Single-molecule Michaelis-Menten equations.
Kou, S C; Cherayil, Binny J; Min, Wei; English, Brian P; Xie, X Sunney
2005-10-20
This paper summarizes our present theoretical understanding of single-molecule kinetics associated with the Michaelis-Menten mechanism of enzymatic reactions. Single-molecule enzymatic turnover experiments typically measure the probability density f(t) of the stochastic waiting time t for individual turnovers. While f(t) can be reconciled with ensemble kinetics, it contains more information than the ensemble data; in particular, it provides crucial information on dynamic disorder, the apparent fluctuation of the catalytic rates due to the interconversion among the enzyme's conformers with different catalytic rate constants. In the presence of dynamic disorder, f(t) exhibits a highly stretched multiexponential decay at high substrate concentrations and a monoexponential decay at low substrate concentrations. We derive a single-molecule Michaelis-Menten equation for the reciprocal of the first moment of f(t), 1/, which shows a hyperbolic dependence on the substrate concentration [S], similar to the ensemble enzymatic velocity. We prove that this single-molecule Michaelis-Menten equation holds under many conditions, in particular when the intercoversion rates among different enzyme conformers are slower than the catalytic rate. However, unlike the conventional interpretation, the apparent catalytic rate constant and the apparent Michaelis constant in this single-molecule Michaelis-Menten equation are complicated functions of the catalytic rate constants of individual conformers. We also suggest that the randomness parameter r, defined as )2> / t2, can serve as an indicator for dynamic disorder in the catalytic step of the enzymatic reaction, as it becomes larger than unity at high substrate concentrations in the presence of dynamic disorder.
Single molecule Michaelis-Menten equation beyond quasistatic disorder.
Xue, Xiaochuan; Liu, Fei; Ou-Yang, Zhong-Can
2006-09-01
The classic Michaelis-Menten equation describes the catalytic activities for ensembles of enzyme molecules very well. But recent single-molecule experiments showed that the waiting time distribution and other properties of single enzyme molecules were not consistent with the prediction based on the ensemble viewpoint. They have contributed to the slow conformational changes of a single enzyme in the catalytic processes. In this work, we study the general dynamics of single enzymes in the presence of dynamic disorder. We find that, within the time separation regimes, i.e., the slow reaction and nondiffusion limits, the Michaelis-Menten equation holds exactly. In particular, by employing the decoupling approximation we demonstrate analytically that the classic Michaelis-Menten equation is still an excellent approximation in the presence of general dynamic disorder.
Michaelis-Menten equation and detailed balance in enzymatic networks.
Cao, Jianshu
2011-05-12
Many enzymatic reactions in biochemistry are far more complex than the celebrated Michaelis-Menten scheme, but the observed turnover rate often obeys the hyperbolic dependence on the substrate concentration, a relation established almost a century ago for the simple Michaelis-Menten mechanism. To resolve the longstanding puzzle, we apply the flux balance method to predict the functional form of the substrate dependence in the mean turnover time of complex enzymatic reactions and identify detailed balance (i.e., the lack of unbalanced conformational current) as a sufficient condition for the Michaelis-Menten equation to describe the substrate concentration dependence of the turnover rate in an enzymatic network. This prediction can be verified in single-molecule event-averaged measurements using the recently proposed signatures of detailed balance violations. The finding helps analyze recent single-molecule studies of enzymatic networks and can be applied to other external variables, such as force-dependence and voltage-dependence.
Alternative Analysis of the Michaelis-Menten Equations
Krogstad, Harald E.; Dawed, Mohammed Yiha; Tegegne, Tadele Tesfa
2011-01-01
Courses in mathematical modelling are always in need of simple, illustrative examples. The Michaelis-Menten reaction kinetics equations have been considered to be a basic example of scaling and singular perturbation. However, the leading order approximations do not easily show the expected behaviour, and this note proposes a different perturbation…
Alternative Analysis of the Michaelis-Menten Equations
Krogstad, Harald E.; Dawed, Mohammed Yiha; Tegegne, Tadele Tesfa
2011-01-01
Courses in mathematical modelling are always in need of simple, illustrative examples. The Michaelis-Menten reaction kinetics equations have been considered to be a basic example of scaling and singular perturbation. However, the leading order approximations do not easily show the expected behaviour, and this note proposes a different perturbation…
Michel, Denis
2013-01-01
The Michaelis-Menten enzymatic reaction is sufficient to perceive many subtleties of network modeling, including the concentration and time scales separations, the formal equivalence between bulk phase and single-molecule approaches, or the relationships between single-cycle transient probabilities and steady state rates. Seven methods proposed by different authors and yielding the same famous Michaelis-Menten equation, are selected here to illustrate the kinetic and probabilistic use of rate constants and to review basic techniques for handling them. Finally, the general rate of an ordered multistep reaction, of which the Michaelis-Menten reaction is a particular case, is deduced from a Markovian approach.
Michel, Denis; Ruelle, Philippe
2013-01-01
International audience; The Michaelis-Menten enzymatic reaction is sufficient to perceive many subtleties of network modeling, including the concentration and time scales separations, the formal equivalence between bulk phase and single-molecule approaches, or the relationships between single-cycle transient probabilities and steady state rates. Seven methods proposed by different authors and yielding the same famous Michaelis-Menten equation, are selected here to illustrate the kinetic and p...
Ever-fluctuating single enzyme molecules : Michaelis-Menten equation revisited
English, Brian P.; Min, Wei; Oijen, Antoine M. van; Lee, Kang Taek; Luo, Guobin; Sun, Hongye; Cherayil, Binny J.; Kou, S.C.; Xie, X. Sunney
2006-01-01
Enzymes are biological catalysts vital to life processes and have attracted century-long investigation. The classic Michaelis-Menten mechanism provides a highly satisfactory description of catalytic activities for large ensembles of enzyme molecules. Here we tested the Michaelis-Menten equation at
Conformational Nonequilibrium Enzyme Kinetics: Generalized Michaelis-Menten Equation.
Piephoff, D Evan; Wu, Jianlan; Cao, Jianshu
2017-08-03
In a conformational nonequilibrium steady state (cNESS), enzyme turnover is modulated by the underlying conformational dynamics. On the basis of a discrete kinetic network model, we use an integrated probability flux balance method to derive the cNESS turnover rate for a conformation-modulated enzymatic reaction. The traditional Michaelis-Menten (MM) rate equation is extended to a generalized form, which includes non-MM corrections induced by conformational population currents within combined cyclic kinetic loops. When conformational detailed balance is satisfied, the turnover rate reduces to the MM functional form, explaining its general validity. For the first time, a one-to-one correspondence is established between non-MM terms and combined cyclic loops with unbalanced conformational currents. Cooperativity resulting from nonequilibrium conformational dynamics can be achieved in enzymatic reactions, and we provide a novel, rigorous means of predicting and characterizing such behavior. Our generalized MM equation affords a systematic approach for exploring cNESS enzyme kinetics.
Goličnik, Marko
2011-04-15
Various explicit reformulations of time-dependent solutions for the classical two-step irreversible Michaelis-Menten enzyme reaction model have been described recently. In the current study, I present further improvements in terms of a generalized integrated form of the Michaelis-Menten equation for computation of substrate or product concentrations as functions of time for more real-world, enzyme-catalyzed reactions affected by the product. The explicit equations presented here can be considered as a simpler and useful alternative to the exact solution for the generalized integrated Michaelis-Menten equation when fitted to time course data using standard curve-fitting software. Copyright © 2011 Elsevier Inc. All rights reserved.
Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revisited.
English, Brian P; Min, Wei; van Oijen, Antoine M; Lee, Kang Taek; Luo, Guobin; Sun, Hongye; Cherayil, Binny J; Kou, S C; Xie, X Sunney
2006-02-01
Enzymes are biological catalysts vital to life processes and have attracted century-long investigation. The classic Michaelis-Menten mechanism provides a highly satisfactory description of catalytic activities for large ensembles of enzyme molecules. Here we tested the Michaelis-Menten equation at the single-molecule level. We monitored long time traces of enzymatic turnovers for individual beta-galactosidase molecules by detecting one fluorescent product at a time. A molecular memory phenomenon arises at high substrate concentrations, characterized by clusters of turnover events separated by periods of low activity. Such memory lasts for decades of timescales ranging from milliseconds to seconds owing to the presence of interconverting conformers with broadly distributed lifetimes. We proved that the Michaelis-Menten equation still holds even for a fluctuating single enzyme, but bears a different microscopic interpretation.
Bozlee, Brian J.
2007-01-01
The impact of raising Gibbs energy of the enzyme-substrate complex (G[subscript 3]) and the reformulation of the Michaelis-Menten equation are discussed. The maximum velocity of the reaction (v[subscript m]) and characteristic constant for the enzyme (K[subscript M]) will increase with increase in Gibbs energy, indicating that the rate of reaction…
A generalized Michaelis-Menten type equation for the analysis of growth
Lopez, S.; France, J.; Gerrits, W.J.J.; Dhanoa, M.S.; Humphries, D.J.; Dijkstra, J.
2000-01-01
The functional form W = (W0Kc Wf t(c)) /(Kc t(c)), where W is body size at age t, W0 and Wf are the zero- and infinite-time values of W, respectively, and K and c are constants, is derived. This new generalized Michaelis-Menten-type equation provides a flexible model for animal growth capable of
Filobello-Nino, Uriel; Vazquez-Leal, Hector; Benhammouda, Brahim; Hernandez-Martinez, Luis; Khan, Yasir; Jimenez-Fernandez, Victor Manuel; Herrera-May, Agustin Leobardo; Castaneda-Sheissa, Roberto; Pereyra-Diaz, Domitilo; Cervantes-Perez, Juan; Agustin Perez-Sesma, Jose Antonio; Hernandez-Machuca, Sergio Francisco; Cuellar-Hernandez, Leticia
2014-01-01
In this article, Perturbation Method (PM) is employed to obtain a handy approximate solution to the steady state nonlinear reaction diffusion equation containing a nonlinear term related to Michaelis-Menten of the enzymatic reaction. Comparing graphics between the approximate and exact solutions, it will be shown that the PM method is quite efficient.
Filobello-Nino, Uriel; Vazquez-Leal, Hector; Benhammouda, Brahim; Hernandez-Martinez, Luis; Khan, Yasir; Jimenez-Fernandez, Victor Manuel; Herrera-May, Agustin Leobardo; Castaneda-Sheissa, Roberto; Pereyra-Diaz, Domitilo; Cervantes-Perez, Juan; Agustin Perez-Sesma, Jose Antonio; Hernandez-Machuca, Sergio Francisco; Cuellar-Hernandez, Leticia
2014-01-01
In this article, Perturbation Method (PM) is employed to obtain a handy approximate solution to the steady state nonlinear reaction diffusion equation containing a nonlinear term related to Michaelis-Menten of the enzymatic reaction. Comparing graphics between the approximate and exact solutions, it will be shown that the PM method is quite efficient.
Solution of the Michaelis-Menten equation using the decomposition method.
Sonnad, Jagadeesh R; Goudar, Chetan T
2009-01-01
We present a low-order recursive solution to the Michaelis-Menten equation using the decomposition method. This solution is algebraic in nature and provides a simpler alternative to numerical approaches such as differential equation evaluation and root-solving techniques that are currently used to compute substrate concentration in the Michaelis-Menten equation. A detailed characterization of the errors in substrate concentrations computed from decomposition, Runge-Kutta, and bisection methods over a wide range of s(0) : K(m) values was made by comparing them with highly accurate solutions obtained using the Lambert W function. Our results indicated that solutions obtained from the decomposition method were usually more accurate than those from the corresponding classical Runge-Kutta methods. Moreover, these solutions required significantly fewer computations than the root-solving method. Specifically, when the stepsize was 0.1% of the total time interval, the computed substrate concentrations using the decomposition method were characterized by accuracies on the order of 10(-8) or better. The algebraic nature of the decomposition solution and its relatively high accuracy make this approach an attractive candidate for computing substrate concentration in the Michaelis-Menten equation.
Carvalho,Nakédia M. F.; Pires, Bianca M.; Antunes,Octavio A. C.; Roberto B Faria; Osório,Renata E. H. M. B.; Clovis Piovezan; Ademir Neves
2010-01-01
The Michaelis-Menten equation is used in many biochemical and bioinorganic kinetic studies involving homogeneous catalysis. Otherwise, it is known that determination of Michaelis-Menten parameters K M, Vmax, and k cat by the well-known Lineweaver-Burk double reciprocal linear equation does not produce the best values for these parameters. In this paper we present a discussion on different linear equations which can be used to calculate these parameters and we compare their results with the va...
Enzyme Kinetics and the Michaelis-Menten Equation
Biaglow, Andrew; Erickson, Keith; McMurran, Shawnee
2010-01-01
The concepts presented in this article represent the cornerstone of classical mathematical biology. The central problem of the article relates to enzyme kinetics, which is a biochemical system. However, the theoretical underpinnings that lead to the formation of systems of time-dependent ordinary differential equations have been applied widely to…
Enzyme Kinetics and the Michaelis-Menten Equation
Biaglow, Andrew; Erickson, Keith; McMurran, Shawnee
2010-01-01
The concepts presented in this article represent the cornerstone of classical mathematical biology. The central problem of the article relates to enzyme kinetics, which is a biochemical system. However, the theoretical underpinnings that lead to the formation of systems of time-dependent ordinary differential equations have been applied widely to…
Schnell, Santiago
2014-01-01
The Michaelis-Menten equation is generally used to estimate the kinetic parameters, V and K(M), when the steady-state assumption is valid. Following a brief overview of the derivation of the Michaelis-Menten equation for the single-enzyme, single-substrate reaction, a critical review of the criteria for validity of the steady-state assumption is presented. The application of the steady-state assumption makes the implicit assumption that there is an initial transient during which the substrate concentration remains approximately constant, equal to the initial substrate concentration, while the enzyme-substrate complex concentration builds up. This implicit assumption is known as the reactant stationary assumption. This review presents evidence showing that the reactant stationary assumption is distinct from and independent of the steady-state assumption. Contrary to the widely believed notion that the Michaelis-Menten equation can always be applied under the steady-state assumption, the reactant stationary assumption is truly the necessary condition for validity of the Michaelis-Menten equation to estimate kinetic parameters. Therefore, the application of the Michaelis-Menten equation only leads to accurate estimation of kinetic parameters when it is used under experimental conditions meeting the reactant stationary assumption. The criterion for validity of the reactant stationary assumption does not require the restrictive condition of choosing a substrate concentration that is much higher than the enzyme concentration in initial rate experiments. © 2013 FEBS.
Klinman, Judith P
2014-01-01
The final arbiter of enzyme mechanism is the ability to establish and test a kinetic mechanism. Isotope effects play a major role in expanding the scope and insight derived from the Michaelis-Menten equation. The integration of isotope effects into the formalism of the Michaelis-Menten equation began in the 1970s and has continued until the present. This review discusses a family of eukaryotic copper proteins, including dopamine β-monooxygenase, tyramine β-monooxygenase and peptidylglycine α-amidating enzyme, which are responsible for the synthesis of neuroactive compounds, norepinephrine, octopamine and C-terminally carboxamidated peptides, respectively. The review highlights the results of studies showing how combining kinetic isotope effects with initial rate parameters permits the evaluation of: (a) the order of substrate binding to multisubstrate enzymes; (b) the magnitude of individual rate constants in complex, multistep reactions; (c) the identification of chemical intermediates; and (d) the role of nonclassical (tunnelling) behaviour in C-H activation. © 2013 FEBS.
Nakédia M. F. Carvalho
2010-01-01
Full Text Available The Michaelis-Menten equation is used in many biochemical and bioinorganic kinetic studies involving homogeneous catalysis. Otherwise, it is known that determination of Michaelis-Menten parameters K M, Vmax, and k cat by the well-known Lineweaver-Burk double reciprocal linear equation does not produce the best values for these parameters. In this paper we present a discussion on different linear equations which can be used to calculate these parameters and we compare their results with the values obtained by the more reliable nonlinear least-square fit.
Reeve, Russell; Turner, J Rick
2013-05-01
The Hill equation is often used in dose-response or exposure-response modeling. Aliases for the Hill model include the Emax model, and the Michaelis-Menten model. There is confusion about the appropriate parameterization, how to interpret the parameters, what the meaning is of the various parameterizations found in the literature, and which parameterization best approximates the statistical inferences produced when fitting the Hill equation to data. In this paper, we present several equivalent versions of the Hill model; show that they are equivalent in terms of yielding the same prediction for a given dose, and are equivalent to the four-parameter logistic model in this same sense; and deduce which parameterization is optimal in the sense of having the least statistical curvature and preferable multicollinearity.
Liao, Fei; Tian, Kao-Cong; Yang, Xiao; Zhou, Qi-Xin; Zeng, Zhao-Chun; Zuo, Yu-Ping
2003-03-01
The reliability of kinetic substrate quantification by nonlinear fitting of the enzyme reaction curve to the integrated Michaelis-Menten equation was investigated by both simulation and preliminary experimentation. For simulation, product absorptivity epsilon was 3.00 mmol(-1) L cm(-1) and K(m) was 0.10 mmol L(-1), and uniform absorbance error sigma was randomly inserted into the error-free reaction curve of product absorbance A(i) versus reaction time t(i) calculated according to the integrated Michaelis-Menten equation. The experimental reaction curve of arylesterase acting on phenyl acetate was monitored by phenol absorbance at 270 nm. Maximal product absorbance A(m) was predicted by nonlinear fitting of the reaction curve to Eq. (1) with K(m) as constant. There were unique A(m) for best fitting of both the simulated and experimental reaction curves. Neither the error in reaction origin nor the variation of enzyme activity changed the background-corrected value of A(m). But the range of data under analysis, the background absorbance, and absorbance error sigma had an effect. By simulation, A(m) from 0.150 to 3.600 was predicted with reliability and linear response to substrate concentration when there was 80% consumption of substrate at sigma of 0.001. Restriction of absorbance to 0.700 enabled A(m) up to 1.800 to be predicted at sigma of 0.001. Detection limit reached A(m) of 0.090 at sigma of 0.001. By experimentation, the reproducibility was 4.6% at substrate concentration twice the K(m), and A(m) linearly responded to phenyl acetate with consistent absorptivity for phenol, and upper limit about twice the maximum of experimental absorbance. These results supported the reliability of this new kinetic method for enzymatic analysis with enhanced upper limit and precision.
About and beyond the Henri-Michaelis-Menten rate equation for single-substrate enzyme kinetics.
Bajzer, Zeljko; Strehler, Emanuel E
2012-01-20
For more than a century the simple single-substrate enzyme kinetics model and related Henri-Michaelis-Menten (HMM) rate equation have been thoroughly explored in various directions. In the present paper we are concerned with a possible generalization of this rate equation recently proposed by F. Kargi (BBRC 382 (2009) 157-159), which is assumed to be valid both in the case that the total substrate or enzyme is in excess and the quasi-steady-state is achieved. We demonstrate that this generalization is grossly inadequate and propose another generalization based on application of the quasi-steady-state condition and conservation equations for both enzyme and substrate. The standard HMM equation is derived by (a) assuming the quasi-steady-state condition, (b) applying the conservation equation only for the enzyme, and (c) assuming that the substrate concentration at quasi-steady-state can be approximated by the total substrate concentration [S](0). In our formula the rate is already expressed through [S](0), and we only assume that when quasi-steady-state is achieved the amount of product formed is negligible compared to [S](0). Numerical simulations show that our formula is generally more accurate than the HMM formula and also can provide a good approximation when the enzyme is in excess, which is not the case for the HMM formula. We show that the HMM formula can be derived from our expression by further assuming that the total enzyme concentration is negligible compared to [S](0). Copyright © 2011 Elsevier Inc. All rights reserved.
Goličnik, Marko
2011-06-01
Many pharmacodynamic processes can be described by the nonlinear saturation kinetics that are most frequently based on the hyperbolic Michaelis-Menten equation. Thus, various time-dependent solutions for drugs obeying such kinetics can be expressed in terms of the Lambert W(x)-omega function. However, unfortunately, computer programs that can perform the calculations for W(x) are not widely available. To avoid this problem, the replacement of the integrated Michaelis-Menten equation with an empiric integrated 1--exp alternative model equation was proposed recently by Keller et al. (Ther Drug Monit. 2009;31:783-785), although, as shown here, it was not necessary. Simulated concentrations of model drugs obeying Michaelis-Menten elimination kinetics were generated by two approaches: 1) calculation of time-course data based on an approximation equation W2*(x) performed using Microsoft Excel; and 2) calculation of reference time-course data based on an exact W(x) function built in to the Wolfram Mathematica. I show here that the W2*(x) function approximates the actual W(x) accurately. W2*(x) is expressed in terms of elementary mathematical functions and, consequently, it can be easily implemented using any of the widely available software. Hence, with the example of a hypothetical drug, I demonstrate here that an equation based on this approximation is far better, because it is nearly equivalent to the original solution, whereas the same characteristics cannot be fully confirmed for the 1--exp model equation. The W2*(x) equation proposed here might have an important role as a useful shortcut in optional software to estimate kinetic parameters from experimental data for drugs, and it might represent an easy and universal analytical tool for simulating and designing dosing regimens.
Costa, Rafael S; Machado, Daniel; Rocha, Isabel; Ferreira, Eugénio C
2010-05-01
The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis-Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action, convenience kinetics, lin-log and power-law). Using the mechanistic model for Escherichia coli central carbon metabolism as a benchmark, we investigate the alternative modeling approaches through comparative simulations analyses. The good dynamic behavior and the powerful predictive capabilities obtained using the hybrid model composed of Michaelis-Menten and the approximate lin-log kinetics indicate that this is a possible suitable approach to model complex large-scale networks where the exact rate laws are unknown. 2010 Elsevier Ireland Ltd. All rights reserved.
Stroberg, Wylie; Schnell, Santiago
2016-12-01
The conditions under which the Michaelis-Menten equation accurately captures the steady-state kinetics of a simple enzyme-catalyzed reaction is contrasted with the conditions under which the same equation can be used to estimate parameters, KM and V, from progress curve data. Validity of the underlying assumptions leading to the Michaelis-Menten equation are shown to be necessary, but not sufficient to guarantee accurate estimation of KM and V. Detailed error analysis and numerical "experiments" show the required experimental conditions for the independent estimation of both KM and V from progress curves. A timescale, tQ, measuring the portion of the time course over which the progress curve exhibits substantial curvature provides a novel criterion for accurate estimation of KM and V from a progress curve experiment. It is found that, if the initial substrate concentration is of the same order of magnitude as KM, the estimated values of the KM and V will correspond to their true values calculated from the microscopic rate constants of the corresponding mass-action system, only so long as the initial enzyme concentration is less than KM. Copyright © 2016 Elsevier B.V. All rights reserved.
Golicnik, Marko
2011-01-01
The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate "V", and the Michaelis constant "K"[subscript M]) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to…
Golicnik, Marko
2011-01-01
The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate "V", and the Michaelis constant "K"[subscript M]) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to…
Pulkkinen, O
2016-01-01
Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessi...
Liao, Fei; Zhu, Xiao-Yun; Wang, Yong-Mei; Zuo, Yu-Ping
2005-01-31
The estimation of enzyme kinetic parameters by nonlinear fitting reaction curve to the integrated Michaelis-Menten rate equation ln(S(0)/S)+(S(0)-S)/K(m)=(V(m)/K(m))xt was investigated and compared to that by fitting to (S(0)-S)/t=V(m)-K(m)x[ln(S(0)/S)/t] (Atkins GL, Nimmo IA. The reliability of Michaelis-Menten constants and maximum velocities estimated by using the integrated Michaelis-Menten equation. Biochem J 1973;135:779-84) with uricase as the model. Uricase reaction curve was simulated with random absorbance error of 0.001 at 0.075 mmol/l uric acid. Experimental reaction curve was monitored by absorbance at 293 nm. For both CV and deviation kinetic parameters and applicable for the characterization of enzyme inhibitors.
The integrated Michaelis-Menten rate equation: déjà vu or vu jàdé?
Goličnik, Marko
2013-08-01
A recent article of Johnson and Goody (Biochemistry, 2011;50:8264-8269) described the almost-100-years-old paper of Michaelis and Menten. Johnson and Goody translated this classic article and presented the historical perspective to one of incipient enzyme-reaction data analysis, including a pioneering global fit of the integrated rate equation in its implicit form to the experimental time-course data. They reanalyzed these data, although only numerical techniques were used to solve the model equations. However, there is also the still little known algebraic rate-integration equation in a closed form that enables direct fitting of the data. Therefore, in this commentary, I briefly present the integral solution of the Michaelis-Menten rate equation, which has been largely overlooked for three decades. This solution is expressed in terms of the Lambert W function, and I demonstrate here its use for global nonlinear regression curve fitting, as carried out with the original time-course dataset of Michaelis and Menten.
Liu, Ai-Lin; Zhou, Ting; He, Feng-Yun; Xu, Jing-Juan; Lu, Yu; Chen, Hong-Yuan; Xia, Xing-Hua
2006-06-01
We firstly transformed the traditional Michaelis-Menten equation into an off-line form which can be used for evaluating the Michaelis-Menten constant after the enzymatic reaction. For experimental estimation of the kinetics of enzymatic reactions, we have developed a facile and effective method by integrating an enzyme microreactor into direct-printing polymer microchips. Strong nonspecific adsorption of proteins was utilized to effectively immobilize enzymes onto the microchannel wall, forming the integrated on-column enzyme microreactor in a microchip. The properties of the integrated enzyme microreactor were evaluated by using the enzymatic reaction of glucose oxidase (GOx) with its substrate glucose as a model system. The reaction product, hydrogen peroxide, was electrochemically (EC) analyzed using a Pt microelectrode. The data for enzyme kinetics using our off-line form of the Michaelis-Menten equation was obtained (K(m) = 2.64 mM), which is much smaller than that reported in solution (K(m) = 6.0 mM). Due to the hydrophobic property and the native mesoscopic structure of the poly(ethylene terephthalate) film, the immobilized enzyme in the microreactor shows good stability and bioactivity under the flowing conditions.
Pulkkinen, Otto; Metzler, Ralf
2015-12-04
Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessible to experiments and not specific to the exact source of the concentration fluctuations.
Padayachee, Letrisha; Pillay, Ché S
2016-07-01
The thioredoxin system, consisting of thioredoxin reductase, thioredoxin and NADPH, is present in most living organisms and reduces a large array of target protein disulfides. The insulin reduction assay is commonly used to characterise thioredoxin activity in vitro, but it is not clear whether substrate saturation datasets from this assay should be fitted and modeled with the Michaelis-Menten equation (thioredoxin enzyme model), or fitted to the thioredoxin system with insulin reduction described by mass-action kinetics (redox couple model). We utilized computational modeling and in vitro assays to determine which of these approaches yield consistent and accurate kinetic parameter sets for insulin reduction. Using computational modeling, we found that fitting to the redox couple model, rather than to the thioredoxin enzyme model, resulted in consistent parameter sets over a range of thioredoxin reductase concentrations. Furthermore, we established that substrate saturation in this assay was due to the progressive redistribution of the thioredoxin moiety into its oxidised form. We then confirmed these results in vitro using the yeast thioredoxin system. This study shows how consistent parameter sets for thioredoxin activity can be obtained regardless of the thioredoxin reductase concentration used in the insulin reduction assay, and validates computational systems biology modeling studies that have described the thioredoxin system with the redox couple modeling approach.
Bezerra, Rui M F; Pinto, Paula A; Fraga, Irene; Dias, Albino A
2016-03-01
To determine initial velocities of enzyme catalyzed reactions without theoretical errors it is necessary to consider the use of the integrated Michaelis-Menten equation. When the reaction product is an inhibitor, this approach is particularly important. Nevertheless, kinetic studies usually involved the evaluation of other inhibitors beyond the reaction product. The occurrence of these situations emphasizes the importance of extending the integrated Michaelis-Menten equation, assuming the simultaneous presence of more than one inhibitor because reaction product is always present. This methodology is illustrated with the reaction catalyzed by alkaline phosphatase inhibited by phosphate (reaction product, inhibitor 1) and urea (inhibitor 2). The approach is explained in a step by step manner using an Excel spreadsheet (available as a template in Appendix). Curve fitting by nonlinear regression was performed with the Solver add-in (Microsoft Office Excel). Discrimination of the kinetic models was carried out based on Akaike information criterion. This work presents a methodology that can be used to develop an automated process, to discriminate in real time the inhibition type and kinetic constants as data (product vs. time) are achieved by the spectrophotometer. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.
Sakoda, M; Hiromi, K
1976-09-01
The best-fit values of the Michaelis constant (Km) and the maximum velocity (V) in the Michaelis-Menten equation can be obtained by the method of least squares with the Taylor expansion for the sum of squares of the absolute residual, i.e., the difference between the observed velocity and the corresponding velocity by calculation. This method makes it possible to determine the values of Km and V not in a trial-and-error manner but in a deductive and unique manner after some iterative procedures starting from arbitrary approximate values of Km and V. These values can be said to be uniquely determined for a set of data as the finally converged values are no longer dependent upon the initial approximate values of Km and V. It is also very important to obtain initial approximate values of parameters for the application of the method described above. A simple method is proposed to estimate the approximate values of parameters involved in fractional functions. The method of rearrangement after canceling of denominator of a fractional function can be utilized to obtain approximate values, not only for cases of two unknown parameters such as the Michaelis-Menten equation, but also for cases with more than two unknowns.
Amyloid-like fibril elongation follows michaelis-menten kinetics
Milto, Katazyna; Botyriute, Akvile; Smirnovas, Vytautas
2013-01-01
... are. We obtained experimental data on insulin amyloid-like fibril elongation at the conditions where other processes which may impact kinetics of fibril formation are minor and fitted it using Michaelis-Menten equation...
Michaelis-Menten dynamics in protein subnetworks
Rubin, Katy J
2016-01-01
To understand the behaviour of complex systems it is often necessary to use models that describe the dynamics of subnetworks. It has previously been established using projection methods that such subnetwork dynamics generically involves memory of the past, and that the memory functions can be calculated explicitly for biochemical reaction networks made up of unary and binary reactions. However, many established network models involve also Michaelis-Menten kinetics, to describe e.g. enzymatic reactions. We show that the projection approach to subnetwork dynamics can be extended to such networks, thus significantly broadening its range of applicability. To derive the extension we construct a larger network that represents enzymes and enzyme complexes explicitly, obtain the projected equations, and finally take the limit of fast enzyme reactions that gives back Michaelis-Menten kinetics. The crucial point is that this limit can be taken in closed form. The outcome is a simple procedure that allows one to obtain ...
Michaelis-Menten dynamics in protein subnetworks.
Rubin, Katy J; Sollich, Peter
2016-05-07
To understand the behaviour of complex systems, it is often necessary to use models that describe the dynamics of subnetworks. It has previously been established using projection methods that such subnetwork dynamics generically involves memory of the past and that the memory functions can be calculated explicitly for biochemical reaction networks made up of unary and binary reactions. However, many established network models involve also Michaelis-Menten kinetics, to describe, e.g., enzymatic reactions. We show that the projection approach to subnetwork dynamics can be extended to such networks, thus significantly broadening its range of applicability. To derive the extension, we construct a larger network that represents enzymes and enzyme complexes explicitly, obtain the projected equations, and finally take the limit of fast enzyme reactions that gives back Michaelis-Menten kinetics. The crucial point is that this limit can be taken in closed form. The outcome is a simple procedure that allows one to obtain a description of subnetwork dynamics, including memory functions, starting directly from any given network of unary, binary, and Michaelis-Menten reactions. Numerical tests show that this closed form enzyme elimination gives a much more accurate description of the subnetwork dynamics than the simpler method that represents enzymes explicitly and is also more efficient computationally.
Bezerra, Rui M F; Fraga, Irene; Dias, Albino A
2013-01-01
Enzyme kinetic parameters are usually determined from initial rates nevertheless, laboratory instruments only measure substrate or product concentration versus reaction time (progress curves). To overcome this problem we present a methodology which uses integrated models based on Michaelis-Menten equation. The most severe practical limitation of progress curve analysis occurs when the enzyme shows a loss of activity under the chosen assay conditions. To avoid this problem it is possible to work with the same experimental points utilized for initial rates determination. This methodology is illustrated by the use of integrated kinetic equations with the well-known reaction catalyzed by alkaline phosphatase enzyme. In this work nonlinear regression was performed with the Solver supplement (Microsoft Office Excel). It is easy to work with and track graphically the convergence of SSE (sum of square errors). The diagnosis of enzyme inhibition was performed according to Akaike information criterion. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.
Legitimacy of the stochastic Michaelis-Menten approximation.
Sanft, K R; Gillespie, D T; Petzold, L R
2011-01-01
Michaelis-Menten kinetics are commonly used to represent enzyme-catalysed reactions in biochemical models. The Michaelis-Menten approximation has been thoroughly studied in the context of traditional differential equation models. The presence of small concentrations in biochemical systems, however, encourages the conversion to a discrete stochastic representation. It is shown that the Michaelis-Menten approximation is applicable in discrete stochastic models and that the validity conditions are the same as in the deterministic regime. The authors then compare the Michaelis-Menten approximation to a procedure called the slow-scale stochastic simulation algorithm (ssSSA). The theory underlying the ssSSA implies a formula that seems in some cases to be different from the well-known Michaelis-Menten formula. Here those differences are examined, and some special cases of the stochastic formulas are confirmed using a first-passage time analysis. This exercise serves to place the conventional Michaelis-Menten formula in a broader rigorous theoretical framework.
Lu, Jian; Dong, Yuxia; Ng, Emily C; Siehl, Daniel L
2017-05-01
One of applications of directed evolution is to desensitize an enzyme to an inhibitor. kcat,1/KM and KI are three dimensions that when multiplied measure an enzyme's intrinsic capacity for catalysis in the presence of an inhibitor. The ideal values for the individual dimensions depend on substrate and inhibitor concentrations under the conditions of the application. When attempting to optimize those values by directed evolution, (kcat/KM)*KI can be an informative parameter for evaluating libraries of variants, but throughput is limited. We describe a manipulation of the Michaelis-Menten equation for competitive inhibition that isolates (kcat/KM)*KI on one side of the equation. If velocity is measured at constant enzyme and substrate concentrations with two different inhibitor concentrations (one of which can be 0), the data are sufficient to calculate (kcat/KM)*KI with just two rate measurements. The procedure is validated by correlating values obtained by the rapid method with those obtained by substrate saturation kinetics. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
Optimal designs for Michaelis-Menten kinetic studies.
Matthews, J N S; Allcock, G C
2004-02-15
Many reactions in enzymology are governed by the Michaelis-Menten equation. Characterising these reactions requires the estimation of the parameters K(M) and V(max) which determine the Michaelis-Menten equation and this is done by observing rates of reactions at a set of substrate concentrations. The choice of substrate concentrations is investigated by determining Bayesian D-optimal designs for a model in which residuals have a normal distribution with constant variance. Designs which focus on alternative quantities, such as K(M) or the ratio V(max)/K(M) are also considered. The effect on the optimal designs of alternative error distributions is also considered.
Reexamining Michaelis-Menten Enzyme Kinetics for Xanthine Oxidase
Bassingthwaighte, James B.; Chinn, Tamara M.
2013-01-01
Abbreviated expressions for enzyme kinetic expressions, such as the Michaelis-Menten (M-M) equations, are based on the premise that enzyme concentrations are low compared with those of the substrate and product. When one does progress experiments, where the solute is consumed during conversion to form a series of products, the idealized conditions…
Reexamining Michaelis-Menten Enzyme Kinetics for Xanthine Oxidase
Bassingthwaighte, James B.; Chinn, Tamara M.
2013-01-01
Abbreviated expressions for enzyme kinetic expressions, such as the Michaelis-Menten (M-M) equations, are based on the premise that enzyme concentrations are low compared with those of the substrate and product. When one does progress experiments, where the solute is consumed during conversion to form a series of products, the idealized conditions…
Michaelis-Menten relations for complex enzymatic networks.
Kolomeisky, Anatoly B
2011-04-21
Most biological processes are controlled by complex systems of enzymatic chemical reactions. Although the majority of enzymatic networks have very elaborate structures, there are many experimental observations indicating that some turnover rates still follow a simple Michaelis-Menten relation with a hyperbolic dependence on a substrate concentration. The original Michaelis-Menten mechanism has been derived as a steady-state approximation for a single-pathway enzymatic chain. The validity of this mechanism for many complex enzymatic systems is surprising. To determine general conditions when this relation might be observed in experiments, enzymatic networks consisting of coupled parallel pathways are investigated theoretically. It is found that the Michaelis-Menten equation is satisfied for specific relations between chemical rates, and it also corresponds to a situation with no fluxes between parallel pathways. Our results are illustrated for a simple model. The importance of the Michaelis-Menten relationship and derived criteria for single-molecule experimental studies of enzymatic processes are discussed.
Michaelis-Menten kinetics under non-isothermal conditions.
Lervik, Anders; Kjelstrup, Signe; Qian, Hong
2015-01-14
We extend the celebrated Michaelis-Menten kinetics description of an enzymatic reaction taking into consideration the presence of a thermal driving force. A coupling of chemical and thermal driving forces is expected from the principle of non-equilibrium thermodynamics, and specifically we obtain an additional term to the classical Michaelis-Menten kinetic equation, which describes the coupling in terms of a single parameter. A companion equation for the heat flux is also derived, which actually can exist even in the absence of a temperature difference. Being thermodynamic in nature, this result is general and independent of the detailed mechanism of the coupling. Conditions for the experimental verification of the new equation are discussed.
Dutta, Annwesha; Chowdhury, Debashish
2017-05-01
The sequence of amino acid monomers in the primary structure of a protein is decided by the corresponding sequence of codons (triplets of nucleic acid monomers) on the template messenger RNA (mRNA). The polymerization of a protein, by incorporation of the successive amino acid monomers, is carried out by a molecular machine called ribosome. We develop a stochastic kinetic model that captures the possibilities of mis-reading of mRNA codon and prior mis-charging of a tRNA. By a combination of analytical and numerical methods, we obtain the distribution of the times taken for incorporation of the successive amino acids in the growing protein in this mathematical model. The corresponding exact analytical expression for the average rate of elongation of a nascent protein is a 'biologically motivated' generalization of the Michaelis-Menten formula for the average rate of enzymatic reactions. This generalized Michaelis-Menten-like formula (and the exact analytical expressions for a few other quantities) that we report here display the interplay of four different branched pathways corresponding to selection of four different types of tRNA.
The Michaelis-Menten-Stueckelberg Theorem
Alexander N. Gorban
2011-05-01
Full Text Available We study chemical reactions with complex mechanisms under two assumptions: (i intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS and (ii they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE. Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the “rarefied gas” limit or the “molecular chaos” hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density (low density of elementary events. This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann H-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.
Kumar, Ashutosh; Dua, Arti
2015-01-01
Recent fluorescence spectroscopy measurements of the turnover time distribution of single-enzyme turnover kinetics of $\\beta$-galactosidase provide evidence of Michaelis-Menten kinetics at low substrate concentration. However, at high substrate concentrations, the dimensionless variance of the turnover time distribution shows systematic deviations from the Michaelis-Menten prediction. This difference is attributed to conformational fluctuations in both the enzyme and the enzyme-substrate complex and to the possibility of both parallel and off-pathway kinetics. Here, we use the chemical master equation to model the kinetics of a single fluctuating enzyme that can yield a product through either parallel or off-pathway mechanisms. An exact expression is obtained for the turnover time distribution from which the mean turnover time and randomness parameters are calculated. The parallel and off-pathway mechanisms yield strikingly different dependences of the mean turnover time and the randomness parameter on the su...
Noise slows the rate of Michaelis-Menten reactions.
Van Dyken, J David
2017-10-07
Microscopic randomness and the small volumes of living cells combine to generate random fluctuations in molecule concentrations called "noise". Here I investigate the effect of noise on biochemical reactions obeying Michaelis-Menten kinetics, concluding that substrate noise causes these reactions to slow. I derive a general expression for the time evolution of the joint probability density of chemical species in arbitrarily connected networks of non-linear chemical reactions in small volumes. This equation is a generalization of the chemical master equation (CME), a common tool for investigating stochastic chemical kinetics, extended to reaction networks occurring in small volumes, such as living cells. I apply this equation to a generalized Michaelis-Menten reaction in an open system, deriving the following general result: 〈p〉≤p¯ and 〈s〉≥s¯, where s¯ and p¯ denote the deterministic steady-state concentration of reactant and product species, respectively, and 〈s〉 and 〈p〉 denote the steady-state ensemble average over independent realizations of a stochastic reaction. Under biologically realistic conditions, namely when substrate is degraded or diluted by cell division, 〈p〉≤p¯. Consequently, noise slows the rate of in vivo Michaelis-Menten reactions. These predictions are validated by extensive stochastic simulations using Gillespie's exact stochastic simulation algorithm. I specify the conditions under which these effects occur and when they vanish, therefore reconciling discrepancies among previous theoretical investigations of stochastic biochemical reactions. Stochastic slowdown of reaction flux caused by molecular noise in living cells may have functional consequences, which the present theory may be used to quantify. Copyright © 2017 Elsevier Ltd. All rights reserved.
A note on the reverse Michaelis-Menten kinetics
Wang, Gangsheng [ORNL; Post, Wilfred M [ORNL
2013-01-01
We theoretically derive a general equation describing the enzyme kinetics that can be further simplified to the typical Michaelis-Menten (M-M) kinetics and the reverse M-M equation (RM-M) proposed by Schimel and Weintraub (2003). We discuss the conditions under which the RM-M is valid with this theoretical derivation. These conditions are contrary to the assumptions of Schimel and Weintraub (2003) and limit the applicability of the model in field soil environments. Nonetheless, Schimel and Weintraub s RM-M model is useful and has the ability to produce a non-linear response of SOM decomposition to enzyme concentration consistent with observations. Regardless of the theoretical basis, if we assume that the M-M and the RM-M could be equivalent, our sensitivity analysis indicates that enzyme plays a more sensitive role in the M-M kinetics compared with in the RM-M kinetics.
Amyloid-like fibril elongation follows michaelis-menten kinetics.
Milto, Katazyna; Botyriute, Akvile; Smirnovas, Vytautas
2013-01-01
A number of proteins can aggregate into amyloid-like fibrils. It was noted that fibril elongation has similarities to an enzymatic reaction, where monomers or oligomers would play a role of substrate and nuclei/fibrils would play a role of enzyme. The question is how similar these processes really are. We obtained experimental data on insulin amyloid-like fibril elongation at the conditions where other processes which may impact kinetics of fibril formation are minor and fitted it using Michaelis-Menten equation. The correlation of the fit is very good and repeatable. It speaks in favour of enzyme-like model of fibril elongation. In addition, obtained [Formula: see text] and [Formula: see text] values at different conditions may help in better understanding influence of environmental factors on the process of fibril elongation.
Enzymatic reactions in microfluidic devices: Michaelis-Menten kinetics.
Ristenpart, William D; Wan, Jiandi; Stone, Howard A
2008-05-01
Kinetic rate constants for enzymatic reactions are typically measured with a series of experiments at different substrate concentrations in a well-mixed container. Here we demonstrate a microfluidic technique for measuring Michaelis-Menten rate constants with only a single experiment. Enzyme and substrate are brought together in a coflow microfluidic device, and we establish analytically and numerically that the initial concentration of product scales with the distance x along the channel as x5/2. Measurements of the initial rate of product formation, combined with the quasi-steady rate of product formation further downstream, yield the rate constants. We corroborate the x5/2 scaling result experimentally using the bioluminescent reaction between ATP and luciferase/luciferin as a model system.
Kumar, Ashutosh; Maity, Hiranmay; Dua, Arti
2015-07-09
Recent fluorescence spectroscopy measurements of the turnover time distribution of single-enzyme turnover kinetics of β-galactosidase provide evidence of Michaelis-Menten kinetics at low substrate concentration. However, at high substrate concentrations, the dimensionless variance of the turnover time distribution shows systematic deviations from the Michaelis-Menten prediction. This difference is attributed to conformational fluctuations in both the enzyme and the enzyme-substrate complex and to the possibility of both parallel- and off-pathway kinetics. Here, we use the chemical master equation to model the kinetics of a single fluctuating enzyme that can yield a product through either parallel- or off-pathway mechanisms. An exact expression is obtained for the turnover time distribution from which the mean turnover time and randomness parameters are calculated. The parallel- and off-pathway mechanisms yield strikingly different dependences of the mean turnover time and the randomness parameter on the substrate concentration. In the parallel mechanism, the distinct contributions of enzyme and enzyme-substrate fluctuations are clearly discerned from the variation of the randomness parameter with substrate concentration. From these general results, we conclude that an off-pathway mechanism, with substantial enzyme-substrate fluctuations, is needed to rationalize the experimental findings of single-enzyme turnover kinetics of β-galactosidase.
Tang, J. Y
2015-01-01
The Michaelis-Menten kinetics and the reverse Michaelis-Menten kinetics are two popular mathematical formulations used in many land biogeochemical models to describe how microbes and plants would...
Uso de equações lineares na determinação dos parâmetros de Michaelis-Menten
Carvalho,Nakédia M. F.; Pires, Bianca M.; Antunes,Octavio A. C.; Roberto B Faria; Osório,Renata E. H. M. B.; Piovezan, Clovis; Neves,Ademir
2010-01-01
The Michaelis-Menten equation is used in many biochemical and bioinorganic kinetic studies involving homogeneous catalysis. Otherwise, it is known that determination of Michaelis-Menten parameters K M, Vmax, and k cat by the well-known Lineweaver-Burk double reciprocal linear equation does not produce the best values for these parameters. In this paper we present a discussion on different linear equations which can be used to calculate these parameters and we compare their results with the va...
Stochastic mapping of the Michaelis-Menten mechanism.
Dóka, Éva; Lente, Gábor
2012-02-07
The Michaelis-Menten mechanism is an extremely important tool for understanding enzyme-catalyzed transformation of substrates into final products. In this work, a computationally viable, full stochastic description of the Michaelis-Menten kinetic scheme is introduced based on a stochastic equivalent of the steady-state assumption. The full solution derived is free of restrictions on amounts of substance or parameter values and is used to create stochastic maps of the Michaelis-Menten mechanism, which show the regions in the parameter space of the scheme where the use of the stochastic kinetic approach is inevitable. The stochastic aspects of recently published examples of single-enzyme kinetic studies are analyzed using these maps.
Role of substrate unbinding in Michaelis-Menten enzymatic reactions.
Reuveni, Shlomi; Urbakh, Michael; Klafter, Joseph
2014-03-25
The Michaelis-Menten equation provides a hundred-year-old prediction by which any increase in the rate of substrate unbinding will decrease the rate of enzymatic turnover. Surprisingly, this prediction was never tested experimentally nor was it scrutinized using modern theoretical tools. Here we show that unbinding may also speed up enzymatic turnover--turning a spotlight to the fact that its actual role in enzymatic catalysis remains to be determined experimentally. Analytically constructing the unbinding phase space, we identify four distinct categories of unbinding: inhibitory, excitatory, superexcitatory, and restorative. A transition in which the effect of unbinding changes from inhibitory to excitatory as substrate concentrations increase, and an overlooked tradeoff between the speed and efficiency of enzymatic reactions, are naturally unveiled as a result. The theory presented herein motivates, and allows the interpretation of, groundbreaking experiments in which existing single-molecule manipulation techniques will be adapted for the purpose of measuring enzymatic turnover under a controlled variation of unbinding rates. As we hereby show, these experiments will not only shed first light on the role of unbinding but will also allow one to determine the time distribution required for the completion of the catalytic step in isolation from the rest of the enzymatic turnover cycle.
Mechanistic interpretation of conventional Michaelis-Menten parameters in a transporter system.
Vivian, Diana; Polli, James E
2014-11-20
The aim was to elucidate how steps in drug translocation by a solute carrier transporter impact Michaelis-Menten parameters Km, Ki, and Vmax. The first objective was to derive a model for carrier-mediated substrate translocation and perform sensitivity analysis with regard to the impact of individual microrate constants on Km, Ki, and Vmax. The second objective was to compare underpinning microrate constants between compounds translocated by the same transporter. Equations for Km, Ki, and Vmax were derived from a six-state model involving unidirectional transporter flipping and reconfiguration. This unidirectional model is applicable to co-transporter type solute carriers, like the apical sodium-dependent bile acid transporter (ASBT) and the proton-coupled peptide cotransporter (PEPT1). Sensitivity analysis identified the microrate constants that impacted Km, Ki, and Vmax. Compound comparison using the six-state model employed regression to identify microrate constant values that can explain observed Km and Vmax values. Results yielded some expected findings, as well as some unanticipated effects of microrate constants on Km, Ki, and Vmax. Km and Ki were found to be equal for inhibitors that are also substrates. Additionally, microrate constant values for certain steps in transporter functioning influenced Km and Vmax to be low or high. Copyright © 2014 Elsevier B.V. All rights reserved.
Oscillatory enzyme reactions and Michaelis-Menten kinetics.
Goldbeter, Albert
2013-09-02
Oscillations occur in a number of enzymatic systems as a result of feedback regulation. How Michaelis-Menten kinetics influences oscillatory behavior in enzyme systems is investigated in models for oscillations in the activity of phosphofructokinase (PFK) in glycolysis and of cyclin-dependent kinases in the cell cycle. The model for the PFK reaction is based on a product-activated allosteric enzyme reaction coupled to enzymatic degradation of the reaction product. The Michaelian nature of the product decay term markedly influences the period, amplitude and waveform of the oscillations. Likewise, a model for oscillations of Cdc2 kinase in embryonic cell cycles based on Michaelis-Menten phosphorylation-dephosphorylation kinetics shows that the occurrence and amplitude of the oscillations strongly depend on the ultrasensitivity of the enzymatic cascade that controls the activity of the cyclin-dependent kinase. Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.
Design issues for the Michaelis-Menten model.
López-Fidalgo, J; Wong, Weng Kee
2002-03-07
We discuss design issues for the Michaelis-Menten model and use geometrical arguments to find optimal designs for estimating a subset of the model parameters, or a linear combination of the parameters. We propose multiple-objective optimal designs when the parameters have different levels of interest to the researcher. In addition, we compare six commonly used sequence designs in the biological sciences for estimating parameters and, propose optimal choices for the parameters for geometric designs using closed-form efficiency formulas.
Robust and efficient designs for the Michaelis-Menten model
Dette, Holger; Biedermann, Stefanie
2002-01-01
For the Michaelis-Menten model, we determine designs that maximize the minimum of the D-efficiencies over a certain interval for the nonlinear parameter. The best two point designs can be found explicitly, and a characterization is given when these designs are optimal within the class of all designs. In most cases of practical interest, the determined designs are highly efficient and robust with respect to misspecification of the nonlinear parameter. The results are illustrated and applied in...
Optimal designs for the Michaelis Menten model with correlated observations
Dette, Holger; Kunert, Joachim
2012-01-01
In this paper we investigate the problem of designing experiments for weighted least squares analysis in the Michaelis Menten model. We study the structure of exact D-optimal designs in a model with an autoregressive error structure. Explicit results for locally D-optimal are derived for the case where 2 observations can be taken per subject. Additionally standardized maximin D-optimal designs are obtained in this case. The results illustrate the enormous difficulties to find e...
Optimal design for goodness-of-fit of the Michaelis-Menten enzyme kinetic function
Wong, Weng Kee; Melas, Viatcheslav B.; Dette, Holger
2004-01-01
We construct efficient designs for the Michaelis-Menten enzyme kinetic model capable of checking model assumption. An extended model, called EMAX model is also considered for this purpose. This model is widely used in pharmacokinetics and reduces to the Michaelis- Menten model for a specific choice of the parameter setting. Our strategy is to find efficient designs for estimating the parameters in the EMAX model and at the same time test the validity of the Michaelis-Menten model against the ...
Determination of individual cell Michaelis-Menten constants.
Sunray, Merav; Zurgil, Naomi; Shafran, Yana; Deutsch, Mordechai
2002-01-01
A novel methodology for the measurement and analysis of apparent K(M) (Michaelis-Menten constant) and V(MAX) values of individual cells is suggested. It is based on a mathematical model that considers substrate influx into the cell, its intracellular enzymatic hydrolysis, and the product efflux. The mathematical formulation was approximated linearly in order to analyze intracellular substrate conversion characteristics via Michaelis-Menten theory. Utilizing static cytometry, the time dependence of the fluorescence intensity [FI(t)] emitted from prelocalized and defined FDA stained cells was recorded. This required frequent periodical measurements of the same cells, which are sequentially exposed to various fluorogenic substrate concentrations. Model simulations correlated with experimental results. Differences in distributions of individual K(M) and V(MAX) values of cells incubated with and without PHA were evident. Average K(M) and V(MAX) values of PHA-stimulated cells increased by 99% and 540%, respectively. This study may provide a tool for assessing intracellular enzymatic activity in individual intact cells under defined physiologic conditions. This may open new vistas in various areas, giving answers to critical questions arising in the field of cell and developmental biology, immunology, oncology, and pharmacology. Copyright 2001 Wiley-Liss, Inc.
Michaelis-Menten kinetics of stiripentol in normal humans.
Levy, R H; Loiseau, P; Guyot, M; Blehaut, H M; Tor, J; Moreland, T A
1984-08-01
Michaelis-Menten kinetic parameters for stiripentol, and anticonvulsant, were assessed in six normal volunteers. Stiripentol was administered orally three times a day in dosage increments of 600, 1,200, and 1,800 mg/day for consecutive periods of 3, 4, and 7 days, respectively. Stiripentol steady-state levels at the three dosing rates increased more than proportionally with dose. The mean +/- SD oral clearance of stiripentol at 600 mg/day (1,090 +/- 624 L/day) was significantly greater (p less than 0.01) than at 1,200 (506 +/- 219 L/day) or 1,800 (405 +/- 151 L/day) mg/day. Average steady-state concentrations predicted from individually determined Vm and Km parameters were in good agreement with experimentally observed levels, indicating that the kinetics of stiripentol are of the Michaelis-Menten type. The mean Vm, Km, and Vm/Km ratio were 2,299 +/- 490 mg/day, 2.20 +/- 1.28 mg/L, and 1,241 +/- 837 L/day, respectively. Neuropsychological tests carried out before and after 14 days of stiripentol treatment showed a significant decline in verbal learning ability (p = 0.038) and a significant improvement in a test of memory and attention (p less than 0.01).
廖飞; 杨晓; 周岐新; 曾昭淳; 左渝萍
2003-01-01
Objective: To investigate the reliability for fast estimation of Michaelis-Menten constant (Km) with calibrated specific activity at only two medium concentrations of substrate by both simulation and experimentation with arylesterase (ArE)as model. Methods: Initial rates were simulated by randomly inserting uniform absolute error, and the experimental initial rates of ArE were determined by measuring the increaser of product absorbance. Calibrated specific activities at two substrate concentrations were obtained by regression analysis, and Km was calculated according to Michaelis-Menten equation. Results: By simulation with calibrated specific activities at two medium substrate concentrations, Km could be calculated according to Michaelis-Menten equation with reasonable precision and accuracy. By experimentation with substrates of 2-naphthyl acetate, phenyl acetate, and p-nitrophenyl acetate, there were no differences between the mean and SD of Km of ArE for either substrate by this linear kinetic method and the Lineweaver-Burk plot. Conclusion: This linear kinetic method was reliable for fast estimation of the Km of some specified enzyme on its substrate of lower solubility or lower sensitivity for quantification by common methods.
Explicit reformulations of time-dependent solution for a Michaelis-Menten enzyme reaction model.
Golicnik, Marko
2010-11-01
The exact closed-form solution to the Michaelis-Menten equation is expressed in terms of the Lambert W(x) function. However, the utility of this solution is limited because the W(x) function is not widely available in curve-fitting software. Based on various approximations to the W(x) function, different explicit equations expressed in terms of the elementary functions are proposed here as useful shortcuts to fit time depletion of substrate concentration directly to progress curves using commonly available nonlinear regression computer programs. The results are compared with those obtained by fitting other algebraic equations that have been proposed previously in the literature. 2010 Elsevier Inc. All rights reserved.
Stochastic Total Quasi-Steady-State Approximation for the Michaelis-Menten Scheme
Galstyan, Vahe
2015-01-01
In biochemical systems the Michaelis-Menten (MM) scheme is one of the best-known models of the enzyme- catalyzed kinetics. In the academic literature the MM approximation has been thoroughly studied in the context of differential equation models. At the level of the cell, however, molecular fluctuations have many important consequences, and thus, a stochastic investigation of the MM scheme is often necessary. In their work Barik et al. [Biophysical Journal, 95, 3563-3574, (2008)] presented a stochastic approximation of the MM scheme. They suggested a substitution of the propensity function in the reduced master equation with the total quasi-steady- state approximation (tQSSA) rate. The justification of the substitution, however, was provided for a special case only and did not cover the whole parameter domain of the tQSSA. In this manuscript we present a derivation of the stochastic tQSSA that is valid for the entire tQSSA parameter domain.
Analysis of noise-induced bistability in Michaelis Menten single-step enzymatic cycle
Remondini, Daniel; Bazzani, Armando; Castellani, Gastone; Maritan, Amos
2011-01-01
In this paper we study noise-induced bistability in a specific circuit with many biological implications, namely a single-step enzymatic cycle described by Michaelis Menten equations with quasi-steady state assumption. We study the system both with a Master Equation formalism, and with the Fokker-Planck continuous approximation, characterizing the conditions in which the continuous approach is a good approximation of the exact discrete model. An analysis of the stationary distribution in both cases shows that bimodality can not occur in such a system. We discuss which additional requirements can generate stochastic bimodality, by coupling the system with a chemical reaction involving enzyme production and turnover. This extended system shows a bistable behaviour only in specific parameter windows depending on the number of molecules involved, providing hints about which should be a feasible system size in order that such a phenomenon could be exploited in real biological systems.
Non-Michaelis-Menten kinetics in cytochrome P450-catalyzed reactions.
Atkins, William M
2005-01-01
The cytochrome P450 monooxygenases (CYPs) are the dominant enzyme system responsible for xenobiotic detoxification and drug metabolism. Several CYP isoforms exhibit non-Michaelis-Menten, or "atypical," steady state kinetic patterns. The allosteric kinetics confound prediction of drug metabolism and drug-drug interactions, and they challenge the theoretical paradigms of allosterism. Both homotropic and heterotropic ligand effects are now widely documented. It is becoming apparent that multiple ligands can simultaneously bind within the active sites of individual CYPs, and the kinetic parameters change with ligand occupancy. In fact, the functional effect of any specific ligand as an activator or inhibitor can be substrate dependent. Divergent approaches, including kinetic modeling and X-ray crystallography, are providing new information about how multiple ligand binding yields complex CYP kinetics.
Thiopentone elimination in newborn infants: exploring Michaelis-Menten kinetics.
Larsson, P; Anderson, B J; Norman, E; Westrin, P; Fellman, V
2011-04-01
Thiopentone elimination has been described using Michaelis-Menten pharmacokinetics in adults after prolonged infusion or overdose, but there are few reports of elimination in neonates. Time-concentration profiles for neonates (n=37) given single-dose thiopentone were examined using both first-order (constant clearance) and mixed-order (Michaelis-Menten) elimination processes using nonlinear mixed effects models. These profiles included a 33-week post-menstrual age (PMA) neonate given an overdose. A two-compartment mamillary model was used to fit data. Parameter estimates were standardized to a 70 kg person using allometric models. There were 197 observations available for analysis from neonates with a mean post-menstrual age of 35 (SD 4.5) weeks and a mean weight of 2.5 (SD 0.9) kg. They were given a mean thiopentone dose of 3 (SD 0.4) mg/kg as a rapid bolus. Clearance at 26 weeks PMA was 0.015 l/min/70 kg and increased to 0.119 l/min/70 kg by 42 weeks PMA. The maximum rate of elimination (V(max)) at 26 weeks PMA was 0.22 mg/min/70 kg and increased to 4.13 mg/min/70 kg by 42 weeks PMA. These parameter estimates are approximately 40% adult values at term gestation. The Michaelis constant (K(m)) was 28.3 [between subject variability (BSV) 46.4%, 95% confidence interval (CI) 4.49-99.2] mg/l; intercompartment clearance was 0.44 (BSV 97.5%, 95% CI 0.27-0.63) l/min/70 kg; central volume of distribution was 46.4 (BSV 29.2%, 95% CI 41.7-59.8) l/70 kg; peripheral volume of distribution was 95.7 (BSV 70.3%, 95% CI 61.3-128) l/70 kg. Both first-order and mixed-order processes satisfactorily described elimination. First-order elimination adequately described the time-concentration profile in the premature neonate given an overdose. Clearance is immature in the pre-term neonate although there is rapid maturation around 40 weeks PMA, irrespective of post-natal age. © 2011 The Authors. Acta Anaesthesiologica Scandinavica © 2011 The Acta Anaesthesiologica Scandinavica Foundation.
Time-dependent corrections to effective rate and event statistics in Michaelis-Menten kinetics
Sinitsyn, N. A.; Nemenman, I.
2010-01-01
We generalize the concept of the geometric phase in stochastic kinetics to a noncyclic evolution. Its application is demonstrated on kinetics of the Michaelis-Menten reaction. It is shown that the nonperiodic geometric phase is responsible for the correction to the Michaelis-Menten law when parameters, such as a substrate concentration, are changing with time. We apply these ideas to a model of chemical reactions in a bacterial culture of a growing size, where the geometric correction qualita...
Relation between pulmonary clearance and particle burden: a Michaelis-Menten-like kinetic model.
Yu, R. C.; Rappaport, S.M.
1996-01-01
OBJECTIVES: To test the validity of a Michaelis-Menten-like kinetic model of pulmonary clearance of insoluble dusts. METHODS: Data were investigated from studies of pulmonary clearance in F344 rats exposed to antimony trioxide (Sb2O3), photocopy test toner, polyvinyl chloride powder (PVC), and diesel exhaust particles. The Michaelis-Menten-like model was used to develop a relation in which the pulmonary clearance half time was a linear function of lung burden. After combining all data, linear...
Extending the kinetic solution of the classic Michaelis-Menten model of enzyme action
BISPO, Jose Ailton Conceicao; Bonafe, Carlos Francisco Sampaio; SOUZA, Volnei Brito de; SILVA, Joao Batista de Almeida e; CARVALHO, Giovani Brandao Mafra de
2011-01-01
The principal aim of studies of enzyme-mediated reactions has been to provide comparative and quantitative information on enzyme-catalyzed reactions under distinct conditions. The classic Michaelis-Menten model (Biochem Zeit 49:333, 1913) for enzyme kinetic has been widely used to determine important parameters involved in enzyme catalysis, particularly the Michaelis-Menten constant (K (M) ) and the maximum velocity of reaction (V (max) ). Subsequently, a detailed treatment of the mechanisms ...
Kosmidis, Kosmas; Karalis, Vangelis; Argyrakis, Panos; Macheras, Panos
2004-09-01
Two different approaches were used to study the kinetics of the enzymatic reaction under heterogeneous conditions to interpret the unusual nonlinear pharmacokinetics of mibefradil. Firstly, a detailed model based on the kinetic differential equations is proposed to study the enzymatic reaction under spatial constraints and in vivo conditions. Secondly, Monte Carlo simulations of the enzyme reaction in a two-dimensional square lattice, placing special emphasis on the input and output of the substrate were applied to mimic in vivo conditions. Both the mathematical model and the Monte Carlo simulations for the enzymatic reaction reproduced the classical Michaelis-Menten (MM) kinetics in homogeneous media and unusual kinetics in fractal media. Based on these findings, a time-dependent version of the classic MM equation was developed for the rate of change of the substrate concentration in disordered media and was successfully used to describe the experimental plasma concentration-time data of mibefradil and derive estimates for the model parameters. The unusual nonlinear pharmacokinetics of mibefradil originates from the heterogeneous conditions in the reaction space of the enzymatic reaction. The modified MM equation can describe the pharmacokinetics of mibefradil as it is able to capture the heterogeneity of the enzymatic reaction in disordered media.
Chaudhury, Srabanti; Cherayil, Binny J
2007-09-14
Single-molecule equations for the Michaelis-Menten [Biochem. Z. 49, 333 (1913)] mechanism of enzyme action are analyzed within the Wilemski-Fixman [J. Chem. Phys. 58, 4009 (1973); 60, 866 (1974)] approximation after the effects of dynamic disorder--modeled by the anomalous diffusion of a particle in a harmonic well--are incorporated into the catalytic step of the reaction. The solution of the Michaelis-Menten equations is used to calculate the distribution of waiting times between successive catalytic turnovers in the enzyme beta-galactosidase. The calculated distribution is found to agree qualitatively with experimental results on this enzyme obtained at four different substrate concentrations. The calculations are also consistent with measurements of correlations in the fluctuations of the fluorescent light emitted during the course of catalysis, and with measurements of the concentration dependence of the randomness parameter.
André Rosa Martins
2014-11-01
Full Text Available The enzymatic processes according Michaelis-Menten kinetics have been studied from various approaches to describe the inhibition state. Proposals for inhibition were compared from a generic process, where kinetic constants have received unitary values, and the numeric value of the concentration of substrate was ten (10 times higher than the numerical value of the concentration of enzyme. For each inhibition model proposed, numerical solutions were obtained from nonlinear system of ordinary differential equations, generating results presents by graphs showing the variation of the enzyme and enzyme complexes, also the variation of substrate and product of the reaction. Also, was designed a model with performance, indicating similar behavior to that seen in the Michaelis-Menten kinetics, where complex of reaction is rapidly formed and throughout the process, tends to decay to zero. Thus, in this new proposed model, the effect of inhibition starts at zero and, throughout the process, tends to the nominal value of the initial enzyme concentration. Such responses have proved to be valid for different values of enzyme concentration and process time, showing robustness. The proposed model was applied to the hydrolysis of disaccharides, providing a setting with conservation of mass of the model at the end of the process regarding the responses of the carbohydrate concentration.
The original Michaelis constant: translation of the 1913 Michaelis-Menten paper.
Michaelis, Leonor; Menten, Maud Leonora; Johnson, Kenneth A; Goody, Roger S
2011-10-04
Nearly 100 years ago Michaelis and Menten published their now classic paper [Michaelis, L., and Menten, M. L. (1913) Die Kinetik der Invertinwirkung. Biochem. Z. 49, 333-369] in which they showed that the rate of an enzyme-catalyzed reaction is proportional to the concentration of the enzyme-substrate complex predicted by the Michaelis-Menten equation. Because the original text was written in German yet is often quoted by English-speaking authors, we undertook a complete translation of the 1913 publication, which we provide as Supporting Information . Here we introduce the translation, describe the historical context of the work, and show a new analysis of the original data. In doing so, we uncovered several surprises that reveal an interesting glimpse into the early history of enzymology. In particular, our reanalysis of Michaelis and Menten's data using modern computational methods revealed an unanticipated rigor and precision in the original publication and uncovered a sophisticated, comprehensive analysis that has been overlooked in the century since their work was published. Michaelis and Menten not only analyzed initial velocity measurements but also fit their full time course data to the integrated form of the rate equations, including product inhibition, and derived a single global constant to represent all of their data. That constant was not the Michaelis constant, but rather V(max)/K(m), the specificity constant times the enzyme concentration (k(cat)/K(m) × E(0)).
Accuracy of the Michaelis-Menten approximation when analysing effects of molecular noise.
Lawson, Michael J; Petzold, Linda; Hellander, Andreas
2015-05-06
Quantitative biology relies on the construction of accurate mathematical models, yet the effectiveness of these models is often predicated on making simplifying approximations that allow for direct comparisons with available experimental data. The Michaelis-Menten (MM) approximation is widely used in both deterministic and discrete stochastic models of intracellular reaction networks, owing to the ubiquity of enzymatic activity in cellular processes and the clear biochemical interpretation of its parameters. However, it is not well understood how the approximation applies to the discrete stochastic case or how it extends to spatially inhomogeneous systems. We study the behaviour of the discrete stochastic MM approximation as a function of system size and show that significant errors can occur for small volumes, in comparison with a corresponding mass-action system. We then explore some consequences of these results for quantitative modelling. One consequence is that fluctuation-induced sensitivity, or stochastic focusing, can become highly exaggerated in models that make use of MM kinetics even if the approximations are excellent in a deterministic model. Another consequence is that spatial stochastic simulations based on the reaction-diffusion master equation can become highly inaccurate if the model contains MM terms. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
eduction for Michaelis-Menten-Henri kinetics in the presence of diffusion
Leonid V. Kalachev
2007-05-01
Full Text Available The Michaelis-Menten-Henri (MMH mechanism is one of the paradigm reaction mechanisms in biology and chemistry. In its simplest form, it involves a substrate that reacts (reversibly with an enzyme, forming a complex which is transformed (irreversibly into a product and the enzyme. Given these basic kinetics, a dimension reduction has traditionally been achieved in two steps, by using conservation relations to reduce the number of species and by exploiting the inherent fast-slow structure of the resulting equations. In the present article, we investigate how the dynamics change if the species are additionally allowed to diffuse. We study the two extreme regimes of large diffusivities and of small diffusivities, as well as an intermediate regime in which the time scale of diffusion is comparable to that of the fast reaction kinetics. We show that reduction is possible in each of these regimes, with the nature of the reduction being regime dependent. Our analysis relies on the classical method of matched asymptotic expansions to derive approximations for the solutions that are uniformly valid in space and time.
Burchardt, Malte; Träuble, Markus; Wittstock, Gunther
2009-06-15
The formalism for simulating scanning electrochemical microscopy (SECM) experiments by boundary element methods in three space coordinates has been extended to allow consideration of nonlinear boundary conditions. This is achieved by iteratively refining the boundary conditions that are encoded in a boundary condition matrix. As an example, the simulations are compared to experimental approach curves in the SECM feedback mode toward samples modified with glucose oxidase (GOx). The GOx layer was prepared by the layer-by-layer assembly of polyelectrolytes using glucose oxidase as one of the polyelectrolytes. The comparison of the simulated and experimental curves showed that under a wide range of experimentally accessible conditions approximations of the kinetics at the sample by first order models yield misleading results. The approach curves differ also qualitatively from curves calculated with first order models. As a consequence, this may lead to severe deviations when such curves are fitted to first order kinetic models. The use of linear approximations to describe the enzymatic reaction in SECM feedback experiments is justified only if the ratio of the mediator and Michaelis-Menten constant is equal to or smaller than 0.1 (deviation less than 10%).
Time-dependent corrections to effective rate and event statistics in Michaelis-Menten kinetics.
Sinitsyn, N A; Nemenman, I
2010-11-01
The authors generalise the concept of the geometric phase in stochastic kinetics to a non-cyclic evolution. Its application is demonstrated on kinetics of the Michaelis-Menten reaction. It is shown that the non-periodic geometric phase is responsible for the correction to the Michaelis-Menten law when parameters, such as a substrate concentration, are changing with time. The authors apply these ideas to a model of chemical reactions in a bacterial culture of a growing size, where the geometric correction qualitatively changes the outcome of the reaction kinetics.
Pereira, Félix Monteiro; Oliveira, Samuel Conceição
2016-11-01
In this article, the occurrence of dead core in catalytic particles containing immobilized enzymes is analyzed for the Michaelis-Menten kinetics. An assessment of numerical methods is performed to solve the boundary value problem generated by the mathematical modeling of diffusion and reaction processes under steady state and isothermal conditions. Two classes of numerical methods were employed: shooting and collocation. The shooting method used the ode function from Scilab software. The collocation methods included: that implemented by the bvode function of Scilab, the orthogonal collocation, and the orthogonal collocation on finite elements. The methods were validated for simplified forms of the Michaelis-Menten equation (zero-order and first-order kinetics), for which analytical solutions are available. Among the methods covered in this article, the orthogonal collocation on finite elements proved to be the most robust and efficient method to solve the boundary value problem concerning Michaelis-Menten kinetics. For this enzyme kinetics, it was found that the dead core can occur when verified certain conditions of diffusion-reaction within the catalytic particle. The application of the concepts and methods presented in this study will allow for a more generalized analysis and more accurate designs of heterogeneous enzymatic reactors.
Reduction for Michaelis-Menten-Henri kinetics in the presence of diffusion.
Kalachev, L.V.; Kaper, H.G.; Kaper, T.J.; Popovic, N.; Zagaris, A.
2007-01-01
Abstract: The Michaelis-Menten-Henri (MMH) mechanism is one of the paradigm reaction mechanisms in biology and chemistry. In its simplest form, it involves a substrate that reacts (reversibly) with an enzyme, forming a complex which is transformed (irreversibly) into a product and the enzyme. Given
Reduction for Michaelis-Menten-Henri kinetics in the presence of diffusion
A. Zagaris (Antonios); L.V. Kalachev; H.G. Kaper; T.J. Kaper (Tasso Joost); N. Popovic
2007-01-01
textabstractThe Michaelis-Menten-Henri (MMH) mechanism is one of the paradigm reaction mechanisms in biology and chemistry. In its simplest form, it involves a substrate that reacts (reversibly) with an enzyme, forming a complex which is transformed (irreversibly) into a product and the enzyme.
A Simple Classroom Teaching Technique to Help Students Understand Michaelis-Menten Kinetics
Runge, Steven W.; Hill, Brent J. F.; Moran, William M.
2006-01-01
A new, simple classroom technique helps cell biology students understand principles of Michaelis-Menten enzyme kinetics. A student mimics the enzyme and the student's hand represents the enzyme's active site. The catalytic event is the transfer of marbles (substrate molecules) by hand from one plastic container to another. As predicted, increases…
A two-substrate Michaelis-Menten model for the growth of self-replicating polymers.
Ferreira, R
1987-10-07
A two-substrate Michaelis-Menten model is proposed for the growth of autocatalytic self-replicating polymers. Selective growth depends on the existence of two complementary pairs of monomers. Discrimination among sequences results from different products of binding constants, KCGnKAUm. The results support an earlier renormalization group treatment (Ferreira & Tsallis, 1985).
A Simple Classroom Teaching Technique to Help Students Understand Michaelis-Menten Kinetics
Runge, Steven W.; Hill, Brent J. F.; Moran, William M.
2006-01-01
A new, simple classroom technique helps cell biology students understand principles of Michaelis-Menten enzyme kinetics. A student mimics the enzyme and the student's hand represents the enzyme's active site. The catalytic event is the transfer of marbles (substrate molecules) by hand from one plastic container to another. As predicted, increases…
Goličnik, Marko
2011-09-01
The exact closed-form solutions to the integrated rate equations for one-compartment pharmacokinetic models that obey Michaelis-Menten elimination kinetics were derived recently (Tang and Xiao in J Pharmacokin Pharmacodyn 34:807-827, 2007). These solutions are expressed in terms of the Lambert W(x)-omega function; however, unfortunately, most of the available computer programs are not set up to handle equations that involve the W(x) function. Therefore, in this article, I provide alternative explicit analytical equations expressed in terms of elementary mathematical functions that accurately approximate exact solutions and can be simply calculated using any optional standard software.
A Squared Michaelis-Menten Function of Substrate Concentration for Plant Mitochondrial Respiration 1
James, Alan T.; Wiskich, Joseph T.; Dry, Ian B.
1990-01-01
Dry and Wiskich ([1987] Arch Biochem Biophys 257: 92-99) have published data showing the response of plant mitochondrial respiration to increasing additions of oxaloacetate or malate when these substrates have been depleted by inhibition of succinate dehydrogenase by malonate, and coenzyme A (CoA) has been sequestered as acetyl-CoA by pyruvate dehydrogenase. In the presence of 2-oxoglutarate, it is shown that the response is given by a Michaelis-Menten curve, but in its absence, when malate has to supply substrate for dehydrogenation as well as to liberate CoA via malate dehydrogenase and citrate synthase, the response is presumably the product of two Michaelis-Menten functions, which can be approximated by the square of a single function. PMID:16667257
Wenzhen Gan
2013-01-01
Full Text Available This paper is concerned with the asymptotical behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition. By taking food ingestion and species' moving into account, the model is further coupled with Michaelis-Menten type functional response and nonlocal delay. Sufficient conditions are derived for the global stability of the positive steady state and the semitrivial steady state of the proposed problem by using the Lyapunov functional. Our results show that intraspecific competition benefits the coexistence of prey and predator. Furthermore, the introduction of Michaelis-Menten type functional response positively affects the coexistence of prey and predator, and the nonlocal delay is harmless for stabilities of all nonnegative steady states of the system. Numerical simulations are carried out to illustrate the main results.
Global stability of enzymatic chains of full reversible Michaelis-Menten reactions.
Belgacem, Ismail; Gouzé, Jean-Luc
2013-09-01
We consider a chain of metabolic reactions catalyzed by enzymes, of reversible Michaelis-Menten type with full dynamics, i.e. not reduced with any quasi-steady state approximations. We study the corresponding dynamical system and show its global stability if the equilibrium exists. If the system is open, the equilibrium may not exist. The main tool is monotone systems theory. Finally we study the implications of these results for the study of coupled genetic-metabolic systems.
Robustness of optimal designs for the Michaelis-Menten model under a variation of criteria
Dette, Holger; Kiss, Christine; Wong, Weng Kee
2009-01-01
The Michaelis-Menten model has and continues to be one of the most widely used models in many diverse fields. In the biomedical sciences, the model continues to be ubiquitous in biochemistry, enzyme kinetics studies, nutrition science and in the pharmaceutical sciences. Despite its wide ranging applications across disciplines, design issues for this model are given short shrift. This paper focuses on design issues and provides a variety of optimal designs of this model. In addition, we ...
Wenzhen Gan; Canrong Tian; Qunying Zhang; Zhigui Lin
2013-01-01
This paper is concerned with the asymptotical behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition. By taking food ingestion and species' moving into account, the model is further coupled with Michaelis-Menten type functional response and nonlocal delay. Sufficient conditions are derived for the global stability of the positive steady state and the semitrivial steady state of the proposed problem by using the Lyapunov functional. Our results show...
Optimal Designs for Discriminating Between some Extensions of the Michaelis-Menten Model
Jesus Lopez Fidalgo; Chiara Tommasi; Camelia Trandafir
2005-01-01
In this paper some results on the problem of computing optimal designs for discriminating between rival models are provided. Using T-optimality for two rival models a compound criterion is developed to discriminate between more than two models. Surprising results arise when T-optimal designs are compared with classical c-optimal designs for nonlinear models. In particular, some practical deviations of the Michaelis-Menten model are considered in order to measure and compare efficiencies of di...
Tang, Sanyi; Xiao, Yanni
2007-12-01
The purpose of this article is to provide the analytical solutions of one-compartment models with Michaelis-Menten elimination kinetics for three different inputs (single intravenous dose, multiple-dose bolus injection and constant). All analytical solutions obtained in present paper can be described by the well defined Lambert W function which can be easily implemented in most mathematical softwares such as Matlab and Maple. These results will play an important role in fitting the Michaelis-Menten parameters and in designing a dosing regimen to maintain steady-state plasma concentrations. In particular, the analytical periodic solution for multi-dose inputs is also given, and we note that the maximum and minimum values of the periodic solution depends on the Michaelis-Menten parameters, dose and time interval of drug administration. In practice, it is important to maintain a concentration above the minimum therapeutic level at all times without exceeding the minimum toxic concentration. Therefore, the one-compartment model with therapeutic window is proposed, and further the existence of periodic solution, analytical expression and its period are analyzed. The analytical formula of period plays a key role in designing a dose regimen to maintain the plasma concentration within a specified range over long periods of therapy. Finally, the completely analytical solution for the constant input rate is derived and discussed which depends on the relations between constant input rate and maximum rate of change of concentration.
Widmer, L A; Stelling, J; Doyle, F J
2013-10-28
Using the (slow-scale) linear noise approximation, we give parameter-independent bounds to the substrate and product intrinsic noise variance for the stochastic Michaelis-Menten approximation at steady state.
无
2012-01-01
In this paper,the existence of eight periodic solutions to a Michaelis-Menten-type predator-prey system with delay and harvesting in patch environment is established using the analytical techniques and Mawhin's coincidence degree theory.
Single-molecule enzymology à la Michaelis-Menten.
Grima, Ramon; Walter, Nils G; Schnell, Santiago
2014-01-01
Over the past 100 years, deterministic rate equations have been successfully used to infer enzyme-catalysed reaction mechanisms and to estimate rate constants from reaction kinetics experiments conducted in vitro. In recent years, sophisticated experimental techniques have been developed that begin to allow the measurement of enzyme-catalysed and other biopolymer-mediated reactions inside single cells at the single-molecule level. Time-course data obtained using these methods are considerably noisy because molecule numbers within cells are typically quite small. As a consequence, the interpretation and analysis of single-cell data requires stochastic methods, rather than deterministic rate equations. Here, we concisely review both experimental and theoretical techniques that enable single-molecule analysis, with particular emphasis on the major developments in the field of theoretical stochastic enzyme kinetics, from its inception in the mid-20th century to its modern-day status. We discuss the differences between stochastic and deterministic rate equation models, how these depend on enzyme molecule numbers and substrate inflow into the reaction compartment, and how estimation of rate constants from single-cell data is possible using recently developed stochastic approaches. © 2013 FEBS.
Mafrica, Stefano; Godiot, Stéphanie; Menouni, Mohsine; Boyron, Marc; Expert, Fabien; Juston, Raphaël; Marchand, Nicolas; Ruffier, Franck; Viollet, Stéphane
2015-03-09
In this paper, we present: (i) a novel analog silicon retina featuring auto-adaptive pixels that obey the Michaelis-Menten law, i.e. V=V(m) I(n)/I(n)+σ(n); (ii) a method of characterizing silicon retinas, which makes it possible to accurately assess the pixels' response to transient luminous changes in a ±3-decade range, as well as changes in the initial steady-state intensity in a 7-decade range. The novel pixel, called M(2)APix, which stands for Michaelis-Menten Auto-Adaptive Pixel, can auto-adapt in a 7-decade range and responds appropriately to step changes up to ±3 decades in size without causing any saturation of the Very Large Scale Integration (VLSI) transistors. Thanks to the intrinsic properties of the Michaelis-Menten equation, the pixel output always remains within a constant limited voltage range. The range of the Analog to Digital Converter (ADC) was therefore adjusted so as to obtain a Least Significant Bit (LSB) voltage of 2.35mV and an effective resolution of about 9 bits. The results presented here show that the M(2)APix produced a quasi-linear contrast response once it had adapted to the average luminosity. Differently to what occurs in its biological counterparts, neither the sensitivity to changes in light nor the contrast response of the M(2)APix depend on the mean luminosity (i.e. the ambient lighting conditions). Lastly, a full comparison between the M(2)APix and the Delbrück auto-adaptive pixel is provided.
Bentz, Joe; Tran, Thuy Thanh; Polli, Joseph W; Ayrton, Andrew; Ellens, Harma
2005-10-01
Typically, the kinetics of membrane transport is analyzed using the steady-state Michaelis-Menten (or Eadie-Hofstee or Hanes) equations. This approach has been successful when the substrate is picked up from the aqueous phase, like a water-soluble enzyme, for which the Michaelis-Menten steady-state analysis was developed. For membrane transporters whose substrate resides in the lipid bilayer of the plasma membrane, like P-glycoprotein (P-gp), there has been no validation of the accuracy of the steady-state analysis because the elementary rate constants for transport were not known. Recently, we fitted the mass action elementary kinetic rate constants of P-gp transport of three different drugs through a confluent monolayer of MDCKII-hMDR1 cells. With these elementary rate constants in hand, we use computer simulations to assess the accuracy of the steady-state Michaelis-Menten parameters. This limits the simulation to parameter ranges known to be physiologically relevant. Using over 2,300 different vectors of initial elementary parameters spanning the space bounded by the three drugs, which defines 2,300 "virtual substrates", the concentrations of substrate transported were calculated and fitted to Eadie-Hofstee plots. Acceptable plots were obtained for 1,338 cases. The fitted steady-state Vmax values from the analysis correlated to within a factor of 2-3 with the values predicted from the elementary parameters. However, the fitted Km value could be generated by a wide range of underlying "molecular" Km values. This is because of the convolution of the drug passive permeability kinetics into the fitted Km. This implies that Km values measured in simpler systems, e.g., microsomes or proteoliposomes, even if accurate, would not predict the Km values for the confluent monolayer system or, by logical extension, in vivo. Reliable in vitro-in vivo extrapolation seems to require using the elementary rate constants rather than the Michaelis-Menten steady-state parameters.
Ochab-Marcinek, Anna
2010-04-21
The study of biochemical pathways usually focuses on a small section of a protein interactions network. Two distinct sources contribute to the noise in such a system: intrinsic noise, inherent in the studied reactions, and extrinsic noise generated in other parts of the network or in the environment. We study the effect of extrinsic noise entering the system through a nonlinear uptake reaction which acts as a nonlinear filter. Varying input noise intensity varies the mean of the noise after the passage through the filter, which changes the stability properties of the system. The steady-state displacement due to small noise is independent on the kinetics of the system but it only depends on the nonlinearity of the input function. For monotonically increasing and concave input functions such as the Michaelis-Menten uptake rate, we give a simple argument based on the small-noise expansion, which enables qualitative predictions of the steady-state displacement only by inspection of experimental data: when weak and rapid noise enters the system through a Michaelis-Menten reaction, then the graph of the system's steady states vs. the mean of the input signal always shifts to the right as noise intensity increases. We test the predictions on two models of lac operon, where TMG/lactose uptake is driven by a Michaelis-Menten enzymatic process. We show that as a consequence of the steady state displacement due to fluctuations in extracellular TMG/lactose concentration the lac switch responds in an asymmetric manner: as noise intensity increases, switching off lactose metabolism becomes easier and switching it on becomes more difficult. (c) 2009 Elsevier Ltd. All rights reserved.
Perturbation theory in the catalytic rate constant of the Henri-Michaelis-Menten enzymatic reaction.
Bakalis, Evangelos; Kosmas, Marios; Papamichael, Emmanouel M
2012-11-01
The Henry-Michaelis-Menten (HMM) mechanism of enzymatic reaction is studied by means of perturbation theory in the reaction rate constant k (2) of product formation. We present analytical solutions that provide the concentrations of the enzyme (E), the substrate (S), as well as those of the enzyme-substrate complex (C), and the product (P) as functions of time. For k (2) small compared to k (-1), we properly describe the entire enzymatic activity from the beginning of the reaction up to longer times without imposing extra conditions on the initial concentrations E ( o ) and S ( o ), which can be comparable or much different.
Michaelis-Menten speeds up tau-leaping under a wide range of conditions.
Wu, Sheng; Fu, Jin; Cao, Yang; Petzold, Linda
2011-04-07
This paper examines the benefits of Michaelis-Menten model reduction techniques in stochastic tau-leaping simulations. Results show that although the conditions for the validity of the reductions for tau-leaping remain the same as those for the stochastic simulation algorithm (SSA), the reductions result in a substantial speed-up for tau-leaping under a different range of conditions than they do for SSA. The reason of this discrepancy is that the time steps for SSA and for tau-leaping are determined by different properties of system dynamics.
Michaelis-Menten speeds up tau-leaping under a wide range of conditions
Wu, Sheng; Fu, Jin; Cao, Yang; Petzold, Linda
2011-04-01
This paper examines the benefits of Michaelis-Menten model reduction techniques in stochastic tau-leaping simulations. Results show that although the conditions for the validity of the reductions for tau-leaping remain the same as those for the stochastic simulation algorithm (SSA), the reductions result in a substantial speed-up for tau-leaping under a different range of conditions than they do for SSA. The reason of this discrepancy is that the time steps for SSA and for tau-leaping are determined by different properties of system dynamics.
Standardization of α-L-iduronidase enzyme assay with Michaelis-Menten kinetics.
Ou, Li; Herzog, Tyler L; Wilmot, Carrie M; Whitley, Chester B
2014-02-01
The lack of methodological uniformity in enzyme assays has been a long-standing difficulty, a problem for bench researchers, for the interpretation of clinical diagnostic tests, and an issue for investigational drug review. Illustrative of the problem, α-L-iduronidase enzyme catalytic activity is frequently measured with the substrate 4-methylumbelliferyl-α-L-iduronide (4MU-iduronide); however, final substrate concentrations used in different assays vary greatly, ranging from 25 μM to 1425 μM (Km ≈ 180 μM) making it difficult to compare results between laboratories. In this study, α-L-iduronidase was assayed with 15 different substrate concentrations. The resulting activity levels from the same specimens varied greatly with different substrate concentrations but, as a group, obeyed the expectations of Michaelis-Menten kinetics. Therefore, for the sake of improved comparability, it is proposed that α-L-iduronidase enzyme assays should be conducted either (1) under substrate saturating conditions; or (2) when concentrations are significantly below substrate saturation, with results standardized by arithmetic adjustment that considers Michaelis-Menten kinetics. The approach can be generalized to many other enzyme assays. Copyright © 2013 Elsevier Inc. All rights reserved.
A comparison of the parameter estimating procedures for the Michaelis-Menten model.
Tseng, S J; Hsu, J P
1990-08-23
The performance of four parameter estimating procedures for the estimation of the adjustable parameters in the Michaelis-Menten model, the maximum initial rate Vmax, and the Michaelis-Menten constant Km, including Lineweaver & Burk transformation (L-B), Eadie & Hofstee transformation (E-H), Eisenthal & Cornish-Bowden transformation (ECB), and Hsu & Tseng random search (H-T) is compared. The analysis of the simulated data reveals the followings: (i) Vmax can be estimated more precisely than Km. (ii) The sum of square errors, from the smallest to the largest, follows the sequence H-T, E-H, ECB, L-B. (iii) Considering the sum of square errors, relative error, and computing time, the overall performance follows the sequence H-T, L-B, E-H, ECB, from the best to the worst. (iv) The performance of E-H and ECB are on the same level. (v) L-B and E-H are appropriate for pricesly measured data. H-T should be adopted for data whose error level are high. (vi) Increasing the number of data points has a positive effect on the performance of H-T, and a negative effect on the performance of L-B, E-H, and ECB.
Bueno, Paulo R; Watanabe, Ailton M; Faria, Ronaldo C; Santos, Márcio L; Riccardi, Carla S
2010-12-16
A piezoelectric detection of enzyme-modified surface was performed under Michaelis-Menten presumptions of steady-state condition. The approach herein presented showed promise in the study of enzymatic kinetics by measuring the frequency changes associated with mass changes at the piezoelectric crystal surface. Likewise, real-time frequency shifts, that is, dΔf/dt, indicated the rate of products formation from enzymatic reaction. In this paper, acetylcholinesterase was used as the enzymatic model and acetylcholine as substrate. The enzymatic rate has its maximum value for a short time during the kinetic reaction, for instance, during the first ten minutes of the reaction time scale. The values found for the kinetic constant rate and Michaelis-Menten constant were (1.4 ± 0.8) 10(5) s(-1) and (5.2 ± 3) 10(-4) M, respectively, in agreement with the values found in classical Michaelis-Menten kinetic experiments.
Extended Parker-Sochacki method for Michaelis-Menten enzymatic reaction model.
Abdelrazik, Ismail M; Elkaranshawy, Hesham A
2016-03-01
In this article, a new approach--namely, the extended Parker-Sochacki method (EPSM)--is presented for solving the Michaelis-Menten nonlinear enzymatic reaction model. The Parker-Sochacki method (PSM) is combined with a new resummation method called the Sumudu-Padé resummation method to obtain approximate analytical solutions for the model. The obtained solutions by the proposed approach are compared with the solutions of PSM and the Runge-Kutta numerical method (RKM). The comparison proves the practicality, efficiency, and correctness of the presented approach. It serves as a basis for solving other nonlinear biochemical reaction models in the future. Copyright © 2015 Elsevier Inc. All rights reserved.
Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches.
Hadeler, Karl Peter
2013-01-01
The Michaelis-Menten (MM) function is a fractional linear function depending on two positive parameters. These can be estimated by nonlinear or linear least squares methods. The non-linear methods, based directly on the defect of the MM function, can fail and not produce any minimizer. The linear methods always produce a unique minimizer which, however, may not be positive. Here we give sufficient conditions on the data such that the nonlinear problem has at least one positive minimizer and also conditions for the minimizer of the linear problem to be positive. We discuss in detail the models and equilibrium relations of a classical operator-repressor system, and we extend our approach to the MM problem with leakage and to reversible MM kinetics. The arrangement of the sufficient conditions exhibits the important role of data that have a concavity property (chemically feasible data).
Reith, David; Medlicott, Natalie J; Kumara De Silva, Rohana; Yang, Lin; Hickling, Jeremy; Zacharias, Mathew
2009-01-01
1. The aim of the present study was to perform an in vivo estimation of the Michaelis-Menten constants of the major metabolic pathways of paracetamol (APAP). 2. A two-occasion, single-dose cross-over trial was performed using 60 and 90 mg/kg doses of APAP in healthy patients undergoing third molar dental extraction. Plasma samples were collected over 24 h and urine was collected for 8 h after dosing. Twenty patients were enrolled in the study and complete data for plasma and urine were available for both doses for 13 volunteers who were included in the analysis; seven of the volunteers were men, the median age (range) was 22 years (19-31) and the median weight (range) was 68 kg (50-86). 3. The mean (95% CI) k(m) for APAP glucuronidation was 6.89 mmol/L (3.57-10.22) and the V(max) was 0.97 mmol/h per kg (0.65-1.28). The k(m) for APAP sulphation was 0.097 mmol/L (0.041-0.152) and the V(max) was 0.011 mmol/h per kg (0.009-0.013). For the combined excretion of APAP-cysteine and APAP-mercapturate, the k(m) was 0.303 mmol/L (0.131-0.475) and the V(max) was 0.004 mmol/h per kg (0.002-0.005). 4. The estimates for in vivo Michaelis-Menten constants for APAP glucuronidation and sulphation were in the order of those reported previously using in vitro methods.
Coluzzi, Barbara; Bersani, Enrico
2016-01-01
We recall the perturbation expansion for Michaelis-Menten kinetics, beyond the standard quasi-steady-state approximation (sQSSA). Against this background, we are able to appropriately apply the alternative approach to the study of singularly perturbed differential equations that is based on the renormalization group (SPDERG), by clarifying similarities and differences. In the present demanding situation, we directly renormalize the bare initial condition value for the substrate. Our main results are: i) the 2nd order SPDERG uniform approximations to the correct solutions contain, up to 1st order, the same outer components as the known perturbation expansion ones; ii) the differential equation to be solved for the derivation of the 1st order outer substrate component is simpler within the SPDERG approach; iii) the approximations better reproduce the numerical solutions of the original problem in a region encompassing the matching one, because of the 2nd order terms in the inner components, calculated here for ...
Moffitt, Jeffrey R; Bustamante, Carlos
2014-01-01
Enzyme-catalyzed reactions are naturally stochastic, and precision measurements of these fluctuations, made possible by single-molecule methods, promise to provide fundamentally new constraints on the possible mechanisms underlying these reactions. We review some aspects of statistical kinetics: a new field with the goal of extracting mechanistic information from statistical measures of fluctuations in chemical reactions. We focus on a widespread and important statistical measure known as the randomness parameter. This parameter is remarkably simple in that it is the squared coefficient of variation of the cycle completion times, although it places significant limits on the minimal complexity of possible enzymatic mechanisms. Recently, a general expression has been introduced for the substrate dependence of the randomness parameter that is for rate fluctuations what the Michaelis-Menten expression is for the mean rate of product generation. We discuss the information provided by the new kinetic parameters introduced by this expression and demonstrate that this expression can simplify the vast majority of published models. © 2013 FEBS.
Michaelis-Menten kinetics in shear flow: Similarity solutions for multi-step reactions.
Ristenpart, W D; Stone, H A
2012-03-01
Models for chemical reaction kinetics typically assume well-mixed conditions, in which chemical compositions change in time but are uniform in space. In contrast, many biological and microfluidic systems of interest involve non-uniform flows where gradients in flow velocity dynamically alter the effective reaction volume. Here, we present a theoretical framework for characterizing multi-step reactions that occur when an enzyme or enzymatic substrate is released from a flat solid surface into a linear shear flow. Similarity solutions are developed for situations where the reactions are sufficiently slow compared to a convective time scale, allowing a regular perturbation approach to be employed. For the specific case of Michaelis-Menten reactions, we establish that the transversally averaged concentration of product scales with the distance x downstream as x(5/3). We generalize the analysis to n-step reactions, and we discuss the implications for designing new microfluidic kinetic assays to probe the effect of flow on biochemical processes.
Müller, R; Babel, W
1980-01-01
Investigations of the 3-hexulosephosphate synthase (HPS) from different methylotrophic bacteria have revealed apparent discrepancies in kinetic behaviour. In all methanol-utilizing species investigated by us the kinetic characteristics showed intermediary plateau regions. Therefore, this behaviour is assumed to be a general feature of the HPS from all non-methane-utilizing methylotrophic bacteria. However, this assumption is in contrast to the results of other authors. Both for Methylomonas M15 (SAHM et al. 1976) and Methylomonas aminofaciens 77a (KATO et al. 1977, 1978) MICHAELIS-MENTEN kinetics of the HPS were stated. To check the validity of our assumption we have analyzed the kinetic data given by others. Indications of the existence of intermediary plateau regions could be found with the enzyme from Arthrobacter globiformis (BYKOVSKAYA and VORONKOV 1977) and Methylomonas aminofaciens 77a (KATO et al. 1978). Furthermore, biphasic ARRHENIUS plots indicate a multiple character of the HPS from these species as could already be demonstrated with the enzyme from Bacterium MB 58 and Pseudomonas oleovorans. In addition, causes which may obscure the detection of intermediary plateau regions are demonstrated.
Lee, Hye Jin; Wark, Alastair W; Goodrich, Terry T; Fang, Shiping; Corn, Robert M
2005-04-26
Real-time surface plasmon resonance (SPR) imaging measurements of surface enzymatic reactions on DNA microarrays are analyzed using a kinetics model that couples the contributions of both enzyme adsorption and surface enzyme reaction kinetics. For the case of a 1:1 binding of an enzyme molecule (E) to a surface-immobilized substrate (S), the overall enzymatic reaction can be described in terms of classical Langmuir adsorption and Michaelis-Menten concepts and three rate constants: enzyme adsorption (k(a)), enzyme desorption (k(d)) and enzyme catalysis (k(cat)). In contrast to solution enzyme kinetics, the amount of enzyme in solution is in excess as compared to the amount of substrate on the surface. Moreover, the surface concentration of the intermediary enzyme-substrate complex (ES) is not constant with time, but goes to zero as the reaction is completed. However, kinetic simulations show that the fractional surface coverage of ES on the remaining unreacted sites does reach a steady-state value throughout the course of the surface reaction. This steady-state value approaches the Langmuir equilibrium value for cases where k(a)[E] > k(cat). Experiments using the 3' --> 5' exodeoxyribonuclease activity of Exonuclease III on double-stranded DNA microarrays as a function of temperature and enzyme concentration are used to demonstrate how this model can be applied to quantitatively analyze the SPR imaging data.
Park, Soohyung; Agmon, Noam
2008-05-15
We develop a uniform theory for the many-particle diffusion-control effects on the Michaelis-Menten scheme in solution, based on the Gopich-Szabo relaxation-time approximation (Gopich, I. V.; Szabo, A. J. Chem. Phys. 2002, 117, 507). We extend the many-particle simulation algorithm to the Michaelis-Menten case by utilizing the Green function previously derived for excited-state reversible geminate recombination with different lifetimes (Gopich, I. V.; Agmon, N. J. Chem. Phys. 2000, 110, 10433). Running the simulation for representative parameter sets in the time domain and under steady-state conditions, we find poor agreement with classical kinetics but excellent agreement with some of the modern theories for bimolecular diffusion-influenced reactions. Our simulation algorithm can be readily extended to the biologically interesting case of dense patches of membrane-bound enzymes.
Simon Brown
2010-06-01
Full Text Available The behavior of enzyme-catalyzed reactions is not made clear to many students by the standard mathematical description of enzyme kinetics. An enzyme-machine analogy is described that has made the details of the Michaelis-Menten mechanism and the associated kinetics more accessible with minimal use of mathematics. Students taught using the analogy appear to have fewer of the misconceptions than those taught using a more mathematical approach.
Putz, Mihai V
2011-04-13
The conceptual and practical issues regarding the reduction of the Haldane-Radić enzymic mechanism, specific for cholinesterase kinetics, to the consecrated or logistically modified Michaelis-Menten kinetics, specific for some mutant enzymes, are here clarified as due to the limited initial substrate concentration, through detailed initial rate and progress curve analysis, even when other classical conditions for such equivalence are not entirely fulfilled.
Simon Brown
2010-01-01
The behavior of enzyme-catalyzed reactions is not made clear to many students by the standard mathematical description of enzyme kinetics. An enzyme-machine analogy is described that has made the details of the Michaelis-Menten mechanism and the associated kinetics more accessible with minimal use of mathematics. Students taught using the analogy appear to have fewer of the misconceptions than those taught using a more mathematical approach.
2009-01-01
A different view of Henri-Michaelis-Menten (HMM) enzyme kinetics is presented. In the first part of the paper, a simplified but useful description that stresses the cyclic nature of the catalytic process is introduced. The time-dependence of the substrate concentration after the initial transient phase is derived in a simple way that dispenses the mathematical technique known as quasi-steady-state approximation. In the second part of the paper an exact one-dimensional formulation of HMM kinet...
Mihai V. Putz
2011-04-01
Full Text Available The conceptual and practical issues regarding the reduction of the Haldane-Radić enzymic mechanism, specific for cholinesterase kinetics, to the consecrated or logistically modified Michaelis-Menten kinetics, specific for some mutant enzymes, are here clarified as due to the limited initial substrate concentration, through detailed initial rate and progress curve analysis, even when other classical conditions for such equivalence are not entirely fulfilled.
Eberwein, Jennifer; Shen, Weijun; Jenerette, G Darrel
2017-05-11
China experiences some of the highest rates of anthropogenic nitrogen deposition globally, with further increases projected. Understanding of soil feedbacks to the combined anthropogenic influences of climate change and nitrogen deposition in these systems is critical to improve predictive abilities for future climate scenarios. Here we used a Michaelis-Menten substrate-based kinetics framework to explore how soil CO2 production (Rsoil) responds to changes in temperature and available soil nitrogen (N) by combining field experiments with laboratory manipulations from sites experiencing elevated rates of anthropogenic N deposition but varying in soil N availabiltiy. The temperature sensitivity of Rsoil was strongly influenced by labile C additions. Furthermore, estimation of the temperature response of the Michaelis-Menten parameters supports the use of substrate-based kinetics in modeling efforts. Results from both field and laboratory experiments demonstrated a general decrease in Rsoil with increasing soil available N that was variably dependent on carbon (C) availability. Both the field and the laboratory measurements demonstrated a consistent decrease in the Michaelis-Menten parameter kM with increasing soil available N, indicating an increase in the efficiency of soil C decomposition with increasing N. Furthermore, these results provide evidence of interactions between N deposition and temperature sensitivity, which could influence C storage under combined anthropogenic global change drivers.
Sinitsyn, Nikolai A [Los Alamos National Laboratory
2008-01-01
We generalize the concept of the geometric phase in stochastic kinetics to a noncyclic evolution. Its application is demonstrated on kinetics of the Michaelis-Menten reaction. It is shown that the noncyclic geometric phase is responsible for the correction to the Michaelis-Menten law when parameters, such as a substrate concentration, are changing with time. We also discuss a model, where this correction qualitatively changes the outcome of reaction kinetics.
Yan, Xiaoyu; Krzyzanski, Wojciech
2012-04-01
The Michaelis-Menten (M-M) approximation of the target-mediated drug disposition (TMDD) pharmacokinetic (PK) model was derived based on the rapid binding (RB) or quasi steady-state (QSS) assumptions that implied that the target and drug binding and dissociation were in equilibrium. However, the initial dose for an IV bolus injection for the M-M model did not account for a fraction bound to the target. We postulated a correction to an initial condition that was consistent with the assumptions underlying the M-M approximation. We determined that the difference between the injected dose and one that should be used for the initial condition is equal to the amount of drug bound to the target upon reaching the equilibrium. We also observed that the corrected initial condition made the internalization rate constant an identifiable parameter that was not for the original M-M model. Finally, we performed a simulation exercise to check if the correction will impact the model performance and the bias of the M-M parameter estimates. We used literature data to simulate plasma drug concentrations described by the RB/QSS TMDD model. The simulated data were refitted by both models. All the parameters estimated from the original M-M model were substantially biased. On the other hand, the corrected M-M is able to accurately estimate these parameters except for equilibrium constant K(m). Weighted sum of square residual and Akaike information criterion suggested a better performance of the corrected M-M model compared with the original M-M model. Further studies are necessary to determine the importance of this correction for the M-M model applications to analysis of TMDD driven PK data.
Statistical reconstruction of transcription factor activity using Michaelis-Menten kinetics.
Khanin, R; Vinciotti, V; Mersinias, V; Smith, C P; Wit, E
2007-09-01
The basic building block of a gene regulatory network consists of a gene encoding a transcription factor (TF) and the gene(s) it regulates. Considerable efforts have been directed recently at devising experiments and algorithms to determine TFs and their corresponding target genes using gene expression and other types of data. The underlying problem is that the expression of a gene coding for the TF provides only limited information about the activity of the TF, which can also be controlled posttranscriptionally. In the absence of a reliable technology to routinely measure the activity of regulators, it is of great importance to understand whether this activity can be inferred from gene expression data. We here develop a statistical framework to reconstruct the activity of a TF from gene expression data of the target genes in its regulatory module. The novelty of our approach is that we embed the deterministic Michaelis-Menten model of gene regulation in this statistical framework. The kinetic parameters of the gene regulation model are inferred together with the profile of the TF regulator. We also obtain a goodness-of-fit test to verify the fit of the model. The model is applied to a time series involving the Streptomyces coelicolor bacterium. We focus on the transcriptional activator cdaR, which is partly responsible for the production of a particular type of antibiotic. The aim is to reconstruct the activity profile of this regulator. Our approach can be extended to include more complex regulatory relationships, such as multiple regulatory factors, competition, and cooperativity.
Selection between Michaelis-Menten and target-mediated drug disposition pharmacokinetic models.
Yan, Xiaoyu; Mager, Donald E; Krzyzanski, Wojciech
2010-02-01
Target-mediated drug disposition (TMDD) models have been applied to describe the pharmacokinetics of drugs whose distribution and/or clearance are affected by its target due to high binding affinity and limited capacity. The Michaelis-Menten (M-M) model has also been frequently used to describe the pharmacokinetics of such drugs. The purpose of this study is to investigate conditions for equivalence between M-M and TMDD pharmacokinetic models and provide guidelines for selection between these two approaches. Theoretical derivations were used to determine conditions under which M-M and TMDD pharmacokinetic models are equivalent. Computer simulations and model fitting were conducted to demonstrate these conditions. Typical M-M and TMDD profiles were simulated based on literature data for an anti-CD4 monoclonal antibody (TRX1) and phenytoin administered intravenously. Both models were fitted to data and goodness of fit criteria were evaluated for model selection. A case study of recombinant human erythropoietin was conducted to qualify results. A rapid binding TMDD model is equivalent to the M-M model if total target density R ( tot ) is constant, and R ( tot ) K ( D ) /(K ( D ) + C) ( 2 ) < 1 where K ( D ) represents the dissociation constant and C is the free drug concentration. Under these conditions, M-M parameters are defined as: V ( max ) = k ( int ) R ( tot ) V ( c ) and K ( m ) = K ( D ) where k ( int ) represents an internalization rate constant, and V ( c ) is the volume of the central compartment. R ( tot ) is constant if and only if k ( int ) = k ( deg,) where k ( deg ) is a degradation rate constant. If the TMDD model predictions are not sensitive to k ( int ) or k ( deg ) parameters, the condition of R ( tot ) K ( D ) /(K ( D ) + C) ( 2 ) < 1 alone can preserve the equivalence between rapid binding TMDD and M-M models. The model selection process for drugs that exhibit TMDD should involve a full mechanistic model as well as reduced models. The best model
Biphasic character of ribosomal translocation and non-Michaelis-Menten kinetics of translation.
Xie, Ping
2014-12-01
We study theoretically the kinetics of mRNA translocation in the wild-type (WT) Escherichia coli ribosome, which is composed of a small 30S and large 50S subunit, and the ribosomes with mutations to some intersubunit bridges such as B1a, B4, B7a, and B8. The theoretical results reproduce well the available in vitro experimental data on the biphasic kinetics of the forward mRNA translocation catalyzed by elongation factor G (EF-G) hydrolyzing GTP, which can be best fit by the sum of two exponentials, and the monophasic kinetics of the spontaneous reverse mRNA translocation in the absence of the elongation factor, which can be best fit by a single-exponential function, in both the WT and mutant ribosomes. We show that both the mutation-induced increase in the maximal rate of the slow phase for the forward mRNA translocation and that in the rate of the spontaneous reverse mRNA translocation result from a reduction in the intrinsic energy barrier to resist the rotational movements between the two subunits, giving the same degree of increase in the two rates. The mutation-induced increase in the maximal rate of the fast phase for the forward mRNA translocation results mainly from the increase in the rate of the ribosomal unlocking, a conformational change in the ribosome that widens the mRNA channel for the mRNA translocation to take place, which could be partly due to the effect of the mutation on the intrasubunit 30S head rotation. Moreover, we study the translation rate of the WT and mutant ribosomes. It is shown that the translation rate versus the concentration of EF-G-GTP does not follow the Michaelis-Menten (MM) kinetics, which is in sharp contrast to the general property of other enzymes that the rate of the enzymatic reaction versus the concentration of a substrate follows the MM kinetics. The physical origin of this non-MM kinetics for the ribosome is revealed.
Differences in Michaelis-Menten kinetics for different cultivars of maize during cyanide removal.
Yu, Xiao-Zhang; Gu, Ji-Dong
2007-06-01
Knowledge of the kinetic parameters, the half-saturation constant (K(m)) and the maximum metabolic capacity (v(max)), is very useful for the characterization of enzymes and biochemical processes. Little is known about rates of which vegetation metabolizes environmental chemicals. It is known, however, that vascular plants possess an enzyme system that detoxifies cyanide by converting it into the amino acid asparagine. This study investigated the differences in Michaelis-Menten kinetics of cyanide removal by different cultivars of maize. Detached leaves (1.0 g fresh weight) of seven different cultivars of maize (Zea mays L.) were kept in glass vessels with 100mL of aqueous solution spiked with potassium cyanide at 25+/-0.5 degrees C for 28 h. Four treatment concentrations of cyanide were used, ranging from 0.43 to 7.67 mgCNL(-1). The disappearance of cyanide from the aqueous solution was analyzed spectrophotometrically. Realistic values of K(m) and v(max) were estimated by a computer program using non-linear regression treatment. Lineweaver-Burk plots were also used to estimate the kinetic parameters for comparison. Using non-linear regression treatments, values of v(max) and K(m) were found to be between 10.80 and 22.80 mgCNkg(-1)h(-1), and 2.57 and 7.09 mgCNL(-1), respectively. The highest v(max) was achieved by the cultivars HengFen 1, followed by NongDa 108. The lowest v(max) was demonstrated by JingKe 8. The highest K(m) was found in NongDa 108, followed by HengFen 1. The lowest K(m) was associated with JingKe 8. Results from this study indicated that significant removal of cyanide from an aqueous solution was observed in the presence of plant materials without apparent phytotoxicity, even at the high concentration of cyanide used in this study. All maize cultivars used in this study were able to metabolize cyanide efficiently, although with different metabolic capacities. Results also showed a small variation of metabolic rates between the different cultivars
Hum, Ryan J; Jha, Prabhat; McGahan, Anita M; Cheng, Yu-Ling
2012-12-13
Life expectancy has risen sharply in the last 50 years. We applied the classic Michaelis-Menten enzyme kinetics to demonstrate a novel mathematical relationship of income to childhood (aged 0-5 years) and adult (aged 15-60 years) survival. We treat income as a substrate that is catalyzed to increase survival (from technologies that income buys) for 180 countries from 1970 and 2007. Michaelis-Menten kinetics permit estimates of maximal survival and, uniquely, the critical income needed to achieve half of the period-specific maximum. Maximum child and adult survival rose by about 1% per year. Critical incomes fell by half for children, but doubled for men. HIV infection and smoking account for some, but not all, of the rising critical incomes for adult survival. Altering the future cost curve for adult survival will require more widespread use of current interventions, most notably tobacco control, but also research to identify practicable low-cost drugs, diagnostics, and strategies.DOI:http://dx.doi.org/10.7554/eLife.00051.001.
Youdim, K; Dodia, R
2010-04-01
Non-linear dose-exposure (supra-proportionality) occurs when plasma drug concentrations increase in a non-linear fashion with increasing dose. To predict the likelihood of this, an understanding is required of the K(M), which reflects a drug ability to saturate a specific enzyme involved in its metabolism. This study assessed the accuracy of K(M) and V(max) determinations for compounds using a substrate-depletion approach with those determined using the product-formation approach, using both recombinant human cytochrome P450 (CYP) enzymes and human liver microsomes. For the vast majority of the compounds studied, the K(M)'s using recombinant CYPs and human liver microsomes in the two approaches predicted within two-fold. Further comparisons between the K(M) and V(max)-values were made between those measured using the product-formation approach and those estimated following simultaneous fitting of the Michaelis-Menten equation to all substrate depletion plots. In each case values were comparable. In conclusion, the current study showed the substrate-depletion approach can be used to estimate K(M) and V(max) using both human liver microsomes and recombinant P450s. Estimation of these parameters during early discovery will aid in the understanding of dosages at which non-linearity may occur, but potentially aid predictions of likely clinical drug-drug interactions.
磁流变阻尼器的米氏模型及试验验证%MICHAELIS-MENTEN MODEL OF MAGNETORHEOLOGICAL DAMPER AND TEST VERIFICATION
张香成; 徐赵东; 王绍安; 沙凌峰
2013-01-01
为研究磁流变阻尼器(MRD)非线性滞回性能的影响因素,建立精确的MRD力学模型,对MRD进行力学性能试验,并基于米氏方程提出一个综合考虑电流、位移和频率影响的力学模型——米氏模型.对所提模型和传统经典力学模型进行数值模拟,并与试验结果进行对比分析,结果表明:该模型可以模拟MRD的非线性滞回性能、体现位移和频率对阻尼力及非线性滞回性能的影响.%To find the effect factors of the nonlinear hysteresis capability of a magnetorheological damper (MRD) and establish a precise mathematical model, a Michaelis-Menten (MM) Model was presented based on the MM equation which considers the effects of current, amplitude and frequency. Numerical simulations of the MM Model and traditional classical mathematic model were carried out to compare with the test results. Comparison results indicate that the MM Model could simulate the hysteresis capability of MRD and reflect the effects of current, amplitude and frequency on damping force and nonlinear hysteresis capability.
Bezerra, Rui M F; Dias, Albino A
2004-03-01
The kinetics of exoglucanase (Cel7A) from Trichoderma reesei was investigated in the presence of cellobiose and 24 different enzyme/Avicel ratios for 47 h, in order to establish which of the eight available kinetic models best explained the factors involved. The heterogeneous catalysis was studied and the kinetic parameters were estimated employing integrated forms of Michaelis-Menten equations through the use of nonlinear least squares. It was found that cellulose hydrolysis follows a model that takes into account competitive inhibition by cellobiose (final product) with the following parameters: Km = 3.8 mM, Kic = 0.041 mM, kcat = 2 h-1 (5.6 x 10-4 s-1). Other models, such as mixed type inhibition and those incorporating improvements concerning inhibition by substrate and parabolic inhibition, increased the modulation performance very slightly. The results support the hypothesis that nonproductive enzyme substrate complexes, parabolic inhibition, and enzyme inactivation (Selwyn test) are not the principal constraints in enzymatic cellulose hydrolysis. Under our conditions, the increment in hydrolysis was not significant for substrate/enzyme ratios <6.5.
Utilization of Integrated Michaelis-Menten Equation to Determine Kinetic Constants
Bezerra, Rui M. F.; Dias, Albino A.
2007-01-01
Students of biochemistry and related biosciences are urged to solve problems where kinetic parameters are calculated from initial rates obtained at different substrate concentrations. Troubles begin when they go to the laboratory to perform kinetic experiments and realize that usual laboratory instruments do not measure initial rates but only…
Utilization of Integrated Michaelis-Menten Equation to Determine Kinetic Constants
Bezerra, Rui M. F.; Dias, Albino A.
2007-01-01
Students of biochemistry and related biosciences are urged to solve problems where kinetic parameters are calculated from initial rates obtained at different substrate concentrations. Troubles begin when they go to the laboratory to perform kinetic experiments and realize that usual laboratory instruments do not measure initial rates but only…
Wu, Xiaotian; Li, Jun; Nekka, Fahima
2015-04-01
The current study aims to provide the closed form solutions of one-compartment open models exhibiting simultaneous linear and nonlinear Michaelis-Menten elimination kinetics for single- and multiple-dose intravenous bolus administrations. It can be shown that the elimination half-time ([Formula: see text]) has a dose-dependent property and is upper-bounded by [Formula: see text] of the first-order elimination model. We further analytically distinguish the dominant role of different elimination pathways in terms of model parameters. Moreover, for the case of multiple-dose intravenous bolus administration, the existence and local stability of the periodic solution at steady state are established. The closed form solutions of the models are obtained through a newly introduced function motivated by the Lambert W function.
Yan, Shaomin; Wu, Guang
2011-10-01
In this study, we attempted to use the neural network to model a quantitative structure-K(m) (Michaelis-Menten constant) relationship for beta-glucosidase, which is an important enzyme to cut the beta-bond linkage in glucose while K(m) is a very important parameter in enzymatic reactions. Eight feedforward backpropagation neural networks with different layers and neurons were applied for the development of predictive model, and twenty-five different features of amino acids were chosen as predictors one by one. The results show that the 20-1 feedforward backpropagation neural network can serve as a predictive model while the normalized polarizability index as well as the amino-acid distribution probability can serve as the predictors. This study threw lights on the possibility of predicting the K(m) in beta-glucosidases based on their amino-acid features.
Garneau-Tsodikova, Sylvie; Shkel, Irina A; Tsodikov, Oleg V
2009-04-15
Most enzyme kinetic experiments are carried out under pseudo-first-order conditions, that is, when one of the reactant species (the enzyme or the substrate) is in a large excess of the other species. More accurate kinetic information about the system can be gained without the restrictions of the pseudo-first-order conditions. We present a practical and general method of analysis of the common two-step rapid equilibrium Michaelis-Menten mechanism. The formalism is exact in that it does not involve any other approximations such as the steady-state, limitations on the reactant concentrations or on reaction times. We apply this method to the global analysis of kinetic progress curves for bovine alkaline phosphatase assays carried out under both pseudo-first-order and pseudo-second-order conditions.
Houston, J B; Kenworthy, K E
2000-03-01
Strategies for the prediction of in vivo drug clearance from in vitro drug metabolite kinetic data are well established for the rat. In this animal species, metabolism rate-substrate concentration relationships can commonly be described by the classic hyperbola consistent with the Michaelis-Menten model and simple scaling of the parameter intrinsic clearance (CL(int) - the ratio of V(max) to K(m)) is particularly valuable. The in vitro scaling of kinetic data from human tissue is more complex, particularly as many substrates for cytochrome P450 (CYP) 3A4, the dominant human CYP, show nonhyperbolic metabolism rate-substrate concentration curves. This review critically examines these types of data, which require the adoption of an enzyme model with multiple sites showing cooperative binding for the drug substrate, and considers the constraints this kinetic behavior places on the prediction of in vivo pharmacokinetic characteristics, such as metabolic stability and inhibitory drug interaction potential. The cases of autoactivation and autoinhibition are discussed; the former results in an initial lag in the rate-substrate concentration profile to generate a sigmoidal curve whereas the latter is characterized by a convex curve as V(max) is not maintained at high substrate concentrations. When positive cooperativity occurs, we suggest the use of CL(max), the maximal clearance resulting from autoactivation, as a substitute for CL(int). The impact of heteroactivation on this approach is also of importance. In the case of negative cooperativity, care in using the V(max)/K(m) approach to CL(int) determination must be taken. Examples of substrates displaying each type of kinetic behavior are discussed for various recombinant CYP enzymes, and possible artifactual sources of atypical rate-concentration curves are outlined. Finally, the consequences of ignoring atypical Michaelis-Menten kinetic relationships are examined, and the inconsistencies reported for both different
Gejl, Michael; Rungby, Jørgen; Brock, Birgitte; Gjedde, Albert
2014-08-01
Glucagon-like peptide-1 (GLP-1) is a potent insulinotropic incretin hormone with both pancreatic and extrapancreatic effects. Studies of GLP-1 reveal significant effects in regions of brain tissue that regulate appetite and satiety. GLP-1 mimetics are used for the treatment of type 2 diabetes mellitus. GLP-1 interacts with peripheral functions in which the autonomic nervous system plays an important role, and emerging pre-clinical findings indicate a potential neuroprotective role of the peptide, for example in models of stroke and in neurodegenerative disorders. A century ago, Leonor Michaelis and Maud Menten described the steady-state enzyme kinetics that still apply to the multiple receptors, transporters and enzymes that define the biochemical reactions of the brain, including the glucose-dependent impact of GLP-1 on blood-brain glucose transfer and metabolism. This MiniReview examines the potential of GLP-1 as a molecule of interest for the understanding of brain energy metabolism and with reference to the impact on brain metabolism related to appetite and satiety regulation, stroke and neurodegenerative disorders. These effects can be understood only by reference to the original formulation of the Michaelis-Menten equation as applied to a chain of kinetically controlled steps. Indeed, the effects of GLP-1 receptor activation on blood-brain glucose transfer and brain metabolism of glucose depend on the glucose concentration and relative affinities of the steps both in vitro and in vivo, as in the pancreas. © 2014 Nordic Association for the Publication of BCPT (former Nordic Pharmacological Society).
Verlindo de Araujo, Bibiana; Farias da Silva, Cristófer; Costa, Teresa Dalla
2010-01-01
the determination of oral bioavailability of drugs which follow nonlinear pharmacokinetics is difficult and few methods are available. In this work, an alternative approach to determine oral bioavailability of voriconazole (VRC), used as a model drug, is presented. VRC pharmacokinetics was investigated in Wistar rats after p.o. (40 mg/kg) and i.v. administration (2.5, 5 and 10 mg/kg). VRC elimination showed saturation in all doses investigated, except the lower i.v. dose in which case a 3-compartment model with linear elimination adequately fitted the data. Data for the 2 higher i.v. doses were best described by a 3-compartment model with Michaelis-Menten elimination. A 1-compartment disposition with a saturable metabolic elimination model described the oral profile. VRC absolute oral bioavailability was determined by simultaneous fitting of the i.v. and oral profiles. the Michaelis constant and the maximum velocity estimated after 5 and 10 mg/kg i.v. dosing were 0.54 +/- 0.25 microg/ml and 2.53 +/- 0.54 microg/h, and 0.62 +/- 0.12 microg/ml and 2.74 +/- 0.84 microg/h, respectively. VRC oral bioavailability was determined to be 82.8%. the approach presented is an alternative for determining the bioavailability of drugs with similar nonlinear behavior. 2010 S. Karger AG, Basel.
Lee, Byung-Yo; Kwon, Kwang-Il; Kim, Min-Soo; Baek, In-Hwan
2016-08-01
Etanercept was approved by the Food and Drug Administration (FDA) in 2010 as a biologic agent for the treatment of rheumatoid arthritis (RA). The aim of the study was to investigate the pharmacokinetic properties of etanercept after intravenous and subcutaneous injection in rats. The plasma concentration of etanercept was determined using an enzyme-linked immunosorbent assay (ELISA). Intravenous and subcutaneous administration of 2 mg/kg of etanercept to rats showed that etanercept was slowly absorbed (time to reach the peak drug concentration [T max] = 1.60 days, bioavailability [F] = 47.18 %) and slowly eliminated (half-life [t 1/2], 2.33 days after intravenous administration and 3.31 days after subcutaneous administration). The area under the curve values on day 13 (AUC13day) were 121.25 ± 14.37 and 48.56 ± 6.78 μg day/mL after intravenous and subcutaneous administration, respectively. A two-compartment model with Michaelis-Menten elimination kinetics (V max = 94.28 µg/day; K m = 10.88 µg/mL) was used to describe the pharmacokinetic profile of etanercept. Our results describe the pharmacokinetic profile of etanercept, and these results could be used for the development of etanercept biosimilars.
Choi, I Y; Lee, S P; Kim, S G; Gruetter, R
2001-06-01
Glucose is the major substrate that sustains normal brain function. When the brain glucose concentration approaches zero, glucose transport across the blood-brain barrier becomes rate limiting for metabolism during, for example, increased metabolic activity and hypoglycemia. Steady-state brain glucose concentrations in alpha-chloralose anesthetized rats were measured noninvasively as a function of plasma glucose. The relation between brain and plasma glucose was linear at 4.5 to 30 mmol/L plasma glucose, which is consistent with the reversible Michaelis-Menten model. When the model was fitted to the brain glucose measurements, the apparent Michaelis-Menten constant, Kt, was 3.3 +/- 1.0 mmol/L, and the ratio of the maximal transport rate relative to CMRglc, Tmax/CMRglc, was 2.7 +/- 0.1. This Kt is comparable to the authors' previous human data, suggesting that glucose transport kinetics in humans and rats are similar. Cerebral blood flow (CBF) was simultaneously assessed and constant above 2 mmol/L plasma glucose at 73 +/- 6 mL 100 g(-1) min(-1). Extrapolation of the reversible Michaelis-Menten model to hypoglycemia correctly predicted the plasma glucose concentration (2.1 +/- 0.6 mmol/L) at which brain glucose concentrations approached zero. At this point, CBF increased sharply by 57% +/- 22%, suggesting that brain glucose concentration is the signal that triggers defense mechanisms aimed at improving glucose delivery to the brain during hypoglycemia.
Meyer, Markus R; Orschiedt, Tina; Maurer, Hans H
2013-02-27
The pharmacokinetics of various important drugs are known to be significantly influenced by the human ABC transporter P-glycoprotein (P-gp), which may lead to clinically relevant drug-drug interactions. In contrast to therapeutic drugs, emerging drugs of abuse (DOA) are sold and consumed without any safety pharmacology testing. Only some studies on their metabolism were published, but none about their affinity to the transporter systems. Therefore, 47 DOAs from various classes were tested for their P-gp affinity using human P-gp (hP-gp) to predict possible drug-drug interactions. DOAs were initially screened for general hP-gp affinity and further characterized by modeling classic Michaelis-Menten kinetics and assessing their K(m) and V(max) values. Among the tested drugs, 12 showed a stimulation of ATPase activity. The most intensive stimulating DOAs were further investigated and compared with the known P-gp model substrates sertraline and verapamil. ATPase stimulation kinetics could be modeled for the entactogen 3,4-methylenedioxy-α-ethylphenethylamine (3,4-BDB), the hallucinogen 2,5-dimethoxy-4-iodoamphetamine (DOI), the abused alkaloid glaucine, the opioid-like drugs N-iso-propyl-1,2-diphenylethylamine (NPDPA), and N-(1-phenylcyclohexyl)-3-ethoxypropanamine (PCEPA), with K(m) and V(max) values within the same range as for verapamil or sertraline. As a consequence interactions with other drugs being P-gp substrates might be considered to be very likely and further studies should be encouraged. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
Commemorating the 1913 Michaelis-Menten paper Die Kinetik der Invertinwirkung: three perspectives.
Deichmann, Ute; Schuster, Stefan; Mazat, Jean-Pierre; Cornish-Bowden, Athel
2014-01-01
Methods and equations for analysing the kinetics of enzyme-catalysed reactions were developed at the beginning of the 20th century in two centres in particular; in Paris, by Victor Henri, and, in Berlin, by Leonor Michaelis and Maud Menten. Henri made a detailed analysis of the work in this area that had preceded him, and arrived at a correct equation for the initial rate of reaction. However, his approach was open to the important objection that he took no account of the hydrogen-ion concentration (a subject largely undeveloped in his time). In addition, although he wrote down an expression for the initial rate of reaction and described the hyperbolic form of its dependence on the substrate concentration, he did not appreciate the great advantages that would come from analysis in terms of initial rates rather than time courses. Michaelis and Menten not only placed Henri's analysis on a firm experimental foundation, but also defined the experimental protocol that remains standard today. Here, we review this development, and discuss other scientific contributions of these individuals. The three parts have different authors, as indicated, and do not necessarily agree on all details, in particular about the relative importance of the contributions of Michaelis and Menten on the one hand and of Henri on the other. Rather than force the review into an unrealistic consensus, we consider it appropriate to leave the disagreements visible. © 2013 FEBS.
Estimation of Michaelis-Menten constant of efflux transporter considering asymmetric permeability.
Sugano, Kiyohiko; Shirasaka, Yoshiyuki; Yamashita, Shinji
2011-10-14
It was previously reported that the apparent K(m) values of P-gp in apical to basal (A to B) and basal to apical (B to A) directions were different. The purpose of the present study was to derive a theoretical framework by which this asymmetric concentration-permeability profile can be explained using a single intrinsic K(m) value. A three compartment model was used to represent the apical, cytosol and basal compartments. The difference of passive permeability and the surface areas between the apical and basolateral membrane were explicitly taken into account. Applying the steady state approximation and considering the mass balance in the cytosol compartment, an open analytical solution was obtained. By using this equation, the asymmetric concentration-permeability profile was appropriately reproduced. In addition, the expression level dependency of apparent K(m) was also reproduced. Copyright © 2011 Elsevier B.V. All rights reserved.
Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem.
Rotbart, Tal; Reuveni, Shlomi; Urbakh, Michael
2015-12-01
We study the effect of restart, and retry, on the mean completion time of a generic process. The need to do so arises in various branches of the sciences and we show that it can naturally be addressed by taking advantage of the classical reaction scheme of Michaelis and Menten. Stopping a process in its midst-only to start it all over again-may prolong, leave unchanged, or even shorten the time taken for its completion. Here we are interested in the optimal restart problem, i.e., in finding a restart rate which brings the mean completion time of a process to a minimum. We derive the governing equation for this problem and show that it is exactly solvable in cases of particular interest. We then continue to discover regimes at which solutions to the problem take on universal, details independent forms which further give rise to optimal scaling laws. The formalism we develop, and the results obtained, can be utilized when optimizing stochastic search processes and randomized computer algorithms. An immediate connection with kinetic proofreading is also noted and discussed.
Specificity of non-Michaelis-Menten enzymes: necessary information for analyzing metabolic pathways.
Cornish-Bowden, Athel; Cárdenas, María Luz
2010-12-16
The specificity of an enzyme obeying the Michaelis−Menten equation is normally measured by comparing the kcat/Km for different substrates, but this is inappropriate for enzymes with a Hill coefficient h different from 1. The obvious alternative of generalizing Km in the expression as K0.5, the substrate concentration for half-saturation, is better, but it is not entirely satisfactory either, and here we show that kcat/K0.5(h) gives satisfactory results for analyzing the kinetic behavior of metabolic pathways. The importance of using kcat/K0.5(h) increases with the value of h, but even when h is small, it makes an appreciable difference, as illustrated for the mammalian hexokinases. Reinterpretation of data for the specificity of these enzymes in terms of the proposed definition indicates that hexokinase D, often believed highly specific for glucose, and accordingly called “glucokinase”, actually has the lowest preference for glucose over fructose of the four isoenzymes found in mammals.
Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem
Rotbart, Tal; Reuveni, Shlomi; Urbakh, Michael
2015-12-01
We study the effect of restart, and retry, on the mean completion time of a generic process. The need to do so arises in various branches of the sciences and we show that it can naturally be addressed by taking advantage of the classical reaction scheme of Michaelis and Menten. Stopping a process in its midst—only to start it all over again—may prolong, leave unchanged, or even shorten the time taken for its completion. Here we are interested in the optimal restart problem, i.e., in finding a restart rate which brings the mean completion time of a process to a minimum. We derive the governing equation for this problem and show that it is exactly solvable in cases of particular interest. We then continue to discover regimes at which solutions to the problem take on universal, details independent forms which further give rise to optimal scaling laws. The formalism we develop, and the results obtained, can be utilized when optimizing stochastic search processes and randomized computer algorithms. An immediate connection with kinetic proofreading is also noted and discussed.
Yunxian Dai; Yiping Lin; Huitao Zhao
2014-01-01
We consider a predator-prey system with Michaelis-Menten type functional response and two delays. We focus on the case with two unequal and non-zero delays present in the model, study the local stability of the equilibria and the existence of Hopf bifurcation, and then obtain explicit formulas to determine the properties of Hopf bifurcation by using the normal form method and center manifold theorem. Special attention is paid to the global continuation of local Hopf bifurcation when the delay...
Machado, Eustáquio José
2014-01-01
A equação hiperbólica, conhecida no contexto bioquímico como o modelo de Michaelis-Menten, é utilizada para descrever a velocidade de reações químicas envolvendo enzimas (cinética enzimática). Este estudo teve como objetivo comparar os ajustes do modelo de Michaelis-Menten (1913) que fez uso de dois modelos não-lineares e quatro modelos linearizados. Os dois modelos não-lineares (um utilizou o método clássico assintotico usual e o outro fez uso da abordagem "bootstrap"). Os modelos linearizad...
Heering, Hendrik A
2012-10-01
Deconvolution of protein film voltammetric data by fitting multiple components (sigmoids, derivative peaks) often is ambiguous when features are partially overlapping, due to exchangeability between the width and the number of components. Here, a new method is presented to obtain the width of the components. This is based on the equivalence between the sigmoidal catalytic response as function of electrode potential, and the classical saturation curve obtained for the enzyme activity as function of the soluble substrate concentration, which is also sigmoidal when plotted versus log[S]. Thus, analysis of the catalytic voltammogram with Lineweaver-Burk, Eadie-Hofstee, and Hanes-Woolf plots is feasible. This provides a very sensitive measure of the cooperativity number (Hill coefficient), which for electrons equals the apparent (fractional) number of electrons that determine the width, and thereby the number of components (kinetic phases). This analysis is applied to the electrocatalytic oxygen reduction by Paracoccus denitrificans cytochrome aa(3) (cytochrome c oxidase). Four partially overlapping kinetic phases are observed that (stepwise) increase the catalytic efficiency with increasingly reductive potential. Translated to cell biology, the activity of the terminal oxidase stepwise adapts to metabolic demand for oxidative phosphorylation. Copyright © 2011 Elsevier B.V. All rights reserved.
Moaty Sayed, A A; Hussein, M A; Becker, T
2010-04-01
Lattice Boltzmann models (LBM) are rapidly showing their ability to simulate a lot of fluid dynamics problems that previously required very complex approaches. This study presents a LBM for simulating diffusion-advection transport of substrate in a 2-D laminar flow. The model considers the substrate influx into a set of active cells placed inside the flow field. A new innovative method was used to simulate the cells activity using the LBM by means of Michaelis-Menten kinetics. The model is validated with some numerical benchmark problems and proved highly accurate results. After validation the model was used to simulate the transport of oxygen substrates that diffuse in water to feed a set of active cartilage cells inside a new designed bioreactor.
Fowler, Stephen; Guerini, Elena; Qiu, NaHong; Cleary, Yumi; Parrott, Neil; Greig, Gerard; Mallalieu, Navita L
2017-01-01
Basimglurant, a novel mGlu5-negative allosteric modulator under development for the treatment of major depressive disorder, is cleared via cytochrome P450 (P450)-mediated oxidative metabolism. Initial enzyme phenotyping studies indicated that CYP3A4/5 dominates basimglurant metabolism and highlights a risk for drug-drug interactions when it is comedicated with strong CYP3A4/5 inhibitors or inactivators; however, a clinical drug-drug interaction (DDI) study using the potent and selective CYP3A4/5 inhibitor ketoconazole resulted in an area under the curve (AUC) AUCi/AUC ratio of only 1.24. A further study using the CYP3A4 inducer carbamazepine resulted in an AUCi/AUC ratio of 0.69. More detailed in vitro enzyme phenotyping and kinetics studies showed that, at the low concentrations attained clinically, basimglurant metabolic clearance is catalyzed mainly by CYP1A2. The relative contributions of the enzymes were estimated as 70:30 CYP1A2:CYP3A4/5. Using this information, a clinical study using the CYP1A2 inhibitor fluvoxamine was performed, resulting in an AUCi/AUC ratio of 1.60, confirming the role of CYP1A2 and indicating a balanced DDI risk profile. Basimglurant metabolism kinetics show enzyme dependency: CYP1A2-mediated metabolism follows Michaelis-Menten kinetics, whereas CYP3A4 and CYP3A5 follow sigmoidal kinetics [with similar constant (KM) and S50 values]. The interplay of the different enzyme kinetics leads to changing fractional enzyme contributions to metabolism with substrate concentration, even though none of the metabolic enzymes is saturated. This example demonstrates the relevance of non-Michaelis-Menten P450 enzyme kinetics and highlights the need for a thorough understanding of metabolism enzymology to make accurate predictions for human metabolism in vivo. Copyright © 2016 by The American Society for Pharmacology and Experimental Therapeutics.
Yusof, Siti R; Abbott, N Joan; Avdeef, Alex
2017-08-30
Most studies of blood-brain barrier (BBB) permeability and transport are conducted at a single pH, but more detailed information can be revealed by using multiple pH values. A pH-dependent biophysical model was applied to the mechanistic analysis of published pH-dependent BBB luminal uptake data from three opioid derivatives in rat: pentazocine (Suzuki et al., 2002a, 2002b), naloxone (Suzuki et al., 2010a), and oxycodone (Okura et al., 2008). Two types of data were processed: in situ brain perfusion (ISBP) and brain uptake index (BUI). The published perfusion data were converted to apparent luminal permeability values, Papp, and analyzed by the pCEL-X program (Yusof et al., 2014), using the pH-dependent Crone-Renkin equation (pH-CRE) to determine the impact of cerebrovascular flow on the Michaelis-Menten transport parameters (Avdeef and Sun, 2011). For oxycodone, the ISBP data had been measured at pH7.4 and 8.4. The present analysis indicates a 7-fold lower value of the cerebrovascular flow velocity, Fpf, than that expected in the original study. From the pyrilamine-inhibited data, the flow-corrected passive intrinsic permeability value was determined to be P0=398×10(-6)cm·s(-1). The uptake data indicate that the neutral form of oxycodone is affected by a transporter at pH8.4. The extent of the cation uptake was less certain from the available data. For pentazocine, the brain uptake by the BUI method had been measured at pH5.5, 6.5, and 7.4, in a concentration range 0.1-40mM. Under similar conditions, ISBP data were also available. The pH-CRE determined values of Fpf from both methods were nearly the same, and were smaller than the expected value in the original publication. The transport of the cationic pentazocine was not fully saturated at pH5.5 at 40mM. The transport of the neutral species at pH7.4 appeared to reach saturation at 40mM pentazocine concentration, but not at 12mM. In the case of naloxone, a pH-dependent Michaelis-Menten equation (p
Longatte, Guillaume; Guille-Collignon, Manon; Lemaître, Frédéric
2017-06-15
In the past years, many strategies have been implemented to benefit from oxygenic photosynthesis to harvest photosynthetic electrons and produce a significant photocurrent. Therefore, electrochemical tools were considered and have globally relied on the electron transfer(s) between the photosynthetic chain and a collecting electrode. In this context, we recently reported the implementation of an electrochemical set-up at the preparative scale to produce photocurrents from a Chlamydomonas reinhardtii algae suspension with an appropriate mediator (2,6-DCBQ) and a carbon gauze as the working electrode. In the present work, we wish to describe a mathematical modeling of the recorded photocurrents to better understand the effects of the experimental conditions on the photosynthetic extraction of electrons. In that way, we established a general model of an electrocatalytic mechanism at the preparative scale (that is, assuming a homogenous bulk solution at any time and a constant diffusion layer, both assumptions being valid under forced convection) in which the chemical step involves a Michaelis-Menten-like behaviour. Dependences of transient and steady-state corresponding currents were analysed as a function of different parameters by means of zone diagrams. This model was tested to our experimental data related to photosynthesis. The corresponding results suggest that competitive pathways beyond photosynthetic harvesting alone should be taken into account. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Li, Albert P; Schlicht, Kari E
2014-01-01
A higher throughput platform was developed for the determination of K(M) values for isoformselective P450 substrates in human hepatocytes via incubation of the hepatocytes with substrates in 384- well plates and metabolite quantification by RapidFire™ mass spectrometry. Isoform-selective P450 substrates were incubated at 8 concentrations in triplicate with cryopreserved human hepatocytes from 16 donors. The metabolic pathways examined were the CYP1A2-catalyzed tacrine 1-hydroxylation, CYP2B6-catalyzed bupropion hydroxylation, CYP2C8-catalyzed amodiaquine N-deethylation, CYP2C9- catalyzed diclofenac 4'-hydroxylation, CYP2D6-catalyzed dextromethorphan O-demethylation, and CYP3A4-catalyzed midazolam 1'-hydroxylation. Typical saturation enzyme kinetics was observed for all the pathways evaluated. Individual differences in the apparent V(max) and K(M) values were observed among the human hepatocytes from each of the 16 individual donors, with no statistically significant gender- or age-associated differences. A "composite" K(M) value was calculated for each of the pathways via normalizing the individual activities to their respective V(max) values to develop "relative activities" followed by Michaelis-Menten analysis of the mean relative activities of the 16 donors at each of the 8 substrate concentrations. The resulting "composite" K(M) values for the P450 substrates may be used to guide in vitro P450 inhibition and induction studies and kinetic modeling of in vivo drug-drug interaction.
André Rosa Martins
2015-01-01
.... One model was obtained, among the evaluated proposals, with performance indicating behavior similar to the classical Michaelis-Menten model, where the reaction complex is rapidly formed and, along...
Gattu, Srikanth; Crihfield, Cassandra L; Holland, Lisa A
2017-01-03
Phospholipid nanogels enhance the stability and performance of the exoglycosidase enzyme neuraminidase and are used to create a fixed zone of enzyme within a capillary. With nanogels, there is no need to covalently immobilize the enzyme, as it is physically constrained. This enables rapid quantification of Michaelis-Menten constants (KM) for different substrates and ultimately provides a means to quantify the linkage (i.e., 2-3 versus 2-6) of sialic acids. The fixed zone of enzyme is inexpensive and easily positioned in the capillary to support electrophoresis mediated microanalysis using neuraminidase to analyze sialic acid linkages. To circumvent the limitations of diffusion during static incubation, the incubation period is reproducibly achieved by varying the number of forward and reverse passes the substrate makes through the stationary fixed zone using in-capillary electrophoretic mixing. A KM value of 3.3 ± 0.8 mM (Vmax, 2100 ± 200 μM/min) was obtained for 3'-sialyllactose labeled with 2-aminobenzoic acid using neuraminidase from Clostridium perfringens that cleaves sialic acid monomers with an α2-3,6,8,9 linkage, which is similar to values reported in the literature that required benchtop analyses. The enzyme cleaves the 2-3 linkage faster than the 2-6, and a KM of 2 ± 1 mM (Vmax, 400 ± 100 μM/min) was obtained for the 6'-sialyllactose substrate. An alternative neuraminidase selective for 2-3 sialic acid linkages generated a KM value of 3 ± 2 mM (Vmax, 900 ± 300 μM/min) for 3'-sialyllactose. With a knowledge of Vmax, the method was applied to a mixture of 2-3 and 2-6 sialyllactose as well as 2-3 and 2-6 sialylated triantennary glycan. Nanogel electrophoresis is an inexpensive, rapid, and simple alternative to current technologies used to distinguish the composition of 3' and 6' sialic acid linkages.
Igamberdiev, Abir U; Roussel, Marc R
2012-03-01
Rubisco, the most abundant protein serving as the primary engine generating organic biomass on Earth, is characterized by a low catalytic constant (in higher plants approx. 3s(-1)) and low specificity for CO(2) leading to photorespiration. We analyze here why this enzyme evolved as the main carbon fixation engine. The high concentration of Rubisco exceeding the concentration of its substrate CO(2) by 2-3 orders of magnitude makes application of Michaelis-Menten kinetics invalid and requires alternative kinetic approaches to describe photosynthetic CO(2) assimilation. Efficient operation of Rubisco is supported by a strong flux of CO(2) to the chloroplast stroma provided by fast equilibration of bicarbonate and CO(2) and forwarding the latter to Rubisco reaction centers. The main part of this feedforward mechanism is a thylakoidal carbonic anhydrase associated with photosystem II and pumping CO(2) from the thylakoid lumen in coordination with the rate of electron transport, water splitting and proton gradient across the thylakoid membrane. This steady flux of CO(2) limits photosynthesis at saturating CO(2) concentrations. At low ambient CO(2) and correspondingly limited capacity of the bicarbonate pool in the stroma, its depletion at the sites of Rubisco is relieved by utilizing O(2) instead of CO(2), i.e. by photorespiration, a process which supplies CO(2) back to Rubisco and buffers the redox state and energy level in the chloroplast. Thus, the regulation of Rubisco function aims to keep steady non-equilibrium levels of CO(2), NADPH/NADP and ATP/ADP in the chloroplast stroma and to optimize the condition of homeostatic photosynthetic flux of matter and energy. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.
Sudhamalla, Babu; Kumar, Mahesh; Roy, Karnati R; Kumar, R Sunil; Bhuyan, Abani K
2013-11-01
It is known that tandem domains of enzymes can carry out catalysis independently or by collaboration. In the case of cysteine proteases, domain sequestration abolishes catalysis because the active site residues are distributed in both domains. The validity of this argument is tested here by using isolated human ribosomal protein S4, which has been recently identified as an unorthodox cysteine protease. Cleavage of the peptide substrate Z-FR↓-AMC catalyzed by recombinant C-terminal domain of human S4 (CHS4) is studied by fluorescence-monitored steady-state and stopped-flow kinetic methods. Proteolysis and autoproteolysis were analyzed by electrophoresis. The CHS4 domain comprised of sequence residues 116-263 has been cloned and ovreexpressed in Escherichia coli. The purified domain is enzymatically active. Barring minor differences, steady-state kinetic parameters for catalysis by CHS4 are very similar to those for full-length human S4. Further, stopped-flow transient kinetics of pre-steady-state substrate binding shows that the catalytic mechanism for both full-length S4 and CHS4 obeys the Michaelis-Menten model adequately. Consideration of the evolutionary domain organization of the S4e family of ribosomal proteins indicates that the central domain (residues 94-170) within CHS4 is indispensable. The C-terminal domain can carry out catalysis independently and as efficiently as the full-length human S4 does. Localization of the enzyme function in the C-terminal domain of human S4 provides the only example of a cysteine endoprotease where substrate-mediated intramolecular domain interaction is irrelevant for catalytic activity. Copyright © 2013 Elsevier B.V. All rights reserved.
Yu, Xiao-Zhang; Zhang, Xue-Hong
2016-07-01
Hydroponic experiments were conducted with different species of plants (rice, maize, soybean and willow) exposed to ferri-cyanide to investigate the half-saturation constant (K M ) and the maximal metabolic capacity (v max ) involved in phyto-assimilation. Three varieties for each testing species were collected from different origins. Measured concentrations show that the uptake rates responded biphasically to ferri-cyanide treatments by showing increases linearly at low and almost constant at high concentrations from all treatments, indicating that phyto-assimilation of ferri-cyanide followed the Michaelis-Menten kinetics. Using non-linear regression, the highest v max was by rice, followed by willows. The lowest v max was found for soybean. All plants, except maize (DY26) and rice (XJ12), had a similar K M value, suggesting the same enzyme was active in phyto-assimilation of ferri-cyanide. Transcript level, by real-time quantitative PCR, of enzymes involved in degradation of cyanides showed that the analyzed genes were differently expressed during different cyanides exposure. The expression of CAS and ST genes responded positively to KCN exposure, suggesting that β-CAS and ST pathways were two possible pathways for cyanide detoxification in rice. The transcript level of NIT and ASPNASE genes also showed a remarkable up-regulation to KCN, implying the contribution to the pool of amino acid aspartate, which is an end product of CN metabolism. Up-regulation of GS genes suggests that acquisition of ammonium released from cyanide degradation may be an additional nitrogen source for plant nutrition. Results also revealed that the expressions of these genes, except for GS, were relatively constant during iron cyanide exposure, suggesting that they are likely metabolized by plants through a non-defined pathway rather than the β-CAS pathway.
Blum, Philipp; Hunkeler, Daniel; Weede, Matthias; Beyer, Christof; Grathwohl, Peter; Morasch, Barbara
2009-04-01
At a former wood preservation plant severely contaminated with coal tar oil, in situ bulk attenuation and biodegradation rate constants for several monoaromatic (BTEX) and polyaromatic hydrocarbons (PAH) were determined using (1) classical first order decay models, (2) Michaelis-Menten degradation kinetics (MM), and (3) stable carbon isotopes, for o-xylene and naphthalene. The first order bulk attenuation rate constant for o-xylene was calculated to be 0.0025 d - 1 and a novel stable isotope-based first order model, which also accounted for the respective redox conditions, resulted in a slightly smaller biodegradation rate constant of 0.0019 d - 1 . Based on MM-kinetics, the o-xylene concentration decreased with a maximum rate of kmax = 0.1 µg/L/d. The bulk attenuation rate constant of naphthalene retrieved from the classical first order decay model was 0.0038 d - 1 . The stable isotope-based biodegradation rate constant of 0.0027 d - 1 was smaller in the reduced zone, while residual naphthalene in the oxic part of the plume further downgradient was degraded at a higher rate of 0.0038 d - 1 . With MM-kinetics a maximum degradation rate of kmax = 12 µg/L/d was determined. Although best fits were obtained by MM-kinetics, we consider the carbon stable isotope-based approach more appropriate as it is specific for biodegradation (not overall attenuation) and at the same time accounts for the dominant electron-accepting process. For o-xylene a field based isotope enrichment factor ɛfield of - 1.4 could be determined using the Rayleigh model, which closely matched values from laboratory studies of o-xylene degradation under sulfate-reducing conditions.
Blum, Philipp; Hunkeler, Daniel; Weede, Matthias; Beyer, Christof; Grathwohl, Peter; Morasch, Barbara
2009-04-01
At a former wood preservation plant severely contaminated with coal tar oil, in situ bulk attenuation and biodegradation rate constants for several monoaromatic (BTEX) and polyaromatic hydrocarbons (PAH) were determined using (1) classical first order decay models, (2) Michaelis-Menten degradation kinetics (MM), and (3) stable carbon isotopes, for o-xylene and naphthalene. The first order bulk attenuation rate constant for o-xylene was calculated to be 0.0025 d(-1) and a novel stable isotope-based first order model, which also accounted for the respective redox conditions, resulted in a slightly smaller biodegradation rate constant of 0.0019 d(-1). Based on MM-kinetics, the o-xylene concentration decreased with a maximum rate of k(max)=0.1 microg/L/d. The bulk attenuation rate constant of naphthalene retrieved from the classical first order decay model was 0.0038 d(-1). The stable isotope-based biodegradation rate constant of 0.0027 d(-1) was smaller in the reduced zone, while residual naphthalene in the oxic part of the plume further downgradient was degraded at a higher rate of 0.0038 d(-1). With MM-kinetics a maximum degradation rate of k(max)=12 microg/L/d was determined. Although best fits were obtained by MM-kinetics, we consider the carbon stable isotope-based approach more appropriate as it is specific for biodegradation (not overall attenuation) and at the same time accounts for the dominant electron-accepting process. For o-xylene a field based isotope enrichment factor epsilon(field) of -1.4 could be determined using the Rayleigh model, which closely matched values from laboratory studies of o-xylene degradation under sulfate-reducing conditions.
Button, D K; Robertson, Betsy; Gustafson, Elizabeth; Zhao, Xiaoming
2004-09-01
A theory for solute uptake by whole cells was derived with a focus on the ability of oligobacteria to sequester nutrients. It provided a general relationship that was used to obtain the kinetic constants for in situ marine populations in the presence of naturally occurring substrates. In situ affinities of 0.9 to 400 liters g of cells(-1) h(-1) found were up to 10(3) times smaller than those from a "Marinobacter arcticus " isolate, but springtime values were greatly increased by warming. Affinities of the isolate for usual polar substrates but not for hydrocarbons were diminished by ionophores. A kinetic curve or Monod plot was constructed from the best available data for cytoarchitectural components of the isolate by using the theory together with concepts and calculations from first principles. The order of effect of these components on specific affinity was membrane potential > cytoplasmic enzyme concentration > cytoplasmic enzyme affinity > permease concentration > area of the permease site > translation coefficient > porin concentration. Component balance was influential as well; a small increase in cytoplasmic enzyme concentration gave a large increase in the effect of permease concentration. The effect of permease concentration on specific affinity was large, while the effect on K(m) was small. These results are in contrast to the Michaelis-Menten theory as applied by Monod that has uptake kinetics dependent on the quality of the permease molecules, with K(m) as an independent measure of affinity. Calculations demonstrated that most oligobacteria in the environment must use multiple substrates simultaneously to attain sufficient energy and material for growth, a requirement consistent with communities largely comprising few species.
Leonard, Erin M; Marentette, Julie R; Balshine, Sigal; Wood, Chris M
2014-03-01
Traditionally, water quality guidelines/criteria are based on lethality tests where results are expressed as a function of waterborne concentrations (e.g. LC50). However, there is growing interest in the use of uptake and binding relationships, such as biotic ligand models (BLM), and in bioaccumulation parameters, such as critical body residue values (e.g. CBR50), to predict metal toxicity in aquatic organisms. Nevertheless, all these approaches only protect species against physiological death (e.g. mortality, failed recruitment), and do not consider ecological death which can occur at much lower concentrations when the animal cannot perform normal behaviours essential for survival. Therefore, we investigated acute (96 h) Ni toxicity in two freshwater fish species, the round goby (Neogobius melanostomus) and rainbow trout (Oncorhynchus mykiss) and compared LC, BLM, and CBR parameters for various organs, as well as behavioural responses (spontaneous activity). In general, round goby were more sensitive. Ni bioaccumulation displayed Michaelis-Menten kinetics in most tissues, and round goby gills had lower Kd (higher binding affinity) but similar Bmax (binding site density) values relative to rainbow trout gills. Round goby also accumulated more Ni than did trout in most tissues at a given exposure concentration. Organ-specific 96 h acute CBR values tended to be higher in round goby but 96 h acute CBR50 and CBR10 values in the gills were very similar in the two species. In contrast, LC50 and LC10 values were significantly higher in rainbow trout. With respect to BLM parameters, gill log KNiBL values for bioaccumulation were higher by 0.4-0.8 log units than the log KNiBL values for toxicity in both species, and both values were higher in goby (more sensitive). Round goby were also more sensitive with respect to the behavioural response, exhibiting a significant decline of 63-75 % in movements per minute at Ni concentrations at and above only 8 % of the LC50 value
Long, Cormac G; Gilbertson, John D; Vijayaraghavan, Ganesh; Stevenson, Keith J; Pursell, Christopher J; Chandler, Bert D
2008-08-06
Thiol monolayer-protected Au clusters (MPCs) were prepared using dendrimer templates, deposited onto a high-surface-area titania, and then the thiol stabilizers were removed under H2/N2. The resulting Au catalysts were characterized with transmission electron microscopy, X-ray photoelectron spectroscopy, and infrared spectroscopy of adsorbed CO. The Au catalysts prepared via this route displayed minimal particle agglomeration during the deposition and activation steps. Structural data obtained from the physical characterization of the Au catalysts were comparable to features exhibited from a traditionally prepared standard Au catalyst obtained from the World Gold Council (WGC). A differential kinetic study of CO oxidation catalysis by the MPC-prepared Au and the standard WGC catalyst showed that these two catalyst systems have essentially the same reaction order and Arrhenius apparent activation energies (28 kJ/mol). However, the MPC-prepared Au catalyst shows 50% greater activity for CO oxidation. Using a Michaelis-Menten approach, the oxygen binding constants for the two catalyst systems were determined and found to be essentially the same within experimental error. To our knowledge, this kinetic evaluation is the first experimental determination of oxygen binding by supported Au nanoparticle catalysts under working conditions. The values for the oxygen binding equilibrium constant obtained from the Michaelis-Menten treatment (ca. 29-39) are consistent with ultra-high-vacuum measurements on model catalyst systems and support density functional theory calculations for oxygen binding at corner or edge atoms on Au nanoparticles and clusters.
Zhou, Chuanzheng; Chattopadhyaya, Jyoti
2010-04-02
In this study, 12 different native or LNA, carba-LNA-modified dinucleoside phosphates were designed as simple chemical models to study how carba-LNA modifications improve the 3'-exonuclease (SVPDE in this study) resistance of internucleotidic phosphate compared to those exhibited by LNA-modified and the native counterparts. Michaelis-Menten kinetic studies for dimers 3 - 7, in which the LNA or carba-LNA modifications are located at the 5'-end, showed that (i) increased 3'-exonuclease resistance of (5')[LNA-T](p)T (3) compared to the native (5')T(p)T (1) was mainly attributed to steric hindrance imposed by the LNA modification that retards the nuclease binding (K(M)) and (ii) digestion of (5')[carba-LNA-dT](p)T (4) and (5')[LNA-T](p)T (3), however, exhibit similar K(M)s, whereas the former shows a 100x decrease in K(cat) and is hence more stable than the latter. By studying the correlation between log k(cat) and pK(a) of the departing 3'(or 6')-OHs for 3-7, we found the pK(a) of 3'-OH of carba-LNA-T was 1.4 pK(a) units higher than that of LNA-T, and this relatively less acidic character of the 3'-OH in the former leads to the 100x decrease in the catalytic efficiency for the digestion of (5')[carba-LNA-T](p)T (4). In contrast, Michaelis-Menten kinetic studies for dimers 9-12, with the LNA or carba-LNA modifications at the 3'-end, showed that the digestion of (5')T(p)[LNA-T] (9) exhibited similar K(M) but k(cat) decreased around 40 times compared to that of the native (5')T(p)T (1). Similar k(cat) values have been observed for digestion of (5')T(p)[carba-LNA-T] (10) and (5')T(p)[LNA-T] (9). The higher stability of carba-LNA modified dimer 10 compared with LNA modified dimer 9 comes solely from the increased K(M).
André Rosa Martins
2015-06-01
Full Text Available ResumoOs processos enzimáticos que seguem o modelo cinético de Michaelis-Menten foram estudados a partir de diferentes propostas para descrever a etapa de inibição reversível. As propostas de inibição foram comparadas a partir de um processo genérico, onde as constantes cinéticas receberam valores unitários e o valor numérico da concentração de substrato foi dez (10 vezes superior ao valor numérico da concentração de enzima. Para cada proposta de modelo de inibição foram obtidas soluções numéricas a partir de sistema não linear de equações diferenciais ordinárias, gerando gráficos que apresentaram, separadamente, a variação das concentrações da enzima, dos complexos enzimáticos, do substrato e do produto da reação. Foi obtido um modelo, dentre as propostas avaliadas, com desempenho indicando comportamento similar ao verificado no modelo clássico de Michaelis-Menten, onde o complexo de reação é rapidamente formado e, ao longo do processo, decai até tender a zero. Em contrapartida, diferentemente do modelo clássico, na nova proposta de modelo o efeito de inibição começa em zero e, ao longo do processo, tende ao valor nominal da concentração inicial da enzima. Tais respostas mostraram-se válidas para valores distintos de concentração de enzima e de tempo de processo, mostrando robustez e indicando uma tendência do somatório do substrato e do produto atingir o valor nominal da concentração inicial do substrato ao longo do tempo de processamento.
Sims, Paul A.
2009-01-01
The King-Altman method of deriving rate equations for enzymatic reactions is applied to the derivation of the Michaelis-Menten equation, along with an explanation for how (or why) the King-Altman method works in this case. The slightly more complicated cases of competitive inhibition and a two-substrate enzyme-catalyzed reaction are then treated…
Sims, Paul A.
2009-01-01
The King-Altman method of deriving rate equations for enzymatic reactions is applied to the derivation of the Michaelis-Menten equation, along with an explanation for how (or why) the King-Altman method works in this case. The slightly more complicated cases of competitive inhibition and a two-substrate enzyme-catalyzed reaction are then treated…
Introducing Michaelis-Menten Kinetics through Simulation
Halkides, Christopher J.; Herman, Russell
2007-01-01
We describe a computer tutorial that introduces the concept of the steady state in enzyme kinetics. The tutorial allows students to produce graphs of the concentrations of free enzyme, enzyme-substrate complex, and product versus time in order to learn about the approach to steady state. By using a range of substrate concentrations and rate…
The Michaelis-Menten-Stueckelberg Theorem
Gorban, Alexander N.; Muhammad Shahzad
2011-01-01
We study chemical reactions with complex mechanisms under two assumptions: (i) intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS) and (ii) they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE). Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without mic...
Introducing Michaelis-Menten Kinetics through Simulation
Halkides, Christopher J.; Herman, Russell
2007-01-01
We describe a computer tutorial that introduces the concept of the steady state in enzyme kinetics. The tutorial allows students to produce graphs of the concentrations of free enzyme, enzyme-substrate complex, and product versus time in order to learn about the approach to steady state. By using a range of substrate concentrations and rate…
Leonard, Erin M; Wood, Chris M
2013-06-01
We investigated the bioaccumulation and acute toxicity (48 h or 96 h) of Ni in four freshwater invertebrate species in two waters with hardness of 40 (soft water) and 140 mg L(-1) as CaCO(3) (hard water). Sensitivity order (most to least) was Lymnaea stagnalis > Daphnia pulex > Lumbriculus variegatus > Chironomus riparius. In all cases water hardness was protective against acute Ni toxicity with LC(50) values 3-3.5× higher in the hard water vs. soft water. In addition, higher water hardness significantly reduced Ni bioaccumulation in these organisms suggesting that competition by Ca and Mg for uptake at the biotic ligand may contribute to higher metal resistance. CBR50 values (Critical Body Residues) were less dependent on water chemistry (i.e. more consistent) than LC(50) values within and across species by ~2 fold. These data support one of the main advantages of the Tissue Residue Approach (TRA) where tissue concentrations are generally less variable than exposure concentrations with respect to toxicity. Whole body Ni bioaccumulation followed Michaelis-Menten kinetics in all organisms, with greater hardness tending to decrease B(max) with no consistent effect on K(d). Across species, acute Ni LC(50) values tended to increase with both K(d) and B(max) values - i.e. more sensitive species exhibited higher binding affinity and lower binding capacity for Ni, but there was no correlation with body size. With respect to biotic ligand modeling, log K(NiBL) values derived from Ni bioaccumulation correlated well with log K(NiBL) values derived from toxicity testing. Both whole body Na and Mg levels were disturbed, suggesting that disruption of ionoregulatory homeostasis is a mechanism of acute Ni toxicity. In L. stagnalis, Na depletion was a more sensitive endpoint than mortality, however, the opposite was true for the other organisms. This is the first study to show the relationship between Na and Ni. Copyright © 2013 Elsevier Inc. All rights reserved.
Gumowski, I
1977-01-01
A class of differential equations with pure delay and a hyperbolic nonlinearity, analogous to the Michaelis-Menten term in chemical reaction kinetics, is examined. Conditions for the existence of periodic solutions are established. The amplitude and period dependences on the equation parameters are estimated analytically. A mixed analytico-numerical approach is used in the computations, because a straightforward integration of the equations is numerically ill conditioned. (11 refs).
Double perturbation series in the differential equations of enzyme kinetics
Fraser, Simon J.
1998-07-01
The connection between combined singular and ordinary perturbation methods and slow-manifold theory is discussed using the Michaelis-Menten model of enzyme catalysis as an example. This two-step mechanism is described by a planar system of ordinary differential equations (ODEs) with a fast transient and a slow "steady-state" decay mode. The systems of scaled nonlinear ODEs for this mechanism contain a singular (η) and an ordinary (ɛ) perturbation parameter: η multiplies the velocity component of the fast variable and dominates the fast-mode perturbation series; ɛ controls the decay toward equilibrium and dominates the slow-mode perturbation series. However, higher order terms in both series contain η and ɛ. Finite series expansions partially decouple the system of ODEs into fast-mode and slow-mode ODEs; infinite series expansions completely decouple these ODEs. Correspondingly, any slow-mode ODE approximately describes motion on M, the linelike slow manifold of the system, and in the infinite series limit this description is exact. Thus the perturbation treatment and the slow-manifold picture of the system are closely related. The functional equation for M is solved automatically with the manipulative language MAPLE. The formal η and ɛ single perturbation expansions for the slow mode yield the same double (η,ɛ) perturbation series expressions to given order. Generalizations of this procedure are discussed.
Modeling of Bacillus spores: Inactivation and Outgrowth
2011-03-01
52 Michaelis - Menten Kinetics ...of repair mechanism [36]. These models were based on Michaelis - Menten kinetics , which is also the foundation of the work in this research Michaelis ...catalyzed reactions. Michaelis - Menten kinetics is a model of enzyme kinetics . The Michaelis - Menten equation describes the rates of enzymatic reactions by
More Nuts and Bolts of Michaelis-Menten Enzyme Kinetics
Lechner, Joseph H.
2011-01-01
Several additions to a classroom activity are proposed in which an "enzyme" (the student) converts "substrates" (nut-bolt assemblies) into "products" (separated nuts and bolts) by unscrewing them. (Contains 1 table.)
More Nuts and Bolts of Michaelis-Menten Enzyme Kinetics
Lechner, Joseph H.
2011-01-01
Several additions to a classroom activity are proposed in which an "enzyme" (the student) converts "substrates" (nut-bolt assemblies) into "products" (separated nuts and bolts) by unscrewing them. (Contains 1 table.)
A nonlinear viscoelastic constitutive equation - Yield predictions in multiaxial deformations
Shay, R. M., Jr.; Caruthers, J. M.
1987-01-01
Yield stress predictions of a nonlinear viscoelastic constitutive equation for amorphous polymer solids have been obtained and are compared with the phenomenological von Mises yield criterion. Linear viscoelasticity theory has been extended to include finite strains and a material timescale that depends on the instantaneous temperature, volume, and pressure. Results are presented for yield and the correct temperature and strain-rate dependence in a variety of multiaxial deformations. The present nonlinear viscoelastic constitutive equation can be formulated in terms of either a Cauchy or second Piola-Kirchhoff stress tensor, and in terms of either atmospheric or hydrostatic pressure.
Hezbollah: The Dynamics of Recruitment
2011-05-19
fundamental Michaelis - Menten kinetic interaction of the enzyme- substrate complex over time. As substrates are converted by enzymes 0 to the intermediate... Michaelis - Menten , Sensitivity Analysis, Nonlinear Differential Equations 16. PRICE CODE 17. SECURITY CLASSIFICATION UNCLASSIFIED OF REPORT 18...Illustrations Figures Figure 1. Concentration over time for the Michaelis - Menten equations. ...................................... 38 Figure 2
Input-output relations in biological systems: measurement, information and the Hill equation.
Frank, Steven A
2013-01-01
Biological systems produce outputs in response to variable inputs. Input-output relations tend to follow a few regular patterns. For example, many chemical processes follow the S-shaped Hill equation relation between input concentrations and output concentrations. That Hill equation pattern contradicts the fundamental Michaelis-Menten theory of enzyme kinetics. I use the discrepancy between the expected Michaelis-Menten process of enzyme kinetics and the widely observed Hill equation pattern of biological systems to explore the general properties of biological input-output relations. I start with the various processes that could explain the discrepancy between basic chemistry and biological pattern. I then expand the analysis to consider broader aspects that shape biological input-output relations. Key aspects include the input-output processing by component subsystems and how those components combine to determine the system's overall input-output relations. That aggregate structure often imposes strong regularity on underlying disorder. Aggregation imposes order by dissipating information as it flows through the components of a system. The dissipation of information may be evaluated by the analysis of measurement and precision, explaining why certain common scaling patterns arise so frequently in input-output relations. I discuss how aggregation, measurement and scale provide a framework for understanding the relations between pattern and process. The regularity imposed by those broader structural aspects sets the contours of variation in biology. Thus, biological design will also tend to follow those contours. Natural selection may act primarily to modulate system properties within those broad constraints.
Nonstop Selection for High and Stable Crop Yield by Two Prognostic Equations to Reduce Yield Losses
Dionysia A. Fasoula
2012-09-01
Full Text Available Yield losses occurring at the field level, whether due to plant diseases or abiotic stresses, reveal reduced stability of the crop yield potential. The paper argues that the stability of crop yield potential is a trait with a clear genetic component, which can be successfully selected for at the single-plant level and incorporated into high-yielding cultivars. Two novel selection equations with prognostic power are presented, capable to objectively phenotype and evaluate individual plants in real field conditions in the absence of the masking effects of interplant competition and soil heterogeneity. The equations predict performance at the crop stand through the key concept of coefficient of homeostasis and are equally useful for early generation selection and for nonstop selection within finished cultivars in order to continuously incorporate the adaptive (genetic or epigenetic responses of plants. Exploitation of adaptive responses acquires particular importance in view of the climate change effects on crop productivity and the changing biotic or abiotic micro-environments. Cotton is used as a case study to highlight the potential of nonstop selection for increasing crop yield and for the gradual build-up of disease resistance. In addition, the paper envisions and proposes the formation of international networks of researchers focusing on specific diseases as, for example, the cereal root-rot or the cotton Verticillium wilt that will concurrently use the proposed strategy in their respective environments to select for resistant genotypes, while gaining a deeper understanding of the nature of the genetic or epigenetic changes at the phenotypic and genomic levels.
Reboucas, G.F.; Moraes Goncalves, de T.; Martines, M.L.; Azevedo Junior, J.; Koops, W.J.
2008-01-01
This study aimed to calculate new accumulated and daily functions based on the Michaelis-Menten equation to estimate the 305-days production of Gir cows using test day milk yields. Data consisted of 7,412 lactation records of 3,416 Gir cows (Bos indicus) collected from 1987 to 2004 in 51 herds
Reboucas, G.F.; Moraes Goncalves, de T.; Martines, M.L.; Azevedo Junior, J.; Koops, W.J.
2008-01-01
This study aimed to calculate new accumulated and daily functions based on the Michaelis-Menten equation to estimate the 305-days production of Gir cows using test day milk yields. Data consisted of 7,412 lactation records of 3,416 Gir cows (Bos indicus) collected from 1987 to 2004 in 51 herds assis
B. Godongwana
2010-01-01
Full Text Available This paper presents an analytical model of substrate mass transfer through the lumen of a membrane bioreactor. The model is a solution of the convective-diffusion equation in two dimensions using a regular perturbation technique. The analysis accounts for radial-convective flow as well as axial diffusion of the substrate specie. The model is applicable to the different modes of operation of membrane bioreactor (MBR systems (e.g., dead-end, open-shell, or closed-shell mode, as well as the vertical or horizontal orientation. The first-order limit of the Michaelis-Menten equation for substrate consumption was used to test the developed model against available analytical results. The results obtained from the application of this model, along with a biofilm growth kinetic model, will be useful in the derivation of an efficiency expression for enzyme production in an MBR.
Maggi, F.M.; Riley, W.J.
2009-06-01
The theoretical formulation of biological kinetic reactions in isotopic applications often assume first-order or Michaelis-Menten-Monod kinetics under the quasi-steady-state assumption to simplify the system kinetics. However, isotopic e ects have the same order of magnitude as the potential error introduced by these simpli cations. Both formulations lead to a constant fractionation factor which may yield incorrect estimations of the isotopic effect and a misleading interpretation of the isotopic signature of a reaction. We have analyzed the isotopic signature of denitri cation in biogeochemical soil systems by Menyailo and Hungate [2006], where high {sup 15}N{sub 2}O enrichment during N{sub 2}O production and inverse isotope fractionation during N{sub 2}O consumption could not be explained with first-order kinetics and the Rayleigh equation, or with the quasi-steady-state Michaelis-Menten-Monod kinetics. When the quasi-steady-state assumption was relaxed, transient Michaelis-Menten-Monod kinetics accurately reproduced the observations and aided in interpretation of experimental isotopic signatures. These results may imply a substantial revision in using the Rayleigh equation for interpretation of isotopic signatures and in modeling biological kinetic isotope fractionation with first-order kinetics or quasi-steady-state Michaelis-Menten-Monod kinetics.
Lu, Yanfei; Lekszycki, Tomasz
2016-10-01
During fracture healing, a series of complex coupled biological and mechanical phenomena occurs. They include: (i) growth and remodelling of bone, whose Young's modulus varies in space and time; (ii) nutrients' diffusion and consumption by living cells. In this paper, we newly propose to model these evolution phenomena. The considered features include: (i) a new constitutive equation for growth simulation involving the number of sensor cells; (ii) an improved equation for nutrient concentration accounting for the switch between Michaelis-Menten kinetics and linear consumption regime; (iii) a new constitutive equation for Young's modulus evolution accounting for its dependence on nutrient concentration and variable number of active cells. The effectiveness of the model and its predictive capability are qualitatively verified by numerical simulations (using COMSOL) describing the healing of bone in the presence of damaged tissue between fractured parts.
Faridi, A; Murawska, D; Golian, A; Mottaghitalab, M; Gitoee, A; Lopez, S; France, J
2014-04-01
In this study, 2 alternative growth functions, the Lomolino and the extreme value function (EVF), are introduced and their ability to predict body, carcass, and breast weight in ducks evaluated. A comparative study was carried out of these equations with standard growth functions: Gompertz, exponential, Richards, and generalized Michaelis-Menten. Goodness of fit of the functions was evaluated using R(2), mean square error, Akaike information criterion, and Bayesian information criterion, whereas bias factor, accuracy factor, Durbin-Watson statistic, and number of runs of sign were the criteria used for analysis of residuals. Results showed that predictive performance of all functions was acceptable, though the Richards and exponential equations failed to converge in a few cases for both male and female ducks. Based on goodness-of-fit statistics, the Richards, Gompertz, and EVF were the best equations whereas the worst fits to the data were obtained with the exponential. Analysis of residuals indicated that, for the different traits investigated, the least biased and the most accurate equations were the Gompertz, EVF, Richards, and generalized Michaelis-Menten, whereas the exponential was the most biased and least accurate. Based on the Durbin-Watson statistic, all models generally behaved well and only the exponential showed evidence of autocorrelation for all 3 traits investigated. Results showed that with all functions, estimated final weights of males were higher than females for the body, carcass, and breast weight profiles. The alternative functions introduced here have desirable advantages including flexibility and a low number of parameters. However, because this is probably the first study to apply these functions to predict growth patterns in poultry or other animals, further analysis of these new models is suggested.
A stochastic differential equation for exposure yields a beta distribution.
Flynn, Michael R
2004-07-01
This paper presents a stochastic differential equation for exposure based on a modified version of the standard dilution ventilation equation. An equilibrium solution is obtained with the assumption that variability in the rate of change of concentration is proportional to the product of concentration and one minus concentration. Appropriate definitions for concentration are used to ensure a physically consistent model. The probability distribution for exposure that results is the standard beta distribution. This model is supported by several exposure data sets, which fit the beta distribution well. Issues regarding parameter estimation for the beta distribution, and application of the model are presented. Recommendations are made for simultaneously collecting contaminant generation rate information, ventilation rates, and time-dependent breathing-zone tracer concentrations, in addition to the exposure data.
Generalized elastic model yields a fractional Langevin equation description.
Taloni, Alessandro; Chechkin, Aleksei; Klafter, Joseph
2010-04-23
Starting from a generalized elastic model which accounts for the stochastic motion of several physical systems such as membranes, (semi)flexible polymers, and fluctuating interfaces among others, we derive the fractional Langevin equation (FLE) for a probe particle in such systems, in the case of thermal initial conditions. We show that this FLE is the only one fulfilling the fluctuation-dissipation relation within a new family of fractional Brownian motion equations. The FLE for the time-dependent fluctuations of the donor-acceptor distance in a protein is shown to be recovered. When the system starts from nonthermal conditions, the corresponding FLE, which does not fulfill the fluctuation-dissipation relation, is derived.
Karakhim, S A
2012-01-01
The article is dedicated to analysis of equation which expresses apparent Michaelis constant K(m)app) of enzyme-catalysed reactions with activator participation by means of the substrate constant K(s) and rate constant of enzyme-substrate complex decomposition k(cat). It has been shown that although it is possible to record the mechanisms of such reactions as a scheme similar to Michaelis-Menten model and to derive equation of apparent Michaelis constant as K(m(app) = K(s) + k(cat)/k(1), but this approach cannot be used for investigation of all reactions with activator participation. The equation mentioned above is not obeyed in the general case, it may be true for some mechanisms only or under certain ratio of kinetic parameters of enzyme-catalysed reactions.
Development of Optimized Guidelines for Therapeutic Strategies for Organophosphate Poisoning
2011-03-01
Hoang, 1995). Metabolism is a complex mechanism, but is implemented into PBPK models in the form of zero order, first order, or Michaelis - Menten ...kinetics. The Vmax and Km required in the Michaelis - Menten equation are derived from in vitro and in vivo 22 measurements. Most PBPK models...metabolism occurs in the liver and follows Michaelis - Menten kinetics (Hoang, 1995). PBPK modeling of organophosphates The consideration of developing a
Use of Mushroom Tyrosinase to Introduce Michaelis-Menten Enzyme Kinetics to Biochemistry Students
Flurkey, William H.; Inlow, Jennifer K.
2017-01-01
An inexpensive enzyme kinetics laboratory exercise for undergraduate biochemistry students is described utilizing tyrosinase from white button mushrooms. The exercise can be completed in one or two three-hour lab sessions. The optimal amounts of enzyme, substrate (catechol), and inhibitor (kojic acid) are first determined, and then kinetic data is…
The Impact of Deviation from Michaelis-Menten Saturation on Mathematical Model Stability Properties
Blackwell, Charles; Kliss, Mark (Technical Monitor)
1998-01-01
Based on purely abstract ecological theory, it has been argued that a system composed of two or more consumers competing for the same resource cannot persist. By analysis on a Monod format mathematical model, Hubble and others demonstrated that this assertion is true for all but very special cases of such competing organisms which are determined by an index formed by a grouping of. the parameters which characterize the biological processes of the competing organisms. In the laboratory, using a bioreactor, Hansen and Hubble obtained confirmatory results for several cases of two competing species, and they characterized it as "qualitative confirmation" of the assertion. This result is amazing, since the analysis required the exact equality of the hey index, and it seems certain that no pair of organism species could have exactly equal values. It is quite plausible, however, that pairs of organism species could have approximately equal indices, and the question of how different they could be and still have coexistence of the two (or more) presents itself. In this paper, the pursuit of this question and a compatible resolution is presented.
Multi-system Nernst-Michaelis-Menten model applied to bioanodes formed from sewage sludge.
Rimboud, Mickaël; Desmond-Le Quemener, Elie; Erable, Benjamin; Bouchez, Théodore; Bergel, Alain
2015-11-01
Bioanodes were formed under constant polarization at -0.2 V/SCE from fermented sewage sludge. Current densities reached were 9.3±1.2 A m(-2) with the whole fermented sludge and 6.2±0.9 A m(-2) with the fermented sludge supernatant. The bioanode kinetics was analysed by differentiating among the contributions of the three redox systems identified by voltammetry. Each system ensured reversible Nernstian electron transfer but around a different central potential. The global overpotential required to reach the maximum current plateau was not imposed by slow electron transfer rates but was due to the potential range covered by the different redox systems. The microbial communities of the three bioanodes were analysed by 16S rRNA gene pyrosequencing. They showed a significant microbial diversity around a core of Desulfuromonadales, the proportion of which was correlated with the electrochemical performance of the bioanodes. Copyright © 2015 Elsevier Ltd. All rights reserved.
The Nuts and Bolts of Michaelis-Menten Enzyme Kinetics: Suggestions and Clarifications
Silverstein, Todd
2011-01-01
Matthew Junker's recent article describes a useful and effective enzyme kinetics application and analogy in which students simulate enzyme activity by unscrewing nut-bolt "substrate molecules", thus, converting them into separate nuts and bolts "products". A number of suggestions and corrections are presented that improve the clarity and accuracy…
Non-Michaelis-Menten kinetics model for conductance of low-conductance potassium ion channels.
Tolokh, Igor S; Tolokh, Illya I; Cho, Hee Cheol; D'Avanzo, Nazzareno; Backx, Peter H; Goldman, Saul; Gray, C G
2005-02-01
A reduced kinetics model is proposed for ion permeation in low-conductance potassium ion channels with zero net electrical charge in the selectivity filter region. The selectivity filter is assumed to be the only conductance-determining part of the channel. Ion entry and exit rate constants depend on the occupancy of the filter due to ion-ion interactions. The corresponding rates are assumed slow relative to the rates of ion motion between binding sites inside the filter, allowing a reduction of the kinetics model of the filter by averaging the entry and exit rate constants over the states with a particular occupancy number. The reduced kinetics model for low-conductance channels is described by only three states and two sets of effective rate constants characterizing transitions between these states. An explicit expression for the channel conductance as a function of symmetrical external ion concentration is derived under the assumption that the average electrical mobility of ions in the selectivity filter region in a limited range of ion concentrations does not depend on these concentrations. The simplified conductance model is shown to provide a good description of the experimentally observed conductance-concentration curve for the low-conductance potassium channel Kir2.1, and also predicts the mean occupancy of the selectivity filter of this channel. We find that at physiological external ion concentrations this occupancy is much lower than the value of two ions observed for one of the high-conductance potassium channels, KcsA.
Stability in a diffusive food chain model with Michaelis-Menten functional response
Lin, Zhigui; Pedersen, Michael
2004-01-01
This paper deals with the behavior of positive solutions to a reaction-diffusion system with homogeneous Neumann boundary conditions describing a three species food chain. A sufficient condition for the local asymptotical stability is given by linearization and also a sufficient condition...... for the global asymptotical stability is given by a Lyapunov function. Our result shows that the equilibrium solution is globally asymptotically stable if the net birth rate of the first species is big enough and the net death rate of the third species is neither too big nor too small. (C) 2004 Elsevier Ltd. All...
Estudio de bioequivalencia de teofilina considerando cinética de Michaelis-Menten
Fagiolino, Pietro; Turlier, M.; Payssé, Helena; Aiache, Jean-Marc
1994-01-01
Se presenta un estudio de bioequivalencia de dos formas farmacéuticas de Teofilina de liberación prolongada, teniendo en cuenta la cinética no lineal de eliminación de esta droga. Una dosis de 300 mg de Teofilina fue administrada a 12 voluntarios sanos, en un diseno aleatorio, cruzado y compensado. Se utilizó una forma farmacéutica elixir, a los efectos de estimar los parámetros farmacocinéticos de eliminación en cada individuo. Como parámetros de evaluación de la biodisponibilidad se utilizó...
The Nuts and Bolts of Michaelis-Menten Enzyme Kinetics: Suggestions and Clarifications
Silverstein, Todd
2011-01-01
Matthew Junker's recent article describes a useful and effective enzyme kinetics application and analogy in which students simulate enzyme activity by unscrewing nut-bolt "substrate molecules", thus, converting them into separate nuts and bolts "products". A number of suggestions and corrections are presented that improve the clarity and accuracy…
Hadamard Transform Time-of-Flight Mass Spectrometry
2010-01-26
determined by direct fitting of the initial rates data to the Michaelis - Menten equation. Excellent agreement is shown amongst the values indicating that...of VGVKVR by trypsin at pH 8.5. The dashed red line in the figure shows a best fit to the Michaelis - Menten equation for the data collected. The
Hadamard Transform Time-of-Flight Spectroscopy
2010-01-26
system presented in Figure 13 were determined by direct fitting of the initial rates data to the Michaelis - Menten equation. Excellent agreement is...trypsin at pH 8.5. The dashed red line in the figure shows a best fit to the Michaelis - Menten equation for the data collected. The error bars in
Yield stress of duplex stainless steel specimens estimated using a compound Hall–Petch equation
Noriaki Hirota, Fuxing Yin, Tsukasa Azuma and Tadanobu Inoue
2010-01-01
Full Text Available In this study, the 0.2% yield stress of duplex stainless steel was evaluated using a compound Hall–Petch equation. The compound Hall–Petch equation was derived from four types of duplex stainless steel, which contained 0.2–64.4 wt% δ-ferrite phase, had different chemical compositions and were annealed at different temperatures. Intragranular yield stress was measured with an ultra-microhardness tester and evaluated with the yield stress model proposed by Dao et al. Grain size, volume fraction and texture were monitored by electron backscattering diffraction measurement. The kγ constant in the compound equation for duplex stainless steel agrees well with that for γ-phase SUS316L steel in the temperature range of 1323–1473 K. The derived compound Hall–Petch equation predicts that the yield stress will be in good agreement with the experimental results for the Cr, Mn, Si, Ni and N solid-solution states. We find that the intragranular yield stress of the δ-phase of duplex stainless steel is rather sensitive to the chemical composition and annealing conditions, which is attributed to the size misfit parameter.
Jensen, Michael Gejl; Lerche, Susanne; Egefjord, Lærke
2013-01-01
hypoglycemia study and our previous hyperglycemia study to estimate the Michaelis-Menten constants of glucose transport and metabolism. The GLP-1 treatment lowered the vascular volume of brain tissue. Loading data from hypo- to hyperglycemia into the Michaelis-Menten equation, we found increased maximum...
Simulation Models of Leaf Area Index and Yield for Cotton Grown with Different Soil Conditioners.
Lijun Su
Full Text Available Simulation models of leaf area index (LAI and yield for cotton can provide a theoretical foundation for predicting future variations in yield. This paper analyses the increase in LAI and the relationships between LAI, dry matter, and yield for cotton under three soil conditioners near Korla, Xinjiang, China. Dynamic changes in cotton LAI were evaluated using modified logistic, Gaussian, modified Gaussian, log normal, and cubic polynomial models. Universal models for simulating the relative leaf area index (RLAI were established in which the application rate of soil conditioner was used to estimate the maximum LAI (LAIm. In addition, the relationships between LAIm and dry matter mass, yield, and the harvest index were investigated, and a simulation model for yield is proposed. A feasibility analysis of the models indicated that the cubic polynomial and Gaussian models were less accurate than the other three models for simulating increases in RLAI. Despite significant differences in LAIs under the type and amount of soil conditioner applied, LAIm could be described by aboveground dry matter using Michaelis-Menten kinetics. Moreover, the simulation model for cotton yield based on LAIm and the harvest index presented in this work provided important theoretical insights for improving water use efficiency in cotton cultivation and for identifying optimal application rates of soil conditioners.
Valencia, Pedro L; Astudillo-Castro, Carolina; Gajardo, Diego; Flores, Sebastián
2017-04-01
We provide initial rate data from enzymatic reaction experiments and tis processing to estimate the kinetic parameters from the substrate uncompetitive inhibition equation using the median method published by Eisenthal and Cornish-Bowden (Cornish-Bowden and Eisenthal, 1974; Eisenthal and Cornish-Bowden, 1974). The method was denominated the direct linear plot and consists in the calculation of the median from a dataset of kinetic parameters Vmax and Km from the Michaelis-Menten equation. In this opportunity we present the procedure to applicate the direct linear plot to the substrate uncompetitive inhibition equation; a three-parameter equation. The median method is characterized for its robustness and its insensibility to outlier. The calculations are presented in an Excel datasheet and a computational algorithm was developed in the free software Python. The kinetic parameters of the substrate uncompetitive inhibition equation Vmax , Km and Ks were calculated using three experimental points from the dataset formed by 13 experimental points. All the 286 combinations were calculated. The dataset of kinetic parameters resulting from this combinatorial was used to calculate the median which corresponds to the statistic estimator of the real kinetic parameters. A comparative statistical analyses between the median method and the least squares was published in Valencia et al. [3].
Design optimality for models defined by a system of ordinary differential equations.
Rodríguez-Díaz, Juan M; Sánchez-León, Guillermo
2014-09-01
Many scientific processes, specially in pharmacokinetics (PK) and pharmacodynamics (PD) studies, are defined by a system of ordinary differential equations (ODE). If there are unknown parameters that need to be estimated, the optimal experimental design approach offers quality estimators for the different objectives of the practitioners. When computing optimal designs the standard procedure uses the linearization of the analytical expression of the ODE solution, which is not feasible when this analytical form does not exist. In this work some methods to solve this problem are described and discussed. Optimal designs for two well-known example models, Iodine and Michaelis-Menten, have been computed using the proposed methods. A thorough study has been done for a specific two-parameter PK model, the biokinetic model of ciprofloxacin and ofloxacin, computing the best designs for different optimality criteria and numbers of points. The designs have been compared according to their efficiency, and the goodness of the designs for the estimation of each parameter has been checked. Although the objectives of the paper are focused on the optimal design field, the methodology can be used as well for a sensitivity analysis of ordinary differential equation systems.
Optimal experiment selection for parameter estimation in biological differential equation models
Transtrum Mark K
2012-07-01
Full Text Available Abstract Background Parameter estimation in biological models is a common yet challenging problem. In this work we explore the problem for gene regulatory networks modeled by differential equations with unknown parameters, such as decay rates, reaction rates, Michaelis-Menten constants, and Hill coefficients. We explore the question to what extent parameters can be efficiently estimated by appropriate experimental selection. Results A minimization formulation is used to find the parameter values that best fit the experiment data. When the data is insufficient, the minimization problem often has many local minima that fit the data reasonably well. We show that selecting a new experiment based on the local Fisher Information of one local minimum generates additional data that allows one to successfully discriminate among the many local minima. The parameters can be estimated to high accuracy by iteratively performing minimization and experiment selection. We show that the experiment choices are roughly independent of which local minima is used to calculate the local Fisher Information. Conclusions We show that by an appropriate choice of experiments, one can, in principle, efficiently and accurately estimate all the parameters of gene regulatory network. In addition, we demonstrate that appropriate experiment selection can also allow one to restrict model predictions without constraining the parameters using many fewer experiments. We suggest that predicting model behaviors and inferring parameters represent two different approaches to model calibration with different requirements on data and experimental cost.
Liu Jian; Wang Hai-Yan; Bao Jing-Dong
2013-01-01
A minimal system-plus-reservoir model yielding a nonergodic Langevin equation is proposed,which originates from the cubic-spectral density of environmental oscillators and momentum-dependent coupling.This model allows ballistic diffusion and classical localization simultaneously,in which the fluctuation-dissipation relation is still satisfied but the Khinchin theorem is broken.The asymptotical equilibrium for a nonergodic system requires the initial thermal equilibrium,however,when the system starts from nonthermal conditions,it does not approach the equilibration even though a nonlinear potential is used to bound the particle,this can be confirmed by the zeroth law of thermodynamics.In the dynamics of Brownian localization,due to the memory damping function inducing a constant term,our results show that the stationary distribution of the system depends on its initial preparation of coordinate rather than momentum.The coupled oscillator chain with a fixed end boundary acts as a heat bath,which has long been used in studies of collinear atom/solid-surface scattering and lattice vibration,we investigate this problem from the viewpoint of nonergodicity.
Nijland, G.O.; Schouls, J.; Goudriaan, J.
2008-01-01
Any agricultural production process is characterized by input¿output relations. In this paper we show that the production functions of Liebig, Mitscherlich and Liebscher for the relation between nutrient supply and crop production can be regarded as special variants of one 'integrated model'. The
Huang, Hsuan-Ming; Ismail-Beigi, Faramarz; Muzic, Raymond F
2011-08-01
A new model is introduced that individually resolves the delivery, transport, and phosphorylation steps of metabolism of glucose and its analogs in skeletal muscle by interpreting dynamic positron emission tomography (PET) data. The model uniquely utilizes information obtained from the competition between glucose and its radiolabeled analogs. Importantly, the model avoids use of a lumped constant which may depend on physiological state. Four basic physiologic quantities constitute our model parameters, including the fraction of total tissue space occupied by interstitial space (f(IS)), a flow-extraction product and interstitial (IS(g)) and intracellular (IC(g)) glucose concentrations. Using the values of these parameters, cellular influx (CI) and efflux (CE) of glucose, glucose phosphorylation rate (PR), and maximal transport (V(G)) and phosphorylation capacities (V(H)) can all be determined. Herein, the theoretical derivation of our model is addressed and characterizes its properties via simulation. Specifically, the model performance is evaluated by simulation of basal and euglycemic hyperinsulinemic (EH) conditions. In fitting the model-generated, synthetic data (including noise), mean estimates of all but IC(g) of the parameter values are within 5% of their values for both conditions. In addition, mean errors of CI, PR, and V(G) are less than 5% whereas those of VH and CE are not. It is concluded that under the conditions tested, the novel model can provide accurate parameter estimates and physiological quantities, except IC(g) and two quantities that are dependent on IC(g), namely CE and VH. However, the ability to estimate IC(g) seems to improve with increases in intracellular glucose concentrations as evidenced by comparing IC(g) estimates under basal vs EH conditions.
Nijland, G.O.; Schouls, J.; Goudriaan, J.
2008-01-01
Any agricultural production process is characterized by input¿output relations. In this paper we show that the production functions of Liebig, Mitscherlich and Liebscher for the relation between nutrient supply and crop production can be regarded as special variants of one 'integrated model'. The mo
Sheiner, L B; Beal, S L
1980-12-01
Individual pharmacokinetic par parameters quantify the pharmacokinetics of an individual, while population pharmacokinetic parameters quantify population mean kinetics, interindividual variability, and residual intraindividual variability plus measurement error. Individual pharmacokinetics are estimated by fitting individual data to a pharmacokinetic model. Population pharmacokinetic parameters are estimated either by fitting all individual's data together as though there was no individual kinetic differences (the naive pooled data approach), or by fitting each individual's data separately, and then combining the individual parameter estimates (the two-stage approach). A third approach, NONMEM, takes a middle course between these, and avoids shortcomings of each of them. A data set consisting of 124 steady-state phenytoin concentration-dosage pairs from 49 patients, obtained in the routine course of their therapy, was analyzed by each method. The resulting population parameter estimates differ considerably (population mean Km, for example, is estimated as 1.57, 5.36, and 4.44 micrograms/ml by the naive pooled data, two-stage, and NONMEN approaches, respectively). Simulations of the data were analyzed to investigate these differences. The simulations indicate that the pooled data approach fails to estimate variabilities and produces imprecise estimates of mean kinetics. The two-stage approach produces good estimates of mean kinetics, but biased and imprecise estimates of interindividual variability. NONMEN produces accurate and precise estimates of all parameters, and also reasonable confidence intervals for them. This performance is exactly what is expected from theoretical considerations and provides empirical support for the use of NONMEM when estimating population pharmacokinetics from routine type patient data.
Constructing stochastic models from deterministic process equations by propensity adjustment
Wu Jialiang
2011-11-01
Full Text Available Abstract Background Gillespie's stochastic simulation algorithm (SSA for chemical reactions admits three kinds of elementary processes, namely, mass action reactions of 0th, 1st or 2nd order. All other types of reaction processes, for instance those containing non-integer kinetic orders or following other types of kinetic laws, are assumed to be convertible to one of the three elementary kinds, so that SSA can validly be applied. However, the conversion to elementary reactions is often difficult, if not impossible. Within deterministic contexts, a strategy of model reduction is often used. Such a reduction simplifies the actual system of reactions by merging or approximating intermediate steps and omitting reactants such as transient complexes. It would be valuable to adopt a similar reduction strategy to stochastic modelling. Indeed, efforts have been devoted to manipulating the chemical master equation (CME in order to achieve a proper propensity function for a reduced stochastic system. However, manipulations of CME are almost always complicated, and successes have been limited to relative simple cases. Results We propose a rather general strategy for converting a deterministic process model into a corresponding stochastic model and characterize the mathematical connections between the two. The deterministic framework is assumed to be a generalized mass action system and the stochastic analogue is in the format of the chemical master equation. The analysis identifies situations: where a direct conversion is valid; where internal noise affecting the system needs to be taken into account; and where the propensity function must be mathematically adjusted. The conversion from deterministic to stochastic models is illustrated with several representative examples, including reversible reactions with feedback controls, Michaelis-Menten enzyme kinetics, a genetic regulatory motif, and stochastic focusing. Conclusions The construction of a stochastic
Bayesian inference of baseline fertility and treatment effects via a crop yield-fertility model.
Hungyen Chen
Full Text Available To effectively manage soil fertility, knowledge is needed of how a crop uses nutrients from fertilizer applied to the soil. Soil quality is a combination of biological, chemical and physical properties and is hard to assess directly because of collective and multiple functional effects. In this paper, we focus on the application of these concepts to agriculture. We define the baseline fertility of soil as the level of fertility that a crop can acquire for growth from the soil. With this strict definition, we propose a new crop yield-fertility model that enables quantification of the process of improving baseline fertility and the effects of treatments solely from the time series of crop yields. The model was modified from Michaelis-Menten kinetics and measured the additional effects of the treatments given the baseline fertility. Using more than 30 years of experimental data, we used the Bayesian framework to estimate the improvements in baseline fertility and the effects of fertilizer and farmyard manure (FYM on maize (Zea mays, barley (Hordeum vulgare, and soybean (Glycine max yields. Fertilizer contributed the most to the barley yield and FYM contributed the most to the soybean yield among the three crops. The baseline fertility of the subsurface soil was very low for maize and barley prior to fertilization. In contrast, the baseline fertility in this soil approximated half-saturated fertility for the soybean crop. The long-term soil fertility was increased by adding FYM, but the effect of FYM addition was reduced by the addition of fertilizer. Our results provide evidence that long-term soil fertility under continuous farming was maintained, or increased, by the application of natural nutrients compared with the application of synthetic fertilizer.
Vosika, Z.; Mitić, V. V.; Vasić, A.; Lazović, G.; Matija, L.; Kocić, Lj. M.
2017-03-01
In this paper, Caputo based Michaelis-Menten kinetic model based on Time Scale Calculus (TSC) is proposed. The main reason for its consideration is a study of tumor cells population growth dynamics. In the particular case discrete-continuous time kinetics, Michaelis-Menten model is numerically treated, using a new algorithm proposed by authors, called multistep generalized difference transformation method (MSGDETM). In addition numerical simulations are performed and is shown that it represents the upgrade of the multi-step variant of generalized differential transformation method (MSGDTM). A possible conditions for its further development are discussed and possible experimental verification is described.
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
Generic Enzymatic Rate Equation%酶反应速率方程的普适形式
徐岷涓; 朱晓梅; 林保宏; 敖平
2011-01-01
Kinetic modeling of large-scale metabolic network require a generic enzymatic rate equation. In the generic form, kinetic parameters are clear and precise enough to correlate to experimental data and construct a database. Such a uniform form is easy to deal with arbitrary number of substrates and products in computation of dynamic modeling. The generic rate equation is symmetrical in both directions of reversible reaction and formally exact under the quasi-steady state condition. Here presented the rigorous derivation of generic rate equation from further three classical enzymatic rate equations and discussed the characters and uses of the generic form.%酶反应速率方程的普适形式是应用于相互关联的大规模代谢途径动力学建模的重要方法.把酶反应速率方程写成Michaelis-Menten-King-Altman方程形式可以使得动力学参数(或函数)容易与数据库中的实验数据相接轨,并可以处理任意数量的底物和产物,有利于大规模的计算.普适形式可以同时描述正、负反应方向,并能精确地用于准稳态条件.展示了在三类生物体系中广泛存在的酶反应机制中普适方程的严格推导过程,并讨论了普适方程的特点,针对不可逆反应酶反应产生的产物抑制效应可以自然消除,总结了在普适速率方程中体现调节剂的作用和协同作用.
Rezaei, Abolfazl; Mohammadi, Zargham
2017-10-01
The safe groundwater yield plays a major role in the appropriate management of groundwater systems, particularly in (semi-)arid areas like Iran. This study incorporates both the water balance equation and the water table fluctuation to estimate the annual safe yield of the unconfined aquifer in the eastern part of the Kaftar Lake, an Iranian semiarid region. Firstly, the water balance year 2002-03, owing same water table elevation at the beginning and year-end, was chosen from the monthly representative groundwater hydrograph of the aquifer to be taken into account as a basic water year for determining the safe yield. Then the ratio of the total groundwater pumping to the annual groundwater recharge in the selected water balance year together with the quantity of total recharge occurred in the wet period (October to May) of the year of interest were applied to evaluate the annual safe yield at the initiation of the dry period (June to September) of the year of interest. Knowing the annual safe groundwater withdrawal rate at the initiation of each dry period could be helpful to decision makers in managing groundwater resources conservation. Analysis results indicate that to develop a safe management strategy in the aquifer; the ratio of the annual groundwater withdrawal to the annually recharged volume should not exceed 0.69. In the water year 2003-04 where the ratio is equal to 0.52, the water table raised up (about 0.48 m) while the groundwater level significantly declined (about 1.54 m) over the water year 2007-08 where the ratio of the annual groundwater withdrawal to the annually recharged volume (i.e., 2.76) is larger than 0.69.
Rong, Youmin; Zhang, Guojun; Huang, Yu
2016-10-01
Inherent strain analysis has been successfully applied to predict welding deformations of large-scale structural components, while thermal-elastic-plastic finite element method is rarely used for its disadvantages of long calculation period and large storage space. In this paper, a hybrid model considering nonlinear yield stress curves and multi-constraint equations to thermal-elastic-plastic analysis is further proposed to predict welding distortions and residual stresses of large-scale structures. For welding T-joint structural steel S355JR by metal active gas welding, the published experiment results of temperature and displacement fields are applied to illustrate the credibility of the proposed integration model. By comparing numerical results of four different cases with the experiment results, it is verified that prediction precision of welding deformations and residual stresses is apparently improved considering the power-law hardening model, and computational time is also obviously shortened about 30.14% using multi-constraint equations. On the whole, the proposed hybrid method can be further used to precisely and efficiently predict welding deformations and residual stresses of large-scale structures.
Zheljazkov, Valtcho D; Astatkie, Tess; Jeliazkova, Ekaterina A; Schlegel, Vicki
2012-01-01
The objective of this study was to evaluate the effect of 15 distillation times (DT), ranging from 1.25 to 960 min, on oil yield, essential oil profiles, and antioxidant capacity of male J. scopulorum trees. Essential oil yields were 0.07% at 1.25 min DT and reached a maximum of 1.48% at 840 min DT. The concentrations of alpha-thujene (1.76-2.75%), alpha-pinene (2.9-8.7%), sabinene (45-74.7%), myrcene (2.4-3.4%), and para-cymene (0.8-3.1%) were highest at the shortest DT (1.5 to 5 min) and decreased with increasing DT. Cis-sabinene hydrate (0.5-0.97%) and linalool plus trans-sabinene (0.56-1.6%) reached maximum levels at 40 min DT. Maximum concentrations of limonene (2.3-2.8%) and pregeijerene-B (0.06-1.4%) were obtained at 360-480 min DT, and 4-terpinenol (0.7-5.7%) at 480 min DT. Alpha-terpinene (0.16-2.9%), gamma-terpinene (0.3-4.9%) and terpinolene (0.3-1.4%) reached maximum at 720 min DT. The concentrations of delta-cadinene (0.06-1.65%), elemol (0-6.0%), and 8-alpha-acetoxyelemol (0-4.4%) reached maximum at 840 min DT. The yield of the essential oil constituents increased with increasing DT. Only linalool/transsabinene hydrate reached a maximum yield at 360 min DT. Maximum yields of the following constituents were obtained at 720 min DT: alpha-thujene, alpha-pinene, camphene, sabinene, myrcene, alpha-terpinene, para-cimene, limonene, gamma-terpinene, terpinolene, and 4-terpinenol. At 840 min DT, cis-sabinene hydrate, prejeijerene-B, gamma muurolene, delta-cadinene, reached maximum. At 960 min DT, maximum yields of beta-pinene, elemol, alphaeudesmol/betaeudesmol, 8-alpha-acetoxyelemol were reached. These changes were adequately modeled by either the Michaelis-Menten or the Power (Convex) nonlinear regression models. Oils from the 480 min DT showed higher antioxidant activity compared to samples collected at 40, 160, or 960 min DT. These results show the potential for obtaining essential oils with various compositions and antioxidant capacity from male J
Ramzi Othman
2015-01-01
Full Text Available In several industrial applications, metallic structures are facing impact loads. Therefore, there is an important need for developing constitutive equations which take into account the strain rate sensitivity of their mechanical properties. The Johnson-Cook equation was widely used to model the strain rate sensitivity of metals. However, it implies that the yield and flow stresses are linearly increasing in terms of the logarithm of strain rate. This is only true up to a threshold strain rate. In this work, a three-constant constitutive equation, assuming an apparent activation volume which decreases as the strain rate increases, is applied here for some metals. It is shown that this equation fits well the experimental yield and flow stresses for a very wide range of strain rates, including quasi-static, high, and very high strain rates (from 10−5 to 5 × 104 s−1. This is the first time that a constitutive equation is showed to be able to fit the yield stress over a so large strain rate range while using only three material constants.
Chowdhury, Debashish
2014-01-01
Cytoskeletal motor proteins move on filamentous tracks by converting input chemical energy that they derive by catalyzing the hydrolysis of ATP. The ATPase site is the analogue of an engine and hydrolysis of ATP is the analogue of burning of chemical fuel. Moreover, the functional role of a segment of the motor is analogous to that of the transmission system of an automobile, which consists of a shaft, gear, clutch, etc. The operation of the engine is intrinsically 'noisy' and the motor faces a molecular 'hailstorm' in the aqueous medium. In this commemorative review, we celebrate the centenary of Michaelis and Menten's landmark paper of 1913 and the golden jubilee of Monod and colleagues classic paper of 1963 by highlighting their relevance with respect to explaining the operational mechanisms of the engine and the transmission system, respectively, of cytoskeletal motors. © 2013 FEBS.
Her, Cheenou; Alonzo, Aaron P.; Vang, Justin Y.; Torres, Ernesto; Krishnan, V. V.
2015-01-01
Enzyme kinetics is an essential part of a chemistry curriculum, especially for students interested in biomedical research or in health care fields. Though the concept is routinely performed in undergraduate chemistry/biochemistry classrooms using other spectroscopic methods, we provide an optimized approach that uses a real-time monitoring of the…
Her, Cheenou; Alonzo, Aaron P.; Vang, Justin Y.; Torres, Ernesto; Krishnan, V. V.
2015-01-01
Enzyme kinetics is an essential part of a chemistry curriculum, especially for students interested in biomedical research or in health care fields. Though the concept is routinely performed in undergraduate chemistry/biochemistry classrooms using other spectroscopic methods, we provide an optimized approach that uses a real-time monitoring of the…
Jensen, Michael Gejl; Rungby, Jørgen; Brock, Birgitte;
2014-01-01
Glucagon-like peptide-1 (GLP-1) is a potent insulinotropic incretin hormone with pancreatic and extrapancreatic effects. Studies reveal significant effects in regions of brain tissue that regulate appetite and satiety. The effects cause that mimetics of GLP-1 serves as treatment of type 2 diabete...... and in vivo, as in pancreas. The apparent neuroprotective potential of GLP-1, indirectly acting through changes of cerebral blood flow, glucose metabolism or brain glucose concentration, or all of these, is worthy of close attention....
SBMLsqueezer: A CellDesigner plug-in to generate kinetic rate equations for biochemical networks
Schröder Adrian
2008-04-01
Full Text Available Abstract Background The development of complex biochemical models has been facilitated through the standardization of machine-readable representations like SBML (Systems Biology Markup Language. This effort is accompanied by the ongoing development of the human-readable diagrammatic representation SBGN (Systems Biology Graphical Notation. The graphical SBML editor CellDesigner allows direct translation of SBGN into SBML, and vice versa. For the assignment of kinetic rate laws, however, this process is not straightforward, as it often requires manual assembly and specific knowledge of kinetic equations. Results SBMLsqueezer facilitates exactly this modeling step via automated equation generation, overcoming the highly error-prone and cumbersome process of manually assigning kinetic equations. For each reaction the kinetic equation is derived from the stoichiometry, the participating species (e.g., proteins, mRNA or simple molecules as well as the regulatory relations (activation, inhibition or other modulations of the SBGN diagram. Such information allows distinctions between, for example, translation, phosphorylation or state transitions. The types of kinetics considered are numerous, for instance generalized mass-action, Hill, convenience and several Michaelis-Menten-based kinetics, each including activation and inhibition. These kinetics allow SBMLsqueezer to cover metabolic, gene regulatory, signal transduction and mixed networks. Whenever multiple kinetics are applicable to one reaction, parameter settings allow for user-defined specifications. After invoking SBMLsqueezer, the kinetic formulas are generated and assigned to the model, which can then be simulated in CellDesigner or with external ODE solvers. Furthermore, the equations can be exported to SBML, LaTeX or plain text format. Conclusion SBMLsqueezer considers the annotation of all participating reactants, products and regulators when generating rate laws for reactions. Thus, for
Non-steady state population kinetics of intravenous phenytoin.
Frame, B; Beal, S L
1998-08-01
This observational study explored the effects of demographics, sickness, and polypharmacy on the non-steady state population pharmacokinetics of intravenous phenytoin. One hundred fifteen patients were studied. Models were developed using the NONMEM program with hybrid first-order conditional estimation. A Michaelis-Menten model with delayed induction was preferred over a Michaelis-Menten model without induction, a Michaelis-Menten model with immediate induction, or a linear model with delayed induction. When the data were fit to a Michaelis-Menten model with delayed induction, the volume of distribution (Vd) was found to depend on weight and serum albumin. The Vd was estimated to be 0.95 l/kg, assuming an albumin level of 3 g/dl. The Michaelis-Menten constant (km) was estimated to be 7.9 mg/l. The baseline maximum metabolic rate was 580 mg/day for a 70-kg patient. The average time to onset of induction was 59.5 hours. If a fever developed after induction began, it increased the extent of induction. This model was evaluated retrospectively in 26 additional patients, yielding a mean prediction error of -0.4 mg/l (-3.0-2.2 mg/l) and a mean absolute prediction error of 4.7 mg/l (3.2-6.2 mg/l) based on two-level feedback. Given the large interindividual variances in maximum metabolic rate, phenytoin levels should be measured frequently.
Andric, Pavle; Meyer, Anne S.; Jensen, Peter Arendt
2010-01-01
, during 96 h of reaction. When glucose was removed by dialysis during the enzymatic hydrolysis, the cellulose conversion rates and glucose yields increased. In fact, with dialytic in situ glucose removal, the rate of enzyme-catalyzed glucose release during 48-72 h of reaction recovered from 20......-40% to become approximate to 70% of the rate recorded during 6-24 h of reaction. Although Michaelis-Menten kinetics do not suffice to model the kinetics of the complex multi-enzymatic degradation of cellulose, the data for the glucose inhibition were surprisingly well described by simple Michaelis......-Menten inhibition models without great significance of the inhibition mechanism. Moreover, the experimental in situ removal of glucose could be simulated by a Michaelis-Menten inhibition model. The data provide an important base for design of novel reactors and operating regimes which include continuous product...
E. E. De Figueiredo
2015-03-01
Full Text Available In the semi arid Cariri region of the state of Paraiba, Brazil, runoff is of the Hortonian type generated by excess of rainfall over infiltration capacity, and soil erosion is governed by rainfall intensity and sediment size. However, the governing sediment transport mechanism is not well understood. Sediment transport generally depends on the load of sediment provided by soil erosion and on the transport capacity of the flow. The latter is mainly governed by mechanisms such as water shear stress, or stream power. Accordingly, the load of sediment transported by the flow may vary depending on the mechanism involved in the equation of estimation. Investigation of the sediment transport capacity of the flow via a distributed physically-based model is an important and necessary task, but quite rare in semi-arid climates, and particularly in the Cariri region of the state of Paraíba/Brazil. In this study, the equations of Yalin, Engelund & Hansen, Laursen, DuBoys and Bagnold have been coupled with the MOSEE distributed physically based model aiming at identifying the mechanisms leading to the best model simulations when compared with data observed at various basin scales and land uses in the study region. The results obtained with the investigated methods were quite similar and satisfactory suggesting the feasibility of the mechanisms involved, but the observed values were better represented with Bagnold’s equation, which is physically grounded on the stream power, and we recommend it for simulations of similar climate, runoff generation mechanisms and sediment characteristics as in the study region.
Diagnosis of Enzyme Inhibition Using Excel Solver: A Combined Dry and Wet Laboratory Exercise
Dias, Albino A.; Pinto, Paula A.; Fraga, Irene; Bezerra, Rui M. F.
2014-01-01
In enzyme kinetic studies, linear transformations of the Michaelis-Menten equation, such as the Lineweaver-Burk double-reciprocal transformation, present some constraints. The linear transformation distorts the experimental error and the relationship between "x" and "y" axes; consequently, linear regression of transformed data…
Enzymatic Production of Ceramide from Sphingomyelin
Zhang, Long; Hellgren, Lars; Xu, Xuebing
activity. After seven recycles, immobilized enzyme retains around 70% of its initial activity. Through kinetic study, it has been found that the hydrolysis reactions catalyzed by both soluble and immobilized enzyme follow the Michaelis-Menten equation. The presentation will describe the research background...
Diagnosis of Enzyme Inhibition Using Excel Solver: A Combined Dry and Wet Laboratory Exercise
Dias, Albino A.; Pinto, Paula A.; Fraga, Irene; Bezerra, Rui M. F.
2014-01-01
In enzyme kinetic studies, linear transformations of the Michaelis-Menten equation, such as the Lineweaver-Burk double-reciprocal transformation, present some constraints. The linear transformation distorts the experimental error and the relationship between "x" and "y" axes; consequently, linear regression of transformed data…
Religionsvidenskabelige sonderinger. Festskrift i anledning af et 10 års jubilæum
Andersen, Vagn
2001-01-01
]mirtazapine pB throughout the forebrain; use of the multireceptor version of the Michaelis-Menten equation indicated that 42% of [(11)C]mirtazapine binding in cortical regions is displaceable by yohimbine. Thus, PET studies confirm that [(11)C]mirtazapine affects alpha(2)-adrenoceptor binding sites in living...
Ketobemidone prodrugs for buccal delivery
Hansen, L.B.; Christrup, Lona Louring; Bundgaard, H.
1992-01-01
conditions ensuring maximal esterase activity, was studied as a function of ester concentration at 37°C. The kinetics of hydrolysis could be accounted for in terms of the Michaelis-Menten equation and the rate parameters K(m) and V(max) were determined. Due to the occurrence of zero-order kinetics...
Rasmussen, Peter Have; Knudsen, I.; Elmholt, S.
2002-01-01
the Hanes-Wolf transformation of the Michaelis-Menten equation. Soil samples from 6 to 13 cm depth were collected in the early spring as undisturbed blocks from 10 arable soils with different physico-chemical properties and cultivation history. Significant correlations were found between soil suppresiveness...
Linear parameter estimation of rational biokinetic functions
Doeswijk, T.G.; Keesman, K.J.
2009-01-01
For rational biokinetic functions such as the Michaelis-Menten equation, in general, a nonlinear least-squares method is a good estimator. However, a major drawback of a nonlinear least-squares estimator is that it can end up in a local minimum. Rearranging and linearizing rational biokinetic
This work describes the development of a physiologically based pharmacokinetic (PBPK) model of deltamethrin, a type II pyrethroid, in the developing male Sprague-Dawley rat. Generalized Michaelis-Menten equations were used to calculate metabolic rate constants and organ weights ...
This work describes the development of a physiologically based pharmacokinetic (PBPK) model of deltamethrin, a type II pyrethroid, in the developing male Sprague-Dawley rat. Generalized Michaelis-Menten equations were used to calculate metabolic rate constants and organ weights ...
Author template for journal articles
Bojan
2012-03-08
Mar 8, 2012 ... ... reported the isolation of the B. fibrisolvens linoleate isomerase by differential centri- ... The fractional conversions of LA for each step were 12.11, 19.43, 8.79 and .... S data range to the Michaelis-Menten equation. The Kmof.
Inferring latent gene regulatory network kinetics
González, Javier; Vujačić, Ivan; Wit, Ernst
2013-01-01
Regulatory networks consist of genes encoding transcription factors (TFs) and the genes they activate or repress. Various types of systems of ordinary differential equations (ODE) have been proposed to model these networks, ranging from linear to Michaelis-Menten approaches. In practice, a serious d
DE KOK, LJ; RENNENBERG, H; KUIPER, PJC
1991-01-01
Spinach (Spinacia oleracea) leaves formed an active sink for atmospheric H2S. Upon short-term exposure, H2S flux to the leaves showed saturation kinetics with respect to the H2S concentrations and could be described by the Michaelis-Menten equation. The kinetics of H2S flux to spinach leaves were
Gómez-Uribe, Carlos A; Verghese, George C; Tzafriri, Abraham R
2008-12-28
Widely different time scales are common in systems of chemical reactions and can be exploited to obtain reduced models applicable to the time scales of interest. These reduced models enable more efficient computation and simplify analysis. A classic example is the irreversible enzymatic reaction, for which separation of time scales in a deterministic mass action kinetics model results in approximate rate laws for the slow dynamics, such as that of Michaelis-Menten. Recently, several methods have been developed for separation of slow and fast time scales in chemical master equation (CME) descriptions of stochastic chemical kinetics, yielding separate reduced CMEs for the slow variables and the fast variables. The paper begins by systematizing the preliminary step of identifying slow and fast variables in a chemical system from a specification of the slow and fast reactions in the system. The authors then present an enhanced time-scale-separation method that can extend the validity and improve the accuracy of existing methods by better accounting for slow reactions when equilibrating the fast subsystem. The resulting method is particularly accurate in systems such as enzymatic and protein interaction networks, where the rates of the slow reactions that modify the slow variables are not a function of the slow variables. The authors apply their methodology to the case of an irreversible enzymatic reaction and show that the resulting improvements in accuracy and validity are analogous to those obtained in the deterministic case by using the total quasi-steady-state approximation rather than the classical Michaelis-Menten. The other main contribution of this paper is to show how mass fluctuation kinetics models, which give approximate evolution equations for the means, variances, and covariances of the concentrations in a chemical system, can feed into time-scale-separation methods at a variety of stages.
Kinetics of atrazine, deisopropylatrazine, and deethylatrazine soil biodecomposers.
la Cecilia, Daniele; Maggi, Federico
2016-12-01
Twenty-two experimental sets were used to determine the biodecomposition parameters of atrazine (ATZ), deisopropylatrazine (DIATZ), and deethylatrazine (DEATZ) by inverse solution of Michaelis-Menten-Monod kinetic equations. The averaged maximum specific growth rate (μ), Michaelis-Menten half-saturation concentration (K), and biomass yield (Y) ranged between 2.00 × 10(-7) and 4.62 × 10(-5) 1/s, 3.43 × 10(-6) and 1.39 × 10(1) mol/L, and 1.20 × 10(2) and 2.98 × 10(5) mg-wet-Bio/mol-Subs, respectively. Parameters grouped by reaction pathway appeared clustered by aerobic and anaerobic catabolic breakdown, and were poorly correlated between each other (R ranging from -0.27 to 0.63, p ≥ 0.05). The tested bacterial strains decomposed ATZ, DIATZ, and DEATZ relatively rapidly in laboratory conditions, with an half-life (t1/2) ranging between 3 and 6 days. Numerical modeling showed that ATZ, DIATZ, and DEATZ half-lives were particularly sensitive to their initial concentration and the initial microbial biomass concentration. This study suggests that these bacterial strains can effectively be used or enhanced for bioremediation of agricultural soils where atrazine has been applied as long as these bacteria already coexist in or can integrate with the local soil microbial population at a given location. Copyright © 2016 Elsevier Ltd. All rights reserved.
马中良; 李艳利; 鲍真真; 王旻
2005-01-01
在生物化学试验中,酶的米氏常数的测定实验是经典的实验.通过Km 测定这一实验的改进,指导学生怎样认识和把握理论知识,并将之应用科学研究中.在生物化学实验教学中,注意提高学生的动手能力,提高解决问题和分析问题的能力,从而形成对待实验结果和教材的正确观点.
林中; 苏银法
2004-01-01
目的: 获得(一级并行)米氏消除药物静脉注射给药时的血药浓度近似解.方法: 根据四阶Runge-Kutta算法,采用Excel软件编写基于药动学参数的程序.结果:输出某周期或稳态任一次给药后的预期血药浓度.结论:方法操作简单,结果可靠,可作为(一级并行)米氏消除药物静脉注射给药时药动学方程的数值解法.
苏银法; 杜乐燕
2006-01-01
目的获得(一级并行)米氏消除药物血管外给药时的血药浓度近似值.方法根据四阶Runge-Kutta算法,采用Excel软件编写基于药动学参数的血药浓度近似解表格程序.结果通过实例演示,可以输出第n周期(或稳态)第s次血管外给药后每间隔0.005 h的预期血药浓度.结论该法是(一级并行)米氏消除药物血管外给药动力学方程的一种可靠的数值解法.
祁兵; 黄大贶
2003-01-01
@@ Michaelis-Menten消除动力学(下称米氏型消除)是非线性药物动力学中的重要部分.大量临床研究表明[1],呈药动学非线性特征的药物,尤有必要进行血药浓度监测.本文对静注多次给药情况下的稳态动力学特征进行了研究,得到了稳态浓度存在的必要条件及稳态浓度的精确表达式,为临床用药提供了理论依据.
Goudar, Chetan T
2011-10-01
We have identified an error in the published integral form of the modified Michaelis-Menten equation that accounts for endogenous substrate production. The correct solution is presented and the error in both the substrate concentration, S, and the kinetic parameters Vm , Km , and R resulting from the incorrect solution was characterized. The incorrect integral form resulted in substrate concentration errors as high as 50% resulting in 7-50% error in kinetic parameter estimates. To better reflect experimental scenarios, noise containing substrate depletion data were analyzed by both the incorrect and correct integral equations. While both equations resulted in identical fits to substrate depletion data, the final estimates of Vm , Km , and R were different and Km and R estimates from the incorrect integral equation deviated substantially from the actual values. Another observation was that at R = 0, the incorrect integral equation reduced to the correct form of the Michaelis-Menten equation. We believe this combination of excellent fits to experimental data, albeit with incorrect kinetic parameter estimates, and the reduction to the Michaelis-Menten equation at R = 0 is primarily responsible for the incorrectness to go unnoticed. However, the resulting error in kinetic parameter estimates will lead to incorrect biological interpretation and we urge the use of the correct integral form presented in this study.
Kinetics of propionate conversion in anaerobic continuously stirred tank reactors
Bangsø Nielsen, Henrik; Mladenovska, Zuzana; Ahring, Birgitte Kiær
2008-01-01
(max), and the half saturation constant, K-m, were initially estimated by applying the integrated Michaelis-Menten equation. A(max) was in the range from 22.8 to 29.1 mu mol gVS(-1) h(-1) while K-m, was in the range from 0.46-0.95 mM. In general, A(max) gave a good reflection of the reactor performances. Secondly...
Xu, Xuebing; Balchen, Steen; Høy, Carl-Erik
1998-01-01
with the Michaelis-Menten equation, while the acyl migration is proportional to time within the range of 20% (mole) acyl migration (MLM-type: Mf=0.2225T, R²=0.9868; LML-type: Mf =0.5618T, R²=0.9961). As water content (wt%, on the enzyme basis) increased from 3.0% to 11.6% for MLM-type and from 3.0% to 7.2% for LML...
Modeling Heavy Metal Removal in Wetlands.
1992-05-01
1976 a,b,c) and Pettersson (1976) treated heavy metals uptake according to Michaelis-Menten kinetics ( Lehninger , 1975), discussed later in detail...copper kinetics equation as used in this modeling effort is presented below, after Lehninger (1975): dv_ dV, Ca (5) dt dt C.+K, where: v = rate of copper...the bulk solution, Cb, using either the Lineweaver-Burk double reciprocal or Eadie-Hofstee graphical methods ( Lehninger , 1975). Nielsen (1976 b) used
A Century of Enzyme Kinetic Analysis, 1913 to 2013
Johnson, Kenneth A.
2013-01-01
This review traces the history and logical progression of methods for quantitative analysis of enzyme kinetics from the 1913 Michaelis and Menten paper to the application of modern computational methods today. Following a brief review of methods for fitting steady state kinetic data, modern methods are highlighted for fitting full progress curve kinetics based upon numerical integration of rate equations, including a re-analysis of the original Michaelis-Menten full time course kinetic data. ...
Asymptotic Behaviour Near a Nonlinear Sink
Calder, Matt S
2010-01-01
In this paper, we will explore an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This procedure is indifferent to resonance in the eigenvalues. Moreover, we will address the writing of one component in terms of the other in the case of a planar system. Examples will be given, notably the Michaelis-Menten mechanism of enzyme kinetics.
Zebin Wang
2012-04-01
Full Text Available A response study and the effects of different parameters (pH, temperature and enzyme dose on kinetics of isolated soy protein hydrolysis by a trypsin-like endopeptidase (TL1 were conducted. Degree of hydrolysis (%DH data varied at different times under different hydrolysis conditions. Fitting the kinetics data to Michaelis-Menten kinetics model did not result in reasonable kinetic parameters, which implied that Michaelis-Menten kinetics was invalid for such a hydrolysis process. A kinetics model proposed by (Gonzalez-Tello, Camacho, Jurado, Paez, & Guadix, 1994 was found to fit the kinetics curve well and resulted in acceptable model parameters. A simple simulation example was performed to demonstrate the concept of how the kinetics equation could be applied in process engineering.
Gonze, Didier; Abou-Jaoudé, Wassim; Ouattara, Djomangan Adama; Halloy, José
2011-01-01
The recent advance of genetic studies and the rapid accumulation of molecular data, together with the increasing performance of computers, led researchers to design more and more detailed mathematical models of biological systems. Many modeling approaches rely on ordinary differential equations (ODE) which are based on standard enzyme kinetics. Michaelis-Menten and Hill functions are indeed commonly used in dynamical models in systems and synthetic biology because they provide the necessary nonlinearity to make the dynamics nontrivial (i.e., limit-cycle oscillations or multistability). For most of the systems modeled, the actual molecular mechanism is unknown, and the enzyme equations should be regarded as phenomenological. In this chapter, we discuss the validity and accuracy of these approximations. In particular, we focus on the validity of the Michaelis-Menten function for open systems and on the use of Hill kinetics to describe transcription rates of regulated genes. Our discussion is illustrated by numerical simulations of prototype systems, including the Repressilator (a genetic oscillator) and the Toggle Switch model (a bistable system). We systematically compare the results obtained with the compact version (based on Michaelis-Menten and Hill functions) with its corresponding developed versions (based on "elementary" reaction steps and mass action laws). We also discuss the use of compact approaches to perform stochastic simulations (Gillespie algorithm). On the basis of these results, we argue that using compact models is suitable to model qualitatively biological systems.
QE+QSS for Derivation of Kinetic Equations and Stiffness Removing
Gorban, A N
2010-01-01
We present the general formalism of the Quasiequilibrium approximation (QE) with the proof of the persistence of entropy production in the QE approximation. We demonstrate, how to apply this formalism to chemical kinetics and describe the difference between QE and Quasi--Steady--State (QSS) approximations. The celebrated QSS "Michaelis--Menten" kinetics is, as a matter of fact, the "Briggs-Haldane" kinetics. Michaelis and Menten used the QE assumption that all intermediate complexes are in fast equilibrium with free substrates and enzyme. Similar approach was developed by Stuekelberg (1952) for the Boltzmann kinetics. Following them, we combine the QE (fast equilibria) and the QSS (small amounts) approaches and study the general kinetics with fast intermediates present in small amount. We prove the representation of the rate of an elementary reaction as a product of the Boltzmann factor (purely thermodynamic) and the kinetic factor, and found the basic relations between kinetic factors. In the practice of mod...
Oldiges Marco
2009-01-01
Full Text Available Abstract Background To understand the dynamic behavior of cellular systems, mathematical modeling is often necessary and comprises three steps: (1 experimental measurement of participating molecules, (2 assignment of rate laws to each reaction, and (3 parameter calibration with respect to the measurements. In each of these steps the modeler is confronted with a plethora of alternative approaches, e. g., the selection of approximative rate laws in step two as specific equations are often unknown, or the choice of an estimation procedure with its specific settings in step three. This overall process with its numerous choices and the mutual influence between them makes it hard to single out the best modeling approach for a given problem. Results We investigate the modeling process using multiple kinetic equations together with various parameter optimization methods for a well-characterized example network, the biosynthesis of valine and leucine in C. glutamicum. For this purpose, we derive seven dynamic models based on generalized mass action, Michaelis-Menten and convenience kinetics as well as the stochastic Langevin equation. In addition, we introduce two modeling approaches for feedback inhibition to the mass action kinetics. The parameters of each model are estimated using eight optimization strategies. To determine the most promising modeling approaches together with the best optimization algorithms, we carry out a two-step benchmark: (1 coarse-grained comparison of the algorithms on all models and (2 fine-grained tuning of the best optimization algorithms and models. To analyze the space of the best parameters found for each model, we apply clustering, variance, and correlation analysis. Conclusion A mixed model based on the convenience rate law and the Michaelis-Menten equation, in which all reactions are assumed to be reversible, is the most suitable deterministic modeling approach followed by a reversible generalized mass action kinetics
Caracterización y digestión anaerobia de las aguas de lavado del aceite de oliva virgen
Borja, R.
1993-04-01
Full Text Available A characterization and kinetic study of the anaerobic digestion of waters from washing of virgin olive oil were carried out. The experimental setup used consisted of a 1;litre thorough mixing bioreactor that was operated at 35 °C and loaded with sepiolite-immobilized biomass at a concentration of 10.8 g VSS/L. The bioreactor worked satisfactorily for a hydraulic retention time of 1.1 to 5.0 days and eliminated more than 92% of the initial COD in all instances.
Guiot's kinetic model was used to determine the macroenergetic parameters of the system, which was found to have a true yield coefficient for the biomass Y = 0.006 g VSS/g COD and a specific rate of substrate uptake for cell maintenance m = 0.072 g COD/g VSS ∙ day.
According to the experimental results obtained, the rate of substrate uptake, Rs (g COD/g VSS ∙ day, was correlated with the concentration of biodegradable substrate, Sb (g COD/L, through an equation of the Michaelis-Menten type.
Se ha efectuado la caracterización y un estudio cinético del proceso de digestión anaerobia de las aguas residuales obtenidas en el lavado del aceite de oliva virgen. El equipo experimental consta de un biorreactor de mezcla completa de 1 litro de volumen y opera a 35 °C con una concentración de biomasa de 10.8 g SSV/L inmovilizada sobre sepiolita. El biorreactor opera de modo satisfactorio en un rango de 5.0 a 1.1 días de tiempo de retención hidráulico, eliminando en todos los casos más del 92% de la DQO inicial.
Se comprueba el modelo cinético propuesto por Guiot y con el auxilio del mismo se determinan los parámetros macroenergéticos de este sistema: Y = 0.006 (g SSV/g DQO, coeficientes de rendimiento verdadero para la biomasa y m = 0.072 (g DQO/g SSV ∙ día, velocidad específica de consumo de sustrato para el mantenimiento celular.
Los datos experimentales obtenidos indican que la velocidad de consumo de sustrato Rs (g DQO/día ∙ g SSV se correlaciona con la
Srichandan, Haragobinda; Pathak, Ashish; Kim, Dong Jin; Lee, Seoung-Won
2014-01-01
A central composite design (CCD) combined with response surface methodology (RSM) was employed for maximizing bioleaching yields of metals (Al, Mo, Ni, and V) from as-received spent refinery catalyst using Acidithiobacillus thiooxidans. Three independent variables, namely initial pH, sulfur concentration, and pulp density were investigated. The pH was found to be the most influential parameter with leaching yields of metals varying inversely with pH. Analysis of variance (ANOVA) of the quadratic model indicated that the predicted values were in good agreement with experimental data. Under optimized conditions of 1.0% pulp density, 1.5% sulfur and pH 1.5, about 93% Ni, 44% Al, 34% Mo, and 94% V was leached from the spent refinery catalyst. Among all the metals, V had the highest maximum rate of leaching (Vmax) according to the Michaelis-Menten equation. The results of the study suggested that two-step bioleaching is efficient in leaching of metals from spent refinery catalyst. Moreover, the process can be conducted with as received spent refinery catalyst, thus making the process cost effective for large-scale applications.
Zhaoxue Tong; Bin Zhao; Guojie Zhao; Hong Shang; Yifu Guan
2014-09-01
Induction of endonucleolytic DNA cleavage is an essential event that links the initiating stimuli to the final effects of cells. The cleavage efficiency and thus the final yield could be affected by many factors, including structures of DNA substrates, composite structures of enzymes–substrates or enzymes–nucleic analogs and so on. However, it is not clear whether a nucleotide derivative-substituted in DNA substrates can influence the efficiency of enzymatic cleavage. To investigate the effect of sugar pucker conformation on DNA–protein interactions, we used 2′--methyl modified nucleotides (OMeN) to modify DNA substrates of isocaudemers BamHI and BglII in this study, and used FRET assay as an efficient method for analysis of enzyme cleavage. Experimental results demonstrated that OMeN-substituted recognition sequences influenced the cleavage rates significantly in a position-dependent manner. OMeN substitutions can reduce the cleavage as expected. Surprisingly, OMeN substitutions can also enhance the cleavage rates. The kinetics parameters of max and m have been obtained by fitting the Michaelis-Menten kinetic equation. These 2′-OMe nucleotides could behave as a regulatory element to modulate the enzymatic activity in vitro, and this property could enrich our understanding about the endonuclease cleavage mechanism and enhance our ability to regulate the enzymatic cleavage efficiency for applications in synthetic biology.
First-order partial differential equations
Rhee, Hyun-Ku; Amundson, Neal R
2001-01-01
This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of mo
Magnus, Wilhelm
2004-01-01
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period
Liu Zhenjie
2009-01-01
Full Text Available This paper investigates the existence of periodic solutions of a ratio-dependent predator-prey diffusion system with Michaelis-Menten functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain suffcient criteria for the existence of periodic solutions for the system. Moreover, when the time scale is chosen as or , the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the methods are unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations.
Integrable Equations on Time Scales
Gurses, Metin; Guseinov, Gusein Sh.; Silindir, Burcu
2005-01-01
Integrable systems are usually given in terms of functions of continuous variables (on ${\\mathbb R}$), functions of discrete variables (on ${\\mathbb Z}$) and recently in terms of functions of $q$-variables (on ${\\mathbb K}_{q}$). We formulate the Gel'fand-Dikii (GD) formalism on time scales by using the delta differentiation operator and find more general integrable nonlinear evolutionary equations. In particular they yield integrable equations over integers (difference equations) and over $q...
Effect of density and planting pattern on yield and yield
alireza yadavi
2009-06-01
Full Text Available In order to evaluate competition ability of Grain maize (Zea mays L. against redroot pigweed (Amaranthus retroflexus L. a field experiment was conducted at Esfahan on 2003. In this research the effect of corn spatial arrangement on yield and yield components of corn (647 Three Way Cross hybrids under different levels of redroot pigweed infestation was investigated. Treatments were arranged in a factorial split experiment based on RCBD with three replications. Factorial arrangement of corn densities (74000 and 111000 plant ha-1 and planting patterns (single row, rectangular twin row and zigzag twin row formed the main plots. Split-plots referred to pigweed densities (0, 4, 8 and 12 plant m-1. Results showed that both grain and biological yield of corn increased as corn density rates increased but rows number per cob, number of grains per row of cob and 1000 grains weight decreased. The effects of planting arrangement on yield and yield components despite rows grain in cob, 1000 seeds weight and harvest index were statistically significant. Corn grain yield and yield components decreased significantly by increasing pigweed density. The effect of redroot pigweed density on corn grain and biological yield loss was predicted using Cousence hyperbolic yield equation. It showed that maximum grain yield loss and biological yield loss happened in single row arrangement and low corn density. Rows number per cob and grain numbers per row in higher corn density treatment showed lower reduction slopes under pigweed competition. In addition, grain rows numbers per cob and corn harvest index in twin arrangement treatments decreased lower than single row treatment under pigweed competition. The results of this research indicated that corn competition ability against redroot pigweed could be increased using dense population (1/5 fold of general density and zigzag twin row arrangement.
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Lloyd K. Williams
1987-01-01
Full Text Available In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second-order ordinary differential equations which are solved herewith.
Prentis, Jeffrey J.
1996-05-01
One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.
Young, C.W. [Applied Research Associates, Inc., Albuquerque, NM (United States)
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.
The compressible adjoint equations in geodynamics: equations and numerical assessment
Ghelichkhan, Siavash; Bunge, Hans-Peter
2016-04-01
The adjoint method is a powerful means to obtain gradient information in a mantle convection model relative to past flow structure. While the adjoint equations in geodynamics have been derived for the conservation equations of mantle flow in their incompressible form, the applicability of this approximation to Earth is limited, because density increases by almost a factor of two from the surface to the Core Mantle Boundary. Here we introduce the compressible adjoint equations for the conservation equations in the anelastic-liquid approximation. Our derivation applies an operator formulation in Hilbert spaces, to connect to recent work in seismology (Fichtner et al (2006)) and geodynamics (Horbach et al (2014)), where the approach was used to derive the adjoint equations for the wave equation and incompressible mantle flow. We present numerical tests of the newly derived equations based on twin experiments, focusing on three simulations. A first, termed Compressible, assumes the compressible forward and adjoint equations, and represents the consistent means of including compressibility effects. A second, termed Mixed, applies the compressible forward equation, but ignores compressibility effects in the adjoint equations, where the incompressible equations are used instead. A third simulation, termed Incompressible, neglects compressibility effects entirely in the forward and adjoint equations relative to the reference twin. The compressible and mixed formulations successfully restore earlier mantle flow structure, while the incompressible formulation yields noticeable artifacts. Our results suggest the use of a compressible formulation, when applying the adjoint method to seismically derived mantle heterogeneity structure.
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
A Century of Enzyme Kinetic Analysis, 1913 to 2013
Johnson, Kenneth A.
2013-01-01
This review traces the history and logical progression of methods for quantitative analysis of enzyme kinetics from the 1913 Michaelis and Menten paper to the application of modern computational methods today. Following a brief review of methods for fitting steady state kinetic data, modern methods are highlighted for fitting full progress curve kinetics based upon numerical integration of rate equations, including a re-analysis of the original Michaelis-Menten full time course kinetic data. Finally, several illustrations of modern transient state kinetic methods of analysis are shown which enable the elucidation of reactions occurring at the active sites of enzymes in order to relate structure and function. PMID:23850893
Chen, Xinyong; Wang, Fengyi; Li, Hongbo; Zhu, Jing; Lv, Xiaotong
2017-01-01
How to explain the effect of seasonal water transfer on the carbon stocks of Baiyangdian wetland is studied. The ecological model of the relationship between the carbon stocks and water depth fluctuation of the reed was established by using STELLA software. For the first time the Michaelis-Menten equation (1) introduced the relation function between the water depth and reed environmental carrying capacity, (2) introduced the concept of suitable growth water depth, and (3) simulated the variation rules of water and reed carbon stocks of artificial adjustment. The model could be used to carry out the research on the optimization design of the ecological service function of the damaged wetland.
[Determination of beta-mannanase activity by viscosimetric and spectrophotometric methods].
Firantas, S G; Venozhinskene, Iu I; Pauliukonis, A B
1982-01-01
The activity of beta-mannanase from Bacillus subtilis was measured viscosimetrically and spectrophotometrically. As substrate galactomannane of Ceratonia siliqua was used. Relationships between the beta-mannanase activity and the substrate concentration as well as the enzyme content were investigated. The kinetic parameters of the enzymes obeying the Michaelis-Menten equation were calculated. It was found viscosimetrically that Vmax of the commercial enzyme preparation was 1.4 mucat/g (at pH 5.8 and 40 degrees) and Km was 0.6 mM. The viscosimetric method shows high sensitivity, whereas the spectrophotometric technique suits mass-scale analyses.
Yankov, D. ; Dobreva, E. ; Beschkov, V. ; Emanuilova, E
Study of optimum conditions and kinetics of starch hydrolysis by means of thermostable ed -amylase.
1986-11-01
The optimum conditions of starch hydrolysis, catalysed by a thermostable ..cap alpha..-amylase (EC 3.2.1.1) produced by the strain Bacillus licheniformis (MB 80) were determined. The kinetic constants in the Michaelis-Menten equation were determined in terms of substrate concentration and dextrose equivalent of the product. It was found that the enzyme action was inhibited by substrate at high concentrations and also by glucose. The enzyme studied is capable of use at an enhanced temperature of 100 degrees C thus enabling higher dextrose equivalents to be obtained than are possible with other less thermostable amylases restricted to temperatures no greater than 95 degrees C. 17 references.
Permeation mechanism of a two-state potassium channel
WANG Xiangqun; ZHAO Tongjun; SONG Yang; ZHAN Yong
2007-01-01
A two-state hopping model was proposed to study the permeation of ion channel.The Nemst equation in equilibrium and the Michaelis-Menten relation in steady state were derived from the two-state kinetic model.The currentvoltage relationship obtained in the symmetrical solutions case was linear when the applied potential was less than 100 mV,which met Ohm's law.The conductance-concentration relationship exhibited the saturation property.Moreover,the characteristic time reaching the steady state of the KcsA channel was also discussed.
A century of enzyme kinetic analysis, 1913 to 2013.
Johnson, Kenneth A
2013-09-02
This review traces the history and logical progression of methods for quantitative analysis of enzyme kinetics from the 1913 Michaelis and Menten paper to the application of modern computational methods today. Following a brief review of methods for fitting steady state kinetic data, modern methods are highlighted for fitting full progress curve kinetics based upon numerical integration of rate equations, including a re-analysis of the original Michaelis-Menten full time course kinetic data. Finally, several illustrations of modern transient state kinetic methods of analysis are shown which enable the elucidation of reactions occurring at the active sites of enzymes in order to relate structure and function.
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Wilmo E. Francisco Jr
2007-10-01
Full Text Available This work aims to study the oxidation of a complex molybdenite mineral which contains pyrite and pyrrotite, by Acidithiobacillus ferrooxidans. This study was performed by respirometric essays and bioleaching in shake flasks. Respirometric essays yielded the kinetics of mineral oxidation. The findings showed that sulfide oxidation followed classical Michaelis-Menten kinetics. Bioleaching in shake flasks allowed evaluation of chemical and mineralogical changes resulting from sulfide oxidation. The results demonstrated that pyrrotite and pyrite were completely oxidized in A. ferrooxidans cultures whereas molybdenite was not consumed. These data indicated that molybdenite was the most recalcitrant sulfide in the sample.
Esterification of phenolic acids catalyzed by lipases immobilized in organogels.
Zoumpanioti, M; Merianou, E; Karandreas, T; Stamatis, H; Xenakis, A
2010-10-01
Lipases from Rhizomucor miehei and Candida antarctica B were immobilized in hydroxypropylmethyl cellulose organogels based on surfactant-free microemulsions consisting of n-hexane, 1-propanol and water. Both lipases kept their catalytic activity, catalyzing the esterification reactions of various phenolic acids including cinnamic acid derivatives. High reaction rates and yields (up to 94%) were obtained when lipase from C. antarctica was used. Kinetic studies have been performed and apparent kinetic constants were determined showing that ester synthesis catalyzed by immobilized lipases occurs via the Michaelis-Menten mechanism.
The Inhibitory Effect of Propranolol and Isoproterenol on Human Plasma Cholinesterase
Ali Awsat Mellati
2002-10-01
Full Text Available The effect of propranolol and isoproterenol on the hydrolysis of 4- nitrophenylbutyrate (PNPB by the purified human plasma cholinesterase was studied. During the hydrolysis of PNPB, enzyme obeyed to Michaelis-Menten model. Propranolol was found to be a competitive inhibitor, and isoproterenol yielded a complex inhibition pattern. It could be explained that the inhibitory effect of propranolol shows noncooperativity between subunits of human plasma cholinesterase upon binding of PNPB. In contrast, isoproternol inhibitory effects indicate more than one type of binding sites on this enzyme.
``Riemann equations'' in bidifferential calculus
Chvartatskyi, O.; Müller-Hoissen, F.; Stoilov, N.
2015-10-01
We consider equations that formally resemble a matrix Riemann (or Hopf) equation in the framework of bidifferential calculus. With different choices of a first-order bidifferential calculus, we obtain a variety of equations, including a semi-discrete and a fully discrete version of the matrix Riemann equation. A corresponding universal solution-generating method then either yields a (continuous or discrete) Cole-Hopf transformation, or leaves us with the problem of solving Riemann equations (hence an application of the hodograph method). If the bidifferential calculus extends to second order, solutions of a system of "Riemann equations" are also solutions of an equation that arises, on the universal level of bidifferential calculus, as an integrability condition. Depending on the choice of bidifferential calculus, the latter can represent a number of prominent integrable equations, like self-dual Yang-Mills, as well as matrix versions of the two-dimensional Toda lattice, Hirota's bilinear difference equation, (2+1)-dimensional Nonlinear Schrödinger (NLS), Kadomtsev-Petviashvili (KP) equation, and Davey-Stewartson equations. For all of them, a recent (non-isospectral) binary Darboux transformation result in bidifferential calculus applies, which can be specialized to generate solutions of the associated "Riemann equations." For the latter, we clarify the relation between these specialized binary Darboux transformations and the aforementioned solution-generating method. From (arbitrary size) matrix versions of the "Riemann equations" associated with an integrable equation, possessing a bidifferential calculus formulation, multi-soliton-type solutions of the latter can be generated. This includes "breaking" multi-soliton-type solutions of the self-dual Yang-Mills and the (2+1)-dimensional NLS equation, which are parametrized by solutions of Riemann equations.
A Finite-Difference Solution of Solute Transport through a Membrane Bioreactor
B. Godongwana
2015-01-01
Full Text Available The current paper presents a theoretical analysis of the transport of solutes through a fixed-film membrane bioreactor (MBR, immobilised with an active biocatalyst. The dimensionless convection-diffusion equation with variable coefficients was solved analytically and numerically for concentration profiles of the solutes through the MBR. The analytical solution makes use of regular perturbation and accounts for radial convective flow as well as axial diffusion of the substrate species. The Michaelis-Menten (or Monod rate equation was assumed for the sink term, and the perturbation was extended up to second-order. In the analytical solution only the first-order limit of the Michaelis-Menten equation was considered; hence the linearized equation was solved. In the numerical solution, however, this restriction was lifted. The solution of the nonlinear, elliptic, partial differential equation was based on an implicit finite-difference method (FDM. An upwind scheme was employed for numerical stability. The resulting algebraic equations were solved simultaneously using the multivariate Newton-Raphson iteration method. The solution allows for the evaluation of the effect on the concentration profiles of (i the radial and axial convective velocity, (ii the convective mass transfer rates, (iii the reaction rates, (iv the fraction retentate, and (v the aspect ratio.
Armstrong, Robert A.
2008-10-01
Pasciak and Gavis were first to propose a model of nutrient uptake that includes both physical transport by diffusion and active biological transport across the cell membrane. While the Pasciak-Gavis model is not complicated mathematically (it can be expressed in closed form as a quadratic equation), its parameters are not so easily interpretable biologically as are the parameters of the Michaelis-Menten uptake model; this lack of transparency is probably the main reason the Pasciak-Gavis model has not been adopted by ecologically oriented modelers. Here I derive a Michaelis-like approximation to the Pasciak-Gavis model, and show how the parameters of the latter map to those of the Michaelis-like model. The derived approximation differs from a pure Michaelis-Menten model in a subtle but potentially critical way: in a pure Michaelis-Menten model, the half-saturation constant for nutrient uptake is independent of the density of transporter (or "porter") proteins on the cell surface, while in the Pasciak-Gavis model and its Michaelis-like approximation, the half-saturation constant does depend on the density of porter proteins. The Pasciak-Gavis model predicts a unique relationship between cell size, nutrient concentration in the medium, the half-saturation constant of porter-limited nutrient uptake, and the resulting rate of uptake; the Michaelis-like approximation preserves the most important feature of that relationship, the size at which porter limitation gives way to diffusion limitation. Finally I discuss the implications for community structure that are implied by the Pasciak-Gavis model and its Michaelis-like approximation.
Kinetic Measurements for Enzyme Immobilization.
Cooney, Michael J
2017-01-01
Enzyme kinetics is the study of the chemical reactions that are catalyzed by enzymes, with a focus on their reaction rates. The study of an enzyme's kinetics considers the various stages of activity, reveals the catalytic mechanism of this enzyme, correlates its value to assay conditions, and describes how a drug or a poison might inhibit the enzyme. Victor Henri initially reported that enzyme reactions were initiated by a bond between the enzyme and the substrate. By 1910, Michaelis and Menten were advancing their work by studying the kinetics of an enzyme saccharase which catalyzes the hydrolysis of sucrose into glucose and fructose. They published their analysis and ever since the Michaelis-Menten equation has been used as the standard to describe the kinetics of many enzymes. Unfortunately, soluble enzymes must generally be immobilized to be reused for long times in industrial reactors. In addition, other critical enzyme properties have to be improved like stability, activity, inhibition by reaction products, and selectivity towards nonnatural substrates. Immobilization is by far the chosen process to achieve these goals.Although the Michaelis-Menten approach has been regularly adapted to the analysis of immobilized enzyme activity, its applicability to the immobilized state is limited by the barriers the immobilization matrix places upon the measurement of compounds that are used to model enzyme kinetics. That being said, the estimated value of the Michaelis-Menten coefficients (e.g., V max, K M) can be used to evaluate effects of immobilization on enzyme activity in the immobilized state when applied in a controlled manner. In this review enzyme activity and kinetics are discussed in the context of the immobilized state, and a few novel protocols are presented that address some of the unique constraints imposed by the immobilization barrier.
... Program Division of Reproductive Health More CDC Sites Low-Yield Cigarettes Recommend on Facebook Tweet Share Compartir ... they compensate when smoking them. Smokers Who Use Low-Yield Cigarettes Many smokers consider smoking low-yield ...
An axiomatic approach to Maxwell's equations
Heras, José A
2016-01-01
This paper suggests an axiomatic approach to Maxwell's equations. The basis of this approach is a theorem formulated for two sets of functions localized in space and time. If each set satisfies a continuity equation then the theorem provides an integral representation for each function. A corollary of this theorem yields Maxwell's equations with magnetic monopoles. It is pointed out that the causality principle and the conservation of electric and magnetic charges are the most fundamental physical axioms underlying these equations. Another application of the corollary yields Maxwell's equations in material media. The theorem is also formulated in the Minkowski space-time and applied to obtain the covariant form of Maxwell's equations with magnetic monopoles and the covariant form of Maxwell's equations in material media. The approach makes use of the infinite-space Green function of the wave equation and is therefore suitable for an advanced course in electrodynamics.
Studies on the kinetics of plasminogen activation by tissue plasminogen activator.
Rånby, M
1982-06-24
The steady-state rate of plasminogen activation by tissue plasminogen activator has been determined at various plasminogen concentrations. A plasmin substrate method similar to that presented by Christensen and Müllertz (Biochim. Biophys. Acta 480 (1977) 257-281) was used. The reaction was studied using one-chain type and two-chain type tissue plasminogen activator, N-terminal glutamic acid and N-terminal lysine plasminogen in the presence and in the absence of fibrin (eight studies). The kinetic data were fitted to a general Wong-Hanes equation and the simplest equation with significant parameters was found. In the absence of fibrin N-terminal glutamic acid plasminogen activation obeyed the Michaelis-Menten rate equation (Km 4.9 and 7.6 micro M and kcat 0.0013 and 0.0078 s-1 for one-chain type and two-chain type tissue plasminogen activator, respectively. In the absence of fibrin the activation of N-terminal lysine plasminogen activation failed to obey the Michaelis-Menten rate equation. Fibrin was found to stimulate greatly (up to 1000-fold) the steady-state activation rate. A theory for the fibrin stimulating mechanism is presented.
谢晶; 刘晓丹
2006-01-01
对香菇分别在273 K、283 K和293 K的密闭容器中氧气和二氧化碳随时间、浓度的变化进行了测定,根据酶动力学原理,利用非线性估计法、多重回归分析分别获得气体成分的变化率曲线和米式方程,从而获得相应的参数,求得反映呼吸状态的呼吸熵动态变化规律以及温度影响参数--活化能,并以此求出在任意温度、有氧呼吸气体环境条件下果蔬的最大呼吸速率,为气调包装系统设计提供理论依据.
Shijian YUAN; Dazhi XIAO; Zhubin HE
2004-01-01
A generalized yield criterion is proposed based on the metal plastic deformation mechanics and the fundamental formula in theory of plasticity. Using the generalized yield criterion, the reason is explained that Mises yield criterion and Tresca yield criterion do not completely match with experimental data. It has been shown that the yield criteria of ductile metals depend not only on the quadratic invariant of the deviatoric stress tensor J2, but also on the cubic invariant of the deviatoric stress tensor J3 and the ratio of the yield stress in pure shear to the yield stress in uniaxial tension k/σs. The reason that Mises yield criterion and Tresca yield criterion are not in good agreement with the experimental data is that the effect of J3 and k/σs is neglected.
Tricomi, Francesco Giacomo
1957-01-01
This classic text on integral equations by the late Professor F. G. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, well-written treatment of the subject at the graduate or advanced undergraduate level. To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the reader to a minimum; a solid foundation in differential and integral calculus, together with some knowledge of the theory of functions is sufficient. The book is divided into four chapters, with two useful
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
2011-03-01
interactions [9] at the Michaelis - Menten state [14]. These interactions enable the protonation of the adenine ring at N3 [9] by the cationic Arg180 of RTA...bound and unbound states. a (top left): overlay of the apo RTA (green, 1IFT [32]) with the oligonucleotide-bound RTA at the Michaelis - Menten state...box atop in the less populated bound conformation (1IFS [32]); d (bottom right): overlay of the oligonucleotide-bound RTA at the Michaelis - Menten state
2009-01-01
with phenyl acetate and paraoxonwere determined by Michaelis - Menten steady state kinetics . The data from four or more independent experiments were fit...paraoxon was followed atA412 for 20 min at room temperature as described above. The data were fit using Michaelis - Menten steady state kinetics to derive...for 4 h at room temperature as described above. The data were fit using Michaelis - Menten steady state kinetics to derive the KM and Vmax values of
Modeling of Complex Mixtures: JP-8 Toxicokinetics
2008-10-01
diffusion, including metabolic loss via the cytochrome P-450 system, described by non-linear Michaelis - Menten kinetics as shown in the following...point. Inhalation and iv were the dose routes for the rat study. The modelers used saturable ( Michaelis - Menten ) kinetics as well as a second... Michaelis - Menten liver metabolic constants for n-decane have been measured (Km = 1.5 mg/L and Vmax = 0.4 mg/hour) using rat liver slices in a vial
Kinetic Study on Flooded Soil Recovery Using Soil Containing Arbuscular Mycorrhizal Fungi
Zainol N.
2016-01-01
Full Text Available The purpose of this research was to determine the kinetic parameters for flooded soil recovery via soil containing Arbuscular Mycorrhizal fungi (AMF. The general procedures of this experiment started by preparation of simulated flooded soil (FS and soil containing AMF (SA. Mixed soil was prepared by mixing FS and SA with ratio 1:1. Onion plant was chosen as a host plant and planted in the mixed soil for 14 days. The plantation was conducted in ambient temperature. The nutrients (nitrogen, phosphorus and potassium concentrations in the soil were tested using HACH Spectrophotomer. The Michaelis-Menten equation was used to study the nutrients recovery in soil. The Lineweaver-Bulk plot was used to solve the Michaelis-Menten equation. From the experiment conducted, the maximum nutrient uptake (Vmax and bonding affinity (Km obtained for nitrogen (N were 6.28mg/l.d and 82.17 mg/l, for phosphorus (P were 9.80 mg/l.d and 60.96 mg/l.d and for potassium (K were 0.07mg/l.d and 4.55mg/l. By comparing the result with other researcher, it showed that the Vmax and Km of nitrogen (N and phosphorus (P obtained were higher than other research. This was because the onion required a high level of N and P in the soil compared to other host plant.
Generalised connections and higher-spin equations
Francia, Dario
2012-01-01
We consider high-derivative equations obtained setting to zero the divergence of the higher-spin curvatures in metric-like form, showing their equivalence to the second-order equations emerging from the tensionless limit of open string field theory, which propagate reducible spectra of particles with different spins. This result can be viewed as complementary to the possibility of setting to zero a single trace of the higher-spin field strengths, which yields an equation known to imply Fronsdal's equation in the compensator form. Higher traces and divergences of the curvatures produce a whole pattern of high-derivative equations whose systematics is also presented.
Yield stress fluids slowly yield to analysis
Bonn, D.; Denn, M.M.
2009-01-01
We are surrounded in everyday life by yield stress fluids: materials that behave as solids under small stresses but flow like liquids beyond a critical stress. For example, paint must flow under the brush, but remain fixed in a vertical film despite the force of gravity. Food products (such as mayon
The Statistical Drake Equation
Maccone, Claudio
2010-12-01
We provide the statistical generalization of the Drake equation. From a simple product of seven positive numbers, the Drake equation is now turned into the product of seven positive random variables. We call this "the Statistical Drake Equation". The mathematical consequences of this transformation are then derived. The proof of our results is based on the Central Limit Theorem (CLT) of Statistics. In loose terms, the CLT states that the sum of any number of independent random variables, each of which may be ARBITRARILY distributed, approaches a Gaussian (i.e. normal) random variable. This is called the Lyapunov Form of the CLT, or the Lindeberg Form of the CLT, depending on the mathematical constraints assumed on the third moments of the various probability distributions. In conclusion, we show that: The new random variable N, yielding the number of communicating civilizations in the Galaxy, follows the LOGNORMAL distribution. Then, as a consequence, the mean value of this lognormal distribution is the ordinary N in the Drake equation. The standard deviation, mode, and all the moments of this lognormal N are also found. The seven factors in the ordinary Drake equation now become seven positive random variables. The probability distribution of each random variable may be ARBITRARY. The CLT in the so-called Lyapunov or Lindeberg forms (that both do not assume the factors to be identically distributed) allows for that. In other words, the CLT "translates" into our statistical Drake equation by allowing an arbitrary probability distribution for each factor. This is both physically realistic and practically very useful, of course. An application of our statistical Drake equation then follows. The (average) DISTANCE between any two neighboring and communicating civilizations in the Galaxy may be shown to be inversely proportional to the cubic root of N. Then, in our approach, this distance becomes a new random variable. We derive the relevant probability density
Yield Improvement in Steel Casting (Yield II)
Richard A. Hardin; Christoph Beckermann; Tim Hays
2002-02-18
This report presents work conducted on the following main projects tasks undertaken in the Yield Improvement in Steel Casting research program: Improvement of Conventional Feeding and Risering Methods, Use of Unconventional Yield Improvement Techniques, and Case Studies in Yield Improvement. Casting trials were conducted and then simulated using the precise casting conditions as recorded by the participating SFSA foundries. These results present a statistically meaningful set of experimental data on soundness versus feeding length. Comparisons between these casting trials and casting trials performed more than forty years ago by Pellini and the SFSA are quite good and appear reasonable. Comparisons between the current SFSA feeding rules and feeding rules based on the minimum Niyama criterion reveal that the Niyama-based rules are generally less conservative. The niyama-based rules also agree better with both the trials presented here, and the casting trails performed by Pellini an d the SFSA years ago. Furthermore, the use of the Niyama criterion to predict centerline shrinkage for horizontally fed plate sections has a theoretical basis according to the casting literature reviewed here. These results strongly support the use of improved feeding rules for horizontal plate sections based on the Niyama criterion, which can be tailored to the casting conditions for a given alloy and to a desired level of soundness. The reliability and repeatability of ASTM shrinkage x-ray ratings was investigated in a statistical study performed on 128 x-rays, each of which were rated seven different times. A manual ''Feeding and Risering Guidelines for Steel Castings' is given in this final report. Results of casting trials performed to test unconventional techniques for improving casting yield are presented. These use a stacked arrangement of castings and riser pressurization to increase the casting yield. Riser pressurization was demonstrated to feed a casting up to
Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes.
Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu; Dua, Arti
2016-08-28
Dynamic co-operativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic co-operativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative co-operativity. For fewer enzymes, dynamic co-operativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, however, suppresses the effect of enzymatic conformational fluctuations such that dynamic co-operativity emerges solely due to the discrete changes in the number of reacting species. These results confirm that the turnover kinetics of fluctuating enzyme based on the parallel-pathway MM mechanism switches over to the single-pathway MM mechanism with the increase in the number of enzymes. For large enzyme numbers, convergence to the exact MM equation occurs in the limit of very high substrate concentration as the stochastic kinetics approaches the deterministic behaviour.
Fock space, symbolic algebra, and analytical solutions for small stochastic systems.
Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A
2015-12-01
Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.
Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes
Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu; Dua, Arti
2016-08-01
Dynamic co-operativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic co-operativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative co-operativity. For fewer enzymes, dynamic co-operativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, however, suppresses the effect of enzymatic conformational fluctuations such that dynamic co-operativity emerges solely due to the discrete changes in the number of reacting species. These results confirm that the turnover kinetics of fluctuating enzyme based on the parallel-pathway MM mechanism switches over to the single-pathway MM mechanism with the increase in the number of enzymes. For large enzyme numbers, convergence to the exact MM equation occurs in the limit of very high substrate concentration as the stochastic kinetics approaches the deterministic behaviour.
Miyamoto, Hirotaka; Matsueda, Satoshi; Moritsuka, Akihiro; Shimokawa, Kenta; Hirata, Haruna; Nakashima, Mikiro; Sasaki, Hitoshi; Fumoto, Shintaro; Nishida, Koyo
2015-10-01
The effect of hypothermia on the in vivo pharmacokinetics of midazolam was evaluated, with a focus on altered metabolism in the liver and binding to serum proteins. Rat primary hepatocytes were incubated with midazolam (which is metabolized mainly by CYP3A2) at 37, 32 or 28 °C. The Michaelis-Menten constant (Km) and maximum velocity (Vmax) of midazolam were estimated using the Michaelis-Menten equation. The Km of CYP3A2 midazolam remained unchanged, but the Vmax decreased at 28 °C. In rats, whose temperature was maintained at 37, 32 or 28 °C by a heat lamp or ice pack, the plasma concentrations of midazolam were higher, whereas those in the brain and liver were unchanged at 28 °C. The tissue/plasma concentration ratios were, however, increased significantly. The unbound fraction of midazolam in serum at 28 °C was half that at 37 °C. These pharmacokinetic changes associated with hypothermic conditions were due to reductions in CYP3A2 activity and protein binding.
Modeling nitrate removal in a denitrification bed.
Ghane, Ehsan; Fausey, Norman R; Brown, Larry C
2015-03-15
Denitrification beds are promoted to reduce nitrate load in agricultural subsurface drainage water to alleviate the adverse environmental effects associated with nitrate pollution of surface water. In this system, drainage water flows through a trench filled with a carbon media where nitrate is transformed into nitrogen gas under anaerobic conditions. The main objectives of this study were to model a denitrification bed treating drainage water and evaluate its adverse greenhouse gas emissions. Field experiments were conducted at an existing denitrification bed. Evaluations showed very low greenhouse gas emissions (mean N2O emission of 0.12 μg N m(-2) min(-1)) from the denitrification bed surface. Field experiments indicated that nitrate removal rate was described by Michaelis-Menten kinetics with the Michaelis-Menten constant of 7.2 mg N L(-1). We developed a novel denitrification bed model based on the governing equations for water flow and nitrate removal kinetics. The model evaluation statistics showed satisfactory prediction of bed outflow nitrate concentration during subsurface drainage flow. The model can be used to design denitrification beds with efficient nitrate removal which in turn leads to enhanced drainage water quality.
A new multi-wavelength model-based method for determination of enzyme kinetic parameters.
Sorouraddin, Mohammad-Hossein; Amini, Kaveh; Naseri, Abdolhossein; Vallipour, Javad; Hanaee, Jalal; Rashidi, Mohammad-Reza
2010-09-01
Lineweaver-Burk plot analysis is the most widely used method to determine enzyme kinetic parameters. In the spectrophotometric determination of enzyme activity using the Lineweaver-Burk plot, it is necessary to find a wavelength at which only the substrate or the product has absorbance without any spectroscopic interference of the other reaction components. Moreover, in this method, different initial concentrations of the substrate should be used to obtain the initial velocities required for Lineweaver-Burk plot analysis. In the present work, a multi-wavelength model-based method has been developed and validated to determine Michaelis-Menten constants for some enzyme reactions. In this method, a selective wavelength region and several experiments with different initial concentrations of the substrate are not required. The absorbance data of the kinetic assays are fitted by non-linear regression coupled to the numeric integration of the related differential equation. To indicate the applicability of the proposed method, the Michaelis-Menten constants for the oxidation of phenanthridine, 6-deoxypenciclovir and xanthine by molybdenum hydroxylases were determined using only a single initial concentration of the substrate, regardless of any spectral overlap.
Modeling networks of coupled enzymatic reactions using the total quasi-steady state approximation.
Andrea Ciliberto
2007-03-01
Full Text Available In metabolic networks, metabolites are usually present in great excess over the enzymes that catalyze their interconversion, and describing the rates of these reactions by using the Michaelis-Menten rate law is perfectly valid. This rate law assumes that the concentration of enzyme-substrate complex (C is much less than the free substrate concentration (S0. However, in protein interaction networks, the enzymes and substrates are all proteins in comparable concentrations, and neglecting C with respect to S0 is not valid. Borghans, DeBoer, and Segel developed an alternative description of enzyme kinetics that is valid when C is comparable to S0. We extend this description, which Borghans et al. call the total quasi-steady state approximation, to networks of coupled enzymatic reactions. First, we analyze an isolated Goldbeter-Koshland switch when enzymes and substrates are present in comparable concentrations. Then, on the basis of a real example of the molecular network governing cell cycle progression, we couple two and three Goldbeter-Koshland switches together to study the effects of feedback in networks of protein kinases and phosphatases. Our analysis shows that the total quasi-steady state approximation provides an excellent kinetic formalism for protein interaction networks, because (1 it unveils the modular structure of the enzymatic reactions, (2 it suggests a simple algorithm to formulate correct kinetic equations, and (3 contrary to classical Michaelis-Menten kinetics, it succeeds in faithfully reproducing the dynamics of the network both qualitatively and quantitatively.
Urmeela Taukoorah
2016-01-01
Full Text Available Aloe vera gel (AVG is traditionally used in the management of diabetes, obesity, and infectious diseases. The present study aimed to investigate the inhibitory potential of AVG against α-amylase, α-glucosidase, and pancreatic lipase activity in vitro. Enzyme kinetic studies using Michaelis-Menten (Km and Lineweaver-Burk equations were used to establish the type of inhibition. The antioxidant capacity of AVG was evaluated for its ferric reducing power, 2-diphenyl-2-picrylhydrazyl hydrate scavenging ability, nitric oxide scavenging power, and xanthine oxidase inhibitory activity. The glucose entrapment ability, antimicrobial activity, and total phenolic, flavonoid, tannin, and anthocyanin content were also determined. AVG showed a significantly higher percentage inhibition (85.56±0.91 of pancreatic lipase compared to Orlistat. AVG was found to increase the Michaelis-Menten constant and decreased the maximal velocity (Vmax of lipase, indicating mixed inhibition. AVG considerably inhibits glucose movement across dialysis tubes and was comparable to Arabic gum. AVG was ineffective against the tested microorganisms. Total phenolic and flavonoid contents were 66.06±1.14 (GAE/mg and 60.95±0.97 (RE/mg, respectively. AVG also showed interesting antioxidant properties. The biological activity observed in this study tends to validate some of the traditional claims of AVG as a functional food.
Taukoorah, Urmeela; Mahomoodally, M. Fawzi
2016-01-01
Aloe vera gel (AVG) is traditionally used in the management of diabetes, obesity, and infectious diseases. The present study aimed to investigate the inhibitory potential of AVG against α-amylase, α-glucosidase, and pancreatic lipase activity in vitro. Enzyme kinetic studies using Michaelis-Menten (K m) and Lineweaver-Burk equations were used to establish the type of inhibition. The antioxidant capacity of AVG was evaluated for its ferric reducing power, 2-diphenyl-2-picrylhydrazyl hydrate scavenging ability, nitric oxide scavenging power, and xanthine oxidase inhibitory activity. The glucose entrapment ability, antimicrobial activity, and total phenolic, flavonoid, tannin, and anthocyanin content were also determined. AVG showed a significantly higher percentage inhibition (85.56 ± 0.91) of pancreatic lipase compared to Orlistat. AVG was found to increase the Michaelis-Menten constant and decreased the maximal velocity (V max) of lipase, indicating mixed inhibition. AVG considerably inhibits glucose movement across dialysis tubes and was comparable to Arabic gum. AVG was ineffective against the tested microorganisms. Total phenolic and flavonoid contents were 66.06 ± 1.14 (GAE)/mg and 60.95 ± 0.97 (RE)/mg, respectively. AVG also showed interesting antioxidant properties. The biological activity observed in this study tends to validate some of the traditional claims of AVG as a functional food. PMID:26880905
Paths of Influence Among Components of Yield in Sorghum ...
equations which express the basic ~Ielation ships between ... First order components on grain yield r68 = P 68 + r67P 78 .... tributed to differential environments and accessions as .... the financial assistance during the course of this study.
department of Agricultural Engineering, University of Ibadan, Nigeria. (Received 28 ... properties, growth and shoot yield of large-green leafy amaranth (Amaranth sp.). Soil moisture ... microorganisms which stimulate the physical processes ... to plants and, consequently, crop establishment ... sustainable soil structure.
evaluate new interspecific genotypes for intensified double cropping of irrigated rice. The experimental ... the performance of the new irrigated .... nursing at a spacing of 20 cm between plants ..... if new technologies, comprising high yielding.
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
The Cauchy problem for the Pavlov equation with large data
Wu, Derchyi
2017-08-01
We prove a local solvability of the Cauchy problem for the Pavlov equation with large initial data by the inverse scattering method. The Pavlov equation arises in studies Einstein-Weyl geometries and dispersionless integrable models. Our theory yields a local solvability of Cauchy problems for a quasi-linear wave equation with a characteristic initial hypersurface.
The Arrhenius equation revisited.
Peleg, Micha; Normand, Mark D; Corradini, Maria G
2012-01-01
The Arrhenius equation has been widely used as a model of the temperature effect on the rate of chemical reactions and biological processes in foods. Since the model requires that the rate increase monotonically with temperature, its applicability to enzymatic reactions and microbial growth, which have optimal temperature, is obviously limited. This is also true for microbial inactivation and chemical reactions that only start at an elevated temperature, and for complex processes and reactions that do not follow fixed order kinetics, that is, where the isothermal rate constant, however defined, is a function of both temperature and time. The linearity of the Arrhenius plot, that is, Ln[k(T)] vs. 1/T where T is in °K has been traditionally considered evidence of the model's validity. Consequently, the slope of the plot has been used to calculate the reaction or processes' "energy of activation," usually without independent verification. Many experimental and simulated rate constant vs. temperature relationships that yield linear Arrhenius plots can also be described by the simpler exponential model Ln[k(T)/k(T(reference))] = c(T-T(reference)). The use of the exponential model or similar empirical alternative would eliminate the confusing temperature axis inversion, the unnecessary compression of the temperature scale, and the need for kinetic assumptions that are hard to affirm in food systems. It would also eliminate the reference to the Universal gas constant in systems where a "mole" cannot be clearly identified. Unless proven otherwise by independent experiments, one cannot dismiss the notion that the apparent linearity of the Arrhenius plot in many food systems is due to a mathematical property of the model's equation rather than to the existence of a temperature independent "energy of activation." If T+273.16°C in the Arrhenius model's equation is replaced by T+b, where the numerical value of the arbitrary constant b is substantially larger than T and T
De Lara, Michel; Oliveros-Ramos, Ricardo; Tam, Jorge
2011-01-01
The World Summit on Sustainable Development (Johannesburg, 2002) encouraged the application of the ecosystem approach by 2010. However, at the same Summit, the signatory States undertook to restore and exploit their stocks at maximum sustainable yield (MSY), a concept and practice without ecosystemic dimension, since MSY is computed species by species, on the basis of a monospecific model. Acknowledging this gap, we propose a definition of "ecosystem viable yields" (EVY) as yields compatible i) with biological viability levels for all time and ii) with an ecosystem dynamics. To the difference of MSY, this notion is not based on equilibrium, but on viability theory, which offers advantages for robustness. For a generic class of multispecies models with harvesting, we provide explicit expressions for the EVY. We apply our approach to the anchovy--hake couple in the Peruvian upwelling ecosystem between the years 1971 and 1981.
Yu, Y.
2016-01-01
Yu, Y.
2016-01-01
A multivariate nonlinear mixed effects method for analyzing energy partitioning in growing pigs
Strathe, Anders Bjerring; Danfær, Allan Christian; Chwalibog, André
2010-01-01
Simultaneous equations have become increasingly popular for describing the effects of nutrition on the utilization of ME for protein (PD) and lipid deposition (LD) in animals. The study developed a multivariate nonlinear mixed effects (MNLME) framework and compared it with an alternative method...... for estimating parameters in simultaneous equations that described energy metabolism in growing pigs, and then proposed new PD and LD equations. The general statistical framework was implemented in the NLMIXED procedure in SAS. Alternative PD and LD equations were also developed, which assumed...... that the instantaneous response curve of an animal to varying energy supply followed the law of diminishing returns behavior. The Michaelis-Menten function was adopted to represent a biological relationship in which the affinity constant (k) represented the sensitivity of PD to ME above maintenance. The approach...
A generalized simplest equation method and its application to the Boussinesq-Burgers equation.
Bilige Sudao
Full Text Available In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs. In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.
A generalized simplest equation method and its application to the Boussinesq-Burgers equation.
Sudao, Bilige; Wang, Xiaomin
2015-01-01
In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.
Static gravitational equations of general relativity and "the fifth force"
Das, A.
2015-10-01
Einstein's static field equations are investigated in various coordinate charts. After comparing Newtonian gravitational theory (in a curvilinear coordinate chart) with various charts of Einstein's static gravitational equations, the most appropriate choice of the coordinate chart for Einstein's static field equations is made. As a consequence, Einstein's equations imply the non-linear potential equation instead of the usual Poisson's equation of the Newtonian theory. Investigating the non-linear potential equation above in the spherically symmetric cases, the corresponding potentials yield scenarios comparable to "the fifth force". Next, static gravitational and electric fields generated by an incoherent charged dust are investigated. The corresponding non-linear potential equation is derived. Finally, the static Einstein-Maxwell-Klein-Gordon equations are explored and again, the corresponding non-linear potential equation is obtained. This potential resembles the static Higgs boson field.
2012-01-01
chloroethene mineralization under nomi- nally anoxic conditions can exhibit saturation type ( Michaelis - Menten ) kinetics over the range of environmentally...relevant concentrations. The Michaelis - Menten parameters, Vmax and ks, are sensitive to a number of environmental factors and vary according to in
Dynamical Systems and Control Theory Inspired by Molecular Biology
2011-02-20
is odd) steady states, there never are more than 2n − 1 steady states, that for parameters near the standard Michaelis - Menten quasi-steady state...conditions, there are at most n + 1 steady states and that for parameters far from the standard Michaelis - Menten quasi-steady state conditions, there is at
The total quasi-steady-state approximation for complex enzyme reactions
Pedersen, Morten Gram; Bersani, A. M.; Bersani, E.
2008-01-01
Biochemistry in general and enzyme kinetics in particular have been heavily influenced by the model of biochemical reactions known as Michaelis-Menten kinetics. Assuming that the complex concentration is approximately constant after a short transient phase leads to the usual Michaelis-Menten (MM...
Plankton Dynamics and Mesoscale Turbulence
2010-06-29
dependending on available nutri- ents through a Holling type-II (or Michaelis - Menten ) functional response, by a Holling type III grazing by zooplankton, by...phytoplankton, using a Michaelis - Menten (or Monod) functional form. The con- stants ρ1 and ρ2 are used to transform phytoplankton biomass into nutrient
PREDICTION OF LACTATION YIELD FROM LAST-RECORD DAY AND AVERAGE DAILY YIELD IN NILI-RAVI BUFFALOES
M. S. Khan, A. U. Hyder, I. R. Bajwa, M. S. Rehman and F. Hassan
2005-10-01
Full Text Available Different adjustment procedures were compared to determine if prediction of lactation milk yield using last record day information could be improved by using information on the average daily milk yield of the recorded lactation. Weekly milk yield records of 993 Nili-Ravi buffaloes for 2704 lactations were used for the study. Comparison of different procedures of lactation milk yield adjustment from partial/incomplete or complete lactations indicated that milk yield predicted from a linear regression equation, or from last test day information, was higher as compared to actual milk yield due to extrapolation to a higher base. Simple linear regression procedure overestimated the yield, especially in the later part of the lactation curve. Most precise adjustments were obtained when last test day and average daily milk yield information were included as predictors. The standard deviation of bias decreased and correlation between actual and predicted lactation milk yield improved with inclusion of average daily milk yield as a predictor along with the last test day milk yield. Last recorded milk yield information along with average daily yield of the recorded lactation period are suggested to be used for standardization of milk yield data in Nili-Ravi buffaloes.
Estimating Corporate Yield Curves
Antionio Diaz; Frank Skinner
2001-01-01
This paper represents the first study of retail deposit spreads of UK financial institutions using stochastic interest rate modelling and the market comparable approach. By replicating quoted fixed deposit rates using the Black Derman and Toy (1990) stochastic interest rate model, we find that the spread between fixed and variable rates of interest can be modeled (and priced) using an interest rate swap analogy. We also find that we can estimate an individual bank deposit yield curve as a spr...
Kinetic energy equations for the average-passage equation system
Johnson, Richard W.; Adamczyk, John J.
1989-01-01
Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.
Kinetic energy equations for the average-passage equation system
Johnson, Richard W.; Adamczyk, John J.
1989-01-01
Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.
Solving Nonlinear Wave Equations by Elliptic Equation
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
Numerical integration methods for large-scale biophysical simulations
Chignola, Roberto; Milotti, Edoardo
2009-01-01
Simulations of biophysical systems inevitably include steps that correspond to time integrations of ordinary differential equations. These equations are often related to enzyme action in the synthesis and destruction of molecular species, and in the regulation of transport of molecules into and out of the cell or cellular compartments. Enzyme action is almost invariably modeled with the quasi-steady-state Michaelis-Menten formula or its close relative, the Hill formula: this description leads to systems of equations that may be stiff and hard to integrate, and poses unusual computational challenges in simulations where a smooth evolution is interrupted by the discrete events that mark the cells' lives. This is the case of a numerical model (Virtual Biophysics Lab - VBL) that we are developing to simulate the growth of three-dimensional tumor cell aggregates (spheroids). The program must be robust and stable, and must be able to accept frequent changes in the underlying theoretical model: here we study the app...
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
The Modified Magnetohydrodynamical Equations
EvangelosChaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similar fashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is done by replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vector potential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vector analysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHD equations.
Initial-value problem for coupled Boussinesq equations and a hierarchy of Ostrovsky equations
Khusnutdinova, K R
2011-01-01
We consider the initial-value problem for a system of coupled Boussinesq equations on the infinite line for localised or sufficiently rapidly decaying initial data, generating sufficiently rapidly decaying right- and left-propagating waves. We study the dynamics of weakly nonlinear waves, and using asymptotic multiple-scales expansions and averaging with respect to the fast time, we obtain a hierarchy of asymptotically exact coupled and uncoupled Ostrovsky equations for unidirectional waves. We then construct a weakly nonlinear solution of the initial-value problem in terms of solutions of the derived Ostrovsky equations within the accuracy of the governing equations, and show that there are no secular terms. When coupling parameters are equal to zero, our results yield a weakly nonlinear solution of the initial-value problem for the Boussinesq equation in terms of solutions of the initial-value problems for two Korteweg-de Vries equations, integrable by the Inverse Scattering Transform. We also perform relev...
George F R Ellis
2007-07-01
The Raychaudhuri equation is central to the understanding of gravitational attraction in astrophysics and cosmology, and in particular underlies the famous singularity theorems of general relativity theory. This paper reviews the derivation of the equation, and its significance in cosmology.
Contemplations on Dirac's equation in quaternionic coordinates
Schuricht, Dirk; Greiter, Martin
2004-11-01
A formulation of Dirac's equation using complex-quaternionic coordinates appears to yield an enormous gain in formal elegance, as there is no longer any need to invoke Dirac matrices. This formulation, however, entails several peculiarities, which we investigate and attempt to interpret.
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Renormalizing Partial Differential Equations
Bricmont, J.; Kupiainen, A.
1994-01-01
In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
Mode decomposition evolution equations.
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2012-03-01
Partial differential equation (PDE) based methods have become some of the most powerful tools for exploring the fundamental problems in signal processing, image processing, computer vision, machine vision and artificial intelligence in the past two decades. The advantages of PDE based approaches are that they can be made fully automatic, robust for the analysis of images, videos and high dimensional data. A fundamental question is whether one can use PDEs to perform all the basic tasks in the image processing. If one can devise PDEs to perform full-scale mode decomposition for signals and images, the modes thus generated would be very useful for secondary processing to meet the needs in various types of signal and image processing. Despite of great progress in PDE based image analysis in the past two decades, the basic roles of PDEs in image/signal analysis are only limited to PDE based low-pass filters, and their applications to noise removal, edge detection, segmentation, etc. At present, it is not clear how to construct PDE based methods for full-scale mode decomposition. The above-mentioned limitation of most current PDE based image/signal processing methods is addressed in the proposed work, in which we introduce a family of mode decomposition evolution equations (MoDEEs) for a vast variety of applications. The MoDEEs are constructed as an extension of a PDE based high-pass filter (Europhys. Lett., 59(6): 814, 2002) by using arbitrarily high order PDE based low-pass filters introduced by Wei (IEEE Signal Process. Lett., 6(7): 165, 1999). The use of arbitrarily high order PDEs is essential to the frequency localization in the mode decomposition. Similar to the wavelet transform, the present MoDEEs have a controllable time-frequency localization and allow a perfect reconstruction of the original function. Therefore, the MoDEE operation is also called a PDE transform. However, modes generated from the present approach are in the spatial or time domain and can be
An extension of the Noether theorem: Accompanying equations possessing conservation laws
Dorodnitsyn, V. A.; Ibragimov, N. H.
2014-02-01
It is shown that the Noether theorem can be extended for some equations associated (accompanying) with Euler-Lagrange equation. Each symmetry of Lagrangian yields a class of accompanying equations possessing conservation law (first integral). The generalization is done for canonical Hamiltonian equations as well.
New Complexiton Solutions of the KdV and Coupled KdV Equations
Pekcan, Aslı
2016-01-01
A new approach to double-sub equation method is introduced to construct novel solutions for the nonlinear partial differential equations. It is applied to the Korteweg-de Vries (KdV) equation and yields new complexiton solutions of both the KdV and coupled KdV equations. The graphs of the solutions are also illustrated.
Roul, Pradip
2016-06-01
This paper presents a new iterative technique for solving nonlinear singular two-point boundary value problems with Neumann and Robin boundary conditions. The method is based on the homotopy perturbation method and the integral equation formalism in which a recursive scheme is established for the components of the approximate series solution. This method does not involve solution of a sequence of nonlinear algebraic or transcendental equations for the unknown coefficients as in some other iterative techniques developed for singular boundary value problems. The convergence result for the proposed method is established in the paper. The method is illustrated by four numerical examples, two of which have physical significance: The first problem is an application of the reaction-diffusion process in a porous spherical catalyst and the second problem arises in the study of steady-state oxygen-diffusion in a spherical cell with Michaelis-Menten uptake kinetics.
Zhenjie Liu
2009-01-01
Full Text Available This paper investigates the existence of periodic solutions of a ratio-dependent predator-prey diffusion system with Michaelis-Menten functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain suffcient criteria for the existence of periodic solutions for the system. Moreover, when the time scale 𝕋 is chosen as ℝ or ℤ, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the methods are unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations.
Escribano, Rubén; Bustos-Ríos, Evelyn; Hidalgo, Pamela; Morales, Carmen E.
2016-09-01
Zooplankton production is critical for understanding marine ecosystem dynamics. This work estimates copepod growth and production in the coastal upwelling and coastal transition zones off central-southern Chile (~35 to 37°S) during a 3-year time series (2004, 2005, and 2006) at a fixed shelf station, and from spring-summer spatial surveys during the same period. To estimate copepod production (CP), we used species-biomasses and associated C-specific growth rates from temperature dependent equations (food-saturated) for the dominant species, which we assumed were maximal growth rates (gmax). Using chlorophyll-a concentrations as a proxy for food conditions, we determined a size-dependent half-saturation constant with the Michaelis-Menten equation to derive growth rates (g) under the effect of food limitation. These food-dependent C-specific growth rates were much lower (absence of bottom-up control, allowing copepods to grow without limitation due to food resources.
Delineamentos experimentais eficientes para estudos de cinética química
Iuri E. P. Ferreira
2014-01-01
Full Text Available In this paper we show how to obtain efficient designs of experiments for fitting Michaelis-Menten and Hill equations useful in chemical studies. The search of exact D-optimal designs by using local and pseudo-Bayesian approaches is considered. Optimal designs were compared to those commonly used in practice using an efficiency measure and theoretical standard errors of the kinetic parameter estimates. In conclusion, the D-optimal designs based on the Hill equation proved efficient for estimating the parameters of both models. Furthermore, these are promising with respect to practical issues, allowing efficient estimation as well as goodness-of-fit tests and comparisons between some kinetic models.
Permeation study of the potassium channel from streptomyces Lividans
XU Xiuzhi; ZHAN Yong; ZHAO Tongjun
2004-01-01
A three-state hopping model is established according to experiments to study permeation of an open-state potassium channel from Streptomyces Lividans (KcsA potassium channel). The master equations are used to characterize the dynamics of the system. In this model, ion conduction involves transitions of three states, with one three-ion state and two two-ion states in the selectivity filter respectively. In equilibrium, the well-known Nernst equation is deduced. It is further shown that the current follows Michaelis-Menten kinetics in steady state. According to the parameters provided by Nelson, the current-voltage relationship is proved to be ohmic and the current-concentration relationship is also obtained reasonably. Additional validation of the model in the characteristic time to reach the steady state for the potassium channel is also discussed. This model lays a possible physical basis for the permeation of ion channel, and opens an avenue for further research.
The Modified Magnetohydrodynamical Equations
Evangelos Chaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similarfashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is doneby replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vectorpotential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vectoranalysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHDequations.
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Fractional Differential Equations
Jianping Zhao
2012-01-01
Full Text Available An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving fractional differential equations.
Correlation Analysis of some Growth, Yield, Yield Components and ...
Keywords: Correlation, Wheat; growth, yield, yield components, grain quality. INTRODUCTION. Wheat ... macaroni, biscuits, cookies, cakes, pasta, noodles and couscous; beer, many .... and 6 WAS which ensured weed free plots. Fertilizer was ...
An introduction to the Dieterici Equation and the van der Waal Equation
Sheldon, John
2003-11-01
The derivation of the ideal gas law by using the kinetic theory of gases is usually presented in an undergraduate physics thermodynamics texts and physical chemistry texts. Following these derivations is the introduction of nonideal effects and the empirical equations of state: the van der Waals equation and the Dieterici equation. These are sometimes are simply given without comment as to the origin of the terms in them. An introduction to a "derivation" of these equations, appropriate for the undergraduate thermodynamics course, is given herein. Empirical equations are not rigorously derived, but rather they are invented, the so-called derivation simply serves to make the empirical terms appear reasonable.The barometric equation is exploited to get an expression for the effective attractive molecular forces. The differential form of the barometric is derived using kinetic theory, then from the barometric equation we get the Dieterici Equation an expansion of the Dieterici Equation, yields the van der Waals Equation of state. The relationship between the empirical constants is also discussed
Scaling of ballistic deposition from a Langevin equation.
Haselwandter, Christoph A; Vvedensky, Dimitri D
2006-04-01
An exact lattice Langevin equation is derived for the ballistic deposition model of surface growth. The continuum limit of this equation is dominated by the Kardar-Parisi-Zhang (KPZ) equation at all length and time scales. For a one-dimensional substrate the solution of the exact lattice Langevin equation yields the KPZ scaling exponents without any extrapolation. For a two-dimensional substrate the scaling exponents are different from those found from computer simulations. This discrepancy is discussed in relation to analytic approaches to the KPZ equation in higher dimensions.
Paek, Seung Weon; Kang, Jae Hyun; Ha, Naya; Kim, Byung-Moo; Jang, Dae-Hyun; Jeon, Junsu; Kim, DaeWook; Chung, Kun Young; Yu, Sung-eun; Park, Joo Hyun; Bae, SangMin; Song, DongSup; Noh, WooYoung; Kim, YoungDuck; Song, HyunSeok; Choi, HungBok; Kim, Kee Sup; Choi, Kyu-Myung; Choi, Woonhyuk; Jeon, JoongWon; Lee, JinWoo; Kim, Ki-Su; Park, SeongHo; Chung, No-Young; Lee, KangDuck; Hong, YoungKi; Kim, BongSeok
2012-03-01
A set of design for manufacturing (DFM) techniques have been developed and applied to 45nm, 32nm and 28nm logic process technologies. A noble technology combined a number of potential confliction of DFM techniques into a comprehensive solution. These techniques work in three phases for design optimization and one phase for silicon diagnostics. In the DFM prevention phase, foundation IP such as standard cells, IO, and memory and P&R tech file are optimized. In the DFM solution phase, which happens during ECO step, auto fixing of process weak patterns and advanced RC extraction are performed. In the DFM polishing phase, post-layout tuning is done to improve manufacturability. DFM analysis enables prioritization of random and systematic failures. The DFM technique presented in this paper has been silicon-proven with three successful tape-outs in Samsung 32nm processes; about 5% improvement in yield was achieved without any notable side effects. Visual inspection of silicon also confirmed the positive effect of the DFM techniques.
Maximizing ROI with yield management
Neil Snyder
2001-01-01
.... the technology is based on the concept of yield management, which aims to sell the right product to the right customer at the right price and the right time therefore maximizing revenue, or yield...
Shortcomings in wheat yield predictions
Semenov, Mikhail A.; Mitchell, Rowan A. C.; Whitmore, Andrew P.; Hawkesford, Malcolm J.; Parry, Martin A. J.; Shewry, Peter R.
2012-06-01
Predictions of a 40-140% increase in wheat yield by 2050, reported in the UK Climate Change Risk Assessment, are based on a simplistic approach that ignores key factors affecting yields and hence are seriously misleading.
张利平; 谢晶
2012-01-01
货架期预测模型可以用来预测蔬菜的货架期.文章通过数学模型讨论蔬菜相关品质,如Vc降解、叶绿素损失、颜色以及质构的变化；介绍不同研究中使用的Arrhenius模型及相关参数或方程,比如Q10、Weibull方程,Michaelis-Menten方程和不同级数的动力学方程,还介绍各个预测模型的局限性.经典的Arrhenius模型结合动力学方程形式有待改进,而Arrhenius方程结合Weibull模型和Michaelis- Menten 方程则有望在新鲜蔬菜货架期中广为应用.%Shelf life prediction model can be used to predict the storage time of certain vegetable. This article discusses relevant qualities of vegetable, such as vitamin C degradation, chlorophyll loss, color and texture changes via mathematical models; Arrhemus model applied in different reaserches is introduced with related parameters or equations, such as Q10,, Weibull mode], Michaehs-Menten equation and kinetic model with different orders used in various studies, while limitations of each prediction models are also investigated. Classical forms of Arrhenius equation combined with kinetic models need to be improved, while models combined with Weibull model and Michaelis-Menten equation were promising used widely in predicting shelf life of fresh vegetables.
Exact solutions for nonlinear foam drainage equation
Zayed, E. M. E.; Al-Nowehy, Abdul-Ghani
2016-09-01
In this paper, the modified simple equation method, the exp-function method, the soliton ansatz method, the Riccati equation expansion method and the ( G^' }/G) -expansion method are used to construct exact solutions with parameters of the nonlinear foam drainage equation. When these parameters are taken to be special values, the solitary wave solutions and the trigonometric function solutions are derived from the exact solutions. The obtained results confirm that the proposed methods are efficient techniques for analytic treatments of a wide variety of nonlinear partial differential equations in mathematical physics. We compare our results together with each other yielding from these integration tools. Also, our results have been compared with the well-known results of others.
Exact solutions for nonlinear foam drainage equation
Zayed, E. M. E.; Al-Nowehy, Abdul-Ghani
2017-02-01
In this paper, the modified simple equation method, the exp-function method, the soliton ansatz method, the Riccati equation expansion method and the ( G^' }/G)-expansion method are used to construct exact solutions with parameters of the nonlinear foam drainage equation. When these parameters are taken to be special values, the solitary wave solutions and the trigonometric function solutions are derived from the exact solutions. The obtained results confirm that the proposed methods are efficient techniques for analytic treatments of a wide variety of nonlinear partial differential equations in mathematical physics. We compare our results together with each other yielding from these integration tools. Also, our results have been compared with the well-known results of others.
Linearized Implicit Numerical Method for Burgers' Equation
Mukundan, Vijitha; Awasthi, Ashish
2016-12-01
In this work, a novel numerical scheme based on method of lines (MOL) is proposed to solve the nonlinear time dependent Burgers' equation. The Burgers' equation is semi discretized in spatial direction by using MOL to yield system of nonlinear ordinary differential equations in time. The resulting system of nonlinear differential equations is integrated by an implicit finite difference method. We have not used Cole-Hopf transformation which gives less accurate solution for very small values of kinematic viscosity. Also, we have not considered nonlinear solvers that are computationally costlier and take more running time.In the proposed scheme nonlinearity is tackled by Taylor series and the use of fully discretized scheme is easy and practical. The proposed method is unconditionally stable in the linear sense. Furthermore, efficiency of the proposed scheme is demonstrated using three test problems.
An analysis of the nonlinear equation = (, ) + (, )$u^2_$ + ℎ(, ) + (, )$
R M Edelstein; K S Govinder
2011-01-01
We use the method of preliminary group classiﬁcation to analyse a particular form of the nonlinear diffusion equation in which the inhomogeneity is quadratic in . The method yields an optimal system of one-dimensional subalgebras. As a result we obtain those explicit forms of the unknown functions , , ℎ and for which the equation admits additional point symmetries.
Structure of Dirac matrices and invariants for nonlinear Dirac equations
2004-01-01
We present invariants for nonlinear Dirac equations in space-time ${\\mathbb R}^{n+1}$, by which we prove that a special choice of the Cauchy data yields free solutions. Our argument works for Klein-Gordon-Dirac equations with Yukawa coupling as well. Related problems on the structure of Dirac matrices are studied.
Differential equations for dummies
Holzner, Steven
2008-01-01
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Fractional Chemotaxis Diffusion Equations
Langlands, T A M
2010-01-01
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding. The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macro-molecular crowding or other obstacles.
K. Banoo
1998-01-01
equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.
Developmental Partial Differential Equations
Duteil, Nastassia Pouradier; Rossi, Francesco; Boscain, Ugo; Piccoli, Benedetto
2015-01-01
In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's evolution. In other words, the manifold's evolution depends on the solution to the PDE, and vice versa the differential operator of the PDE depends on the manifold's geometry. DPDE is used to study a diffusion equation with source on a growing surface whose gro...
Differential equations I essentials
REA, Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.
Ordinary differential equations
Pontryagin, Lev Semenovich
1962-01-01
Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.
Dimension 7 operators in the b{yields}s transition
Chalons, G. [Karlsruhe Univ. (T.H.) (Germany). Inst. fuer Theoretische Teilchenphysik; Domingo, F. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-03-15
We extend the low-energy effective field theory relevant for b{yields}s transitions up to operators of mass-dimension 7 and compute the associated anomalous-dimension matrix. We then compare our findings to the known results for dimension 6 operators and derive a solution for the renormalization group equations involving operators of dimension 7. We finally apply our analysis to a particularly simple case where the Standard Model is extended by an electroweak-magnetic operator and consider limits on this scenario from the decays B{sub s}{yields}{mu}{sup +}{mu}{sup -} and B{yields}K{nu} anti {nu}.
Jeschke, Anja; Behrens, Jörn
2015-04-01
In tsunami modeling, two different systems of dispersive long wave equations are common: The nonhydrostatic pressure correction for the shallow water equations derived out of the depth-integrated 3D Reynolds-averaged Navier-Stokes equations, and the category of Boussinesq-type equations obtained by an expansion in the nondimensional parameters for nonlinearity and dispersion in the Euler equations. The first system uses as an assumption a linear vertical interpolation of the nonhydrostatic pressure, whereas the second system's derivation includes an quadratic vertical interpolation for the nonhydrostatic pressure. In this case the analytical dispersion relations do not coincide. We show that the nonhydrostatic correction with a quadratic vertical interpolation yields an equation set equivalent to the Serre equations, which are 1D Boussinesq-type equations for the case of a horizontal bottom. Now, both systems yield the same analytical dispersion relation according up to the first order with the reference dispersion relation of the linear wave theory. The adjusted model is also compared to other Boussinesq-type equations. The numerical model with the nonhydrostatic correction for the shallow water equations uses Leapfrog timestepping stabilized with the Asselin filter and the P1-PNC1 finite element space discretization. The numerical dispersion relations are computed and compared by employing a testcase of a standing wave in a closed basin. All numerical values match their theoretical expectations. This work is funded by project ASTARTE - Assessment, Strategy And Risk Reduction for Tsunamis in Europe - FP7-ENV2013 6.4-3, Grant 603839. We acknowledge the support given by Geir K. Petersen from the University of Oslo.
Trends in United States cotton yield productivity since 1980
Cotton is produced in over 30 countries and provides a major fiber source for textile manufacturers. In 2012, the direct market value of 17.0 million bales of U.S. cotton equated to US$ 8.1 billion. The objective of this study was to document trends in U.S. upland cotton yield productivity since 198...
无
2002-01-01
Water yield and sediment yield in the Teba catchment, Spain, were simulated using SWRRB (Simulator for Water Resources in Rural Basins) model. The model is composed of 198 mathematical equations. About 120 items (variables) were input for the simulation, including meteorological and climatic factors, hydrologic factors, topographic factors, parent materials, soils, vegetation, human activities, etc. The simulated results involved surface runoff, subsurface runoff, sediment, peak flow, evapotranspiration, soil water, total biomass,etc. Careful and thorough input data preparation and repeated simulation experiments are the key to get the accurate results. In this work the simulation accuracy for annual water yield prediction reached to 83.68%.``
Genetic relationship between yield and yield components of maize
Nastasić Aleksandra
2010-01-01
Full Text Available One of the objectives of this paper was to determine relationship between grain yield and yield components, in S1 and HS progenies of one early synthetic maize population. Grain yield was in high significant, medium strong and strong association with all studied yield components, in both populations. The strongest correlation was recorded between grain yield and 1000-kernel weight (S1 progenies rg = 0.684; HS progenies rg = 0.633. Between other studied traits, the highest values of genotypic coefficient of correlations were found between 1000-kernel weight and kernel depth in S1 population, and 1000-kernel weight and ear length in HS population. Also, objective of this research was founding the direct and indirect effects of yield components on grain yield. Desirable, high significant influence on grain yield, in path coefficient analysis, was found for 1000-kernel weight and kernel row number, and in S1 and HS progenies, and for ear length in population of S1 progenies. Kernel depth has undesirable direct effect on grain yield, in both populations.
Master-equation approach to stochastic neurodynamics
Ohira, Toru; Cowan, Jack D.
1993-09-01
A master-equation approach to the stochastic neurodynamics proposed by Cowan [in Advances in Neural Information Processing Systems 3, edited by R. P. Lippman, J. E. Moody, and D. S. Touretzky (Morgan Kaufmann, San Mateo, 1991), p. 62] is investigated in this paper. We deal with a model neural network that is composed of two-state neurons obeying elementary stochastic transition rates. We show that such an approach yields concise expressions for multipoint moments and an equation of motion. We apply the formalism to a (1+1)-dimensional system. Exact and approximate expressions for various statistical parameters are obtained and compared with Monte Carlo simulations.
Elimination and recursions in the scattering equations
Carlos Cardona
2016-05-01
Full Text Available We use the elimination theory to explicitly construct the (n−3! order polynomial in one of the variables of the scattering equations. The answer can be given either in terms of a determinant of Sylvester type of dimension (n−3! or a determinant of Bézout type of dimension (n−4!. We present a recursive formula for the Sylvester determinant. Expansion of the determinants yields expressions in terms of Plücker coordinates. Elimination of the rest of the variables of the scattering equations is also presented.
Multicomponent integrable wave equations: II. Soliton solutions
Degasperis, A [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , and Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Rome (Italy); Lombardo, S [School of Mathematics, University of Manchester, Alan Turing Building, Upper Brook Street, Manchester M13 9EP (United Kingdom)], E-mail: antonio.degasperis@roma1.infn.it, E-mail: sara.lombardo@manchester.ac.uk, E-mail: sara@few.vu.nl
2009-09-25
The Darboux-dressing transformations developed in Degasperis and Lombardo (2007 J. Phys. A: Math. Theor. 40 961-77) are here applied to construct soliton solutions for a class of boomeronic-type equations. The vacuum (i.e. vanishing) solution and the generic plane wave solution are both dressed to yield one-soliton solutions. The formulae are specialized to the particularly interesting case of the resonant interaction of three waves, a well-known model which is of boomeronic type. For this equation a novel solution which describes three locked dark pulses (simulton) is introduced.
Mathematical Modeling of Biosensors Based on an Array of Enzyme Microreactors
Juozas Kulys
2006-04-01
Full Text Available This paper presents a two-dimensional-in-space mathematical model ofbiosensors based on an array of enzyme microreactors immobilised on a single electrode.The modeling system acts under amperometric conditions. The microreactors were modeledby particles and by strips. The model is based on the diffusion equations containing a non-linear term related to the Michaelis-Menten kinetics of the enzymatic reaction. The modelinvolves three regions: an array of enzyme microreactors where enzyme reaction as well asmass transport by diffusion takes place, a diffusion limiting region where only the diffusiontakes place, and a convective region, where the analyte concentration is maintained constant.Using computer simulation, the influence of the geometry of the microreactors and of thediffusion region on the biosensor response was investigated. The digital simulation wascarried out using the finite difference technique.
Maciej Leszczyński
2017-01-01
Full Text Available We consider an optimal control problem for a general mathematical model of drug treatment with a single agent. The control represents the concentration of the agent and its effect (pharmacodynamics is modelled by a Hill function (i.e., Michaelis-Menten type kinetics. The aim is to minimize a cost functional consisting of a weighted average related to the state of the system (both at the end and during a fixed therapy horizon and to the total amount of drugs given. The latter is an indirect measure for the side effects of treatment. It is shown that optimal controls are continuous functions of time that change between full or no dose segments with connecting pieces that take values in the interior of the control set. Sufficient conditions for the strong local optimality of an extremal controlled trajectory in terms of the existence of a solution to a piecewise defined Riccati differential equation are given.
Desempenho da matriz híbrida SiO2-quitosana na imobilização da lipase microbiana de Candida rugosa
Aline S Simões
2011-01-01
Full Text Available Lipase from Candida rugosa was immobilized by covalent attachment on hybrid SiO2-chitosan obtained by sol-gel technique. A comparative study between free and immobilized lipase was provided in terms of pH, temperature, kinetic parameters and thermal stability on the olive oil hydrolysis. The pH and temperature for maximum activity shifted from 7.0 and 45 ºC for the free lipase to 7.5 and wide range of temperature (40-50 ºC after immobilization. Kinetics parameters were found to obey Michaelis-Menten equation and K M values indicated that immobilization process reduced the affinity of enzyme-substrate; however Kd values revealed an increase of thermal stability of lipase.
Removing Iron and Manganese Simultaneously from Ground Water Using One-stage Biological Filter
XUE Gang; GAO Pin; GONG Qing-jie
2009-01-01
A novel process for removing iron and manganese simultaneously in ground water, which consisted of simple aeration and one-stage filtration, was developed in this research. It was found that the biological process had much higher manganese removal efficiency than chemical contact oxidation process. At the same time, the optimal operation parameters of aeration and biological filtration such as DO concentration and pH after aeration, filtration rate before and after startup, filtration operation cycle and backwashing rate, etc., were also obtained by experiments. By analyzing water quafity in different positions of filter bed, it was found that the oxidation of Fe2+ in biological filter bed adapted to first-order reaction, whereas the oxidation of Mn2+ conformed to zero-order reaction, which could be explained by Michaelis-Menten enzyme reaction equation when substrate concentration was far more than bacteria amount.
Oddone, S.; Grasselli, M.; Cuellas, A.
2010-07-01
Advances in the design of a bioreactor in the fats and oils industry have permitted the hydrolysis of triglycerides in mild conditions and improved productivity while avoiding the formation of unwanted byproducts. The present work develops a mathematical model that describes the hydrolytic activity of a tubular reactor with immobilized lipases for the production of glycerol and fatty acids from the oil trade. Runge Kuttas numerical method of high order has been applied, considering that there is no accumulation of the substratum in the surface of the membrane, where the enzyme is. At the same time, different equations based on the kinetic model of Michaelis Mentens and the Ping-Pong bi-bi mechanism were examined. Experimental data in discontinuous systems are the basis for the development of the quantitative mathematical model that was used to simulate the process computationally. The obtained results allow for optimizing both the operative variables and the economic aspects of industrial processes. (Author)
Kinetics and mechanism of the oxidation of formic and oxalic acids by quinolinium fluorochromate
Madhu Khurana; Pradeep K Sharma; Kalyan K Banerji
2000-04-01
Kinetics and mechanism of oxidation of formic and oxalic acids by quinolinium fluorochromate (QFC) have been studied in dimethylsulphoxide. The main product of oxidation is carbon dioxide. The reaction is first-order with respect to QFC. Michaelis-Menten type of kinetics were observed with respect to the reductants. The reaction is acid-catalysed and the acid dependence has the form: obs = + [H+]. The oxidation of -deuterioformic acid exhibits a substantial primary kinetic isotope effect (H/D = 6.01 at 303 K). The reaction has been studied in nineteen different organic solvents and the solvent effect has been analysed using Taft’s and Swain’s multiparametric equations. The temperature dependence of the kinetic isotope effect indicates the presence of a symmetrical cyclic transition state in the rate-determining step. Suitable mechanisms have been proposed
Analysis of mathematical modelling on potentiometric biosensors.
Mehala, N; Rajendran, L
2014-01-01
A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.
Decolorization of Direct Black 22 by Aspergillus ficuum
无
2001-01-01
The decolorization of Direct Black 22 by Aspergillus ficuum has been studied. It was found that Aspergillus ficuum could effectively decolorize Direct Black 22 especially when grown as pelleted mycelia. Results showed that the media containing Direct Black 22 at 50 mg/L could be decolorized by 98.05% of the initial color in 24 h. The optimum pH and temperature of decolorization are 4.0 and 33 ℃ respectively. Aeration was quite beneficial to decolorization. Medium composition and the concentration of Direct Black 22 could affect the rate of decolorization. The dye degraded products assayed by UV-visible spectrophotometer and macroscopic observation showed that the decolorization of Direct Black 22 by mycelial pellets includes two important processes: bioadsorption and biodegradation.The degradation experiment agree with the Michaelis-Menten kinetics equation
A mechanical model for the role of the neck linker during kinesin stepping and gating
Wang, HaiYan; He, ChenJuan
2011-12-01
In this paper, considering the different elastic properties in the attached head and the free head, we propose a physical model, in which the free head undergoes a diffusive search in an entropic spring potential formed by undocking the neck linker, and there are asymmetric conformational changes in the attached head formed by docking the neck linker to support the load force and bias the diffusive search to the forward direction. By performing the thermodynamic analysis, we obtain the free energy difference between forward and backward binding sites. And using the Fokker-Planck equation with two absorbing boundaries, we obtain the dependence of the ratio of forward to backward steps on the backward force. Also, within the Michaelis-Menten model, we investigate the dependence of the velocity-load relationship on the effective length of the junction between the two heads. The results show that our model can provide a physical understanding for the processive movement of kinesin.
Effect of hydrodynamics on kinetics of gluconic acid enzymatic production in bubble column reactor
Ramezani Mohammad
2013-01-01
Full Text Available Oxidation of glucose by homogeneous glucose oxidase was performed in rectangular bubble column reactor at 40°C, ambient pressure and pH of 5.5 while superficial gas (oxygen velocity was varied in the homogeneous and transition regime in the range of 0.0014 - 0.0112 m s-1. Effect of superficial gas (oxygen velocity on the apparent reaction rate and its parameters was determined and it was observed that the apparent reaction rate on the basis of volume of the liquid increased with increasing the superficial gas (oxygen velocity. The apparent reaction rate was assumed to be in the form of Michaelis-Menten equation and its apparent kinetic parameters were evaluated by the nonlinear regression method.
Faure, Mathilde; Sotta, Bruno; Gamby, Jean
2014-08-15
Real time monitoring of electrolyte resistance changes during hydrolysis of 4-nitrophenylphosphate (pNPP) by alkaline phosphatase (ALP) bound on paramagnetic-beads was performed into a small dielectric channel. The reaction kinetic fit with a non-competitive substrate-inhibition equation. Michaelis-Menten apparent constant, KM(app), was determined as 0.33±0.06mM and the maximum apparent rate, Vmax(app) as 98±5pMs(-1). The detection limits were 15fM for ALP and 0.75mM for pNPP. This miniaturized device constitutes a powerful tool for analysis of interaction between ligands. Copyright © 2014 Elsevier B.V. All rights reserved.
Hazewinkel, M.
1995-01-01
Dedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an original space-
Shabat, A. B.
2016-12-01
We consider the class of entire functions of exponential type in relation to the scattering theory for the Schrödinger equation with a finite potential that is a finite Borel measure. These functions have a special self-similarity and satisfy q-difference functional equations. We study their asymptotic behavior and the distribution of zeros.
Dissipative Boussinesq equations
Dutykh, D; Dias, Fr\\'{e}d\\'{e}ric; Dutykh, Denys
2007-01-01
The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated numerically.
Hannelore Breckner
2000-01-01
Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.
Differential Equation of Equilibrium
user
than the classical method in the solution of the aforementioned differential equation. Keywords: ... present a successful approximation of shell ... displacement function. .... only applicable to cylindrical shell subject to ..... (cos. 4. 4. 4. 3 β. + β. + β. -. = β. - β x x e ex. AL. xA w. Substituting equations (29); (30) and (31) into.
Applied partial differential equations
Logan, J David
2004-01-01
This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...
Yield and Yield Components of Winter Canola (Brassica napus L. Affected by
M AghaAlikhani
2012-06-01
Full Text Available In order to determine the critical period of weed control and investigation the effect of periodical control and interference of weeds natural population on yield and yield components of winter canola (Brassica napus L. cv. Okapi in west region of Tehran an experiment was carried out at research field of Tarbiat Modarres University, Tehran, Iran on 2004-5 growing season. Fourteen experimental treatments which divided into two sets were arranged in randomized complete blocks design with three replications. In the first set, the crop was kept weedfree from canola emergence time to two-leaf stage (V2, four-leaf stage (V4, six-leaf stage (V6, eight-leaf stage (V8, initiation of flowering (If, %50 of pod set (%50Ps and final harvest (H. In the second set of treatments, weeds were permitted to grow with the crop until above mentioned stages and then related plots kept weed free till end of season. Furthermore two additional treatments known as whole season control and whole season weed infested were established. At mentioned phonological stages in interference treatments weeds were removed, separated to species and measured for dry weight. Also during canola growth season trend of plant height and dry matter distribution were studied. At the end of season canola grain yield and yield components were determined. Results showed that extending interference duration and limiting weed control duration significantly decreased all canola yield components except 1000 grain weight .Furthermore extended weed interference duration up to canola 4-leaf stage decreased %20-70 of grain yield in compare to whole season control. Delayed weed control up to early rosette stage creates decreasing trend in canola grain yield. According to Gompertz and Logistic equations, critical period of weed control in canola was estimated between 25-70 days after emergence of canola.
Systematics in delayed neutron yields
Ohsawa, Takaaki [Kinki Univ., Higashi-Osaka, Osaka (Japan). Atomic Energy Research Inst.
1998-03-01
An attempt was made to reproduce the systematic trend observed in the delayed neutron yields for actinides on the basis of the five-Gaussian representation of the fission yield together with available data sets for delayed neutron emission probability. It was found that systematic decrease in DNY for heavier actinides is mainly due to decrease of fission yields of precursors in the lighter side of the light fragment region. (author)
Kinetics and mechanism of the oxidation of some diols by benzyltrimethylammonium tribromide
Garima Goswami; Seema Kothari; Kalyan K Banerji
2001-02-01
The kinetics of oxidation of five vicinal and four non-vicinal diols, and two of their monoethers by benzyltrimethylammonium tribromide (BTMAB) have been studied in 3:7 (/) acetic acid-water mixture. The vicinal diols yield the carbonyl compounds arising out of the glycol bond fission while the other diols give the hydroxycarbonyl compounds. The reaction is first-order with respect to BTMAB. Michaelis-Menten type kinetics is observed with respect to diol. Addition of benzyltrimethylammonium chloride does not affect the rate. Tribromide ion is postulated to be the reactive oxidizing species. Oxidation of [1,1,2,2-2H4] ethanediol shows the absence of a kinetic isotope effect. The reaction exhibits substantial solvent isotope effect. A mechanism involving a glycol-bond fission has been proposed for the oxidation of the vicinal diols. The other diols are oxidized by a hydride ion transfer to the oxidant, as are the monohydric alcohols.
Impact of biodiversity loss on production in complex marine food webs mitigated by prey-release.
Fung, Tak; Farnsworth, Keith D; Reid, David G; Rossberg, Axel G
2015-03-23
Public concern over biodiversity loss is often rationalized as a threat to ecosystem functioning, but biodiversity-ecosystem functioning (BEF) relations are hard to empirically quantify at large scales. We use a realistic marine food-web model, resolving species over five trophic levels, to study how total fish production changes with species richness. This complex model predicts that BEF relations, on average, follow simple Michaelis-Menten curves when species are randomly deleted. These are shaped mainly by release of fish from predation, rather than the release from competition expected from simpler communities. Ordering species deletions by decreasing body mass or trophic level, representing 'fishing down the food web', accentuates prey-release effects and results in unimodal relationships. In contrast, simultaneous unselective harvesting diminishes these effects and produces an almost linear BEF relation, with maximum multispecies fisheries yield at ≈40% of initial species richness. These findings have important implications for the valuation of marine biodiversity.
Characterization of the anion sensitive ATPase in intact vacuoles of Kalanchoe diagremontiana
Kobza, J.; Uribe, E.G.
1986-04-01
A method for the isolation of intact vacuoles from K. daigremontiana was developed which produced high yields of relatively pure vacuoles as determined by marker enzyme contamination. Upon isolation, the vacuoles were stabilized by the inclusion of 5% (w/v) ficoll. Enzyme activity was insensitive to vanadate and azide but was strongly inhibited by DCCD. Enzyme activity was strictly dependent on the inclusion of Mg/sup 2 +/ and was stimulated by anions as depicted by the series, NO/sub 3//sup -/ < Br/sup -/ < SO/sub 4//sup -/ < HCO/sub 3//sup -/ < Cl/sup -/. It was found that in intact vacuoles the ATPase activity was stimulated by phosphate to a level equivalent to that found with the chloride. The enzyme exhibited Michaelis-Menten kinetics with a Km for Mg-ATP complex of 0.51 mM.
Interdependence of yield and yield components of confectionary sunflower hybrids
Hladni Nada
2011-01-01
Full Text Available The two most important criteria for introducing new confectionary hybrids into production are high seed and protein yield. That is why it is important to find the traits that are measurable, and that at the same time show a strong correlation with seed and protein yield, so that they can be used as a criteria for confectionary hybrid breeding. Results achieved during 2008 at the locations Rimski Šančevi (Region of Vojvodina and Kula (Central Serbia show that the new confectionary hybrids are expressing higher seed yields in comparison to standards (Vranac and Cepko though with a lower seed oil content. A very strong positive correlation was determined between seed yield and seed protein content, kernel content and mass of 1000 seeds. A very strong positive correlation was determined between seed protein content, seed yield and mass of 1000 seeds, with protein yield. This indicates that seed yield, seed protein content and mass of 1000 seeds have a high influence on protein yield. The degree of interdependence between different traits is a sign of direction which is supposed to facilitate better planning of sunflower breeding program.
Classical Equations for Quantum Systems
Gell-Mann, Murray; Gell-Mann, Murray; Hartle, James B.
1993-01-01
The origin of the phenomenological deterministic laws that approximately govern the quasiclassical domain of familiar experience is considered in the context of the quantum mechanics of closed systems such as the universe as a whole. We investigate the requirements for coarse grainings to yield decoherent sets of histories that are quasiclassical, i.e. such that the individual histories obey, with high probability, effective classical equations of motion interrupted continually by small fluctuations and occasionally by large ones. We discuss these requirements generally but study them specifically for coarse grainings of the type that follows a distinguished subset of a complete set of variables while ignoring the rest. More coarse graining is needed to achieve decoherence than would be suggested by naive arguments based on the uncertainty principle. Even coarser graining is required in the distinguished variables for them to have the necessary inertia to approach classical predictability in the presence of t...
Kuksin, Sergei; Maiocchi, Alberto
In this chapter we present a general method of constructing the effective equation which describes the behavior of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a hamiltonian system with a pure imaginary discrete spectrum. The effective equation is obtained by retaining only the resonant terms of the nonlinearity (which may be hamiltonian, or may be not); the assertion that it describes the limiting behavior of small-amplitude solutions is a rigorous mathematical theorem. In particular, the method applies to the three- and four-wave systems. We demonstrate that different possible types of energy transport are covered by this method, depending on whether the set of resonances splits into finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima equation), or is connected (this happens, e.g. in the case of the NLS equation if the space-dimension is at least two). For equations of the first type the energy transition to high frequencies does not hold, while for equations of the second type it may take place. Our method applies to various weakly nonlinear wave systems, appearing in plasma, meteorology and oceanography.
Speaking rate effects on locus equation slope
Berry, Jeff; Weismer, Gary
2013-01-01
A locus equation describes a 1st order regression fit to a scatter of vowel steady-state frequency values predicting vowel onset frequency values. Locus equation coefficients are often interpreted as indices of coarticulation. Speaking rate variations with a constant consonant–vowel form are thought to induce changes in the degree of coarticulation. In the current work, the hypothesis that locus slope is a transparent index of coarticulation is examined through the analysis of acoustic samples of large-scale, nearly continuous variations in speaking rate. Following the methodological conventions for locus equation derivation, data pooled across ten vowels yield locus equation slopes that are mostly consistent with the hypothesis that locus equations vary systematically with coarticulation. Comparable analyses between different four-vowel pools reveal variations in the locus slope range and changes in locus slope sensitivity to rate change. Analyses across rate but within vowels are substantially less consistent with the locus hypothesis. Taken together, these findings suggest that the practice of vowel pooling exerts a non-negligible influence on locus outcomes. Results are discussed within the context of articulatory accounts of locus equations and the effects of speaking rate change. PMID:24535890
MULTILEVEL AUGMENTATION METHODS FOR SOLVING OPERATOR EQUATIONS
Chen Zhongying; Wu Bin; Xu Yuesheng
2005-01-01
We introduce multilevel augmentation methods for solving operator equations based on direct sum decompositions of the range space of the operator and the solution space of the operator equation and a matrix splitting scheme. We establish a general setting for the analysis of these methods, showing that the methods yield approximate solutions of the same convergence order as the best approximation from the subspace. These augmentation methods allow us to develop fast, accurate and stable nonconventional numerical algorithms for solving operator equations. In particular, for second kind equations, special splitting techniques are proposed to develop such algorithms. These algorithms are then applied to solve the linear systems resulting from matrix compression schemes using wavelet-like functions for solving Fredholm integral equations of the second kind. For this special case, a complete analysis for computational complexity and convergence order is presented. Numerical examples are included to demonstrate the efficiency and accuracy of the methods. In these examples we use the proposed augmentation method to solve large scale linear systems resulting from the recently developed wavelet Galerkin methods and fast collocation methods applied to integral equations of the secondkind. Our numerical results confirm that this augmentation method is particularly efficient for solving large scale linear systems induced from wavelet compression schemes.
Differential equations problem solver
Arterburn, David R
2012-01-01
REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and
Ordinary differential equations
Miller, Richard K
1982-01-01
Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,
Pierret, Frédéric
2016-02-01
We derived the equations of Celestial Mechanics governing the variation of the orbital elements under a stochastic perturbation, thereby generalizing the classical Gauss equations. Explicit formulas are given for the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle, and the mean anomaly, which are expressed in term of the angular momentum vector H per unit of mass and the energy E per unit of mass. Together, these formulas are called the stochastic Gauss equations, and they are illustrated numerically on an example from satellite dynamics.
Beginning partial differential equations
O'Neil, Peter V
2011-01-01
A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres
Hyperbolic partial differential equations
Witten, Matthew
1986-01-01
Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Partial differential equations
Friedman, Avner
2008-01-01
This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists.Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of we
Introduction to functional equations
Sahoo, Prasanna K
2011-01-01
Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as possible for students from a variety of disciplines, the book chooses not to focus on functional equations where the unknown functions take on values on algebraic structures such as groups, rings, or fields. However, each chapter includes sections hig
Uncertain differential equations
Yao, Kai
2016-01-01
This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.
Classical equations for quantum systems
Gell-Mann, M. (Theoretical Astrophysics Group (T-6), Los Alamos National Laboratory, Los Alamos, New Mexico 87545) (United States) (Santa Fe Institute, 1660 Old Pecos Trail, Santa Fe, New Mexico 87501); Hartle, J.B. (Department of Physics, University of California enSanta Barbara, Santa Barbara, (California) 93106)
1993-04-15
The origin of the phenomenological deterministic laws that approximately govern the quasiclassical domain of familiar experience is considered in the context of the quantum mechanics of closed systems such as the universe as a whole. A formulation of quantum mechanics is used that predicts probabilities for the individual members of a set of alternative coarse-grained histories that [ital decohere], which means that there is negligible quantum interference between the individual histories in the set. We investigate the requirements for coarse grainings to yield decoherent sets of histories that are quasiclassical, i.e., such that the individual histories obey, with high probability, effective classical equations of motion interrupted continually by small fluctuations and occasionally by large ones. We discuss these requirements generally but study them specifically for coarse grainings of the type that follows a distinguished subset of a complete set of variables while ignoring the rest. More coarse graining is needed to achieve decoherence than would be suggested by naive arguments based on the uncertainty principle. Even coarser graining is required in the distinguished variables for them to have the necessary inertia to approach classical predictability in the presence of the noise consisting of the fluctuations that typical mechanisms of decoherence produce. We describe the derivation of phenomenological equations of motion explicitly for a particular class of models.
A Comparison of IRT Equating and Beta 4 Equating.
Kim, Dong-In; Brennan, Robert; Kolen, Michael
Four equating methods were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional mean squared error (CMSE) difference, and the equipercentile equating property. The four methods were: (1) three parameter logistic (3PL) model true score equating; (2) 3PL observed score equating; (3) beta 4 true…
Growth and yield models for Dahurian larch plantations
Yuan Jinlan
1999-01-01
Several equations were seiected using nonlinear regression analysis for setting up growth and yield models of Dahurian larch (Larix gmelinii Rupr.) plantations. Data of 405 stem analysis trees were collected from 336 temporary plots throughout the Daxing'an Mountains. Results showed that the Richards equation was the best model for estimating tree height, stand mean height and stand dominant height by age; the Power equation was the fittest model for predicting tree volume by DBH and tree height, and the Logarithmic stand volume equation was good for predicting stand volume from age, mean height, basal area and other stand variables. These models can be used to construct volume tables, site index table and other forestry tables for Dahurian plantations.
Accelerated Schwarz iterations for Helmholtz equation
Nagid, Nabila; Belhadj, Hassan; Amattouch, Mohamed Ridouan
2017-01-01
In this paper, the Restricted additive Schwarz (RAS) method is applied to solve Helmholtz equation. To accelerate the RAS iterations, we propose to apply the vector ɛ-algorithm. Some convergence analysis of the proposed method is presented, and applied succeffully to Helmholtz problem. The obtained results show the efficiency of the proposed approach. Moreover, the algorithm yields much faster convergence than the classical Schwarz iterations.
QCD evolution equations for high energy partons in nuclear matter
Kinder-Geiger, Klaus; Geiger, Klaus; Mueller, Berndt
1994-01-01
We derive a generalized form of Altarelli-Parisi equations to decribe the time evolution of parton distributions in a nuclear medium. In the framework of the leading logarithmic approximation, we obtain a set of coupled integro- differential equations for the parton distribution functions and equations for the virtuality (``age'') distribution of partons. In addition to parton branching processes, we take into account fusion and scattering processes that are specific to QCD in medium. Detailed balance between gain and loss terms in the resulting evolution equations correctly accounts for both real and virtual contributions which yields a natural cancellation of infrared divergences.
Specific yield: compilation of specific yields for various materials
Johnson, A.I.
1967-01-01
Specific yield is defined as the ratio of (1) the volume of water that a saturated rock or soil will yield by gravity to (2) the total volume of the rock or soft. Specific yield is usually expressed as a percentage. The value is not definitive, because the quantity of water that will drain by gravity depends on variables such as duration of drainage, temperature, mineral composition of the water, and various physical characteristics of the rock or soil under consideration. Values of specific yields nevertheless offer a convenient means by which hydrologists can estimate the water-yielding capacities of earth materials and, as such, are very useful in hydrologic studies. The present report consists mostly of direct or modified quotations from many selected reports that present and evaluate methods for determining specific yield, limitations of those methods, and results of the determinations made on a wide variety of rock and soil materials. Although no particular values are recommended in this report, a table summarizes values of specific yield, and their averages, determined for 10 rock textures. The following is an abstract of the table. [Table
Incorporating phenology into yield models
Gray, J. M.; Friedl, M. A.
2015-12-01
Because the yields of many crops are sensitive to meteorological forcing during specific growth stages, phenological information has potential utility in yield mapping and forecasting exercises. However, most attempts to explain the spatiotemporal variability in crop yields with weather data have relied on growth stage definitions that do not change from year-to-year, even though planting, maturity, and harvesting dates show significant interannual variability. We tested the hypothesis that quantifying temperature exposures over dynamically determined growth stages would better explain observed spatiotemporal variability in crop yields than statically defined time periods. Specifically, we used National Agricultural and Statistics Service (NASS) crop progress data to identify the timing of the start of the maize reproductive growth stage ("silking"), and examined the correlation between county-scale yield anomalies and temperature exposures during either the annual or long-term average silking period. Consistent with our hypothesis and physical understanding, yield anomalies were more correlated with temperature exposures during the actual, rather than the long-term average, silking period. Nevertheless, temperature exposures alone explained a relatively low proportion of the yield variability, indicating that other factors and/or time periods are also important. We next investigated the potential of using remotely sensed land surface phenology instead of NASS progress data to retrieve crop growth stages, but encountered challenges related to crop type mapping and subpixel crop heterogeneity. Here, we discuss the potential of overcoming these challenges and the general utility of remotely sensed land surface phenology in crop yield mapping.
Coiling of yield stress fluids
Y. Rahmani; M. Habibi; A. Javadi; D. Bonn
2011-01-01
We present an experimental investigation of the coiling of a filament of a yield stress fluid falling on a solid surface. We use two kinds of yield stress fluids, shaving foam and hair gel, and show that the coiling of the foam is similar to the coiling of an elastic rope. Two regimes of coiling (el
Woittiez, Lotte S.; Wijk, van Mark T.; Slingerland, Maja; Noordwijk, van Meine; Giller, Ken E.
2017-01-01
Oil palm, currently the world's main vegetable oil crop, is characterised by a large productivity and a long life span (≥25 years). Peak oil yields of 12 t ha−1 yr−1 have been achieved in small plantations, and maximum theoretical yields as calculated with simulation models are 18.5 t oil ha−1 yr−1,
Boelt, Birte; Studer, Bruno
2010-01-01
Seed yield is a trait of major interest for many fodder and amenity grass species and has received increasing attention since seed multiplication is economically relevant for novel grass cultivars to compete in the commercial market. Although seed yield is a complex trait and affected...... by agricultural practices as well as environmental factors, traits related to seed production reveal considerable genetic variation, prerequisite for improvement by direct or indirect selection. This chapter first reports on the biological and physiological basics of the grass reproduction system, then highlights...... important aspects and components affecting the seed yield potential and the agronomic and environmental aspects affecting the utilization and realization of the seed yield potential. Finally, it discusses the potential of plant breeding to sustainably improve total seed yield in fodder and amenity grasses....
Applied partial differential equations
Logan, J David
2015-01-01
This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...
Frédéric, Pierret
2014-01-01
The equations of celestial mechanics that govern the variation of the orbital elements are completely derived for stochastic perturbation which generalized the classic perturbation equations which are used since Gauss, starting from Newton's equation and it's solution. The six most understandable orbital element, the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle and the mean motion are express in term of the angular momentum vector $\\textbf{H}$ per unit of mass and the energy $E$ per unit of mass. We differentiate those expressions using It\\^o's theory of differential equations due to the stochastic nature of the perturbing force. The result is applied to the two-body problem perturbed by a stochastic dust cloud and also perturbed by a stochastic dynamical oblateness of the central body.
Kinetic equations: computation
Pareschi, Lorenzo
2013-01-01
Kinetic equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity.
Saaty, Thomas L
1981-01-01
Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.
Geometry of differential equations
Khovanskiĭ, A; Vassiliev, V
1998-01-01
This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.
Regularized Structural Equation Modeling.
Jacobucci, Ross; Grimm, Kevin J; McArdle, John J
A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM's utility.
A.I.Arbab
2013-01-01
A unified complex model of Maxwell's equations is presented.The wave nature of the electromagnetic field vector is related to the temporal and spatial distributions and the circulation of charge and current densities.A new vacuum solution is obtained,and a new transformation under which Maxwell's equations are invariant is proposed.This transformation extends ordinary gauge transformation to include charge-current as well as scalar-vector potential.An electric dipole moment is found to be related to the magnetic charges,and Dirac's quantization is found to determine an uncertainty relation expressing the indeterminacy of electric and magnetic charges.We generalize Maxwell's equations to include longitudinal waves.A formal analogy between this formulation and Dirac's equation is also discussed.
Applied partial differential equations
DuChateau, Paul
2012-01-01
Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.
Singular Renormalization Group Equations
Minoru, HIRAYAMA; Department of Physics, Toyama University
1984-01-01
The possible behaviour of the effective charge is discussed in Oehme and Zimmermann's scheme of the renormalization group equation. The effective charge in an example considered oscillates so violently in the ultraviolet limit that the bare charge becomes indefinable.
Problems in differential equations
Brenner, J L
2013-01-01
More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.
Construction of Difference Equations Using Lie Groups
Axford, R.A.
1998-08-01
The theory of prolongations of the generators of groups of point transformations to the grid point values of dependent variables and grid spacings is developed and applied to the construction of group invariant numerical algorithms. The concepts of invariant difference operators and generalized discrete sources are introduced for the discretization of systems of inhomogeneous differential equations and shown to produce exact difference equations. Invariant numerical flux functions are constructed from the general solutions of first order partial differential equations that come out of the evaluation of the Lie derivatives of conservation forms of difference schemes. It is demonstrated that invariant numerical flux functions with invariant flux or slope limiters can be determined to yield high resolution difference schemes. The introduction of an invariant flux or slope limiter can be done so as not to break the symmetry properties of a numerical flux-function.
Relativistic Guiding Center Equations
White, R. B. [PPPL; Gobbin, M. [Euratom-ENEA Association
2014-10-01
In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Stem taper equations for poplars growing on farmland in Sweden
Birger Hjelm
2013-01-01
We developed a simple polynomial taper equation for poplars growing on former farmland in Sweden and also evaluated the performance of some well-known taper equations.In Sweden there is an increasing interest in the use of poplar.Effective management of poplar plantations for high yield production would be facilitated by taper equations providing better predictions of stem volume than currently available equations.In the study a polynomial stem taper equation with five parameters was established for individual poplar trees growing on former farmland.The outputs of the polynomial taper equation were compared with five published equations.Data for fitting the equations were collected from 69 poplar trees growing at 37 stands in central and southern Sweden (lat.55-60° N).The mean age of the stands was 21 years (range 14-43),the mean density 984 stemsha-1 (198-3,493),and the mean diameter at breast height (outside bark) 25 cm (range 12-40).To verify the tested equations,performance of accuracy and precision diameter predictions at seven points along the stem was closely analyzed.Statistics used for evaluation of the equations indicated that the variable exponent taper equation presented by Kozak (1988) performed best and can be recommended.The stem taper equation by Kozak (1988) recommended in the study is likely to be beneficial for optimising the efficiency and profitability of poplar plantation management.The constructed polynomial equation and the segmented equation presented by Max & Burkhart (1976) were second and third ranked.Due to the statistical complexity of Kozak's equation,the constructed polynomial equation is alternatively recommended when a simple model is requested and larger bias is accepted.
Functional Equations and Fourier Analysis
2010-01-01
By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson equation, and the d'Alembert long equation, on compact groups.
YIELD AND YIELD COMPONENTS OF INVESTIGATED RAPESEED HYBRIDS AND CULTIVARS
Milan Pospišil
2014-06-01
Full Text Available To evaluate new winter rapeseed hybrids and cultivars, investigations were conducted at the experimental field of the Faculty of Agriculture, University of Zagreb, in the period 2009/10 - 2011/12. The trial involved 11 hybrids and 5 cultivars rapeseed of 5 seed producers selling seed in Croatia. The studied rapeseed hybrids and cultivars differed significantly in seed and oil yields, oil content and yield components (seed number per silique and 1000 seed weight. However, a number of hybrids rendered identical results, since the differences in the investigated properties were within statistically allowable deviation. Hybrids Traviata and CWH 119 can be singled out based on the achieved seed and oil yields, and the cultivar Ricco and hybrids CWH 119 and PR46W15 for their high oil content in seed. Hybrids with a larger silique number per plant also achieved a higher seed yield.
Historical effects of temperature and precipitation on California crop yields
Lobell, D.B. [Energy and Environment Directorate, Lawrence Livermore National Laboratory, Livermore, CA 94550 (United States); Cahill, K.N. [Interdisciplinary Graduate Program in Environment and Resources, Stanford University, Stanford, CA 94305 (United States); Field, C.B. [Department of Global Ecology, Carnegie Institution, Stanford, CA 94305 (United States)
2007-03-15
For the 1980-2003 period, we analyzed the relationship between crop yield and three climatic variables (minimum temperature, maximum temperature, and precipitation) for 12 major Californian crops: wine grapes, lettuce, almonds, strawberries, table grapes, hay, oranges, cotton, tomatoes, walnuts, avocados, and pistachios. The months and climatic variables of greatest importance to each crop were used to develop regressions relating yield to climatic conditions. For most crops, fairly simple equations using only 2-3 variables explained more than two-thirds of observed yield variance. The types of variables and months identified suggest that relatively poorly understood processes such as crop infection, pollination, and dormancy may be important mechanisms by which climate influences crop yield. Recent climatic trends have had mixed effects on crop yields, with orange and walnut yields aided, avocado yields hurt, and most crops little affected by recent climatic trends. Yield-climate relationships can provide a foundation for forecasting crop production within a year and for projecting the impact of future climate changes.
Interdependence of yield and yield components of confectionary sunflower hybrids
Hladni Nada; Jocić Siniša; Miklič Vladimir; Saftić-Panković Dejana; Kraljević-Balalić Marija
2011-01-01
The two most important criteria for introducing new confectionary hybrids into production are high seed and protein yield. That is why it is important to find the traits that are measurable, and that at the same time show a strong correlation with seed and protein yield, so that they can be used as a criteria for confectionary hybrid breeding. Results achieved during 2008 at the locations Rimski Sancevi (Region of Vojvodina) and Kula (Central Serbia) show t...
Grapevine canopy reflectance and yield
Minden, K. A.; Philipson, W. R.
1982-01-01
Field spectroradiometric and airborne multispectral scanner data were applied in a study of Concord grapevines. Spectroradiometric measurements of 18 experimental vines were collected on three dates during one growing season. Spectral reflectance, determined at 30 intervals from 0.4 to 1.1 microns, was correlated with vine yield, pruning weight, clusters/vine, and nitrogen input. One date of airborne multispectral scanner data (11 channels) was collected over commercial vineyards, and the average radiance values for eight vineyard sections were correlated with the corresponding average yields. Although some correlations were significant, they were inadequate for developing a reliable yield prediction model.
Lagrangian formulation of the one-dimensional Vlasov equation. [in plasma physics
Lewak, G. J.
1974-01-01
A new formulation of the one-dimensional Vlasov equation is derived which is analogous to the Kalman-transformed cold-plasma equations. The equations are shown to yield nonsecular, nonlinear approximations to a source or boundary-value problem. It is suggested that the formulation may have other applications in nonlinear plasma theory.
Gardner's deformations of the graded Korteweg-de Vries equations revisited
Kiselev, A. V.; Krutov, A. O.
2012-01-01
We solve the Gardner deformation problem for the N = 2 supersymmetric a = 4 Korteweg-de Vries equation [P. Mathieu, "Supersymmetric extension of the Korteweg-de Vries equation," J. Math. Phys. 29(11), 2499-2506 (1988)]. We show that a known zero-curvature representation for this super-equation yield
2014-04-04
were determined by Michaelis - Menten steady state kinetics using Prism Graphpad (Irvine, CA). Kinetic data for CMP hydrolysis was used as a metric to...against CMP, paraoxon and phenyl acetate versus G3C9 expression in E. coli (Table 1). A closer examination of the Michaelis - Menten parameters reveals...0.05% BSA 1.09 ± 0.06 45 ± 9 24 ± 5 Table 2. Michaelis - Menten parameters for G3C9 CMP hydrolysis. G3C9 expressed in mammalian cells displayed
Nerve Agent Hydrolysis Activity Designed into a Human Drug Metabolism Enzyme
2011-03-18
inhibition, Michaelis - Menten constants, and rates of reactivation for wild-type and V146H/ L363E hCE1 against racemic cyclosarin and stereoisomers of...0017441.t002 Table 3. Inhibition and Michaelis - Menten constants for wild-type and V146H/L363E hCE1 against stereoisomers of sarin and soman model...6 | Issue 3 | e17441 where Km was the nerve agent model Michaelis - Menten constant, k2 the unimolecular phosphonylation rate constant, v the remaining
Phenytoin dose adjustment in epileptic patients.
Mawer, G E; Mullen, P W; Rodgers, M; Robins, A J; Lucas, S B
1974-04-01
1 A preliminary survey showed that many outpatients with partially controlled epilepsy had serum concentrations of phenytoin below the recommended therapeutic range (10-20 μg/ml). A phenytoin tolerance test was devised with the intention of predicting a more adequate daily dose for such a patient. 2 Fifteen patients were each given an oral test dose of 600 mg phenytoin sodium and the serum concentration of phenytoin was measured at intervals over 48 h; the concentration rose during the first 4 h and decayed between 12-48 h as an almost linear function of time. 3 The serum concentration/time curves were fitted by an interative computer program based on the Michaelis-Menten equation. The mean saturated rate of elimination of phenytoin was 435 mg/day and the serum concentration (K(m)) corresponding with 50% saturation was 3.8 μg/ml. The mean calculated dose of phenytoin sodium required for a steady state serum concentration of 10-20 μg/ml was 345-400 mg/day. 4 The Michaelis-Menten principle was used to predict steady state serum phenytoin concentrations in individual patients receiving daily doses of phenytoin sodium adjusted by steps of 100 mg. The serum concentrations tended to be either too low or too high. The steep relationship between phenytoin concentration and dose indicates that when the concentration reaches 5-10 μg/ml it is then appropriate to adjust dose by small steps of about 25 mg.
A. Agah
2012-12-01
Full Text Available Risk-based assessment methods are commonly used at the contaminated sites by hydrocarbon pollutants. This paper presents the results of a two-dimensional finite volume model of reactive transport of biodegradable BTEX which have been developed for the saturated zone of an unconfined aquifer in the Pump station area of Tehran oil refinery, Iran. The model governing equations were numerically solved by modification of a general commercial software called PHOENICS. To reduce costs in general, many input parameters of a model are often approximated based on the used values in the contaminated sites with same conditions. It was not fully recognised the effect of errors in these inputs on modelling outputs. Thus, a sensitivity analysis was carried out to determine the influence of parameters variability on the results of model. For this analysis, the sensitivity of the model to changes in the dispersivity, distribution coefficient, parameters of Monod, Michaelis-Menten, first- and zero- order kinetics modes on the BTEX contaminant plume were examined by performing several simulations. It was found that the model is sensitive to changes in dispersivity and parameters of Michaelis-Menten, first- and zero- order kinetics model. On the other hand, the predictions for plumes assuming Monod kinetics are similar, even if different values for parameterization are chosen. The reason for this insensibility is that degradation is not limited by microbial kinetics in the simulation, but by dispersive mixing. Quantifying the effect of changes in model input parameters on the modelling results is essential when it is desired to recognise which model parameters are more vital on the fate and transport of reactive pollutants. Furthermore, this process can provide an insight into understanding pollutant transportation mechanisms.
Hargono Hargono
2017-05-01
Full Text Available Starch is a potential substrate for this purpose, but the extra cost is needed to hydrolyze it into reducing sugar. As an alternative to the expensive and energy demanding conventional hydrolysis process, the low-temperature hydrolysis is being studied. Granular Starch Hydrolysing Enzyme (GSHE was used in the process to degrade starch into reducing sugar at 30°C and pH 4. The substrates included bitter cassava flour, sweet cassava starch, and gadung flour. Starch concentrations studied were 50, 100, 150, 200, 250, 300, 350, and 400 g/L, respectively, while concentration of enzyme was 1.5 % (w/w. The optimum condition of the process was hydrolysis using 200 g/L of substrate concentration and enzyme concentration of 1.5% for 12 h. It was found that the reducing sugar was 49.3 g/L and the productivity of reducing sugar (Qrs was 4.11 (gL-1 h-1. Lineweaver-Burk plot of Michaelis-Menten equation was used to study the inhibition kinetics. The Michaelis-Menten constants (Km for these three substrates were determined as 141.64 g/L, 137,64 g/L and 140.84 g/L for bitter cassava flour, sweet cassava starch, and gadung flour, respectively. The value of Vm/Km, which denotes the affinity of the enzyme to the substrate, were determined and compared, and the result showed that the affinity (Vm to the enzyme to this substrate followed the order of sweet cassava starch˃ bitter cassava flour˃ gadung flour, and all are non-competitive inhibitor, while the Ki value was 0.022 h -1.
Modelling atypical CYP3A4 kinetics: principles and pragmatism.
Houston, J Brian; Galetin, Aleksandra
2005-01-15
The Michaelis-Menten model, and the existence of a single active site for the interaction of substrate with drug metabolizing enzyme, adequately describes a substantial number of in vitro metabolite kinetic data sets for both clearance and inhibition determination. However, in an increasing number of cases (involving most notably, but not exclusively, CYP3A4), atypical kinetic features are observed, e.g., auto- and heteroactivation; partial, cooperative, and substrate inhibition; concentration-dependent effector responses (activation/inhibition); limited substrate substitution and inhibitory reciprocity necessitating sub-group classification. The phenomena listed above cannot be readily interpreted using single active site models and the literature indicates that three types of approaches have been adopted. First the 'nai ve' approach of using the Michaelis-Menten model regardless of the kinetic behaviour, second the 'empirical' approach (e.g., employing the Hill or uncompetitive inhibition equations to model homotropic phenomena of sigmoidicity and substrate inhibition, respectively) and finally, the 'mechanistic' approach. The later includes multisite kinetic models derived using the same rapid equilibrium/steady-state assumptions as the single-site model. These models indicate that 2 or 3 binding sites exist for a given CYP3A4 substrate and/or effector. Multisite kinetic models share common features, depending on the substrate kinetics and the nature of the effector response observed in vitro, which allow a generic model to be proposed. Thus although more complex than the other two approaches, they show more utility and can be comprehensively applied in relatively simple versions that can be readily generated from generic model. Multisite kinetic features, observed in isolated hepatocytes as well as in microsomes from hepatic tissue and heterologous expression systems, may be evident in substrate depletion-time profiles as well as in metabolite formation rates
Temperature-sensitive molecularly imprinted microgels with esterase activity%具酯酶活性的温敏型分子印迹微凝胶
王红飞; 杨浩; 张黎明
2011-01-01
Temperature-sensitive molecularly imprinted microgels (MIGs) exhibiting esterase activity were prepared by a reverse emulsion method using dialdehyde dextran-histidine conjugate (PAD-His) as the functional macromonomer and p-nitrophenyl phosphate (NPP) as the stable transition state analogue (TSA) as well as Co2+ as the coordination center. The catalytic activity of MIGs was greatly influenced by the template amount, and could be modulated by temperature. The hydrolysis kinetics ofp-nitrophenyl acetate (NPA) in the presence of MIGs could be described by the Michaelis-Menten equation. The Michaelis-Menten constant and maximium velocity were found to be 2.2×105 mol/L and 2.04×108 mol/h,respectively. In addition, the MIGs were found to have a high catalytic selectivity to NPA.%以双醛葡聚糖-组氨酸偶连物(PAD-His)为功能大单体、过渡态类似物p-硝基苯磷酸酯(NPP)为模板分子、Co2+为中心离子,采用油包水反相乳液法首次制得具有酯酶活性的温敏型分子印迹微凝胶(MIGs).催化水解实验表明,MIGs催化活性受模板分子用量的影响,并可通过温度进行有效调控.MIGs催化p-硝基乙酸苯酯(NPA)水解反应行为可用Michaelis-Menten方程进行描述,其最大催化水解反应速率和Michaelis-Menten常数分别为2.04×10-8 mol/h和2.2×10-5 mol/L,且具有较好的催化选择性.
Scaling Equation for Invariant Measure
LIU Shi-Kuo; FU Zun-Tao; LIU Shi-Da; REN Kui
2003-01-01
An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.
Multiaxial yield behaviour of polypropylene
Lang R.
2010-06-01
Full Text Available In order to characterize the yield behavior of polypropylene as a function of pressure and to verify the applicability of the Drucker-Prager yield function, various tests were conducted to cover a wide range of stress states from uniaxial tension and compression to multiaxial tension and confined compression. Tests were performed below and above the glass transition temperature, to study the combined effect of pressure and temperature. The pressure sensitivity coefficient as an intrinsic material parameter was determined as a function of temperature. Increasing pressure sensitivity values were found with increasing temperature, which can be related to the change in the free volume and thus, to the enhanced molecular mobility. A best-fit Drucker-Prager yield function was applied to the experimental yield stresses and an average error between the predictions and the measurements of 7 % was obtained.
Effect of biofertilizers on yield and yield components of cucumber
Faranak Moshabaki Isfahani
2012-01-01
Full Text Available Biofertilizer is defined as a substance which contains living organisms which, when applied to seed, plant surface, or soil, colonize the rhizosphere or interior of the plant and promote growth by increasing the supply or availability of primary nutrients to the host plant. Biofertilizers are well recognized as an important component of integrated plant nutrient management for sustainable agriculture and hold a great promise improve crop yield. The present study for the sake of evaluating the use of plant growth promoting rhizobacteria produced by Pseudomonas sp. and phosphate bio fertilizers produced by Pseudomonas putida strain P13 and Pantoea agglomerans strain P5 and chemical fertilizers in the separate treatments on yield and yield components of cucumber by using a factorial experiment in completely randomized block design with three repetition were performed in the field. The symbol of P represents chemical fertilizer by amount of respectively (0, 25%, 50%, 75%, 100%, B1 shows plant growth promoting rhizobacteria (PGPR and B2 indicates bio fertilizer-2. The results showed that P1B0 has the most yield, and control treatments has the least yield. P100B1 has the most length of plant and P100B0 has the least length of plant, P25B1 has the most amount of chlorophyll and P75B2 has the least chlorophyll. P75B2 has the most shoots dry weight and P100B0 has the least shoots dry weight. B1P50 has the most shoots fresh weight and P25B2 has the least shoots fresh weight. B1P50 has the most roots dry weight and P100B0 has the least roots dry weight. B1P50 has the most roots fresh weight and P25B2 has the least roots fresh weight. So the results indicate that use of biological fertilizers have caused increase yield and components yield of cucumber.
Florian Ion Tiberiu Petrescu
2015-09-01
Full Text Available This paper presents the dynamic, original, machine motion equations. The equation of motion of the machine that generates angular speed of the shaft (which varies with position and rotation speed is deduced by conservation kinetic energy of the machine. An additional variation of angular speed is added by multiplying by the coefficient dynamic D (generated by the forces out of mechanism and or by the forces generated by the elasticity of the system. Kinetic energy conservation shows angular speed variation (from the shaft with inertial masses, while the dynamic coefficient introduces the variation of w with forces acting in the mechanism. Deriving the first equation of motion of the machine one can obtain the second equation of motion dynamic. From the second equation of motion of the machine it determines the angular acceleration of the shaft. It shows the distribution of the forces on the mechanism to the internal combustion heat engines. Dynamic, the velocities can be distributed in the same way as forces. Practically, in the dynamic regimes, the velocities have the same timing as the forces. Calculations should be made for an engine with a single cylinder. Originally exemplification is done for a classic distribution mechanism, and then even the module B distribution mechanism of an Otto engine type.
Introduction to partial differential equations
Greenspan, Donald
2000-01-01
Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.
Fission yield measurements at IGISOL
Lantz M.
2016-01-01
Full Text Available The fission product yields are an important characteristic of the fission process. In fundamental physics, knowledge of the yield distributions is needed to better understand the fission process. For nuclear energy applications good knowledge of neutroninduced fission-product yields is important for the safe and efficient operation of nuclear power plants. With the Ion Guide Isotope Separator On-Line (IGISOL technique, products of nuclear reactions are stopped in a buffer gas and then extracted and separated by mass. Thanks to the high resolving power of the JYFLTRAP Penning trap, at University of Jyväskylä, fission products can be isobarically separated, making it possible to measure relative independent fission yields. In some cases it is even possible to resolve isomeric states from the ground state, permitting measurements of isomeric yield ratios. So far the reactions U(p,f and Th(p,f have been studied using the IGISOL-JYFLTRAP facility. Recently, a neutron converter target has been developed utilizing the Be(p,xn reaction. We here present the IGISOL-technique for fission yield measurements and some of the results from the measurements on proton induced fission. We also present the development of the neutron converter target, the characterization of the neutron field and the first tests with neutron-induced fission.
Mihara, H; Kurihara, T; Yoshimura, T; Esaki, N
2000-04-01
We have purified three NifS homologs from Escherichia coli, CSD, CsdB, and IscS, that appear to be involved in iron-sulfur cluster formation and/or the biosynthesis of selenophosphate. All three homologs catalyze the elimination of Se and S from L-selenocysteine and L-cysteine, respectively, to form L-alanine. These pyridoxal 5'-phosphate enzymes were inactivated by abortive transamination, yielding pyruvate and a pyridoxamine 5'-phosphate form of the enzyme. The enzymes showed non-Michaelis-Menten behavior for L-selenocysteine and L-cysteine. When pyruvate was added, they showed Michaelis-Menten behavior for L-selenocysteine but not for L-cysteine. Pyruvate significantly enhanced the activity of CSD toward L-selenocysteine. Surprisingly, the enzyme activity toward L-cysteine was not increased as much by pyruvate, suggesting the presence of different rate-limiting steps or reaction mechanisms for L-cysteine desulfurization and the degradation of L-selenocysteine. We substituted Ala for each of Cys358 in CSD, Cys364 in CsdB, and Cys328 in IscS, residues that correspond to the catalytically essential Cys325 of Azotobacter vinelandii NifS. The enzyme activity toward L-cysteine was almost completely abolished by the mutations, whereas the activity toward L-selenocysteine was much less affected. This indicates that the reaction mechanism of L-cysteine desulfurization is different from that of L-selenocysteine decomposition, and that the conserved cysteine residues play a critical role only in L-cysteine desulfurization.
Generalization of Hopf Functional Equation
无
2002-01-01
This paper generalizes the Hopf functional equation in order to apply it to a wider class of not necessarily incompressible fluid flows. We start by defining characteristic functionals of the velocity field, the density field and the temperature field of a compressible field. Using the continuity equation, the Navier-Stokes equations and the equation of energy we derive a functional equation governing the motion of an ideal gas flow and a van der Waals gas flow, and then give some general methods of deriving a functional equation governing the motion of any compressible fluid flow. These functional equations can be considered as the generalization of the Hopf functional equation.
Saffman-Taylor instability in yield stress fluids
Maleki-Jirsaraei, Nahid [Laboratoire de Physique Statistique, Ecole Normale Superieure, 24, Rue Lhomond, F-75231 Paris Cedex 05 (France); Complex Systems Laboratory, Physics Department, Azzahra University, Tehran (Iran, Islamic Republic of); Lindner, Anke [LMDH-PMMH, Ecole de Physique et Chimie de la Ville de Paris, 10 rue Vauquelin, 75231 Paris Cedex 05 (France); Rouhani, Shahin [Physics Department, Sharif University of Technology, Tehran (Iran, Islamic Republic of); Bonn, Daniel [Laboratoire de Physique Statistique, Ecole Normale Superieure, 24, Rue Lhomond, F-75231 Paris Cedex 05 (France); Van der Waals-Zeeman Instituut, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)
2005-04-13
Pushing a fluid with a less viscous one gives rise to the well known Saffman-Taylor instability. This instability is important in a wide variety of applications involving strongly non-Newtonian fluids that often exhibit a yield stress. Here we investigate the Saffmann-Taylor instability in this type of fluid, in longitudinal flows in Hele-Shaw cells. In particular, we study Darcy's law for yield stress fluids. The dispersion equation for the flow is similar to the equations obtained for ordinary viscous fluids but the viscous terms in the dimensionless numbers conditioning the instability now contain the yield stress. This also has repercussions on the wavelength of the instability as it follows from a linear stability analysis. As a consequence of the presence of yield stress, the wavelength of maximum growth is finite even at vanishing velocities. We study Darcy's law and the fingering patterns experimentally for a yield stress fluid in a linear Hele-Shaw cell. The results are in rather good agreement with the theoretical predictions. In addition we observe different regimes that lead to different morphologies of the fingering patterns, in both rectangular and circular Hele-Shaw cells.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Quasirelativistic Langevin equation.
Plyukhin, A V
2013-11-01
We address the problem of a microscopic derivation of the Langevin equation for a weakly relativistic Brownian particle. A noncovariant Hamiltonian model is adopted, in which the free motion of particles is described relativistically while their interaction is treated classically, i.e., by means of action-to-a-distance interaction potentials. Relativistic corrections to the classical Langevin equation emerge as nonlinear dissipation terms and originate from the nonlinear dependence of the relativistic velocity on momentum. On the other hand, similar nonlinear dissipation forces also appear as classical (nonrelativistic) corrections to the weak-coupling approximation. It is shown that these classical corrections, which are usually ignored in phenomenological models, may be of the same order of magnitude, if not larger than, relativistic ones. The interplay of relativistic corrections and classical beyond-the-weak-coupling contributions determines the sign of the leading nonlinear dissipation term in the Langevin equation and thus is qualitatively important.
Boussinesq evolution equations
Bredmose, Henrik; Schaffer, H.; Madsen, Per A.
2004-01-01
This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...
A fast marching algorithm for the factored eikonal equation
Treister, Eran; Haber, Eldad
2016-11-01
The eikonal equation is instrumental in many applications in several fields ranging from computer vision to geoscience. This equation can be efficiently solved using the iterative Fast Sweeping (FS) methods and the direct Fast Marching (FM) methods. However, when used for a point source, the original eikonal equation is known to yield inaccurate numerical solutions, because of a singularity at the source. In this case, the factored eikonal equation is often preferred, and is known to yield a more accurate numerical solution. One application that requires the solution of the eikonal equation for point sources is travel time tomography. This inverse problem may be formulated using the eikonal equation as a forward problem. While this problem has been solved using FS in the past, the more recent choice for applying it involves FM methods because of the efficiency in which sensitivities can be obtained using them. However, while several FS methods are available for solving the factored equation, the FM method is available only for the original eikonal equation. In this paper we develop a Fast Marching algorithm for the factored eikonal equation, using both first and second order finite-difference schemes. Our algorithm follows the same lines as the original FM algorithm and requires the same computational effort. In addition, we show how to obtain sensitivities using this FM method and apply travel time tomography, formulated as an inverse factored eikonal equation. Numerical results in two and three dimensions show that our algorithm solves the factored eikonal equation efficiently, and demonstrate the achieved accuracy for computing the travel time. We also demonstrate a recovery of a 2D and 3D heterogeneous medium by travel time tomography using the eikonal equation for forward modeling and inversion by Gauss-Newton.
Nonlocal electrical diffusion equation
Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.
2016-07-01
In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.
Equations of mathematical physics
Tikhonov, A N
2011-01-01
Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri
Gas Dynamics Equations: Computation
Chen, Gui-Qiang G
2012-01-01
Shock waves, vorticity waves, and entropy waves are fundamental discontinuity waves in nature and arise in supersonic or transonic gas flow, or from a very sudden release (explosion) of chemical, nuclear, electrical, radiation, or mechanical energy in a limited space. Tracking these discontinuities and their interactions, especially when and where new waves arise and interact in the motion of gases, is one of the main motivations for numerical computation for the gas dynamics equations. In this paper, we discuss some historic and recent developments, as well as mathematical challenges, in designing and formulating efficient numerical methods and algorithms to compute weak entropy solutions for the Euler equations for gas dynamics.
Theory of differential equations
Gel'fand, I M
1967-01-01
Generalized Functions, Volume 3: Theory of Differential Equations focuses on the application of generalized functions to problems of the theory of partial differential equations.This book discusses the problems of determining uniqueness and correctness classes for solutions of the Cauchy problem for systems with constant coefficients and eigenfunction expansions for self-adjoint differential operators. The topics covered include the bounded operators in spaces of type W, Cauchy problem in a topological vector space, and theorem of the Phragmén-Lindelöf type. The correctness classes for the Cau
Systematic Equation Formulation
Lindberg, Erik
2007-01-01
A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....
Generalized estimating equations
Hardin, James W
2002-01-01
Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th
Ding Yi
2009-01-01
In this article, the author derives a functional equation η(s)=［(π/4)s-1/2√2/πг(1-s)sin(πs/2)]η(1-s) of the analytic function η(s) which is defined by η(s)=1-s-3-s-5-s+7-s…for complex variable s with Re s>1, and is defined by analytic continuation for other values of s. The author proves (1) by Ramanujan identity (see [1], [3]). Her method provides a new derivation of the functional equation of Riemann zeta function by using Poisson summation formula.
Comparison of Kernel Equating and Item Response Theory Equating Methods
Meng, Yu
2012-01-01
The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…
Test equating methods and practices
Kolen, Michael J
1995-01-01
In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...
Variation principle of piezothermoelastic bodies, canonical equation and homogeneous equation
LIU Yan-hong; ZHANG Hui-ming
2007-01-01
Combining the symplectic variations theory, the homogeneous control equation and isoparametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isoparametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which are often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.
Calculus & ordinary differential equations
Pearson, David
1995-01-01
Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.
Standardized Referente Evapotranspiration Equation
M.D. Mundo–Molina
2009-04-01
Full Text Available In this paper is presented a discussion on the necessity to standardize the Penman–Monteith equations in order to estimate ETo. The proposal is to define an accuracy and standarize equation based in Penman–Monteith. The automated weather station named CIANO (27° 22 ' 144 North latitude and 109" 55' west longitude it was selected tomake comparisons. The compared equations we re: a CIANO weat her station, b Penman–Monteith ASCE (PMA, Penman–Monteith FAO 56 (PM FAO 56, Penman–Monteith estandarizado ASCE (PM Std. ASCE. The results were: a There are important differences between PMA and CIANO weather station. The differences are attributed to the nonstandardization of the equation CIANO weather station, b The coefficient of correlation between both methods was of 0,92, with a standard deviation of 1,63 mm, an average quadratic error of 0,60 mm and one efficiency in the estimation of ETo with respect to the method pattern of 87%.
Modified differential equations
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
2007-01-01
Motivated by the theory of modified differential equations (backward error analysis) an approach for the construction of high order numerical integrators that preserve geometric properties of the exact flow is developed. This summarises a talk presented in honour of Michel Crouzeix.
Equational binary decision diagrams
Groote, J.F.; Pol, J.C. van de
2000-01-01
We incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and tautology checkin
Garkavenko A. S.
2011-08-01
Full Text Available The rate equations of the exciton laser in the system of interacting excitons have been obtained and the inverted population conditions and generation have been derived. The possibility of creating radically new gamma-ray laser has been shown.
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
Generalized reduced magnetohydrodynamic equations
Kruger, S.E.
1999-02-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics.
Hatem Mejjaoli
2008-12-01
Full Text Available We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and tauto
New exact solutions of the Einstein-Maxwell equations for magnetostatic fields
Nisha Goyal; R. K. Gupta
2012-01-01
The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields,which is a coupled system of nonlinear partial differential equations of the second order.The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations.Some of the reduced systems are further studied to obtain the exact solutions.
Examples of Rate-Theory Constitutive Equations Which Unify Elasticity and Plasticity
1979-01-01
Yield Condit.ion, Rate-Type Constitutive Equations, Differential Equations, Non-uniqueness, Lipschitz Condition, Prandtl-Reuss 20. A11STR ACT (Coniliwa...equations. We shall show how elastic behavior can correspond to uniqueness of solutions of such equations; how nonuniqueness of solutioncan...2. Indeed, the Piccard-Lindelof uniqueness theorem3 assures us of this, since a Lipschitz condition will hold when -l//r < s < l/1V. Indeed, as long
Higher-order symmetries and conservation laws of multi-dimensional Gordon-type equations
S Jamal; A H Kara
2011-09-01
In this paper a class of multi-dimensional Gordon-type equations are analysed using a multiplier and homotopy approach to construct conservation laws. The main focus is the analysis of the classical versions of the Gordon-type equations and obtaining higher-order variational symmetries and corresponding conserved quantities. The results are extended to the multi-dimensional Gordontype equations with the two-dimensional Klein–Gordon equation in particular yielding interesting results.
Lie Symmetries of Ishimori Equation
SONG Xu-Xia
2013-01-01
The Ishimori equation is one of the most important (2+1)-dimensional integrable models,which is an integrable generalization of (1+1)-dimensional classical continuous Heisenberg ferromagnetic spin equations.Based on importance of Lie symmetries in analysis of differential equations,in this paper,we derive Lie symmetries for the Ishimori equation by Hirota's direct method.
Lectures on partial differential equations
Petrovsky, I G
1992-01-01
Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.
Yield statistics of interpolated superoscillations
Katzav, Eytan; Perlsman, Ehud; Schwartz, Moshe
2017-01-01
Yield optimized interpolated superoscillations have been recently introduced as a means for possibly making the use of the phenomenon of superoscillation practical. In this paper we study how good is a superoscillation that is not optimal. Namely, by how much is the yield decreased when the signal departs from the optimal one. We consider two situations. One is the case where the signal strictly obeys the interpolation requirement and the other is when that requirement is relaxed. In the latter case the yield can be increased at the expense of deterioration of signal quality. An important conclusion is that optimizing superoscillations may be challenging in terms of the precision needed, however, storing and using them is not at all that sensitive. This is of great importance in any physical system where noise and error are inevitable.
THE CONSTITUTIVE EQUATIONS FOR MIXED HARDENING ORTHOTROPIC MATERIAL
LIUTeng-xi; HUANGShi-qing; FUYi-ming
2003-01-01
A dimensionless stress yield criterion is proposed to describe the mixed hardening of orthortropic material ,including kinematic hardening and proportional hardening,and the associated plastic flow law is derived.The generalized effective stress-strain formulae can be obtained correspondingly based on the experimental stress-strain curves in various simple stress states.The initial plastic anisotropy is influenced by the elastic anisotropy.The yield criterion can be reduced to Huber-Mises Criterion for isotropic materials and associated constitutive equations can be degenerated into Prandtl-Reuss equations.