface potential, we have estimated that it corresponds to -0.429 V.
Nicolas Panel
2017-09-01
Full Text Available PDZ domains generally bind short amino acid sequences at the C-terminus of target proteins, and short peptides can be used as inhibitors or model ligands. Here, we used experimental binding assays and molecular dynamics simulations to characterize 51 complexes involving the Tiam1 PDZ domain and to test the performance of a semi-empirical free energy function. The free energy function combined a Poisson-Boltzmann (PB continuum electrostatic term, a van der Waals interaction energy, and a surface area term. Each term was empirically weighted, giving a Linear Interaction Energy or “PB/LIE” free energy. The model yielded a mean unsigned deviation of 0.43 kcal/mol and a Pearson correlation of 0.64 between experimental and computed free energies, which was superior to a Null model that assumes all complexes have the same affinity. Analyses of the models support several experimental observations that indicate the orientation of the α2 helix is a critical determinant for peptide specificity. The models were also used to predict binding free energies for nine new variants, corresponding to point mutants of the Syndecan1 and Caspr4 peptides. The predictions did not reveal improved binding; however, they suggest that an unnatural amino acid could be used to increase protease resistance and peptide lifetimes in vivo. The overall performance of the model should allow its use in the design of new PDZ ligands in the future.
Jakobtorweihen, S.; Zuniga, A. Chaides; Ingram, T.; Gerlach, T.; Keil, F. J.; Smirnova, I.
2014-07-01
Quantitative predictions of biomembrane/water partition coefficients are important, as they are a key property in pharmaceutical applications and toxicological studies. Molecular dynamics (MD) simulations are used to calculate free energy profiles for different solutes in lipid bilayers. How to calculate partition coefficients from these profiles is discussed in detail and different definitions of partition coefficients are compared. Importantly, it is shown that the calculated coefficients are in quantitative agreement with experimental results. Furthermore, we compare free energy profiles from MD simulations to profiles obtained by the recent method COSMOmic, which is an extension of the conductor-like screening model for realistic solvation to micelles and biomembranes. The free energy profiles from these molecular methods are in good agreement. Additionally, solute orientations calculated with MD and COSMOmic are compared and again a good agreement is found. Four different solutes are investigated in detail: 4-ethylphenol, propanol, 5-phenylvaleric acid, and dibenz[a,h]anthracene, whereby the latter belongs to the class of polycyclic aromatic hydrocarbons. The convergence of the free energy profiles from biased MD simulations is discussed and the results are shown to be comparable to equilibrium MD simulations. For 5-phenylvaleric acid the influence of the carboxyl group dihedral angle on free energy profiles is analyzed with MD simulations.
Jakobtorweihen, S.; Ingram, T.; Gerlach, T.; Smirnova, I.; Zuniga, A. Chaides; Keil, F. J.
2014-01-01
Quantitative predictions of biomembrane/water partition coefficients are important, as they are a key property in pharmaceutical applications and toxicological studies. Molecular dynamics (MD) simulations are used to calculate free energy profiles for different solutes in lipid bilayers. How to calculate partition coefficients from these profiles is discussed in detail and different definitions of partition coefficients are compared. Importantly, it is shown that the calculated coefficients are in quantitative agreement with experimental results. Furthermore, we compare free energy profiles from MD simulations to profiles obtained by the recent method COSMOmic, which is an extension of the conductor-like screening model for realistic solvation to micelles and biomembranes. The free energy profiles from these molecular methods are in good agreement. Additionally, solute orientations calculated with MD and COSMOmic are compared and again a good agreement is found. Four different solutes are investigated in detail: 4-ethylphenol, propanol, 5-phenylvaleric acid, and dibenz[a,h]anthracene, whereby the latter belongs to the class of polycyclic aromatic hydrocarbons. The convergence of the free energy profiles from biased MD simulations is discussed and the results are shown to be comparable to equilibrium MD simulations. For 5-phenylvaleric acid the influence of the carboxyl group dihedral angle on free energy profiles is analyzed with MD simulations
Voltammetric quantitation of nitazoxanide by glassy carbon electrode
Rajeev Jain
2013-12-01
Full Text Available The present study reports voltammetric reduction of nitazoxanide in BrittonâRobinson (BâR buffer by cyclic and square-wave voltammetry at glassy carbon electrode. A versatile fully validated voltammetric method for quantitative determination of nitazoxanide in pharmaceutical formulation has been proposed. A squrewave peak current was linear over the nitazoxanide concentration in the range of 20â140Â Âµg/mL. The limit of detection (LOD and limit of quantification (LOQ was calculated to be 5.23Â Î¼g/mL and 17.45Â Î¼g/mL, respectively. Keywords: Nitazoxanide, Squarewave voltammetry, Glassy carbon electrode, Pharmaceutical formulation
Glassy selenium at high pressure: Le Chatelier's principle still works
Brazhkin, V. V.; Tsiok, O. B.
2017-10-01
Selenium is the only easily vitrified elementary substance. Numerous experimental studies of glassy Se (g -Se) at high pressures show a large spread in the data on the compressibility and electrical resistivity of g -Se. Furthermore, H. Liu et al. [Proc. Natl. Acad. Sci. USA 105, 13229 (2008), 10.1073/pnas.0806857105] have arrived at the surprising conclusion that the volume of glass increases during pressure-induced crystallization. We have performed high-precision measurements of the specific volume and electrical resistivity of glassy selenium (g -Se) at high hydrostatic pressures up to 9 GPa. The measured bulk modulus at normal pressure is B =(9.0 5 ±0.15 ) GPa and its pressure derivative is BP'=6.4 ±0.2 . In the pressure range P <3 GPa, glassy selenium has an anomalously large negative second derivative of the bulk modulus. The electrical resistivity of g -Se decreases almost exponentially with increasing pressure and reaches 20 Ω cm at a pressure of 8.75 GPa. The inelastic behavior and weak relaxation of the volume for g -Se begin at pressures above 3.5 GPa; the volume and logarithm of the electrical resistivity relax significantly (logarithmically with the time) at pressures above 8 GPa. Bulk measurements certainly indicate that the volume of g -Se glass in the crystallization pressure range is larger than the volumes of both appearing crystalline phases (by 2% and 4%). Therefore, the "volume expansion phenomenon" suggested in [H. Liu et al., Proc. Natl. Acad. Sci. USA 105, 13229 (2008), 10.1073/pnas.0806857105] is not observed, and the pressure-induced crystallization of glassy selenium is consistent with the laws of thermodynamics.
Thermodynamic Modeling of Gas Transport in Glassy Polymeric Membranes.
Minelli, Matteo; Sarti, Giulio Cesare
2017-08-19
Solubility and permeability of gases in glassy polymers have been considered with the aim of illustrating the applicability of thermodynamically-based models for their description and prediction. The solubility isotherms are described by using the nonequilibrium lattice fluid (NELF) (model, already known to be appropriate for nonequilibrium glassy polymers, while the permeability isotherms are described through a general transport model in which diffusivity is the product of a purely kinetic factor, the mobility coefficient, and a thermodynamic factor. The latter is calculated from the NELF model and mobility is considered concentration-dependent through an exponential relationship containing two parameters only. The models are tested explicitly considering solubility and permeability data of various penetrants in three glassy polymers, PSf, PPh and 6FDA-6FpDA, selected as the reference for different behaviors. It is shown that the models are able to calculate the different behaviors observed, and in particular the permeability dependence on upstream pressure, both when it is decreasing as well as when it is increasing, with no need to invoke the onset of additional plasticization phenomena. The correlations found between polymer and penetrant properties with the two parameters of the mobility coefficient also lead to the predictive ability of the transport model.
Quasi-equilibrium in glassy dynamics: an algebraic view
Franz, Silvio; Parisi, Giorgio
2013-01-01
We study a chain of identical glassy systems in a constrained equilibrium, where each bond of the chain is forced to remain at a preassigned distance to the previous one. We apply this description to mean-field glassy systems in the limit of a long chain where each bond is close to the previous one. We show that this construction defines a pseudo-dynamic process that in specific conditions can formally describe real relaxational dynamics for long times. In particular, in mean-field spin glass models we can recover in this way the equations of Langevin dynamics in the long time limit at the dynamical transition temperature and below. We interpret the formal identity as evidence that in these situations the configuration space is explored in a quasi-equilibrium fashion. Our general formalism, which relates dynamics to equilibrium, puts slow dynamics in a new perspective and opens the way to the computation of new dynamical quantities in glassy systems. (paper)
Hudson, Phillip S; Woodcock, H Lee; Boresch, Stefan
2015-12-03
Carrying out free energy simulations (FES) using quantum mechanical (QM) Hamiltonians remains an attractive, albeit elusive goal. Renewed efforts in this area have focused on using "indirect" thermodynamic cycles to connect "low level" simulation results to "high level" free energies. The main obstacle to computing converged free energy results between molecular mechanical (MM) and QM (ΔA(MM→QM)), as recently demonstrated by us and others, is differences in the so-called "stiff" degrees of freedom (e.g., bond stretching) between the respective energy surfaces. Herein, we demonstrate that this problem can be efficiently circumvented using nonequilibrium work (NEW) techniques, i.e., Jarzynski's and Crooks' equations. Initial applications of computing ΔA(NEW)(MM→QM), for blocked amino acids alanine and serine as well as to generate butane's potentials of mean force via the indirect QM/MM FES method, showed marked improvement over traditional FES approaches.
Patete, Jonathan; Petrofsky, John M; Stepan, Jeffery; Waheed, Abdul; Serafin, Joseph M
2009-01-15
This work describes chemical force microscopy (CFM) studies of specific-ion effects on the aqueous interfacial free energy of hydrophobic monolayers. CFM measurements allow for the characterization of interfacial properties on length scales below 100 nm. The ions chosen span the range of the Hofmeister series, from the kosmotropic Na(2)SO(4) to the chaotropic NaSCN. The salt concentrations used are typical of many laboratory processes such as protein crystallization, 2-3 M. Both aliphatic (terminal methyl) and aromatic (terminal phenyl) monolayers were examined, and rather pronounced differences were observed between the two cases. The specific-ion dependence of the aliphatic monolayer closely follows the Hofmeister series, namely the chaotropic ions lowered the interfacial free energy and the kosmotropic ions increased the interfacial free energy. However, the aromatic monolayer had significant deviations from the Hofmeister series. Possible origins for this difference are discussed.
2015-01-01
Molecular docking is a powerful tool used in drug discovery and structural biology for predicting the structures of ligand–receptor complexes. However, the accuracy of docking calculations can be limited by factors such as the neglect of protein reorganization in the scoring function; as a result, ligand screening can produce a high rate of false positive hits. Although absolute binding free energy methods still have difficulty in accurately rank-ordering binders, we believe that they can be fruitfully employed to distinguish binders from nonbinders and reduce the false positive rate. Here we study a set of ligands that dock favorably to a newly discovered, potentially allosteric site on the flap of HIV-1 protease. Fragment binding to this site stabilizes a closed form of protease, which could be exploited for the design of allosteric inhibitors. Twenty-three top-ranked protein–ligand complexes from AutoDock were subject to the free energy screening using two methods, the recently developed binding energy analysis method (BEDAM) and the standard double decoupling method (DDM). Free energy calculations correctly identified most of the false positives (≥83%) and recovered all the confirmed binders. The results show a gap averaging ≥3.7 kcal/mol, separating the binders and the false positives. We present a formula that decomposes the binding free energy into contributions from the receptor conformational macrostates, which provides insights into the roles of different binding modes. Our binding free energy component analysis further suggests that improving the treatment for the desolvation penalty associated with the unfulfilled polar groups could reduce the rate of false positive hits in docking. The current study demonstrates that the combination of docking with free energy methods can be very useful for more accurate ligand screening against valuable drug targets. PMID:25189630
Suzuki, Yohichi; Tanimura, Yoshitaka
2007-01-01
Electron transfer reaction in a polar solvent is modeled by a solute dipole surrounded by dipolar molecules with simple rotational dynamics posted on the three-dimensional distorted lattice sites. The interaction energy between the solute and solvent dipoles as a reaction coordinate is adopted and free energy landscapes are calculated by generating all possible states for a 26 dipolar system and by employing Wang-Landau sampling algorithm for a 92 dipolar system. For temperatures higher than the energy scale of dipole-dipole interactions, the free energy landscapes for the small reaction coordinate region have quadratic shape as predicted by Marcus [Rev. Mod. Phys. 65, 599 (1993)] whereas for the large reaction coordinate region, the landscapes exhibit a nonquadratic shape. When the temperature drops, small notched structures appear on the free energy profiles because of the frustrated interactions among dipoles. The formation of notched structure is analyzed with statistical approach and it is shown that the amplitude of notched structure depend upon the segment size of the reaction coordinate and is characterized by the interaction energy among the dipoles. Using simulated free energy landscapes, the authors calculate the reaction rates as a function of the energy gap for various temperatures. At high temperature, the reactions rates follow a bell shaped (inverted parabolic) energy gap law in the small energy gap regions, while it becomes steeper than the parabolic shape in a large energy gap regions due to the nonquadratic shape of the free energy landscape. The peak position of parabola also changes as the function of temperature. At low temperature, the profile of the reaction rates is no longer smooth because of the many local minima of the free energy landscape
Huang, Y; Ackers, G K
1996-01-23
A strategy has been developed for quantitatively "translating" the distributions of cooperative free energy between different oxygenation analogs of hemoglobin (Hb). The method was used to resolve the cooperative free energies of all eight carbon monoxide binding intermediates. These parameters of the FeCOHb system were determined by thermodynamic transformation of corresponding free energies obtained previously for all species of the Co/FeCO system, i.e., where cobalt-substituted hemes comprise the unligated sites [Speros, P. C., et al. (1991) Biochemistry 30, 7254-7262]. Using hybridized combinations of normal and cobalt-substituted Hb, ligation analog systems Co/FeX (X = CO, CN) were constructed and experimentally quantified. Energetics of cobalt-induced structural perturbation were determined for all species of both the "mixed metal" Co/Fe system and also the ligated Co/FeCN system. It was found that major energetic perturbations of the Co/Fe hybrid species originate from a pure cobalt substitution effect on the alpha subunits. These perturbations are transduced to the beta subunit within the same dimeric half-tetramer, resulting in alteration of the free energies for binding at the nonsubstituted (Fe) sites. Using the linkage strategy developed in this study along with the determined energetics of these couplings, the experimental assembly free energies for the Co/FeCO species were transformed into cooperative free energies of the 10 Fe/FeCO species. The resulting values were found to distribute according to predictions of a symmetry rule mechanism proposed previously [Ackers, G. K., et al. (1992) Science 255, 54-63]. Their distribution is consistent with accurate CO binding data of normal Hb [Perrella, M., et al. (1990b) Biophys. Chem. 37, 211-223] and also with accurate O2 binding data obtained under the same conditions [Chu, A. H., et al. (1984) Biochemistry 23, 604-617].
Dam, H. van; Leege, P.F.A. de
1987-01-01
An analysis is presented of thermal systems with minimum critical mass, based on the use of materials with optimum neutron moderating and reflecting properties. The optimum fissile material distributions in the systems are obtained by calculations with standard computer codes, extended with a routine for flat fuel importance search. It is shown that in the minimum critical mass configuration a considerable part of the fuel is positioned in the reflector region. For 239 Pu a minimum critical mass of 87 g is found, which is the lowest value reported hitherto. (author)
Muenster, G.
1980-05-01
We derive high temperature cluster expansions for the free energy of vortices in SU(2) and Z 2 lattice gauge theories in 3 and 4 dimensions. The expected behaviour of the vortex free energy is verified. It obeys an area law behaviour. The coefficient of the area is shown to be equal to the string tension between static quarks. We calculate its expansion up to 12th order. For SU(2) in 4 dimensions the result is compared with Monte Carlo calculations of Creutz and is in good agreement at strong and intermediate coupling. (orig.)
Minimum entropy production principle
Maes, C.; Netočný, Karel
2013-01-01
Roč. 8, č. 7 (2013), s. 9664-9677 ISSN 1941-6016 Institutional support: RVO:68378271 Keywords : MINEP Subject RIV: BE - Theoretical Physics http://www.scholarpedia.org/article/Minimum_entropy_production_principle
The free-energy self: a predictive coding account of self-recognition.
Apps, Matthew A J; Tsakiris, Manos
2014-04-01
Recognising and representing one's self as distinct from others is a fundamental component of self-awareness. However, current theories of self-recognition are not embedded within global theories of cortical function and therefore fail to provide a compelling explanation of how the self is processed. We present a theoretical account of the neural and computational basis of self-recognition that is embedded within the free-energy account of cortical function. In this account one's body is processed in a Bayesian manner as the most likely to be "me". Such probabilistic representation arises through the integration of information from hierarchically organised unimodal systems in higher-level multimodal areas. This information takes the form of bottom-up "surprise" signals from unimodal sensory systems that are explained away by top-down processes that minimise the level of surprise across the brain. We present evidence that this theoretical perspective may account for the findings of psychological and neuroimaging investigations into self-recognition and particularly evidence that representations of the self are malleable, rather than fixed as previous accounts of self-recognition might suggest. Copyright © 2013 Elsevier Ltd. All rights reserved.
Free energy landscape and multiple folding pathways of an H-type RNA pseudoknot.
Yunqiang Bian
Full Text Available How RNA sequences fold to specific tertiary structures is one of the key problems for understanding their dynamics and functions. Here, we study the folding process of an H-type RNA pseudoknot by performing a large-scale all-atom MD simulation and bias-exchange metadynamics. The folding free energy landscapes are obtained and several folding intermediates are identified. It is suggested that the folding occurs via multiple mechanisms, including a step-wise mechanism starting either from the first helix or the second, and a cooperative mechanism with both helices forming simultaneously. Despite of the multiple mechanism nature, the ensemble folding kinetics estimated from a Markov state model is single-exponential. It is also found that the correlation between folding and binding of metal ions is significant, and the bound ions mediate long-range interactions in the intermediate structures. Non-native interactions are found to be dominant in the unfolded state and also present in some intermediates, possibly hinder the folding process of the RNA.
Evoli, Stefania
2016-11-10
Human serum albumin possesses multiple binding sites and transports a wide range of ligands that include the anti-inflammatory drug ibuprofen. A complete map of the binding sites of ibuprofen in albumin is difficult to obtain in traditional experiments, because of the structural adaptability of this protein in accommodating small ligands. In this work, we provide a set of predictions covering the geometry, affinity of binding and protonation state for the pharmaceutically most active form (S-isomer) of ibuprofen to albumin, by using absolute binding free energy calculations in combination with classical molecular dynamics (MD) simulations and molecular docking. The most favorable binding modes correctly reproduce several experimentally identified binding locations, which include the two Sudlow\\'s drug sites (DS2 and DS1) and the fatty acid binding sites 6 and 2 (FA6 and FA2). Previously unknown details of the binding conformations were revealed for some of them, and formerly undetected binding modes were found in other protein sites. The calculated binding affinities exhibit trends which seem to agree with the available experimental data, and drastically degrade when the ligand is modeled in a protonated (neutral) state, indicating that ibuprofen associates with albumin preferentially in its charged form. These findings provide a detailed description of the binding of ibuprofen, help to explain a wide range of results reported in the literature in the last decades, and demonstrate the possibility of using simulation methods to predict ligand binding to albumin.
Trickey, Samuel; Karasiev, Valentin
We introduce the concept of tunable orbital-free non-interacting free-energy density functionals and present a generalized gradient approximation (GGA) with a subset of parameters defined from constraints and a few free parameters. Those free parameters are tuned to reproduce reference Kohn-Sham (KS) static-lattice pressures for Al at T=8 kK for bulk densities between 0.6 and 2 g/cm3. The tuned functional then is used in OF molecular dynamics (MD) simulations for Al with densities between 0.1 and 2 g/cm3 and T between 6 and 50 kK to calculate the equation of state and generate configurations for electrical conductivity calculations. The tunable functional produces accurate results. Computationally it is very effective especially at elevated temperature. Kohn-Shiam calculations for such low densities are affordable only up to T=10 kK, while other OF approximations, including two-point functionals, fail badly in that regime. Work supported by US DoE Grant DE-SC0002139.
Alherz, Abdulaziz; Lim, Chern-Hooi; Hynes, James T; Musgrave, Charles B
2018-01-25
We propose a method to approximate the kinetic properties of hydride donor species by relating the nucleophilicity (N) of a hydride to the activation free energy ΔG ⧧ of its corresponding hydride transfer reaction. N is a kinetic parameter related to the hydride transfer rate constant that quantifies a nucleophilic hydridic species' tendency to donate. Our method estimates N using quantum chemical calculations to compute ΔG ⧧ for hydride transfers from hydride donors to CO 2 in solution. A linear correlation for each class of hydrides is then established between experimentally determined N values and the computationally predicted ΔG ⧧ ; this relationship can then be used to predict nucleophilicity for different hydride donors within each class. This approach is employed to determine N for four different classes of hydride donors: two organic (carbon-based and benzimidazole-based) and two inorganic (boron and silicon) hydride classes. We argue that silicon and boron hydrides are driven by the formation of the more stable Si-O or B-O bond. In contrast, the carbon-based hydrides considered herein are driven by the stability acquired upon rearomatization, a feature making these species of particular interest, because they both exhibit catalytic behavior and can be recycled.
Ionic Strength Modulation of the Free Energy Landscape of Aβ40 Peptide Fibril Formation.
Abelein, Axel; Jarvet, Jüri; Barth, Andreas; Gräslund, Astrid; Danielsson, Jens
2016-06-01
Protein misfolding and formation of cross-β structured amyloid fibrils are linked to many neurodegenerative disorders. Although recently developed quantitative approaches have started to reveal the molecular nature of self-assembly and fibril formation of proteins and peptides, it is yet unclear how these self-organization events are precisely modulated by microenvironmental factors, which are known to strongly affect the macroscopic aggregation properties. Here, we characterize the explicit effect of ionic strength on the microscopic aggregation rates of amyloid β peptide (Aβ40) self-association, implicated in Alzheimer's disease. We found that physiological ionic strength accelerates Aβ40 aggregation kinetics by promoting surface-catalyzed secondary nucleation reactions. This promoted catalytic effect can be assigned to shielding of electrostatic repulsion between monomers on the fibril surface or between the fibril surface itself and monomeric peptides. Furthermore, we observe the formation of two different β-structured states with similar but distinct spectroscopic features, which can be assigned to an off-pathway immature state (Fβ*) and a mature stable state (Fβ), where salt favors formation of the Fβ fibril morphology. Addition of salt to preformed Fβ* accelerates transition to Fβ, underlining the dynamic nature of Aβ40 fibrils in solution. On the basis of these results we suggest a model where salt decreases the free-energy barrier for Aβ40 folding to the Fβ state, favoring the buildup of the mature fibril morphology while omitting competing, energetically less favorable structural states.
Bardhan, Jaydeep P; Jungwirth, Pavel; Makowski, Lee
2012-09-28
Two mechanisms have been proposed to drive asymmetric solvent response to a solute charge: a static potential contribution similar to the liquid-vapor potential, and a steric contribution associated with a water molecule's structure and charge distribution. In this work, we use free-energy perturbation molecular-dynamics calculations in explicit water to show that these mechanisms act in complementary regimes; the large static potential (∼44 kJ/mol/e) dominates asymmetric response for deeply buried charges, and the steric contribution dominates for charges near the solute-solvent interface. Therefore, both mechanisms must be included in order to fully account for asymmetric solvation in general. Our calculations suggest that the steric contribution leads to a remarkable deviation from the popular "linear response" model in which the reaction potential changes linearly as a function of charge. In fact, the potential varies in a piecewise-linear fashion, i.e., with different proportionality constants depending on the sign of the charge. This discrepancy is significant even when the charge is completely buried, and holds for solutes larger than single atoms. Together, these mechanisms suggest that implicit-solvent models can be improved using a combination of affine response (an offset due to the static potential) and piecewise-linear response (due to the steric contribution).
Bardhan, Jaydeep P; Knepley, Matthew G; Anitescu, Mihai
2009-03-14
The importance of electrostatic interactions in molecular biology has driven extensive research toward the development of accurate and efficient theoretical and computational models. Linear continuum electrostatic theory has been surprisingly successful, but the computational costs associated with solving the associated partial differential equations (PDEs) preclude the theory's use in most dynamical simulations. Modern generalized-Born models for electrostatics can reproduce PDE-based calculations to within a few percent and are extremely computationally efficient but do not always faithfully reproduce interactions between chemical groups. Recent work has shown that a boundary-integral-equation formulation of the PDE problem leads naturally to a new approach called boundary-integral-based electrostatics estimation (BIBEE) to approximate electrostatic interactions. In the present paper, we prove that the BIBEE method can be used to rigorously bound the actual continuum-theory electrostatic free energy. The bounds are validated using a set of more than 600 proteins. Detailed numerical results are presented for structures of the peptide met-enkephalin taken from a molecular-dynamics simulation. These bounds, in combination with our demonstration that the BIBEE methods accurately reproduce pairwise interactions, suggest a new approach toward building a highly accurate yet computationally tractable electrostatic model.
Parsing of the free energy of aromatic-aromatic stacking interactions in solution
Kostjukov, Viktor V.; Khomytova, Nina M. [Department of Physics, Sevastopol National Technical University, Sevastopol 99053, Crimea (Ukraine); Hernandez Santiago, Adrian A.; Tavera, Anna-Maria Cervantes; Alvarado, Julieta Salas [Faculty of Chemical Sciences, Autonomous University of Puebla, Puebla (Mexico); Evstigneev, Maxim P., E-mail: max_evstigneev@mail.ru [Department of Physics, Sevastopol National Technical University, Sevastopol 99053, Crimea (Ukraine)
2011-10-15
Graphical abstract: Highlights: > A protocol for decomposition of the free energy of aromatic stacking is developed. > The factors stabilizing/destabilizing stacking of aromatic molecules are defined. > Hydrophobic contribution is found to be dominant. - Abstract: We report an analysis of the energetics of aromatic-aromatic stacking interactions for 39 non-covalent reactions of self- and hetero-association of 12 aromatic molecules with different structures and charge states. A protocol for computation of the contributions to the total energy from various energetic terms has been developed and the results are consistent with experiment in 92% of all the systems studied. It is found that the contributions from hydrogen bonds and entropic factors are always unfavorable, whereas contributions from van-der-Waals, electrostatic and/or hydrophobic effects may lead to stabilizing or destabilizing factors depending on the system studied. The analysis carried out in this work provides an answer to the questions 'What forces stabilize/destabilize the stacking of aromatic molecules in aqueous-salt solution and what are their relative importance?'
Parsing of the free energy of aromatic-aromatic stacking interactions in solution
Kostjukov, Viktor V.; Khomytova, Nina M.; Hernandez Santiago, Adrian A.; Tavera, Anna-Maria Cervantes; Alvarado, Julieta Salas; Evstigneev, Maxim P.
2011-01-01
Graphical abstract: Highlights: → A protocol for decomposition of the free energy of aromatic stacking is developed. → The factors stabilizing/destabilizing stacking of aromatic molecules are defined. → Hydrophobic contribution is found to be dominant. - Abstract: We report an analysis of the energetics of aromatic-aromatic stacking interactions for 39 non-covalent reactions of self- and hetero-association of 12 aromatic molecules with different structures and charge states. A protocol for computation of the contributions to the total energy from various energetic terms has been developed and the results are consistent with experiment in 92% of all the systems studied. It is found that the contributions from hydrogen bonds and entropic factors are always unfavorable, whereas contributions from van-der-Waals, electrostatic and/or hydrophobic effects may lead to stabilizing or destabilizing factors depending on the system studied. The analysis carried out in this work provides an answer to the questions 'What forces stabilize/destabilize the stacking of aromatic molecules in aqueous-salt solution and what are their relative importance?'
Abrecht, David G; Schwantes, Jon M
2015-03-03
This paper extends the preliminary linear free energy correlations for radionuclide release performed by Schwantes et al., following the Fukushima-Daiichi Nuclear Power Plant accident. Through evaluations of the molar fractionations of radionuclides deposited in the soil relative to modeled radionuclide inventories, we confirm the initial source of the radionuclides to the environment to be from active reactors rather than the spent fuel pool. Linear correlations of the form In χ = −α ((ΔGrxn°(TC))/(RTC)) + β were obtained between the deposited concentrations, and the reduction potentials of the fission product oxide species using multiple reduction schemes to calculate ΔG°rxn (TC). These models allowed an estimate of the upper bound for the reactor temperatures of TC between 2015 and 2060 K, providing insight into the limiting factors to vaporization and release of fission products during the reactor accident. Estimates of the release of medium-lived fission products 90Sr, 121mSn, 147Pm, 144Ce, 152Eu, 154Eu, 155Eu, and 151Sm through atmospheric venting during the first month following the accident were obtained, indicating that large quantities of 90Sr and radioactive lanthanides were likely to remain in the damaged reactor cores.
Xiang, Zhexin; Soto, Cinque S; Honig, Barry
2002-05-28
In this paper, we introduce a method to account for the shape of the potential energy curve in the evaluation of conformational free energies. The method is based on a procedure that generates a set of conformations, each with its own force-field energy, but adds a term to this energy that favors conformations that are close in structure (have a low rmsd) to other conformations. The sum of the force-field energy and rmsd-dependent term is defined here as the "colony energy" of a given conformation, because each conformation that is generated is viewed as representing a colony of points. The use of the colony energy tends to select conformations that are located in broad energy basins. The approach is applied to the ab initio prediction of the conformations of all of the loops in a dataset of 135 nonredundant proteins. By using an rmsd from a native criterion based on the superposition of loop stems, the average rmsd of 5-, 6-, 7-, and 8-residue long loops is 0.85, 0.92, 1.23, and 1.45 A, respectively. For 8-residue loops, 60 of 61 predictions have an rmsd of less than 3.0 A. The use of the colony energy is found to improve significantly the results obtained from the potential function alone. (The loop prediction program, "Loopy," can be downloaded at http://trantor.bioc.columbia.edu.)
Pliego, Josefredo R.
2017-07-01
The cluster expansion method has been used in the imperfect gas theory for several decades. This paper proposes a cluster expansion of the solvation free energy difference. This difference, which results from a change in the solute-solvent potential energy, can be written as the logarithm of a finite series. Similar to the Mayer function, the terms in the series are related to configurational integrals, which makes the integrand relevant only for configurations of the solvent molecules close to the solute. In addition, the terms involve interaction of solute with one, two, and so on solvent molecules. The approach could be used for hybrid quantum mechanical and molecular mechanics methods or mixed cluster-continuum approximation. A simple form of the theory was applied for prediction of pKa in methanol; the results indicated that three explicit methanol molecules and the dielectric continuum lead to a root of mean squared error (RMSE) of only 1.3 pKa units, whereas the pure continuum solvation model based on density method leads to a RMSE of 6.6 pKa units.
Bardhan, Jaydeep P.; Jungwirth, Pavel; Makowski, Lee
2012-01-01
Two mechanisms have been proposed to drive asymmetric solvent response to a solute charge: a static potential contribution similar to the liquid-vapor potential, and a steric contribution associated with a water molecule's structure and charge distribution. In this work, we use free-energy perturbation molecular-dynamics calculations in explicit water to show that these mechanisms act in complementary regimes; the large static potential (∼44 kJ/mol/e) dominates asymmetric response for deeply buried charges, and the steric contribution dominates for charges near the solute-solvent interface. Therefore, both mechanisms must be included in order to fully account for asymmetric solvation in general. Our calculations suggest that the steric contribution leads to a remarkable deviation from the popular “linear response” model in which the reaction potential changes linearly as a function of charge. In fact, the potential varies in a piecewise-linear fashion, i.e., with different proportionality constants depending on the sign of the charge. This discrepancy is significant even when the charge is completely buried, and holds for solutes larger than single atoms. Together, these mechanisms suggest that implicit-solvent models can be improved using a combination of affine response (an offset due to the static potential) and piecewise-linear response (due to the steric contribution). PMID:23020318
Bardhan, J. P.; Knepley, M. G.; Anitescu, M. (Biosciences Division); ( MCS); (Rush Univ.)
2009-03-01
The importance of electrostatic interactions in molecular biology has driven extensive research toward the development of accurate and efficient theoretical and computational models. Linear continuum electrostatic theory has been surprisingly successful, but the computational costs associated with solving the associated partial differential equations (PDEs) preclude the theory's use in most dynamical simulations. Modern generalized-Born models for electrostatics can reproduce PDE-based calculations to within a few percent and are extremely computationally efficient but do not always faithfully reproduce interactions between chemical groups. Recent work has shown that a boundary-integral-equation formulation of the PDE problem leads naturally to a new approach called boundary-integral-based electrostatics estimation (BIBEE) to approximate electrostatic interactions. In the present paper, we prove that the BIBEE method can be used to rigorously bound the actual continuum-theory electrostatic free energy. The bounds are validated using a set of more than 600 proteins. Detailed numerical results are presented for structures of the peptide met-enkephalin taken from a molecular-dynamics simulation. These bounds, in combination with our demonstration that the BIBEE methods accurately reproduce pairwise interactions, suggest a new approach toward building a highly accurate yet computationally tractable electrostatic model.
Trapped electrons as a free energy source for the auroral kilometric radiation
Louarn, P.; Roux, A.; de Feraudy, H.; Le Queau, D.; Andre, M.; Matson, L.
1990-01-01
Simultaneous measurements of electromagnetic fields and particle distributions, measured during the crossing by the Swedish spacecraft Viking of an auroral kilometric radiation (AKR) source, are presented. It is shown that AKR is generated within an acceleration region characterized by an upward directed parallel electric field, as evidenced by its signature on the proton and electron distributions. From particle observations inside the AKR source it is clear that the potential drop below the spacecraft produces upward moving field-aligned ion beams and a depletion in the density of low energy electrons. The potential drop above the spacecraft produces downward accelerated electrons. A large fraction of these electrons have small parallel velocities; they mirror above the ionosphere. These trapped electrons lie in a region of velocity space which should be empty in a simple adiabatic theory. The authors suggest that these electrons get trapped when they experience a time-varying (or space-varying) parallel electric field. This conclusion is supported by the comparison between the observed electron distribution function and a model distribution function built by applying Liouville theorem. Since trapped electrons can cause positive gradients (∂f e /∂V perpendicular > 0) over a broad range of parallel velocities, around v parallel ∼ 0, it is suggested that they are the free energy source for the AKR. This conclusion is substantiated by an evaluation of the convective growth rate, where the various input parameters have been determined by fitting particle data
Accurate Estimation of the Standard Binding Free Energy of Netropsin with DNA
Hong Zhang
2018-01-01
Full Text Available DNA is the target of chemical compounds (drugs, pollutants, photosensitizers, etc., which bind through non-covalent interactions. Depending on their structure and their chemical properties, DNA binders can associate to the minor or to the major groove of double-stranded DNA. They can also intercalate between two adjacent base pairs, or even replace one or two base pairs within the DNA double helix. The subsequent biological effects are strongly dependent on the architecture of the binding motif. Discriminating between the different binding patterns is of paramount importance to predict and rationalize the effect of a given compound on DNA. The structural characterization of DNA complexes remains, however, cumbersome at the experimental level. In this contribution, we employed all-atom molecular dynamics simulations to determine the standard binding free energy of DNA with netropsin, a well-characterized antiviral and antimicrobial drug, which associates to the minor groove of double-stranded DNA. To overcome the sampling limitations of classical molecular dynamics simulations, which cannot capture the large change in configurational entropy that accompanies binding, we resort to a series of potentials of mean force calculations involving a set of geometrical restraints acting on collective variables.
Manzoni, Francesco; Ryde, Ulf
2018-03-01
We have calculated relative binding affinities for eight tetrafluorophenyl-triazole-thiogalactoside inhibitors of galectin-3 with the alchemical free-energy perturbation approach. We obtain a mean absolute deviation from experimental estimates of only 2-3 kJ/mol and a correlation coefficient (R 2) of 0.5-0.8 for seven relative affinities spanning a range of up to 11 kJ/mol. We also studied the effect of using different methods to calculate the charges of the inhibitor and different sizes of the perturbed group (the atoms that are described by soft-core potentials and are allowed to have differing coordinates). However, the various approaches gave rather similar results and it is not possible to point out one approach as consistently and significantly better than the others. Instead, we suggest that such small and reasonable variations in the computational method can be used to check how stable the calculated results are and to obtain a more accurate estimate of the uncertainty than if performing only one calculation with a single computational setup.
A new approach to the estimation of surface free energy based on Vickers microhardness data
2009-03-01
Full Text Available A relation between surface free energy (σMHV and Meyer’s lines cut-values has been established using Vickers microhardness (MHV method and empirical physical laws. This relation allows the calculation of σMHV only from MHV data. The parameters required are Meyer’s lines cut-values and the mean value of diagonal length of the impression at different loads applied (drealmean. Our study of 12 samples of ultra high molecular weight polyethylene (PE-UHMW showed that the new approach is applicable when the slope value of Meyer’s lines equals 2 (i.e. n = 2. A γ-60Co source was used for the irradiation of 11 samples (one of the samples investigated is un-irradiated at room temperature in air. Doses of 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000 and 1500 kGy were applied. The values of σMHV obtained are in a good agreement with the literature. The dependence of σMHV on the dose applied strictly corresponds to the radiation effects theory. MHV was measured at seven different loads – 0.0123, 0.0245, 0.049, 0.098, 0.196, 0.392, 0.785 N at a loading time of 30 s.
Xu, H.
1999-01-01
In this letter, the Sverjensky-Molling equation derived from a linear free energy relationship is used to calculate the Gibbs free energies of formation of zirconolite crystalline phases (MZrTi 2 O 7 and MHfTi 2 O 7 ) from the known thermodynamic properties of the corresponding aqueous divalent cations (M 2+ ). Sverjensky-Molling equation is expressed as ΔG 0 f,M v X =a M v X ΔG 0 n,M 2+ +b M v X +β M v X r M 2+ , where the coefficients a M v X , b M v X , and β M v X characterize a particular structural family of M v X, r M 2+ is the ionic radius of M 2+ cation, ΔG f,M v X 0 is the standard Gibbs free energy of formation of M v X, and ΔG 0 n,M 2+ is the standard non-solvation energy of cation M 2+ . This relationship can be used to predict the Gibbs free energies of formation of various fictive phases (such as BaZrTi 2 O 7 , SrZrTi 2 O 7 , PbZrTi 2 O 7 , etc.) that may form solid solution with CaZrTi 2 O 7 in actual Synroc-based nuclear waste forms. Based on obtained linear free energy relationships, it is predicted that large cations (e.g., Ba and Ra) prefer to be in perovskite structure, and small cations (e.g., Ca, Zn, and Cd) prefer to be in zirconolite structure. (orig.)
Heimdal, J.; Kaukonen, M.; Srnec, Martin; Rulíšek, Lubomír; Ryde, U.
2011-01-01
Roč. 12, č. 17 (2011), s. 3337-3347 ISSN 1439-4235 R&D Projects: GA MŠk LC512 Institutional research plan: CEZ:AV0Z40550506 Keywords : acidity constants * enzymes * free-energy * perturbation * molecular modelling * reduction potentials Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.412, year: 2011
QUIRYNEN, M; VANDERMEI, HC; BOLLEN, CML; VANDENBOSSCHE, LH; DOORNBUSCH, GI; VANSTEENBERGHE, D; BUSSCHER, HJ
THE INFLUENCE OF SURFACE FREE ENERGY on supra- and subgingival plaque microbiology was examined in 9 patients with functional fixed prostheses supported by endosseous titanium implants. Two abutments (trans-mucosal part of the 2 stage implant) were replaced by either a new titanium abutment or a
Tamura, Yukie; Takamizawa, Toshiki; Shimamura, Yutaka; Akiba, Shunsuke; Yabuki, Chiaki; Imai, Arisa; Tsujimoto, Akimasa; Kurokawa, Hiroyasu; Miyazaki, Masashi
2017-11-29
The influences of air-powder polishing with glycine or sodium bicarbonate powders on shear bond strengths (SBS) and surface-free energies of universal adhesives were examined. Scotchbond Universal Adhesive (SU, 3M ESPE), G-Premio Bond (GP, GC), Adhese Universal (AU, Ivoclar Vivadent), and All-Bond Universal (AB, Bisco) were used in this study. Bovine dentin surfaces were air polished with glycine or sodium bicarbonate powders prior to the bonding procedure, and resin pastes were bonded to the dentin surface using universal adhesives. SBSs were determined after 24-h storage in distilled water at 37°C. Surface-free energy was then determined by measuring contact angles using three test liquids on dentin surfaces. Significantly lower SBSs were observed for dentin that was air-powder polished and surface-free energies were concomitantly lowered. This study indicated that air-powder polishing influences SBSs and surface-free energies. However, glycine powder produced smaller changes in these surface parameters than sodium bicarbonate.
Absolute binding free energy calculations of CBClip host–guest systems in the SAMPL5 blind challenge
Tofoleanu, Florentina; Pickard, Frank C.; König, Gerhard; Huang, Jing; Damjanović, Ana; Baek, Minkyung; Seok, Chaok; Brooks, Bernard R.
2016-01-01
Herein, we report the absolute binding free energy calculations of CBClip complexes in the SAMPL5 blind challenge. Initial conformations of CBClip complexes were obtained using docking and molecular dynamics simulations. Free energy calculations were performed using thermodynamic integration (TI) with soft-core potentials and Bennett’s acceptance ratio (BAR) method based on a serial insertion scheme. We compared the results obtained with TI simulations with soft-core potentials and Hamiltonian replica exchange simulations with the serial insertion method combined with the BAR method. The results show that the difference between the two methods can be mainly attributed to the van der Waals free energies, suggesting that either the simulations used for TI or the simulations used for BAR, or both are not fully converged and the two sets of simulations may have sampled difference phase space regions. The penalty scores of force field parameters of the 10 guest molecules provided by CHARMM Generalized Force Field can be an indicator of the accuracy of binding free energy calculations. Among our submissions, the combination of docking and TI performed best, which yielded the root mean square deviation of 2.94 kcal/mol and an average unsigned error of 3.41 kcal/mol for the ten guest molecules. These values were best overall among all participants. However, our submissions had little correlation with experiments. PMID:27677749
Carlotto, Silvia; Zerbetto, Mirco
2014-01-01
We propose an articulated computational experiment in which both quantum mechanics (QM) and molecular mechanics (MM) methods are employed to investigate environment effects on the free energy surface for the backbone dihedral angles rotation of the small dipeptide N-Acetyl-N'-methyl-L-alanylamide. This computation exercise is appropriate for an…
Ulstrup, Jens
1999-01-01
We discuss a simple model for the environmental reorganisation Gibbs free energy, E-r, in electron transfer between a metalloprotein and a small reaction partner. The protein is represented as a dielectric globule with low dielectric constant, the metal centres as conducting spheres, all embedded...
Zhang, Wanzhu; Dong, Bingzhi
2018-05-20
Natural organic matter (NOM) in micro-polluted water purification using membranes is a critical issue to handle. Understanding the fouling mechanism in the forward osmosis (FO) process, particularly identifying the predominant factor that controls membrane fouling, could have significant effects on exerting the advantages of FO technique. Cellulose triacetate no-woven (CTA-NW) membrane is applied to experiments with a high removal efficiency (> 99%) for the model foulant. Tannic acid (TA) is used as a surrogate foulant for NOM in the membrane fouling process, thus enabling the analysis of the effects of physical and chemical aspects of water flux, retention, and adsorption. The membrane fouling behavior is affected mainly by the combined effects of the osmotic dragging force and the interaction of the pH in the working solution, foulants, and calcium ions, as demonstrated by the water flux loss and the changes of membrane retention and adsorption. The fouled CTA-NW membrane (in PRO mode) could be flux-recovered by > 85% through physical cleaning methods. The interfacial free energy analysis theory was used to analyze the membrane fouling behavior with calculating the interfacial cohesion and adhesion free energies. The cohesion free energy refers to the deposition of foulants (TA or TA combined with calcium ions) on a fouled membrane. In addition, the adhesion free energy could be used to evaluate the interaction between foulants and a clean membrane.
UYEN, HMW; JONGEBLOED, WL; BUSSCHER, HJ
1991-01-01
The strength of adhesion between dental calculus and enamel or dentin surfaces determines the ease with which the calculus can be removed by brushing or professional dental treatment. In this study, we examined the adhesion of canine calculi formed on substrata with different surface free energies
Lili X Peng
2014-02-01
Full Text Available αβ-tubulin dimers need to convert between a 'bent' conformation observed for free dimers in solution and a 'straight' conformation required for incorporation into the microtubule lattice. Here, we investigate the free energy landscape of αβ-tubulin using molecular dynamics simulations, emphasizing implications for models of assembly, and modulation of the conformational landscape by colchicine, a tubulin-binding drug that inhibits microtubule polymerization. Specifically, we performed molecular dynamics, potential-of-mean force simulations to obtain the free energy profile for unpolymerized GDP-bound tubulin as a function of the ∼12° intradimer rotation differentiating the straight and bent conformers. Our results predict that the unassembled GDP-tubulin heterodimer exists in a continuum of conformations ranging between straight and bent, but, in agreement with existing structural data, suggests that an intermediate bent state has a lower free energy (by ∼1 kcal/mol and thus dominates in solution. In agreement with predictions of the lattice model of microtubule assembly, lateral binding of two αβ-tubulins strongly shifts the conformational equilibrium towards the straight state, which is then ∼1 kcal/mol lower in free energy than the bent state. Finally, calculations of colchicine binding to a single αβ-tubulin dimer strongly shifts the equilibrium toward the bent states, and disfavors the straight state to the extent that it is no longer thermodynamically populated.
Application of a linear free energy relationship to crystalline solids of MO2 and M(OH)4
Xu Huifang; Barton, L.L.
1999-01-01
In this letter, a linear free energy relationship developed by Sverjensky and Molling is used to predict the Gibbs free energies of formation of crystalline phases of M 4+ O 2 and M 4+ (OH) 4 from the known thermodynamic properties of aqueous tetravalent cations (M 4+ ). The modified Sverjensky and Molling equation for tetravalent cations is expressed as ΔG 0 f,M v X = a M v X ΔG 0 n,M 4+ + b M v X + β M v X r M 4+ , where the coefficients a M v X , b M v X and β M v X characterize a particular structural family of M v X, r M 4+ is the ionic radius of M 4+ cation, ΔG 0 f,M v X is the standard Gibbs free energy of formation of M v X, and ΔG 0 n,M 4+ is the standard non-solvation energy of cation M 4+ . By fitting the equation to the existing thermodynamic data, the coefficients in the equation for the MO 2 family minerals are estimated to be: a M v X = 0.670, β M v X = 32 (kcal/mol A), and b = -430.02 (kcal/mol). The constrained relationship can be used to predict the standard Gibbs free energies of formation of crystalline phases and fictive phases (i.e., phases which are thermodynamically unstable and do not occur at standard conditions) within the isostructural families of M 4+ O 2 and M 4+ (OH) 4 if the standard Gibbs free energies of formation of the tetravalent cations are known. (orig.)