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.
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.
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.
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.
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.
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.
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.
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…
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.
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.
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…
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...
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.
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
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.
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.
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…
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.
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.
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.
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.
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...
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.
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.
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.
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.
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.
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.
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.
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…
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...
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.
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.
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.
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.
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.
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 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.
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.
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.
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).
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.
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.
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.
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.
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...
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.
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.
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.
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.
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.
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.
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)).
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...
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.
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.
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...
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.
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.
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.
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.
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.
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.
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 ...
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.
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.
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.
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.
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.
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.
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…
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.
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.
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.
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.
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…
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.
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
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.
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...
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.
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.
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.
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
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
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.
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).
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.
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 ...
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.
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%).
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.
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...
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.
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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
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.
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.
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...
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.
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.
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...
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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
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).
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.
Evaluation of rate law approximations in bottom-up kinetic models of metabolism
Du, Bin; Zielinski, Daniel C.; Kavvas, Erol S.
2016-01-01
. These approximate rate laws were: 1) a Michaelis-Menten rate law with measured enzyme parameters, 2) a Michaelis-Menten rate law with approximated parameters, using the convenience kinetics convention, 3) a thermodynamic rate law resulting from a metabolite saturation assumption, and 4) a pure chemical reaction......Background: The mechanistic description of enzyme kinetics in a dynamic model of metabolism requires specifying the numerical values of a large number of kinetic parameters. The parameterization challenge is often addressed through the use of simplifying approximations to form reaction rate laws...... with reduced numbers of parameters. Whether such simplified models can reproduce dynamic characteristics of the full system is an important question. Results: In this work, we compared the local transient response properties of dynamic models constructed using rate laws with varying levels of approximation...
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].
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
2017-01-01
The specific consumption rate of substrate, as well as the associated specific growth rate, is an essential parameter in the mathematical description of substrate-limited microbial growth. In this paper we develop a completely new kinetic model of substrate transport, based on recent knowledge on the structural biology of transport proteins, which correctly describes very accurate experimental results at near-zero substrate concentration values found in the literature, where the widespread Michaelis-Menten model fails. Additionally, our model converges asymptotically to Michaelis-Menten predictions as substrate concentration increases. Instead of the single active site enzymatic reaction of Michaelis-Menten type, the proposed model assumes a multi-site kinetics, simplified as an apparent all-or-none mechanism for the transport, which is controlled by means of the local substrate concentration in the close vicinity of the transport protein. Besides, the model also assumes that this local concentration is not equal to the mean substrate concentration experimentally determined in the culture medium. Instead, we propose that it fluctuates with a mostly exponential distribution of Weibull type. PMID:28187189
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.
Cristiane Fagundes
2013-03-01
Full Text Available In this study, the influence of storage temperature and passive modified packaging (PMP on the respiration rate and physicochemical properties of fresh-cut Gala apples (Malus domestica B. was investigated. The samples were packed in flexible multilayer bags and stored at 2 °C, 5 °C, and 7 °C for eleven days. Respiration rate as a function of CO2 and O2 concentrations was determined using gas chromatography. The inhibition parameters were estimated using a mathematical model based on Michaelis-Menten equation. The following physicochemical properties were evaluated: total soluble solids, pH, titratable acidity, and reducing sugars. At 2 °C, the maximum respiration rate was observed after 150 hours. At 5 °C and 7 °C the maximum respiration rates were observed after 100 and 50 hours of storage, respectively. The inhibition model results obtained showed a clear effect of CO2 on O2 consumption. The soluble solids decreased, although not significantly, during storage at the three temperatures studied. Reducing sugars and titratable acidity decreased during storage and the pH increased. These results indicate that the respiration rate influenced the physicochemical properties.
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.)
Karakhim, S A
2012-01-01
The Slater-Bonner method which is used for graphic determination of substrate constant (Ks) by linear dependence of apparent Michaelis constant (Km(app)) on the limiting rate (V(app)) of enzyme-catalysed reactions with activator participation has been critically analysed. It has been shown that although it is possible to record the mechanisms of such reactions as a scheme similar to Michaelis-Menten model which allow to find correlation Km(app) and V(app) as equation Km(app) = Ks + V(app)/k1[E]0 ([E]0 is a total enzyme concentration, k1 is a rate constant of enzyme-substrate complex formation from free enzyme and substrate) in order to calculate Ks and individual rate constants (k1, k(-1)), but this approach for investigation of all reactions with activator participation ought not to be used. The above equation is not obeyed in general, it may be true for some mechanisms only or under certain ratios of kinetic parameters of enzyme-catalysed reactions.
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.
Modeling helicity dissipation-rate equation
Yokoi, Nobumitsu
2016-01-01
Transport equation of the dissipation rate of turbulent helicity is derived with the aid of a statistical analytical closure theory of inhomogeneous turbulence. It is shown that an assumption on the helicity scaling with an algebraic relationship between the helicity and its dissipation rate leads to the transport equation of the turbulent helicity dissipation rate without resorting to a heuristic modeling.
Cyclodextrin-based artificial oxidases with high rate accelerations and selectivity
Zhou, You; Lindbäck, Emil Anders; Pedersen, Christian Marcus
2014-01-01
Three cyclodextrin derivatives with one to four 2-O-formylmethyl groups attached to the secondary rim were prepared and investigated as catalysts for the oxidation of aminophenols in buffered dilute hydrogen peroxide. The derivatives were found to be Michaelis-Menten catalysts and to give rate ac....... The ability of one of the new artificial enzymes to oxidize selectively one aminophenol from a mixture of two was investigated giving substrate selectivities of up to 16:1. © 2014 Elsevier Ltd. All rights reserved....
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
In situ measurements of volatile aromatic hydrocarbon biodegradation rates in groundwater
Cozzarelli, Isabelle M.; Bekins, Barbara A.; Eganhouse, Robert P.; Warren, Ean; Essaid, Hedeff I.
2010-01-01
Benzene and alkylbenzene biodegradation rates and patterns were measured using an in situ microcosm in a crude-oil contaminated aquifer near Bemidji, Minnesota. Benzene-D6, toluene, ethylbenzene, o-, m- and p-xylenes and four pairs of C 3- and C 4-benzenes were added to an in situ microcosm and studied over a 3-year period. The microcosm allowed for a mass-balance approach and quantification of hydrocarbon biodegradation rates within a well-defined iron-reducing zone of the anoxic plume. Among the BTEX compounds, the apparent order of persistence is ethylbenzene > benzene > m,p-xylenes > o-xylene ≥ toluene. Threshold concentrations were observed for several compounds in the in situ microcosm, below which degradation was not observed, even after hundreds of days. In addition, long lag times were observed before the onset of degradation of benzene or ethylbenzene. The isomer-specific degradation patterns were compared to observations from a multi-year study conducted using data collected from monitoring wells along a flowpath in the contaminant plume. The data were fit with both first-order and Michaelis-Menten models. First-order kinetics provided a good fit for hydrocarbons with starting concentrations below 1 mg/L and Michaelis-Menten kinetics were a better fit when starting concentrations were above 1 mg/L, as was the case for benzene. The biodegradation rate data from this study were also compared to rates from other investigations reported in the literature.
In situ measurements of volatile aromatic hydrocarbon biodegradation rates in groundwater
Cozzarelli, I.M.; Bekins, B.A.; Eganhouse, R.P.; Warren, E.; Essaid, H.I.
2010-01-01
Benzene and alkylbenzene biodegradation rates and patterns were measured using an in situ microcosm in a crude-oil contaminated aquifer near Bemidji, Minnesota. Benzene-D6, toluene, ethylbenzene, o-, m- and p-xylenes and four pairs of C3- and C4-benzenes were added to an in situ microcosm and studied over a 3-year period. The microcosm allowed for a mass-balance approach and quantification of hydrocarbon biodegradation rates within a well-defined iron-reducing zone of the anoxic plume. Among the BTEX compounds, the apparent order of persistence is ethylbenzene > benzene > m,p-xylenes > o-xylene ≥ toluene. Threshold concentrations were observed for several compounds in the in situ microcosm, below which degradation was not observed, even after hundreds of days. In addition, long lag times were observed before the onset of degradation of benzene or ethylbenzene. The isomer-specific degradation patterns were compared to observations from a multi-year study conducted using data collected from monitoring wells along a flowpath in the contaminant plume. The data were fit with both first-order and Michaelis-Menten models. First-order kinetics provided a good fit for hydrocarbons with starting concentrations below 1 mg/L and Michaelis-Menten kinetics were a better fit when starting concentrations were above 1 mg/L, as was the case for benzene. The biodegradation rate data from this study were also compared to rates from other investigations reported in the literature.
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...
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 ...
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.
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.
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.
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...
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
Cristiane Fagundes
2013-03-01
Full Text Available In this study, the influence of storage temperature and passive modified packaging (PMP on the respiration rate and physicochemical properties of fresh-cut Gala apples (Malus domestica B. was investigated. The samples were packed in flexible multilayer bags and stored at 2 °C, 5 °C, and 7 °C for eleven days. Respiration rate as a function of CO2 and O2 concentrations was determined using gas chromatography. The inhibition parameters were estimated using a mathematical model based on Michaelis-Menten equation. The following physicochemical properties were evaluated: total soluble solids, pH, titratable acidity, and reducing sugars. At 2 °C, the maximum respiration rate was observed after 150 hours. At 5 °C and 7 °C the maximum respiration rates were observed after 100 and 50 hours of storage, respectively. The inhibition model results obtained showed a clear effect of CO2 on O2 consumption. The soluble solids decreased, although not significantly, during storage at the three temperatures studied. Reducing sugars and titratable acidity decreased during storage and the pH increased. These results indicate that the respiration rate influenced the physicochemical properties.Neste estudo, a influência da temperatura de armazenamento e da embalagem com atmosfera modificada passiva (AMP na taxa respiratória e nas propriedades físico-químicas de maçãs da variedade Gala (Malus domestica, B. minimamente processadas foi investigada. As amostras foram acondicionadas em embalagens flexíveis e armazenados a 2 °C, 5 °C e 7 °C, durante 11 dias. A taxa de respiração foi gerada para diferentes concentrações de O2 e CO2, obtidas por cromatografia gasosa. Os parâmetros de inibição foram estimados por um modelo matemático baseado na equação de Michaelis-Menten. Foram avaliadas as seguintes propriedades físico-químicas: sólidos solúveis totais, pH, acidez titulável e açúcares redutores. A 2 °C, a taxa de respiração máxima foi
Quick and Easy Rate Equations for Multistep Reactions
Savage, Phillip E.
2008-01-01
Students rarely see closed-form analytical rate equations derived from underlying chemical mechanisms that contain more than a few steps unless restrictive simplifying assumptions (e.g., existence of a rate-determining step) are made. Yet, work published decades ago allows closed-form analytical rate equations to be written quickly and easily for…
Rate equation modelling and investigation of quantum cascade detector characteristics
Saha, Sumit; Kumar, Jitendra
2016-10-01
A simple precise transport model has been proposed using rate equation approach for the characterization of a quantum cascade detector. The resonant tunneling transport is incorporated in the rate equation model through a resonant tunneling current density term. All the major scattering processes are included in the rate equation model. The effect of temperature on the quantum cascade detector characteristics has been examined considering the temperature dependent band parameters and the carrier scattering processes. Incorporation of the resonant tunneling process in the rate equation model improves the detector performance appreciably and reproduces the detector characteristics within experimental accuracy.
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.
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…
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…
Studies on Microwave Heated Drying-rate Equations of Foods
1990-01-01
In order to design various microwave heated drying apparatuses, we must take drying-rate equations which are based on simple drying-rate models. In a previous paper (KUBOTA, et al., 1990), we have studied a convenient microwave heated drying instrument, and studied the simple drying-rate equations of potato and so on by using the simple empirical rate equations that have been reported in previous papers (KUBOTA, 1979-1, 1979-2). In this paper, we studied the microwave drying rate of the const...
Theory of nanolaser devices: Rate equation analysis versus microscopic theory
Lorke, Michael; Skovgård, Troels Suhr; Gregersen, Niels;
2013-01-01
A rate equation theory for quantum-dot-based nanolaser devices is developed. We show that these rate equations are capable of reproducing results of a microscopic semiconductor theory, making them an appropriate starting point for complex device simulations of nanolasers. The input...
Bringing metabolic networks to life: convenience rate law and thermodynamic constraints
Klipp Edda
2006-12-01
Full Text Available Abstract Background Translating a known metabolic network into a dynamic model requires rate laws for all chemical reactions. The mathematical expressions depend on the underlying enzymatic mechanism; they can become quite involved and may contain a large number of parameters. Rate laws and enzyme parameters are still unknown for most enzymes. Results We introduce a simple and general rate law called "convenience kinetics". It can be derived from a simple random-order enzyme mechanism. Thermodynamic laws can impose dependencies on the kinetic parameters. Hence, to facilitate model fitting and parameter optimisation for large networks, we introduce thermodynamically independent system parameters: their values can be varied independently, without violating thermodynamical constraints. We achieve this by expressing the equilibrium constants either by Gibbs free energies of formation or by a set of independent equilibrium constants. The remaining system parameters are mean turnover rates, generalised Michaelis-Menten constants, and constants for inhibition and activation. All parameters correspond to molecular energies, for instance, binding energies between reactants and enzyme. Conclusion Convenience kinetics can be used to translate a biochemical network – manually or automatically - into a dynamical model with plausible biological properties. It implements enzyme saturation and regulation by activators and inhibitors, covers all possible reaction stoichiometries, and can be specified by a small number of parameters. Its mathematical form makes it especially suitable for parameter estimation and optimisation. Parameter estimates can be easily computed from a least-squares fit to Michaelis-Menten values, turnover rates, equilibrium constants, and other quantities that are routinely measured in enzyme assays and stored in kinetic databases.
OPTIMAL CONVERGENCE RATE OF THE LANDAU EQUATION WITH FRICTIONAL FORCE
Liu Shuangqian; Liu Hongxia
2012-01-01
The Cauchy problem of the Landau equation with frictional force is investigated.Based on Fourier analysis and nonlinear energy estimates,the optimal convergence rate to the steady state is obtained under some conditions on initial data.
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...
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 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. ...
Rate equations for sodium catalyzed amorphous silica dissolution
Rimstidt, J. Donald; Zhang, Yilun; Zhu, Chen
2016-12-01
Newly measured amorphous silica dissolution rate data were combined with data from the literature to produce an equation that predicts the dissolution flux (J, mol/m2 s) of amorphous silica as a function of temperature (T, K), sodium concentration (mNa+, molal), and hydrogen ion activity (aH+).
ECONOMETRIC APPROACH TO DIFFERENCE EQUATIONS MODELING OF EXCHANGE RATES CHANGES
Josip Arnerić
2010-12-01
Full Text Available Time series models that are commonly used in econometric modeling are autoregressive stochastic linear models (AR and models of moving averages (MA. Mentioned models by their structure are actually stochastic difference equations. Therefore, the objective of this paper is to estimate difference equations containing stochastic (random component. Estimated models of time series will be used to forecast observed data in the future. Namely, solutions of difference equations are closely related to conditions of stationary time series models. Based on the fact that volatility is time varying in high frequency data and that periods of high volatility tend to cluster, the most successful and popular models in modeling time varying volatility are GARCH type models and their variants. However, GARCH models will not be analyzed because the purpose of this research is to predict the value of the exchange rate in the levels within conditional mean equation and to determine whether the observed variable has a stable or explosive time path. Based on the estimated difference equation it will be examined whether Croatia is implementing a stable policy of exchange rates.
郑丹平; 吴艳阳; 吴群河; 罗昊; 张恒军; 张仁铎
2013-01-01
设计了层状底泥的连续流动培养实验装置,经调试后用于对珠江广州河段的沉积物样品进行连续流动培养实验r通过检测培养出水和稳定状态时硝氮还原速率和氨氮生成速率,运用Michaelis-Menten方程计算珠江底泥的潜在硝氮还原速率和氨氮生成速率,并结合氨氮生成和硝氮还原理论配比分析硝氮还原的主要途径.结果显示,珠江广州河段整体的潜在硝氮还原速率为1410 nmol· (h·mL)-1,硝氮还原动力参数为5.0 mmol·L-1；潜在氨氮生成速率为0.665 nmol·(h·mL)-1,氨氮生成动力参数为0.137 mmol·L-1；厌氧氨氧化作用和硝氮异化还原作用是珠江底泥中硝氮还原的主要途径.%Flow-through reactors ( FTR) were designed and debugged for the incubation experiments of sediment slices. After being constructed, the FTR with sediments were run for different concentrations of nitrate-inflow incubation experiments. Time-series concentrations of nitrate and ammonium were monitored in the outflow, and the nitrate reduction rates (NRR) and ammonium production rates (APR) were calculated when reaching a equilibrium-steady state. After that, the potential maximum nitrate reduction rate and ammonium production rate were calculated out according to Michaelis-Menten equation. The conclusions are as follows: the potential NRR in Pearl River sediment was 1410 nmol· (h·mL)-1, and the kinetic parameter of nitrate reduction was 5. 0 mmol·L-1; the potential APR was 0. 665 nmol· ( h · mL) -1, while the kentic parameter was 0.137 mmol·L-1. The anaerobic ammonium oxidation(Anammox) and the dissimilatory nitrate reduction to ammonium (DNRA) are likely to be the two principle pathways for nitrate reduction in river sediments.
Biological Electric Fields and Rate Equations for Biophotons
Alvermann, M; Swain, J; Widom, A
2014-01-01
Ultraweak bioluminescence - the emission of biophotons - remains an experimentally well-established, but theoretically poorly understood phenomenon. This paper presents several related investigations into the physical process of both spontaneous biophoton emission and delayed luminescence. Since light intensities depend upon the modulus squared of their corresponding electric fields we first make some general estimates about the inherent electric fields within various biological systems. Since photon emission from living matter following an initial excitation ("delayed luminescence") typically does not follow a simple exponential decay law after excitation we discuss such non-exponential decays from a general theoretical perspective and argue that they are often to be expected and why. We then discuss the dynamics behind some nonlinear rate equations, connecting them both to biological growth rates and biophoton emission rates, noting a possible connection with cancer. We then return to non-exponential decay ...
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.
Validation of resting metabolic rate prediction equations for teenagers
Paulo Henrique Santos da Fonseca
2007-09-01
Full Text Available The resting metabolic rate (RMR can be defi ned as the minimum rate of energy spent and represents the main component of the energetic outlay. The purpose of this study is to validate equations to predict the resting metabolic rate in teenagers (103 individuals, being 51 girls and 52 boys, with age between 10 and 17 years from Florianópolis – SC – Brazil. It was measured: the body weight, body height, skinfolds and obtained the lean and body fat mass through bioimpedance. The nonproteic RMR was measured by Weir’s equation (1949, utilizing AeroSport TEEM-100 gas analyzer. The studied equations were: Harry and Benedict (1919, Schofi eld (1985, WHO/FAO/UNU (1985, Henry and Rees (1991, Molnár et al. (1998, Tverskaya et al. (1998 and Müller et al. (2004. In order to study the cross-validation of the RMR prediction equations and its standard measure (Weir 1949, the following statistics procedure were calculated: Pearson’s correlation (r ≥ 0.70, the “t” test with the signifi cance level of p0.05 in relation to the standard measure, with exception of the equations suggested for Tverskaya et al. (1998, and the two models of Müller et al (2004. Even though there was not a signifi cant difference, only the models considered for Henry and Rees (1991, and Molnár et al. (1995 had gotten constant error variation under 5%. All the equations analyzed in the study in girls had not reached criterion of correlation values of 0.70 with the indirect calorimetry. Analyzing the prediction equations of RMR in boys, all of them had moderate correlation coeffi cients with the indirect calorimetry, however below 0.70. Only the equation developed for Tverskaya et al. (1998 presented differences (p ABSTRACT0,05 em relação à medida padrão (Weir 1949, com exceção das equações sugeridas por Tverskaya et al. (1998 e os dois modelos de Müller et al (2004. Mesmo não havendo diferença signifi cativa, somente os modelos propostos por Henry e Rees (1991
Reaction rates for a generalized reaction-diffusion master equation.
Hellander, Stefan; Petzold, Linda
2016-01-01
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach, in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is of the order of the reaction radius of a reacting pair of molecules.
Reaction rates for a generalized reaction-diffusion master equation
Hellander, Stefan; Petzold, Linda
2016-01-01
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach, in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is of the order of the reaction radius of a reacting pair of molecules.
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.
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
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.
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.
Matsushita, K.; Mahmoodi, B.K.; Woodward, M.; Emberson, J.R.; Jafar, T.H.; Jee, S.H.; Polkinghorne, K.R.; Shankar, A.; Smith, D.H.; Tonelli, M.; Warnock, D.G.; Wen, C.P.; Coresh, J.; Gansevoort, R.T.; Hemmelgarn, B.R.; Levey, A.S.; Wetzels, J.F.
2012-01-01
CONTEXT: The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation more accurately estimates glomerular filtration rate (GFR) than the Modification of Diet in Renal Disease (MDRD) Study equation using the same variables, especially at higher GFR, but definitive evidence of its risk
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
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
无
2010-01-01
In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or
Temperature characteristics of quantum dot devices: Rate vs. Master Equation Models
Berg, Tommy Winther; Bischoff, Svend; Magnúsdóttir, Ingibjörg;
2001-01-01
The change of transparency current with temperature for quantum dot devices depends strongly on whether a rate or master equation model is used. The master equation model successfully explains experimental observations of negative characteristic temperatures.......The change of transparency current with temperature for quantum dot devices depends strongly on whether a rate or master equation model is used. The master equation model successfully explains experimental observations of negative characteristic temperatures....
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.
Agbogbo Frank K
2010-03-01
Full Text Available Abstract Background Different mechanistic models have been used in the literature to describe the enzymatic hydrolysis of pretreated biomass. Although these different models have been applied to different substrates, most of these mechanistic models fit into two- and three-parameter mechanistic models. The purpose of this study is to compare the models and determine the activation energy and the enthalpy of adsorption of Trichoderma reesei enzymes on ammonia fibre explosion (AFEX-treated wheat straw. Experimental enzymatic hydrolysis data from AFEX-treated wheat straw were modelled with two- and three-parameter mechanistic models from the literature. In order to discriminate between the models, initial rate data at 49°C were subjected to statistical analysis (analysis of variance and scatter plots. Results For three-parameter models, the HCH-1 model best fitted the experimental data; for two-parameter models Michaelis-Menten (M-M best fitted the experimental data. All the three-parameter models fitted the data better than the two-parameter models. The best three models at 49°C (HCH-1, Huang and M-M were compared using initial rate data at three temperatures (35°, 42° and 49°C. The HCH-1 model provided the best fit based on the F values, the scatter plot and the residual sum of squares. Also, its kinetic parameters were linear in Arrhenius/van't Hoff's plots, unlike the other models. The activation energy (Ea is 47.6 kJ/mol and the enthalpy change of adsorption (ΔH is -118 kJ/mol for T. reesei enzymes on AFEX-treated wheat straw. Conclusion Among the two-parameter models, Michaelis-Menten model provided the best fit compared to models proposed by Humphrey and Wald. For the three-parameter models, HCH-1 provided the best fit because the model includes a fractional coverage parameter (ϕ which accounts for the number of reactive sites covered by the enzymes.
Quantum-Dot Semiconductor Optical Amplifiers: State Space Model versus Rate Equation Model
Hussein Taleb
2013-01-01
Full Text Available A simple and accurate dynamic model for QD-SOAs is proposed. The proposed model is based on the state space theory, where by eliminating the distance dependence of the rate equation model of the QD-SOA; we derive a state space model for the device. A comparison is made between the rate equation model and the state space model under both steady state and transient regimes. Simulation results demonstrate that the derived state space model not only is much simpler and faster than the rate equation model, but also it is as accurate as the rate equation model.
Crank-Nicholson method for rate equations in powder random lasers
García-Ramiro, B.; Illarramendi, M. A.; Zubia, J.
2015-01-01
In this work, we show the resolution of the rate equations in powder random lasers by using the Crank-Nicholson finite difference method. Light propagation in our powders is described by the model of light diffusion. The generalized time-dependent random laser equations describing our system are formed by three differential coupled equations: two diffusion equations for the pump and emitted light and a rate equation for the density of the dopant molecules in the excited state. The system has been solved for two pumping schemes (one-photon and two-photon excitation) and for a wide range of temporal incident pulses (from femtoseconds to nanoseconds).
Kandasamy, Palani; Moitra, Ranabir; Mukherjee, Souti
2015-01-01
Experiments were conducted to determine the respiration rate of tomato at 10, 20 and 30 °C using closed respiration system. Oxygen depletion and carbon dioxide accumulation in the system containing tomato was monitored. Respiration rate was found to decrease with increasing CO2 and decreasing O2 concentration. Michaelis-Menten type model based on enzyme kinetics was evaluated using experimental data generated for predicting the respiration rate. The model parameters that obtained from the respiration rate at different O2 and CO2 concentration levels were used to fit the model against the storage temperatures. The fitting was fair (R2 = 0.923 to 0.970) when the respiration rate was expressed as O2 concentation. Since inhibition constant for CO2 concentration tended towards negetive, the model was modified as a function of O2 concentration only. The modified model was fitted to the experimental data and showed good agreement (R2 = 0.998) with experimentally estimated respiration rate.
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
Shape of the Polymerization Rate in the Prion Equation
Gabriel, Pierre
2010-01-01
We consider a polymerization (fragmentation) model with size-dependent parameters involved in prion proliferation. Using power laws for the different rates of this model, we recover the shape of the polymerization rate using experimental data. The technique used is inspired from an article of Zampieri et al. where the fragmentation dependency on prion strains is investigated. Our improvement is to use power laws for the rates whereas Zampieri et al. used a constant polymerization coefficient and linear fragmentation.
Upper Bounds of the Rates of Decay for Solutions of the Boussinesq Equations
Ying Liu
2011-01-01
In this paper, upper bounds of the L2-decay rate for the Boussinesq equations are considered.Using the L2 decay rate of solutions for the heat equation, and assuming that the solutions of the Boussinesq equations are smooth, we obtain the upper bounds of L2 decay rate for the smooth solutions and difference between the solutions of the Boussinesq equations and those of the heat system with the same initial data. The decay results may then be obtained by passing to the limit of approximating sequences of solutions. The main tool is the Fourier splitting method.
Beyond the Mincer Equation: The Internal Rate of Return to Higher Education in Colombia
García-Suaza, Andrés Felipe; Guataquí, Juan Carlos; Guerra, José Alberto; Maldonado, Darío
2014-01-01
In order to present an estimation of the internal rate of return (IRR) to higher education in Colombia, we take advantage of recent updates on the methodological approach towards earnings equations. In order to overcome the criticism that surrounds interpretations of the education coefficient of Mincer equations as being the rate of return to…
Persson, Inga-Lill; Nilsson, Mats B; Pastor, John; Eriksson, Tobias; Bergström, Roger; Danell, Kjell
2009-10-01
Large herbivores can affect the carbon cycle in boreal forests by changing productivity and plant species composition, which in turn could ultimately alter litter production, nutrient cycling, and the partitioning between aboveground and belowground allocation of carbon. Here we experimentally tested how moose (Alces alces) at different simulated population densities affected belowground respiration rates (estimated as CO2 flux) in young boreal forest stands situated along a site productivity gradient. At high simulated population density, moose browsing considerably depressed belowground respiration rates (24-56% below that of no-moose controls) except during June, where the difference only was 10%. Moose browsing depressed belowground respiration the most on low-productivity sites. Soil moisture and temperature did not affect respiration rates. Impact of moose on belowground respiration was closely linked to litter production and followed Michaelis-Menten dynamics. The main mechanism by which moose decrease belowground respiration rates is likely their effect on photosynthetic biomass (especially decreased productivity of deciduous trees) and total litter production. An increased productivity of deciduous trees along the site productivity gradient causes an unequal effect of moose along the same gradient. The rapid growth of deciduous trees may offer higher resilience against negative effects of moose browsing on litter production and photosynthate allocation to roots.
A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations
Radhakrishnan, K.
1984-01-01
The efficiency of several algorithms used for numerical integration of stiff ordinary differential equations was compared. The methods examined included two general purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes were applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code available for the integration of combustion kinetic rate equations. It is shown that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient then evaluating the temperature by integrating its time-derivative.
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.
Asymptotic solution of nonlinear moment equations for constant-rate aerosol reactors
B. D. Shaw
1998-01-01
Full Text Available Nonlinear evolution equations based upon moments of the aerosol size distribution function are solved asymptotically for constant-rate aerosol reactors (i.e., where condensible monomer is added at a constant rate operating in the free-molecular limit. The governing equations are nondimensionalized and a large parameter that controls nucleation behavior is identified. Asymptotic analyses are developed in terms of this parameter. Comparison of the asymptotic results with direct numerical integration of the governing equations is favorable. The asymptotic results provide a simplified analytical approach to estimating average particle sizes, particle number densities, and peak supersaturation values for constant-rate aerosol reactors.
Emanuele Ricca
2014-01-01
Full Text Available The present paper addresses two crucial features in the industrial development of fructose production by enzymatic hydrolysis of inulin: the use of immobilized biocatalyst in the hydrolysis of crude extracts of chicory roots and the evaluation of the effect of degree of polymerization of inulin on the overall reaction rate. The immobilized biocatalyst consisted of inulinase covalently bound to Sepabeads® supports. It was demonstrated that its catalytic activity towards crude inulin extract (real substrate was much higher than that exhibited towards pure inulin (synthetic solution. Experiments revealed that, in applications of practical interest with real substrate, the activity of immobilized enzyme was as high as 63 % of that of free enzyme in homogeneous solution. This certainly was a driving force to potential industrial application of this immobilized enzyme preparation. Therefore, the effect of pure and crude substrates on the kinetics of the reaction catalysed by the immobilized enzyme was investigated. The kinetic analysis revealed a Michaelis-Menten dependence of the reaction rate on substrate concentration for both pure (high molecular mass and crude (low molecular mass inulin. Interesting results were derived from the comparison of Km and vmax values in the two cases. In particular, it was found that increasing degree of polymerization of the substrate caused vmax decrease and Km increase. After evaluation of mass transport effects, this was mainly associated with a different substrate/ enzyme affinity when exploiting inulin characterized by different (low or high degree of polymerization.
Exact solution to laser rate equations: three-level laser as a Morse-like oscillator
León-Montiel, R. de J.; Moya-Cessa, Héctor M.
2016-08-01
It is shown how the rate equations that model a three-level laser can be cast into a single second-order differential equation, whose form describes a time-dependent harmonic oscillator. Using this result, we demonstrate that the resulting equation can be identified as a Schrödinger equation for a Morse-like potential, thus allowing us to derive exact closed-form expressions for the dynamics of the number of photons inside the laser cavity, as well as the atomic population inversion.
Posttranscriptional expression regulation: what determines translation rates?
Regina Brockmann
2007-03-01
Full Text Available Recent analyses indicate that differences in protein concentrations are only 20%-40% attributable to variable mRNA levels, underlining the importance of posttranscriptional regulation. Generally, protein concentrations depend on the translation rate (which is proportional to the translational activity, TA and the degradation rate. By integrating 12 publicly available large-scale datasets and additional database information of the yeast Saccharomyces cerevisiae, we systematically analyzed five factors contributing to TA: mRNA concentration, ribosome density, ribosome occupancy, the codon adaptation index, and a newly developed "tRNA adaptation index." Our analysis of the functional relationship between the TA and measured protein concentrations suggests that the TA follows Michaelis-Menten kinetics. The calculated TA, together with measured protein concentrations, allowed us to estimate degradation rates for 4,125 proteins under standard conditions. A significant correlation to recently published degradation rates supports our approach. Moreover, based on a newly developed scoring system, we identified and analyzed genes subjected to the posttranscriptional regulation mechanism, translation on demand. Next we applied these findings to publicly available data of protein and mRNA concentrations under four stress conditions. The integration of these measurements allowed us to compare the condition-specific responses at the posttranscriptional level. Our analysis of all 62 proteins that have been measured under all four conditions revealed proteins with very specific posttranscriptional stress response, in contrast to more generic responders, which were nonspecifically regulated under several conditions. The concept of specific and generic responders is known for transcriptional regulation. Here we show that it also holds true at the posttranscriptional level.
Trimming Behavior of H_2-Loaded Silica Fiber Modeled by Rate Equations
无
2003-01-01
Photosensitivity behavior of H2-loaded silica fiber was modeled by rate equations for activated particles. The theoretical deductions give a close explanation to experimental phenomena on post-exposure growth in fiber gratings.
Lorentz Invariance at Finite Temperature and Its Effect on Production Rate and Equation of State
HE Lian-Yi; ZHUANG Peng-Fei
2004-01-01
The effect of Lorentz invariance breaking on the production rate and the equation of state at finite temperature is investigated in the frame of φ3 theory. The invariance breaking significantly changes the off-shell degree at high temperatures.
Rate of Convergence to Barenblatt Profiles for the Fast Diffusion Equation
Fila, Marek; Winkler, Michael; Yanagida, Eiji
2011-01-01
We study the asymptotic behaviour of positive solutions of the Cauchy problem for the fast diffusion equation near the extinction time. We find a continuum of rates of convergence to a self-similar profile. These rates depend explicitly on the spatial decay rates of initial data.
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
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.
Improved decay rates for solutions for a multidimensional generalized Benjamin-Bona-Mahony equation
Said-Houari, Belkacem
2014-01-01
In this paper, we study the decay rates of solutions for the generalized Benjamin-Bona-Mahony equation in multi-dimensional space. For initial data in some L1-weighted spaces, we prove faster decay rates of the solutions. More precisely, using the Fourier transform and the energy method, we show the global existence and the convergence rates of the solutions under the smallness assumption on the initial data and we give better decay rates of the solutions. This result improves early works in J. Differential Equations 158(2) (1999), 314-340 and Nonlinear Anal. 75(7) (2012), 3385-3392. © 2014-IOS Press.
Convergence Rate to Stationary Solutions for Boltzmann Equation with External Force
Seiji UKAI; Tong YANG; Huijiang ZHAO
2006-01-01
For the Boltzmann equation with an external force in the form of the gradient of a potential function in space variable, the stability of its stationary solutions as local Maxwellians was studied by S. Ukai et al. (2005) through the energy method. Based on this stability analysis and some techniques on analyzing the convergence rates to stationary solutions for the compressible Navier-Stokes equations, in this paper, we study the convergence rate to the above stationary solutions for the Boltzmann equation which is a fundamental equation in statistical physics for non-equilibrium rarefied gas. By combining the dissipation from the viscosity and heat conductivity on the fluid components and the dissipation on the non-fluid component through the celebrated H-theorem, a convergence rate of the same order as the one for the compressible Navier-Stokes is obtained by constructing some energy functionals.
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.
Woeger, Julia; Kinoshita, Shunichi; Wolfgang, Eder; Briguglio, Antonino; Hohenegger, Johann
2016-04-01
Operculina complanata was collected in 20 and 50 m depth around the Island of Sesoko belonging to Japans southernmost prefecture Okinawa in a series of monthly sampling over a period of 16 months (Apr.2014-July2015). A minimum of 8 specimens (4 among the smallest and 4 among the largest) per sampling were cultured in a long term experiment that was set up to approximate conditions in the field as closely as possible. A set up allowing recognition of individual specimens enabled consistent documentation of chamber formation, which in combination with μ-CT-scanning after the investigation period permitted the assignment of growth steps to specific time periods. These data were used to fit various mathematical models to describe growth (exponential-, logistic-, generalized logistic-, Gompertz-function) and chamber building rate (Michaelis-Menten-, Bertalanffy- function) of Operculina complanata. The mathematically retrieved maximum lifespan and mean chamber building rate found in cultured Operculina complanata were further compared to first results obtained by the simultaneously conducted "natural laboratory approach". Even though these comparisons hint at a somewhat stunted growth and truncated life spans of Operculina complanata in culture, they represent a possibility to assess and improve the quality of further cultivation set ups, opening new prospects to a better understanding of the their theoretical niches.
Tomlinson, Sean
2016-04-01
The calculation and comparison of physiological characteristics of thermoregulation has provided insight into patterns of ecology and evolution for over half a century. Thermoregulation has typically been explored using linear techniques; I explore the application of non-linear scaling to more accurately calculate and compare characteristics and thresholds of thermoregulation, including the basal metabolic rate (BMR), peak metabolic rate (PMR) and the lower (Tlc) and upper (Tuc) critical limits to the thermo-neutral zone (TNZ) for Australian rodents. An exponentially-modified logistic function accurately characterised the response of metabolic rate to ambient temperature, while evaporative water loss was accurately characterised by a Michaelis-Menten function. When these functions were used to resolve unique parameters for the nine species studied here, the estimates of BMR and TNZ were consistent with the previously published estimates. The approach resolved differences in rates of metabolism and water loss between subfamilies of Australian rodents that haven't been quantified before. I suggest that non-linear scaling is not only more effective than the established segmented linear techniques, but also is more objective. This approach may allow broader and more flexible comparison of characteristics of thermoregulation, but it needs testing with a broader array of taxa than those used here.
Laser Rate Equation Based Filtering for Carrier Recovery in Characterization and Communication
Piels, Molly; Iglesias Olmedo, Miguel; Xue, Weiqi;
2015-01-01
We formulate a semiconductor laser rate equationbased approach to carrier recovery in a Bayesian filtering framework. Filter stability and the effect of model inaccuracies (unknown or un-useable rate equation coefficients) are discussed. Two potential application areas are explored: laser charact...
A new approach to model CW CO$_2$ laser using rate equations
UTPAL NUNDY; SUNIL DAGA; MANOJ KUMAR
2016-12-01
Two popular methods to analyse the operation of CW CO$_2$ lasers use the temperature model and the rate equation model. Among the two, the latter model directly calculates the population densities in the various vibrational levels connected with the lasing action, and provides a clearer illustration of the processes involved. Rate equation models used earlier grouped a number of vibration levels together, on the basis of normal modes of vibrations of CO$_2$. However, such grouping has an inherent disadvantage as it requires that theselevels be in thermal equilibrium. Here we report a new approach for modelling CW CO$_2$ lasers wherein the relevant vibration levels are identified and independently treated. They are connected with each other through theprocesses of excitation, relaxation and radiative transitions. We use the universally accepted rate coefficients to describe these processes. The other distinguishing feature of our model is the methodology adopted for carryingout the calculations. For instance, the CW case being a steady state, all the rate equations are thus equated to zero. In the prior works, researchers derived analytical expressions for the vibration level population densities, thatbecomes quite a tedious task with increasing number of levels. Grouping of the vibration levels helped in restricting the number of equations and this facilitated the derivation of these analytical expressions. We show that insteady state, these rate equations form a set of linear algebric equations. Instead of deriving analytical expressions, these can be elegantly solved using the matrix method. The population inversion calculated in this manner alongwith the relaxation rate of the upper laser level determines the output power of the laser. We have applied the model to an experimental CW laser reported in literature. Our results match the experimentally reported power.
S. C. Oukouomi Noutchie
2014-01-01
Full Text Available We make use of Laplace transform techniques and the method of characteristics to solve fragmentation equations explicitly. Our result is a breakthrough in the analysis of pure fragmentation equations as this is the first instance where an exact solution is provided for the fragmentation evolution equation with general fragmentation rates. This paper is the key for resolving most of the open problems in fragmentation theory including “shattering” and the sudden appearance of infinitely many particles in some systems with initial finite particles number.
A differential equation for the flow rate during silo discharge: Beyond the Beverloo rule
2016-01-01
We present a differential equation for the flow rate of granular materials during the discharge of a silo. This is based in the energy balance of the variable mass system in contrast with the traditional derivations based on heuristic postulates such as the free fall arch. We show that this new equation is consistent with the well known Beverloo rule, providing an independent estimate for the universal Beverloo prefactor. We also find an analytic expression for the pressure under discharging ...
From Langmuir kinetics to first- and second-order rate equations for adsorption.
Liu, Yu; Shen, Liang
2008-10-21
So far, the first- and second-order kinetic equations have been most frequently employed to interpret adsorption data obtained under various conditions, whereas the theoretical origins of these two equations still remain unknown. Using the Langmuir kinetics as a theoretical basis, this study showed that the Langmuir kinetics can be transformed to a polynomial expression of dtheta t /d t = k 1(theta e - theta t ) + k 2(theta e - theta t ) (2), a varying-order rate equation. The sufficient and necessary conditions for simplification of the Langmuir kinetics to the first- and second-order rate equations were put forward, which suggested that the relative magnitude of theta e over k 1/ k 2 governs the simplification of the Langmuir kinetics. In cases where k 1/ k 2 is greater than theta e or k 1/ k 2 is very close to theta e, adsorption kinetics would be reasonably described by the first-order rate equation, whereas the Langmuir kinetics would be reduced to the second-order equation only at k 1/ k 2 Langmuir kinetics indeed is determined by C 0. Detailed C 0-depedent boundary conditions for simplifying the Langmuir kinetics were also established and were verified by experimental data.
Yun, Ji-Yeong; Lee, Jung-Eun; Yang, Kyung-Mi; Cho, Suekyung; Kim, Arim; Kwon, Yong-Uk; Kwon, Yong-Euk; Park, Jin-Byung
2012-01-01
The effects of structural modification of cell wall on the biotransformation capability by recombinant Corynebacterium glutamicum cells, expressing the chnB gene encoding cyclohexanone monooxygenase of Acinetobacter calcoaceticus NCIMB 9871, were investigated. Baeyer-Villiger oxygenation of 2-(2'-acetoxyethyl) cyclohexanone (MW 170 Da) into R-7-(2'-acetoxyethyl)-2-oxepanone was used as a model reaction. The whole-cell biotransformation followed Michaelis-Menten kinetics. The V (max) and K (S) values were estimated as 96.8 U g(-1) of dry cells and 0.98 mM, respectively. The V (max) was comparable with that of cyclohexanone oxygenation, whereas the K (S) was almost eightfold higher. The K (S) value of 2-(2'-acetoxyethyl) cyclohexanone oxygenation was reduced by ca. 30% via altering the cell envelop structure of C. glutamicum with ethambutol, which inhibits arabinosyl transferases involved in the biosynthesis of cell wall arabinogalactan and mycolate layers. The higher whole-cell biotransformation rate was also observed in the oxygenation of ethyl 2-cyclohexanone acetate upon ethambutol treatment of the recombinant C. glutamicum. Therefore, it was assumed that the biotransformation efficiency of C. glutamicum-based biocatalysts, with respect to medium- to large-sized lipophilic organic substrates (MW > ca. 170), can be enhanced by engineering their cell wall outer layers, which are known to function as a formidable barrier to lipophilic molecules.
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.
Soghra ALIASGHARZADEH
2015-10-01
Full Text Available Background: Underweight as a public health problem in young women is associated with nutritional deficiencies, menstrual irregularity, eating disorders, reduced fertility, etc. Since resting metabolic rate (RMR is a necessary compo-nent in the development of nutrition support therapy, therefore we determined the accuracy of commonly used pre-dictive equations against RMR measured by indirect calorimetry among healthy young underweight females.Methods: This cross-sectional study was conducted on 104 underweight females aged 18-30 years old with body mass index (BMI <18.5 kg/m2 in 2013 . After collecting anthropometric data, body composition was measured by bioelec-tric impedance analysis (BIA. RMR was measured by using indirect calorimetry (FitMate™ and was estimated by 10 commonly used predictive equations. Comparisons were conducted using paired t-test. The accuracy of the RMR equations was evaluated on the basis of the percentage of subjects’ predicted RMR within 10% of measured RMR.Results: The mean BMI of subjects was 17.3±1.3 kg/m2. The measured RMR ranged 736-1490 kcal/day (mean 1084.7±175 kcal/day. Findings indicated that except Muller and Abbreviation, other equations significantly over es-timated RMR, compared to measured value (P<0.05. As an individual prediction accuracy, these predictive equations showed poor performance with the highest accuracy rate of 54.8% for Muller equation (22.1% under and 23.1% over-prediction and 43.3% for Abbreviation equation (31.7% under and 25% over-prediction, the percentage bias was 1.8% and 0.63% and RMSE was 162 and 173 kcal/d, respectively.Conclusion: Although Muller equation gave fairly acceptable prediction, more suitable new equations are needed to be developed to help better management of nutritional plans in young underweight people.
Rate-equation model for multi-mode semiconductor lasers with spatial hole burning.
Lenstra, Daan; Yousefi, Mirvais
2014-04-07
We present a set of rate equations for the modal amplitudes and carrier-inversion moments that describe the deterministic multi-mode dynamics of a semiconductor laser due to spatial hole burning. Mutual interactions among the lasing modes, induced by high- frequency modulations of the carrier distribution, are included by carrier-inversion moments for which rate equations are given as well. We derive the Bogatov effect of asymmetric gain suppression in semiconductor lasers and illustrate the potential of the model for a two and three-mode laser by numerical and analytical methods.
On the convergence rate of operator splitting for Hamilton-Jacobi equations with source terms
Jakobsen, Espen R.; Karlsen, Kenneth H.; Risebro, Nils Henrik
2000-02-01
We establish a rate of convergence for a semi-discrete operator splitting method applied to Hamilton-Jacobi equations with source terms. The method is based on sequentially solving a Hamilton-Jacobi equation and an ordinary differential equation. The Hamilton-Jacobi equation is solved exactly while the ordinary differential equation is solved exactly or by an explicit Euler method. We prove that the L{sup {infinity}} error associated with the operator splitting method is bounded by O({delta}t), where {delta}t is the splitting (or time) step. This error bound is an improvement over the existing O((sqroot)({delta}t)) bound due to Souganidis [40]. In the one dimensional case, we present a fully discrete splitting method based on an unconditionally stable front tracking method for homogenuous Hamilton-Jacobi equations. It is proved that this fully discrete splitting method possesses a linear convergence rate. Moreover, numerical results are presented to illustrate the theoreticle convergence results. (author)
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.
Deng, Fang; Finer, Gal; Haymond, Shannon; Brooks, Ellen; Langman, Craig B
2015-03-01
Estimating glomerular filtration rate (eGFR) has become popular in clinical medicine as an alternative to measured GFR (mGFR), but there are few studies comparing them in clinical practice. We determined mGFR by iohexol clearance in 81 consecutive children in routine practice and calculated eGFR from 14 standard equations using serum creatinine, cystatin C, and urea nitrogen that were collected at the time of the mGFR procedure. Nonparametric Wilcoxon test, Spearman correlation, Bland-Altman analysis, bias (median difference), and accuracy (P15, P30) were used to compare mGFR with eGFR. For the entire study group, the mGFR was 77.9 ± 38.8 mL/min/1.73 m(2). Eight of the 14 estimating equations demonstrated values without a significant difference from the mGFR value and demonstrated a lower bias in Bland-Altman analysis. Three of these 8 equations based on a combination of creatinine and cystatin C (Schwartz et al. New equations to estimate GFR in children with CKD. J Am Soc Nephrol 2009;20:629-37; Schwartz et al. Improved equations estimating GFR in children with chronic kidney disease using an immunonephelometric determination of cystatin C. Kidney Int 2012;82:445-53; Chehade et al. New combined serum creatinine and cystatin C quadratic formula for GFR assessment in children. Clin J Am Soc Nephrol 2014;9:54-63) had the highest accuracy with approximately 60% of P15 and 80% of P30. In 10 patients with a single kidney, 7 with kidney transplant, and 11 additional children with short stature, values of the 3 equations had low bias and no significant difference when compared with mGFR. In conclusion, the 3 equations that used cystatin C, creatinine, and growth parameters performed in a superior manner over univariate equations based on either creatinine or cystatin C and also had good applicability in specific pediatric patients with single kidneys, those with a kidney transplant, and short stature. Thus, we suggest that eGFR calculations in pediatric clinical practice
On the validity of the Arrhenius equation for electron attachment rate coefficients.
Fabrikant, Ilya I; Hotop, Hartmut
2008-03-28
The validity of the Arrhenius equation for dissociative electron attachment rate coefficients is investigated. A general analysis allows us to obtain estimates of the upper temperature bound for the range of validity of the Arrhenius equation in the endothermic case and both lower and upper bounds in the exothermic case with a reaction barrier. The results of the general discussion are illustrated by numerical examples whereby the rate coefficient, as a function of temperature for dissociative electron attachment, is calculated using the resonance R-matrix theory. In the endothermic case, the activation energy in the Arrhenius equation is close to the threshold energy, whereas in the case of exothermic reactions with an intermediate barrier, the activation energy is found to be substantially lower than the barrier height.
A simple algebraic cancer equation: calculating how cancers may arise with normal mutation rates
Shibata Darryl
2010-01-01
Full Text Available Abstract Background The purpose of this article is to present a relatively easy to understand cancer model where transformation occurs when the first cell, among many at risk within a colon, accumulates a set of driver mutations. The analysis of this model yields a simple algebraic equation, which takes as inputs the number of stem cells, mutation and division rates, and the number of driver mutations, and makes predictions about cancer epidemiology. Methods The equation [p = 1 - (1 - (1 - (1 - udkNm ] calculates the probability of cancer (p and contains five parameters: the number of divisions (d, the number of stem cells (N × m, the number of critical rate-limiting pathway driver mutations (k, and the mutation rate (u. In this model progression to cancer "starts" at conception and mutations accumulate with cell division. Transformation occurs when a critical number of rate-limiting pathway mutations first accumulates within a single stem cell. Results When applied to several colorectal cancer data sets, parameter values consistent with crypt stem cell biology and normal mutation rates were able to match the increase in cancer with aging, and the mutation frequencies found in cancer genomes. The equation can help explain how cancer risks may vary with age, height, germline mutations, and aspirin use. APC mutations may shorten pathways to cancer by effectively increasing the numbers of stem cells at risk. Conclusions The equation illustrates that age-related increases in cancer frequencies may result from relatively normal division and mutation rates. Although this equation does not encompass all of the known complexity of cancer, it may be useful, especially in a teaching setting, to help illustrate relationships between small and large cancer features.
Convergence rates for dispersive approximation schemes to nonlinear Schr\\"odinger equations
Ignat, Liviu I
2011-01-01
This article is devoted to the analysis of the convergence rates of several numerical approximation schemes for linear and nonlinear Schr\\"odinger equations on the real line. Recently, the authors have introduced viscous and two-grid numerical approximation schemes that mimic at the discrete level the so-called Strichartz dispersive estimates of the continuous Schr\\"odinger equation. This allows to guarantee the convergence of numerical approximations for initial data in L2(R), a fact that can not be proved in the nonlinear setting for standard conservative schemes unless more regularity of the initial data is assumed. In the present article we obtain explicit convergence rates and prove that dispersive schemes fulfilling the Strichartz estimates are better behaved for H^s(R) data if 0 < s < 1/2. Indeed, while dispersive schemes ensure a polynomial convergence rate, non-dispersive ones only yield logarithmic decay rates.
Symmetry analysis of Black-Scholes equation for small values of volatility and rate of return
M. Nadjafikhah
2014-07-01
of volatility and rate of return parameters. A novel method for obtaining the approximate symmetry of a singularly perturbed partial differential equation (PDE is introduced. Further, we compute the optimal system in the singular case. Finally, by combining two methods, a new approach that calculates the approximate generators for admitted Lie groups of asset price is provided.
An estimator for the relative entropy rate of path measures for stochastic differential equations
Opper, Manfred
2017-02-01
We address the problem of estimating the relative entropy rate (RER) for two stochastic processes described by stochastic differential equations. For the case where the drift of one process is known analytically, but one has only observations from the second process, we use a variational bound on the RER to construct an estimator.
Riisgård, Hans Ulrik; Larsen, Poul Scheel; Pleissner, Daniel
2014-01-01
rate (F, l h-1), W (g), and L (mm) as described by the equations: FW = aWb and FL = cLd, respectively. This is done by using available and new experimental laboratory data on M. edulis obtained by members of the same research team using different methods and controlled diets of cultivated algal cells...
Validation of predictive equations for basal metabolic rate in eutrophic and obese subjects
Renata Lopes Krüger
2014-12-01
Full Text Available DOI: http://dx.doi.org/10.5007/1980-0037.2015v17n1p73 Prediction equations for basal metabolic rate (BMR continue to be the most common clinical tool for diet prescription; however, the values estimated may differ from those measured by indirect calorimetry (IC, especially in obese subjects. The objective of this study was to determine the BMR of obese and eutrophic subjects by IC, and to compare the results obtained with those estimated by prediction equations in order to identify whether differences exist between predicted values and those measured by IC. Forty men aged 18 to 30 years were evaluated; of these, 20 were grade 1 obese and 20 were eutrophic. The agreement between the prediction equations and IC was evaluated using Bland-Altman (1986 plots. The results showed a variation between the prediction equations and IC of -19.6% to -91% in obese subjects and of 4.2% to 4.4% in eutrophic subjects. In both groups, the Mifflin-St. Jeor equation (1990 was the most accurate, with a difference of -9.1% compared to IC in obese subjects and of 0.9% in eutrophic subjects. This study indicates the Mifflin-St. Jeor equation to be the most adequate to estimate BMR. However, it is important to measure the BMR of obese subjects more accurately and safely in order to establish the best intervention based on physical exercise and healthy eating.
Cross-Validation of Age-Predicted Maximal Heart Rate Equations Among Female Collegiate Athletes.
Esco, Michael R; Chamberlain, Nik; Flatt, Andrew A; Snarr, Ronald L; Bishop, Phillip A; Williford, Henry N
2015-11-01
The purpose of this study was to determine the accuracy of 3 general and 2 female-specific age-predicted maximal heart rate (HRmax) prediction equations in female collegiate athletes. Thirty female collegiate athletes (age = 21.5 ± 1.9 years, height = 164.7 ± 6.6 cm, weight = 61.3 ± 8.2 kg) participated. HRmax was determined with a maximal graded exercise test and predicted with 3 general equations (Fox et al., Astrand, and Tanaka et al.) and 2 female-specific equations (Fairbarn et al. and Gulati et al.). There was no significant difference between observed HRmax (185.9 ± 5.0 b·min) and the Fairbarn (187.5 ± 1.2 b·min) and Gulati (187.1 ± 1.7 b·min) equations (p = 0.11 and 0.23, respectively). The Fox (198.5 ± 1.9 b·min), Astrand (198.1 ± 1.6 b·min), and Tanaka (193.0 ± 1.4 b·min) equations provided significantly higher estimates compared with observed HRmax (p < 0.001 for each). The standard error of the estimate was similar for all the prediction equations (between 5.0 and 5.4 b·min), but the total error was smallest for Fairbarn and Gulati (5.3 b·min for each) and largest for Fox and Astrand (13.9 and 13.3 b·min, respectively). The 95% limits of agreement of the mean error were similar for all of the prediction equations, with values varying between 9.9 and 10.5 b·min. Because of the wide limits of agreement displayed by each equation, the use of age-predicted methods for estimating HRmax in collegiate female athletes should be performed only with caution.
A differential equation for the flow rate during silo discharge: Beyond the Beverloo rule
Madrid Marcos A.
2017-01-01
Full Text Available We present a differential equation for the flow rate of granular materials during the discharge of a silo. This is based in the energy balance of the variable mass system in contrast with the traditional derivations based on heuristic postulates such as the free fall arch. We show that this new equation is consistent with the well known Beverloo rule, providing an independent estimate for the universal Beverloo prefactor. We also find an analytic expression for the pressure under discharging conditions.
Goldberg, Robert K.; Stouffer, Donald C.
1998-01-01
Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this first paper of a two part report, background information is presented, along with the constitutive equations which will be used to model the rate dependent nonlinear deformation response of the polymer matrix. Strain rate dependent inelastic constitutive models which were originally developed to model the viscoplastic deformation of metals have been adapted to model the nonlinear viscoelastic deformation of polymers. The modified equations were correlated by analyzing the tensile/ compressive response of both 977-2 toughened epoxy matrix and PEEK thermoplastic matrix over a variety of strain rates. For the cases examined, the modified constitutive equations appear to do an adequate job of modeling the polymer deformation response. A second follow-up paper will describe the implementation of the polymer deformation model into a composite micromechanical model, to allow for the modeling of the nonlinear, rate dependent deformation response of polymer matrix composites.
A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate
Min Sun
2014-01-01
Full Text Available A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.
How reliable are the equations for predicting maximal heart rate values in military personnel?
Sporis, Goran; Vucetic, Vlatko; Jukic, Igor; Omrcen, Darija; Bok, Daniel; Custonja, Zrinko
2011-03-01
The purpose of this study was to evaluate the validity and reliability of equations for predicting maximal values of heart rate (HR) in military personnel. Five hundred and nine members of the Croatian Armed Forces (age 29.1 +/- 5.5 years; height 180.1 +/- 6.6 cm; body mass 83.4 +/- 11.3 kg; maximal oxygen uptake [VO2(max)] 49.7 +/- 6.9 mL O2/kg/min) were tested. The graded exercise test with gas exchange measurements was used to determine VO2(max) and maximum HR (HR(max)). The analysis of variance was used to determine the differences between the equations to calculate HR(max). The analysis of variance yielded statistically significant differences between seven HR equations (p max) = 205 - [age/2]) and Fox and Haskell's (HR(max) = 220 - age) equations had the highest correlation with the HRmax obtained by the graded exercise test. The authors recommend using the HR(max) values from the Stevens Creek and the Fox and Haskell equations for the purpose of training, testing, and daily exercise routine in military personnel.
Liu X
2012-10-01
Full Text Available Xun Liu,1,2,* Mu-hua Cheng,3,* Cheng-gang Shi,1 Cheng Wang,1 Cai-lian Cheng,1 Jin-xia Chen,1 Hua Tang,1 Zhu-jiang Chen,1 Zeng-chun Ye,1 Tan-qi Lou11Division of Nephrology, Department of Internal Medicine, The Third Affiliated Hospital of Sun Yet-sun University, Guangzhou, China; 2College of Biology Engineering, South China University of Technology, Guangzhou, China; 3Department of Nuclear Medicine, The Third Affiliated Hospital of Sun Yet-sun University, Guangzhou, China *These authors contributed equally to this paperBackground: Chronic kidney disease (CKD is recognized worldwide as a public health problem, and its prevalence increases as the population ages. However, the applicability of formulas for estimating the glomerular filtration rate (GFR based on serum creatinine (SC levels in elderly Chinese patients with CKD is limited.Materials and methods: Based on values obtained with the technetium-99m diethylenetriaminepentaacetic acid (99mTc-DTPA renal dynamic imaging method, 319 elderly Chinese patients with CKD were enrolled in this study. Serum creatinine was determined by the enzymatic method. The GFR was estimated using the Cockroft–Gault (CG equation, the Modification of Diet in Renal Disease (MDRD equations, the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equation, the Jelliffe-1973 equation, and the Hull equation.Results: The median of difference ranged from −0.3–4.3 mL/min/1.73 m2. The interquartile range (IQR of differences ranged from 13.9–17.6 mL/min/1.73 m2. Accuracy with a deviation less than 15% ranged from 27.6%–32.9%. Accuracy with a deviation less than 30% ranged from 53.6%–57.7%. Accuracy with a deviation less than 50% ranged from 74.9%–81.5%. None of the equations had accuracy up to the 70% level with a deviation less than 30% from the standard glomerular filtration rate (sGFR. Bland–Altman analysis demonstrated that the mean difference ranged from −3.0–2.4 mL/min/1.73 m2. However, the
Hagelaar, G J M; Pitchford, L C [Centre de Physique des Plasmas et de leurs Applications de Toulouse, Universite Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 9 (France)
2005-11-15
Fluid models of gas discharges require the input of transport coefficients and rate coefficients that depend on the electron energy distribution function. Such coefficients are usually calculated from collision cross-section data by solving the electron Boltzmann equation (BE). In this paper we present a new user-friendly BE solver developed especially for this purpose, freely available under the name BOLSIG+, which is more general and easier to use than most other BE solvers available. The solver provides steady-state solutions of the BE for electrons in a uniform electric field, using the classical two-term expansion, and is able to account for different growth models, quasi-stationary and oscillating fields, electron-neutral collisions and electron-electron collisions. We show that for the approximations we use, the BE takes the form of a convection-diffusion continuity-equation with a non-local source term in energy space. To solve this equation we use an exponential scheme commonly used for convection-diffusion problems. The calculated electron transport coefficients and rate coefficients are defined so as to ensure maximum consistency with the fluid equations. We discuss how these coefficients are best used in fluid models and illustrate the influence of some essential parameters and approximations.
Borzykh, A. N.
2017-01-01
The Seidel method for solving a system of linear algebraic equations and an estimate of its convergence rate are considered. It is proposed to change the order of equations. It is shown that the method described in Faddeevs' book Computational Methods of Linear Algebra can deteriorate the convergence rate estimate rather than improve it. An algorithm for establishing the optimal order of equations is proposed, and its validity is proved. It is shown that the computational complexity of the reordering is 2 n 2 additions and (12) n 2 divisions. Numerical results for random matrices of order 100 are presented that confirm the proposed improvement.
Exact solution of rate equations for a two-spin-qubit system
Le Thi Ha Linh; Nguyen Bich Ha [Institute of Materials Science, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Road, Cau Giay District, Hanoi (Viet Nam)], E-mail: linhlth@ims.vast.ac.vn
2009-09-01
The quantum dynamics of a system of two interacting spin-qubits is studied for elaborating the physical mechanism of the quantum information transfer between them. A simple model with their Heisenberg XY exchange interaction is investigated. The rate equations are established. The analytical expressions of their solution are exactly derived. They explicitly demonstrate, how the quantum information encoded into a spin-qubit at the initial time t = 0 is transferred to other one at any time t > 0.
Kuster Jr, George Emil
2016-01-01
In this research, I utilize the theoretical perspective Knowledge In Pieces to identify the knowledge resources students utilize while in the process of completing various differential equations tasks. In addition I explore how this utilization changes over the course of a semester, and how resources related to the concepts of function and rate of change supported the students in completing the tasks. I do so using data collected from a series of task-based individual interviews with two stud...
Characteristics of quantum dash laser under the rate equation model framework
Khan, Mohammed Zahed Mustafa
2010-09-01
The authors present a numerical model to study the carrier dynamics of InAs/InP quantum dash (QDash) lasers. The model is based on single-state rate equations, which incorporates both, the homogeneous and the inhomogeneous broadening of lasing spectra. The numerical technique also considers the unique features of the QDash gain medium. This model has been applied successfully to analyze the laser spectra of QDash laser. ©2010 IEEE.
Montañés Bermúdez, R; Gràcia Garcia, S; Fraga Rodríguez, G M; Escribano Subias, J; Diez de Los Ríos Carrasco, M J; Alonso Melgar, A; García Nieto, V
2014-05-01
The appearance of the K/DOQI guidelines in 2002 on the definition, evaluation and staging of chronic kidney disease (CKD) have led to a major change in how to assess renal function in adults and children. These guidelines, recently updated, recommended that the study of renal function is based, not only on measuring the serum creatinine concentration, but this must be accompanied by the estimation of glomerular filtration rate (GFR) obtained by an equation. However, the implementation of this recommendation in the clinical laboratory reports in the paediatric population has been negligible. Numerous studies have appeared in recent years on the importance of screening and monitoring of patients with CKD, the emergence of new equations for estimating GFR, and advances in clinical laboratories regarding the methods for measuring plasma creatinine and cystatin C, determined by the collaboration between the departments of paediatrics and clinical laboratories to establish recommendations based on the best scientific evidence on the use of equations to estimate GFR in this population. The purpose of this document is to provide recommendations on the evaluation of renal function and the use of equations to estimate GFR in children from birth to 18 years of age. The recipients of these recommendations are paediatricians, nephrologists, clinical biochemistry, clinical analysts, and all health professionals involved in the study and evaluation of renal function in this group of patients.
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.
On the Rate of Relaxation for the Landau Kinetic Equation and Related Models
Bobylev, Alexander; Gamba, Irene M.; Zhang, Chenglong
2017-08-01
We study the rate of relaxation to equilibrium for Landau kinetic equation and some related models by considering the relatively simple case of radial solutions of the linear Landau-type equations. The well-known difficulty is that the evolution operator has no spectral gap, i.e. its spectrum is not separated from zero. Hence we do not expect purely exponential relaxation for large values of time t>0. One of the main goals of our work is to numerically identify the large time asymptotics for the relaxation to equilibrium. We recall the work of Strain and Guo (Arch Rat Mech Anal 187:287-339 2008, Commun Partial Differ Equ 31:17-429 2006), who rigorously show that the expected law of relaxation is \\exp (-ct^{2/3}) with some c > 0. In this manuscript, we find an heuristic way, performed by asymptotic methods, that finds this "law of two thirds", and then study this question numerically. More specifically, the linear Landau equation is approximated by a set of ODEs based on expansions in generalized Laguerre polynomials. We analyze the corresponding quadratic form and the solution of these ODEs in detail. It is shown that the solution has two different asymptotic stages for large values of time t and maximal order of polynomials N: the first one focus on intermediate asymptotics which agrees with the "law of two thirds" for moderately large values of time t and then the second one on absolute, purely exponential asymptotics for very large t, as expected for linear ODEs. We believe that appearance of intermediate asymptotics in finite dimensional approximations must be a generic behavior for different classes of equations in functional spaces (some PDEs, Boltzmann equations for soft potentials, etc.) and that our methods can be applied to related problems.
Validation of predictive equations for glomerular filtration rate in the Saudi population
Al Wakeel Jamal
2009-01-01
Full Text Available Predictive equations provide a rapid method of assessing glomerular filtration rate (GFR. To compare the various predictive equations for the measurement of this parameter in the Saudi population, we measured GFR by the Modification of Diet in Renal Disease (MDRD and Cockcroft-Gault formulas, cystatin C, reciprocal of cystatin C, creatinine clearance, reciprocal of creatinine, and inulin clearance in 32 Saudi subjects with different stages of renal disease. We com-pared GFR measured by inulin clearance and the estimated GFR by the equations. The study included 19 males (59.4% and 13 (40.6% females with a mean age of 42.3 ± 15.2 years and weight of 68.6 ± 17.7 kg. The mean serum creatinine was 199 ± 161 μmol/L. The GFR measured by inulin clearance was 50.9 ± 33.5 mL/min, and the estimated by Cockcroft-Gault and by MDRD equations was 56.3 ± 33.3 and 52.8 ± 32.0 mL/min, respectively. The GFR estimated by MDRD revealed the strongest correlation with the measured inulin clearance (r= 0.976, P= 0.0000 followed by the GFR estimated by Cockcroft-Gault, serum cystatin C, and serum creatinine (r= 0.953, P= 0.0000 (r= 0.787, P= 0.0001 (r= -0.678, P= 0.001, respectively. The reciprocal of cystatin C and serum creatinine revealed a correlation coefficient of 0.826 and 0.93, respectively. Cockroft-Gault for-mula overestimated the GFR by 5.40 ± 10.3 mL/min in comparison to the MDRD formula, which exhibited the best correlation with inulin clearance in different genders, age groups, body mass index, renal transplant recipients, chronic kidney disease stages when compared to other GFR predictive equations.
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....
Hamadou, A.; Thobel, J.-L.; Lamari, S.
2016-10-01
A four level rate equations model for a terahertz optically pumped electrically driven quantum cascade laser is here introduced and used to model the system both analytically and numerically. In the steady state, both in the presence and absence of the terahertz optical field, we solve the resulting nonlinear system of equations and obtain closed form expressions for the levels occupation, population inversion as well as the mid-infrared pump threshold intensity in terms of the device parameters. We also derive, for the first time for this system, an analytical formula for the optical external efficiency and analyze the simultaneous effects of the cavity length and pump intensity on it. At moderate to high pump intensities, we find that the optical external efficiency scales roughly as the reciprocal of the cavity length.
Anita Nordenson
2010-09-01
Full Text Available Anita Nordenson2, Anne Marie Grönberg1,2, Lena Hulthén1, Sven Larsson2, Frode Slinde11Department of Clinical Nutrition, Sahlgrenska Academy at University of Gothenburg, Göteborg, Sweden; 2Department of Internal Medicine/Respiratory Medicine and Allergology, Sahlgrenska Academy at University of Gothenburg, SwedenAbstract: Malnutrition is a serious condition in chronic obstructive pulmonary disease (COPD. Successful dietary intervention calls for calculations of resting metabolic rate (RMR. One disease-specific prediction equation for RMR exists based on mainly male patients. To construct a disease-specific equation for RMR based on measurements in underweight or weight-losing women and men with COPD, RMR was measured by indirect calorimetry in 30 women and 11 men with a diagnosis of COPD and body mass index <21 kg/m2. The following variables, possibly influencing RMR were measured: length, weight, middle upper arm circumference, triceps skinfold, body composition by dual energy x-ray absorptiometry and bioelectrical impedance, lung function, and markers of inflammation. Relations between RMR and measured variables were studied using univariate analysis according to Pearson. Gender and variables that were associated with RMR with a P value <0.15 were included in a forward multiple regression analysis. The best-fit multiple regression equation included only fat-free mass (FFM: RMR (kJ/day = 1856 + 76.0 FFM (kg. To conclude, FFM is the dominating factor influencing RMR. The developed equation can be used for prediction of RMR in underweight COPD patients.Keywords: pulmonary disease, chronic obstructive, basal metabolic rate, malnutrition, body composition
Ji, Misuk; Lee, Yoon-Hee; Kim, Hyesun; Cho, Han-Ik; Yang, Hyun Suk; Navarin, Silvia; Di Somma, Salvatore
2016-01-01
Background Estimated glomerular filtration rate (eGFR) is a widely used index of kidney function. Recently, new formulas such as the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations or the Lund-Malmö equation were introduced for assessing eGFR. We compared them with the Modification of Diet in Renal Disease (MDRD) Study equation in the Korean adult population. Methods The study population comprised 1,482 individuals (median age 51 [42-59] yr, 48.9% males) who received annual physical check-ups during the year 2014. Serum creatinine (Cr) and cystatin C (CysC) were measured. We conducted a retrospective analysis using five GFR estimating equations (MDRD Study, revised Lund-Malmö, and Cr and/or CysC-based CKD-EPI equations). Reduced GFR was defined as eGFR <60 mL/min/1.73 m2. Results For the GFR category distribution, large discrepancies were observed depending on the equation used; category G1 (≥90 mL/min/1.73 m2) ranged from 7.4-81.8%. Compared with the MDRD Study equation, the other four equations overestimated GFR, and CysC-based equations showed a greater difference (-31.3 for CKD-EPICysC and -20.5 for CKD-EPICr-CysC). CysC-based equations decreased the prevalence of reduced GFR by one third (9.4% in the MDRD Study and 2.4% in CKD-EPICysC). Conclusions Our data shows that there are remarkable differences in eGFR assessment in the Korean population depending on the equation used, especially in normal or mildly decreased categories. Further prospective studies are necessary in various clinical settings. PMID:27578504
Maximum Rate of Growth of Enstrophy in Solutions of the Fractional Burgers Equation
Yun, Dongfang
2016-01-01
This investigation is a part of a research program aiming to characterize the extreme behavior possible in hydrodynamic models by probing the sharpness of estimates on the growth of certain fundamental quantities. We consider here the rate of growth of the classical and fractional enstrophy in the fractional Burgers equation in the subcritical, critical and supercritical regime. First, we obtain estimates on these rates of growth and then show that these estimates are sharp up to numerical prefactors. In particular, we conclude that the power-law dependence of the enstrophy rate of growth on the fractional dissipation exponent has the same global form in the subcritical, critical and parts of the supercritical regime. This is done by numerically solving suitably defined constrained maximization problems and then demonstrating that for different values of the fractional dissipation exponent the obtained maximizers saturate the upper bounds in the estimates as the enstrophy increases. In addition, nontrivial be...
Relaxation rates of the linearized Uehling-Uhlenbeck equation for bosons.
Gust, Erich; Reichl, L E
2010-06-01
We linearize the Uehling-Uhlenbeck equation for bosonic gases close to thermal equilibrium under the assumption of a contact interaction characterized by a scattering length a. We show that the spectrum of relaxation rates is similar to that of a classical hard-sphere gas. However, the relaxation rates show a significant dependence on the fugacity z of the gas, increasing by as much as 60% of their classical value for z approaching 1. The relaxation modes are also significantly altered at higher values of z. The relaxation rates and modes are determined by the eigenvalues and eigenvectors of a Fredholm integral operator of the second kind. We derive an analytical form for the kernel of this operator and present numerical results for the first few eigenvalues and eigenvectors.
Bayesian inference for kinetic models of biotransformation using a generalized rate equation.
Ying, Shanshan; Zhang, Jiangjiang; Zeng, Lingzao; Shi, Jiachun; Wu, Laosheng
2017-03-06
Selecting proper rate equations for the kinetic models is essential to quantify biotransformation processes in the environment. Bayesian model selection method can be used to evaluate the candidate models. However, comparisons of all plausible models can result in high computational cost, while limiting the number of candidate models may lead to biased results. In this work, we developed an integrated Bayesian method to simultaneously perform model selection and parameter estimation by using a generalized rate equation. In the approach, the model hypotheses were represented by discrete parameters and the rate constants were represented by continuous parameters. Then Bayesian inference of the kinetic models was solved by implementing Markov Chain Monte Carlo simulation for parameter estimation with the mixed (i.e., discrete and continuous) priors. The validity of this approach was illustrated through a synthetic case and a nitrogen transformation experimental study. It showed that our method can successfully identify the plausible models and parameters, as well as uncertainties therein. Thus this method can provide a powerful tool to reveal more insightful information for the complex biotransformation processes.
Asymptotics of steady states of a selection–mutation equation for small mutation rate
Calsina, Àngel
2013-12-01
We consider a selection-mutation equation for the density of individuals with respect to a continuous phenotypic evolutionary trait. We assume that the competition term for an individual with a given trait depends on the traits of all the other individuals, therefore giving an infinite-dimensional nonlinearity. Mutations are modelled by means of an integral operator. We prove existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. © Royal Society of Edinburgh 2013.
CONVERGENCE RATES FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL FORCES
Qian Jianzhen; Yin Hui
2009-01-01
For the viscous and heat-conductive fluids governed by the compressible NavierStokes equations with external force of general form in R~3, there exist nontrivial stationary solutions provided the external forces are small in suitable norms, which was studied in article[15], and there we also proved the global in time stability of the stationary solutions with respect to initial data in H~3-framework. In this article, the authors investigate the rates of convergence of nonstationary solutions to the corresponding stationary solutions when the initial data are small in H~3 and bounded in L_(6/5).
Rate equation simulation of temporal characteristics of a pulsed dye laser oscillator
S Kundu; K Dasgupta; S Sasikumar; J Singh; A K Ray; S Sinha
2010-11-01
A time-dependent, two-dimensional (in space) rate equation model of a transversely-pumped pulsed dye laser oscillator, which incorporates transverse pump intensity variation in the presence of intracavity dye laser radiation, is proposed to under-stand and predict its temporal behaviour. The model yields output pulses which agree well with experimental results using rhodamine 6G and kiton red dyes. The shape, amplitude and temporal position of the simulated pulse within the pump pulse vary dramatically across the tuning range of each dye depending on the relative gain and loss values.
Utility Rate Equations of Group Population Dynamics in Biological and Social Systems
Yukalov, V I; Sornette, D
2014-01-01
We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human) composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors) and of three groups (cooperators, defectors, and regulators) and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about 10% each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric q...
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.
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.
Optimal decay rates of classical solutions for the full compressible MHD equations
Gao, Jincheng; Tao, Qiang; Yao, Zheng-an
2016-04-01
In this paper, we are concerned with optimal decay rates for higher-order spatial derivatives of classical solutions to the full compressible MHD equations in three-dimensional whole space. If the initial perturbation is small in {H^3}-norm and bounded in {L^q(qin [1, 6/5 ))}-norm, we apply the Fourier splitting method by Schonbek (Arch Ration Mech Anal 88:209-222, 1985) to establish optimal decay rates for the second-order spatial derivatives of solutions and the third-order spatial derivatives of magnetic field in {L^2}-norm. These results improve the work of Pu and Guo (Z Angew Math Phys 64:519-538, 2013).
Rate equations for nitrogen molecules in ultrashort and intense x-ray pulses
Liu, Ji-Cai; Cederbaum, Lorenz S; Cryan, James P; Glownia, James M; Schafer, Kenneth J; Buth, Christian
2015-01-01
We study theoretically the molecular dynamics of nitrogen molecules (N$_2$) exposed to x rays at a wavelength of 1.1 nm (1100 eV photon energy) from the Linac Coherent Light Source (LCLS) free electron laser. Molecular rate equations are derived to describe the intertwined photoionization, decay, and dissociation processes occurring for N2 in intense and ultrafast x rays from LCLS. This model complements our earlier phenomenological approaches, the single-atom, symmetric-sharing, and fragmentation-matrix models of J. Chem. Phys. $\\mathbf{136}$, 214310 (2012). Our rate-equations are used to obtain the effective pulse energy at the sample and the time scale for the dissociation of the metastable dication N$_2^{2+}$. This leads to a very good agreement between the theoretically and experimentally obtained ion yields and, consequently, the average charge states. The effective pulse energy is found to decrease with shortening pulse duration. This variation in the effective pulse energy together with a change in th...
Bevc, Sebastjan; Hojs, Nina; Hojs, Radovan; Ekart, Robert; Gorenjak, Maksimiljan; Puklavec, Ludvik
2017-04-01
Estimating glomerular filtration rate (GFR) in elderly patients is a problem, since they are poorly represented in studies developing GFR equations. Serum cystatin C is a better indicator of GFR than serum creatinine in elderly patients. Therefore the aim of our study was to compare frequently used serum cystatin C based GFR equations with a gold standard ((51) CrEDTA clearance) in elderly chronic kidney disease (CKD) patients. 106 adult Caucasian patients, older than 65 years (58 women, 48 men; mean age 72.5 years), were included. In each patient (51) CrEDTA clearance, serum creatinine (IDMS traceable method) and serum cystatin C (immunonephelometric method) were determined. GFR was estimated using the Simple cystatin C, CKD-EPI cystatin C, CKD-EPI creatinine-cystatin C and BIS2 equation. Mean serum creatinine of our patients was 141.4 ± 41.5 μmol/L, mean serum cystatin C 1.79 ± 0.6 mg/L, mean (51) CrEDTA clearance was 52.2 ± 15.9 mL/min per 1.73 m(2) . Statistically significant correlations between (51) CrEDTA clearance and all formulas were found (P C and BIS2 equation underestimated and CKD-EPI cystatin C and Simple cystatin C equation overestimated measured GFR. All equations lacked precision. Analysis of ability to correctly predict patient's GFR below or above 45 mL/min per 1.73 m(2) showed similar ability for all equations (P = 0.24-0.89). All equations are equally accurate for estimating GFR in elderly Caucasian CKD patients. For daily practice Simple cystatin C equation is most practical.
Yoshimoto Akifumi
2015-01-01
Full Text Available These days, polymer foams, such as polyurethane foam and polystyrene foam, are used in various situations as a thermal insulator or shock absorber. In general, however, their strength is insufficient in high temperature environments because of their low glass transition temperature. Polyimide is a polymer which has a higher glass transition temperature and high strength. Its mechanical properties do not vary greatly, even in low temperature environments. Therefore, polyimide foam is expected to be used in the aerospace industry. Thus, the constitutive equation of polyimide foam that can be applied across a wide range of strain rates and ambient temperature is very useful. In this study, a series of compression tests at various strain rates, from 10−3 to 103 s−1 were carried out in order to examine the effect of strain rate on the compressive properties of polyimide foam. The flow stress of polyimide foam increased rapidly at dynamic strain rates. The effect of ambient temperature on the properties of polyimide foam was also investigated at temperature from − 190 °C to 270°∘C. The flow stress decreased with increasing temperature.
Lainscsek, C.; Rowat, P.; Schettino, L.; Lee, D.; Song, D.; Letellier, C.; Poizner, H.
2012-03-01
Parkinson's disease is a degenerative condition whose severity is assessed by clinical observations of motor behaviors. These are performed by a neurological specialist through subjective ratings of a variety of movements including 10-s bouts of repetitive finger-tapping movements. We present here an algorithmic rating of these movements which may be beneficial for uniformly assessing the progression of the disease. Finger-tapping movements were digitally recorded from Parkinson's patients and controls, obtaining one time series for every 10 s bout. A nonlinear delay differential equation, whose structure was selected using a genetic algorithm, was fitted to each time series and its coefficients were used as a six-dimensional numerical descriptor. The algorithm was applied to time-series from two different groups of Parkinson's patients and controls. The algorithmic scores compared favorably with the unified Parkinson's disease rating scale scores, at least when the latter adequately matched with ratings from the Hoehn and Yahr scale. Moreover, when the two sets of mean scores for all patients are compared, there is a strong (r = 0.785) and significant (p <0.0015) correlation between them.
Marczewski, Adam W
2010-10-05
In the article, a new integrated kinetic Langmuir equation (IKL) is derived. The IKL equation is a simple and easy to analyze but complete analytical solution of the kinetic Langmuir model. The IKL is compared with the nth-order, mixed 1,2-order, and multiexponential kinetic equations. The impact of both equilibrium coverage θ(eq) and relative equilibrium uptake u(eq) on kinetics is explained. A newly introduced Langmuir batch equilibrium factor f(eq) that is the product of both parameters θ(eq)u(eq) is used to determine the general kinetic behavior. The analysis of the IKL equation allows us to understand fully the Langmuir kinetics and explains its relation with respect to the empirical pseudo-first-order (PFO, i.e., Lagergren), pseudo-second-order (PSO), and mixed 1,2-order kinetic equations, and it shows the conditions of their possible application based on the Langmuir model. The dependence of the initial adsorption rate on the system properties is analyzed and compared to the earlier published approximate equations.
Totok R. Biyanto
2016-06-01
Full Text Available Safety Instrumented Function (SIF is implemented on the system to prevent hazard in process industry. In general, most of SIF implementation in process industry works in low demand condition. Safety valuation of SIF that works in low demand can be solved by using quantitative method. The quantitative method is a simplified exponential equation form of MacLaurin series, which can be called simplified equation. Simplified equation used in high demand condition will generate a higher Safety Integrity Level (SIL and it will affect the higher safety cost. Therefore, the value of low or high demand rate limit should be determined to prevent it. The result of this research is a first order equation that can fix the error of SIL, which arises from the usage of simplified equation, without looking the demand rate limit for low and high demand. This equation is applied for SIL determination on SIF with 1oo1 vote. The new equation from this research is λ = 0.9428 λMC + 1.062E−04 H/P, with 5% average of error, where λMC is a value of λ from the simplified equation, Hazardous event frequency (H is a probabilistic frequency of hazard event and P is Probability of Failure on Demand (PFD in Independent Protection Layers (IPLs. The equation generated from this research could correct SIL of SIF in various H and P. Therefore, SIL design problem could be solved and it provides an appropriate SIL.
Hadron Mass Spectra and Decay Rates in a Potential Model with Relativistic Wave Equations.
Namgung, Wuk
Hadron properties of mass spectra and decay rates are calculated in a quark potential model. Wave equations based on the Klein-Gordon and Todorov equations both of which incorporate the feature of relativistic two-body kinematics are used. The wave equations are modified to contain potentials which transform either like a Lorentz scalar or like a time-component of a four-vector. Potentials based on the Fogleman-Lichtenberg-Wills potential which has the properties suggested by QCD of both confinement and asymptotic freedom are used. The potentials, motivated by QCD but otherwise phenomenological, are further generalized to forms which can apply to any color representation. To break the degeneracy between vector and pseudoscalar mesons or between spin-3/2 and spin-1/2 baryons, the essential feature of spin dependence is included in the potentials. The masses of vector and pseudoscalar mesons are calculated with only a small number of adjustable parameters, and good qualitative agreement with experiment is obtained for both heavy and light mesons. Baryons are treated in this framework by making use of a quark-diquark two-body model of baryons. First, diquark properties are calculated without any additional parameters. The g-factors of diquarks and spin-flavor configuration of baryons, which are necessary for the calculation of baryons, are given. Then baryon masses are calculated also without additional parameters. The results of the masses of ground-state baryons are in good qualitative agreement with experiment. Also effective constituent quark masses are obtained using current quark masses as input. The calculated effective constituent quark masses are in the right range of the values that most theoretical estimates have given. The general qualitative features of hadron spectra are similar with the two relativistic wave equations, although there are differences in detail. The Van Royen-Weisskopf formula for electromagnetic decay widths of vector mesons into lepton
Bidding process in online auctions and winning strategy: Rate equation approach
Yang, I.; Kahng, B.
2006-06-01
Online auctions have expanded rapidly over the last decade and have become a fascinating new type of business or commercial transaction in this digital era. Here we introduce a master equation for the bidding process that takes place in online auctions. We find that the number of distinct bidders who bid k times up to the t th bidding progresses, called the k -frequent bidder, seems to scale as nk(t)˜tk-2.4 . The successfully transmitted bidding rate by the k -frequent bidder is likely to scale as qk(t)˜k-1.4 , independent of t for large t . This theoretical prediction is close to empirical data. These results imply that bidding at the last moment is a rational and effective strategy to win in an eBay auction.
Bidding process in online auctions and winning strategy:rate equation approach
Yang, I
2006-01-01
Online auctions have expanded rapidly over the last decade and have become a fascinating new type of business or commercial transaction in this digital era. Here we introduce a master equation for the bidding process that takes place in online auctions. We find that the number of distinct bidders who bid $k$ times, called the $k$-frequent bidder, up to the $t$-th bidding progresses as $n_k(t)\\sim tk^{-2.4}$. The successfully transmitted bidding rate by the $k$-frequent bidder is obtained as $q_k(t) \\sim k^{-1.4}$, independent of $t$ for large $t$. This theoretical prediction is in agreement with empirical data. These results imply that bidding at the last moment is a rational and effective strategy to win in an eBay auction.
Rate equations modeling for hydrogen inventory studies during a real tokamak material thermal cycle
Bonnin, X., E-mail: xavier.bonnin@iter.org [LSPM-CNRS, Université Paris 13, Sorbonne Paris Cité, 99 avenue Jean-Baptiste Clément, F-93430 Villetaneuse (France); Hodille, E. [IRFM, CEA-Cadarache, F-13108 St-Paul-Lez-Durance (France); Ning, N. [LSPM-CNRS, Université Paris 13, Sorbonne Paris Cité, 99 avenue Jean-Baptiste Clément, F-93430 Villetaneuse (France); Sang, C. [School of Physics and Optoelectronics Technology, Dalian University of Technology, Dalian 116024 (China); Grisolia, Ch. [IRFM, CEA-Cadarache, F-13108 St-Paul-Lez-Durance (France)
2015-08-15
Prediction and control of tritium inventory in plasma-facing components (PFCs) is a critical nuclear safety issue for ITER and future fusion devices. This goal can be achieved through rate equations models as presented here. We calibrate our models with thermal desorption spectrometry results to obtain a validated set of material parameters relevant to hydrogen inventory processes in bulk tungsten. The best fits are obtained with two intrinsic trap types, deep and shallow, and an extrinsic trap created by plasma irradiation and plastic deformation of the tungsten matrix associated with blister formation. We then consider a realistic cycle of plasma discharges consisting of 400 s of plasma exposure followed by a resting period of 1000 s, repeating for several hours. This cycle is then closed by a long “overnight” period, thus providing an estimate of the amount of tritium retained in the PFCs after a full day of standard operation.
Population and Asset Distributions in Economically Competitive Activities:a Rate-Equation Approach
KE Jian-Hong; CAI Xiao-Ou; LIN Zhen-Quan
2004-01-01
We introduce a simple asset migration model for the wealth redistribution in economical activities, in which a unit of asset migrates from one individual to another whenever they interact. By means of the mean-field rate equation, we have analysed the dynamic behaviour of the system. In the random migration case, the asset distribution of individuals takes the standard Gaussian form and consistently decreases to zero at the end. As for the system in which only the richer can gain assets from the poorer, it is found that the individual asset distribution is discontinuous at a critical point and only the individuals with asset absolute value less than a cutoff value have a uniform and non-zero distribution. Moreover, the result shows that for the system with migration bias the assets of the individuals may have a cutoff value at each given time, which is different from the system without migration bias.
Rate equation model of phototransduction into the membranous disks of mouse rod cells
Takamoto, Rei; Awazu, Akinori
2015-01-01
A theoretical model was developed to investigate the rod phototransduction process in the mouse. In particular, we explored the biochemical reactions of several chemical components that contribute to the signaling process into/around the membranous disks in the outer segments of the rod cells. We constructed a rate equation model incorporating the molecular crowding effects of rhodopsin according to experimental results, which may hinder the diffusion of molecules on the disk mem- brane. The present model could effectively reproduce and explain the mechanisms of the following phenomena observed in experiments. First, the activations and relaxation of the wild-type mouse rod cell progressed more slowly than those of mutant cells containing half the amount of rhodopsin on the disk membrane. Second, the strong photoactivated state of the cell was sustained for a longer period when the light stimuli were strong. Finally, the lifetime of photoactivation exhibited a logarithmic increase with increasing light streng...
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...
DECAY RATES TOWARD STATIONARY WAVES OF SOLUTIONS FOR DAMPED WAVE EQUATIONS
Fan Lili; Yin Hui; Zhao Huijiang
2008-01-01
This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the half space R+(utt-uxx+ut+f(u)x=0,t>0,z∈R+,(u(0,x)=u0(x)→u+, as x→+∞, (I)(ut(0,x)=u1(x),u(t,0)=ub.For the non-degenerate case,f'(u+)＜0,it is shown in[1]that the above initialboundary value problem admits a unique global solution u(t,x)which converges to the stationary wave φ(x)uniformly in x∈R+as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small.Moreover,by using the space-time weighted energy method initiated by Kawashima and Matsumura[2],the convergence rates(including the algebraic convergence rate and the exponential convergence rate)of u(t,x)toward φ(x)are also obtained in[1].We note,however,that the analysis in[1]relies heavily on the assumption that f'(ub)＜0.The main purpose of this paper is devoted to discussing the case of f'(ub)=0 and we show that similar results still hold for such a case.Our analysis is based on some delicate energy estimates.
Rate equation analysis of nanocrystal-enhanced upconversion in neodymium-doped glass ceramics
Skrzypczak, U.; Pfau, Charlotte; Seifert, G.; Schweizer, Stefan
2014-05-01
Rare-earth ions embedded in glassy matrices are promising materials for photon upconversion processes, e.g. to convert near infrared light to frequencies above the band gap of a solar cell to make it available for electrical power generation. One strategy to optimize the efficiency of such upconversion processes is to embed the active ions in a host matrix with minimal losses to non-radiative relaxation. For the model system of trivalent neodymium in fluorochlorozirconate (FCZ) glass it has been shown recently that a uniform growth of BaCl2 nanocrystals inside such glasses can decrease the probability of multi-phonon relaxation (MPR) drastically, leading to a huge increase in upconversion intensity for monochromatic illumination. To identify the key processes which may enhance or diminish the total upconversion efficiency, a comprehensive description for the optical dynamics of neodymium in FCZ glass ceramics has been developed on the basis of a rate equation system, including ion-photon, ion-phonon, and ion-ion interactions. An effective medium approach is utilized to account for the neodymium located in BaCl2 nanocrystals or the FCZ glass bulk, respectively. The numerous parameters required to enable for a reliable numerical simulation of the processes are obtained from theoretical approaches like Judd-Ofelt theory, as well as from experimental studies of luminescence decay after femtosecond excitation at various wavelengths and luminescence spectra under cw illumination at 800 nm wavelength. This rate equation model enables for a convenient, self-consistent description of all time-resolved and cw experiments on samples with different neodymium concentration. On this basis, the power dependence of upconversion spectra can be simulated in good agreement with the experimental result for 800 nm cw illumination. The model therefore forms an excellent tool for optimizing the upconversion efficiency of rare-earth doped luminescent material also under realistic
Wang, M; Sun, X Z; Tang, S X; Tan, Z L; Pacheco, D
2013-06-01
Water-soluble components of feedstuffs are mainly utilized during the early phase of microbial fermentation, which could be deemed an important determinant of gas production behavior in vitro. Many studies proposed that the fractional rate of degradation (FRD) estimated by fitting gas production curves to mathematical models might be used to characterize the early incubation for in vitro systems. In this study, the mathematical concept of FRD was developed on the basis of the Logistic-Exponential (LE) model, with initial gas volume being zero (LE0). The FRD of the LE0 model exhibits a continuous increase from initial (FRD 0) toward final asymptotic value (FRD F) with longer incubation time. The relationships between the FRD and gas production at incubation times 2, 4, 6, 8, 12 and 24 h were compared for four models, in addition to LE0, Generalization of the Mitscherlich (GM), c th order Michaelis-Menten (MM) and Exponential with a discrete LAG (EXPLAG). A total of 94 in vitro gas curves from four subsets with a wide range of feedstuffs from different laboratories and incubation periods were used for model testing. Results indicated that compared with the GM, MM and EXPLAG models, the FRD of LE0 model consistently had stronger correlations with gas production across the four subsets, especially at incubation times 2, 4, 6, 8 and 12 h. Thus, the LE0 model was deemed to provide a better representation of the early fermentation rates. Furthermore, the FRD 0 also exhibited strong correlations (P < 0.05) with gas production at early incubation times 2, 4, 6 and 8 h across all four subsets. In summary, the FRD of LE0 model provides an alternative to quantify the rate of early stage incubation, and its initial value could be an important starting parameter of rate.
Analytical study of the energy rate balance equation for the magnetospheric storm-ring current
A. L. Clúa de Gonzalez
Full Text Available We present some results of the analytical integration of the energy rate balance equation, assuming that the input energy rate is proportional to the azimuthal interplanetary electric field, E_{y}, and can be described by simple rectangular or triangular functions, as approximations to the frequently observed shapes of E_{y}, especially during the passage of magnetic clouds. The input function is also parametrized by a reconnection-transfer efficiency factor α (which is assumed to vary between 0.1 and 1. Our aim is to solve the balance equation and derive values for the decay parameter τ compatible with the observed Dst peak values. To facilitate the analytical integration we assume a constant value for τ through the main phase of the storm. The model is tested for two isolated and well-monitored intense storms. For these storms the analytical results are compared to those obtained by the numerical integration of the balance equation, based on the interplanetary data collected by the ISEE-3 satellite, with the τ values parametrized close to those obtained by the analytical study. From the best fit between this numerical integration and the observed Dst the most appropriate values of τ are then determined. Although we specifically focus on the main phase of the storms, this numerical integration has been also extended to the recovery phase by an independent adjust. The results of the best fit for the recovery phase show that the values of τ may differ drastically from those corresponding to the main phase. The values of the decay parameter for the main phase of each event, τ_{m}, are found to be very sensitive to the adopted efficiency factor, α, decreasing as this factor increases. For the recovery phase, which is characterized by very low values of the power input, the response function becomes almost independent of the value of α and the resulting values for the decay time
Analytical study of the energy rate balance equation for the magnetospheric storm-ring current
Clúa de Gonzalez, A. L.; Gonzalez, W. D.
1998-11-01
We present some results of the analytical integration of the energy rate balance equation, assuming that the input energy rate is proportional to the azimuthal interplanetary electric field, Ey, and can be described by simple rectangular or triangular functions, as approximations to the frequently observed shapes of Ey, especially during the passage of magnetic clouds. The input function is also parametrized by a reconnection-transfer efficiency factor (which is assumed to vary between 0.1 and 1). Our aim is to solve the balance equation and derive values for the decay parameter compatible with the observed Dst peak values. To facilitate the analytical integration we assume a constant value for through the main phase of the storm. The model is tested for two isolated and well-monitored intense storms. For these storms the analytical results are compared to those obtained by the numerical integration of the balance equation, based on the interplanetary data collected by the ISEE-3 satellite, with the values parametrized close to those obtained by the analytical study. From the best fit between this numerical integration and the observed Dst the most appropriate values of are then determined. Although we specifically focus on the main phase of the storms, this numerical integration has been also extended to the recovery phase by an independent adjust. The results of the best fit for the recovery phase show that the values of may differ drastically from those corresponding to the main phase. The values of the decay parameter for the main phase of each event, m, are found to be very sensitive to the adopted efficiency factor, , decreasing as this factor increases. For the recovery phase, which is characterized by very low values of the power input, the response function becomes almost independent of the value of and the resulting values for the decay time parameter, r, do not vary greatly as varies. As a consequence, the relative values of between the main and the
LI Jiang-tao; XUN Chen; CUI Chun-li; WANG Hui-fang; WU Yi-tai; YUN Ai-hong; JIANG Xiao-feng; MA Jun
2012-01-01
Background The new Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation was developed to address the systematic underestimation of glomerular filtration rate (GFR) by the Modification of Diet in Renal Disease (MDRD) Study equation in patients with relatively well-preserved kidney function.Performance of the new equation in the Chinese population is unknown.The goal of the present study was to compare performance of these two equations in Chinese patients with chronic kidney disease (CKD).Methods We enrolled 450 Chinese patients (239 women and 211 men) with CKD in the present study.The renal dynamic imaging method was used to measure the referenced standard GFR (rGFR) for comparison with estimations using the two equations.Their overall performance was assessed with the Bland-Altman method and receiver-operating characteristics (ROC) analysis.Performance of the two equations in lower and higher estimated GFR (eGFR) subgroups was further investigated.Results Both eGFRs correlated well with rGFR (r=0.88,0.81,P＜0.05).In overall performance,the CKD-EPI equation showed less bias,higher precision and improved accuracy,and was better for detecting CKD.In the higher-eGFR subgroup,the CKD-EPI equation corrected the underestimation of GFR by the abbreviated MDRD equation.Conclusions The CKD-EPI equation outperformed the abbreviated MDRD equation not only in overall performance but also in the subgroups studied.For the present,the CKD-EPI equation appears to be the first-choice prediction equation for estimating GFR.
Comparison of estimated glomerular filtration rate equations at the time of hemodialysis initiation
Min-Jeong Lee
2015-12-01
Conclusions: The eGFR at HD initiation are significantly different according to the used eGFR equations, and the corrected Cockcroft–Gault equation may be the best in defining the eGFR at HD initiation.
M. Rafizadeh; H. Ghasemi; V. Haddadi-Asl
2006-01-01
Due to its mechanical properties and ease of use, vinyl ester resin is enjoying increasing consideration. This resin normally is produced by reaction between epoxy resin and unsaturated carboxylic acid. In the present study, bis-phenol A based epoxy resin and methacrylic acid was used to produce vinyl ester resin. The reaction was conducted under both stoichiometric and non-stoichiometric conditions in the presence of triphenylphosphine as catalyst. The stoichiometric and non-stoichiometric experiments were conducted at 95, 100, 105 and 110℃ and at 90 and 95℃, respectively. The first order rate equation and mechanism based rate equation were examined. Parameters are evaluated by least square method. A comparison of mechanism based rate equation and experimental data show an excellent agreement. Finally, Arrhenius equation and activation energy were presented.
Blufpand, Hester N; Westland, Rik; van Wijk, Joanna A E; Roelandse-Koop, Elianne A; Kaspers, Gertjan J L; Bökenkamp, Arend
2013-12-01
To compare the diagnostic performance of 2 height-independent equations used to calculate estimated glomerular filtration rate (eGFR), those of Pottel (eGFR-Pottel) and the British Columbia Children's Hospital (BCCH) (eGFR-BCCH), with the commonly used Schwartz equation (eGFR-Schwartz). We externally validated eGFR-Pottel and eGFR-BCCH in a well-characterized pediatric patient population (n = 152) and compared their diagnostic performance with that of eGFR-Schwartz using Bland-Altman analysis. All patients underwent glomerular filtration rate measurement using the gold standard single-injection inulin clearance method (GFR-inulin). Median GFR-inulin was 92.0 mL/min/1.73 m² (IQR, 76.1-107.4 mL/min/1.73 m²). Compared with GFR-inulin, the mean bias for eGFR-Schwartz was -10.1 mL/min/1.73 m(2) (95% limits of agreement [LOA], -77.5 to 57.2 mL/min/1.73 m(2)), compared with -12.3 mL/min/1.73 m² (95% LOA, -72.6 to 47.9 mL/min/1.73 m(2)) for eGFR-Pottel and -22.1 mL/min/1.73 m² (95% LOA, -105.0 to 60.8 mL/min/1.73 m(2)) for eGFR-BCCH. eGFR-Pottel showed comparable accuracy to eGFR-Schwartz, with 77% and 76% of estimates within 30% of GFR-inulin, respectively. eGFR-BCCH was less accurate than eGFR-Schwartz (66% of estimates within 30% of GFR-inulin; P Schwartz. eGFR-Pottel is a valid alternative to eGFR-Schwartz in children and could be reported by the laboratory if height data are not available. Copyright © 2013 Mosby, Inc. All rights reserved.
Xun Liu
2014-01-01
Full Text Available Objectives. To evaluate eight modified equations developed in Asiatic populations in type 2 diabetic patients in China. Methods. A total of 209 Chinese patients with type 2 diabetes were recruited. Using the technetium—99m diethylenetriaminepentaacetic acid—glomerular filtration rate (GFR to act as the reference, comparisons of their efficiency to estimate GFR in the subjects were made between various equations. Results. Median of difference of the Chinese equation 1 was the lowest (median of difference, 0.51 mL/min/1.73 m2. Median percent of absolute difference of the Chinese equation 2 was less than those of the other equations (26.97 versus ranged from 32.54 to 37.61 mL/min/1.73 m2, [P<0.001 for all]. Precision of the simplified reexpressed MDRD equation was the best (92.9 mL/min/1.73 m2. Accuracies of the Chinese equation 2 were greater (P<0.05 for all. There was also an improvement in chronic kidney disease (CKD stage misclassification of the Chinese equation 2 (55.0 versus ranged from 61.2 to 64.6%, [P<0.001 for all]. However, the 30% accuracies of all the equations were less than 70%. Conclusions. Our study highlighted a limitation in the use of the above equations in the majority of Chinese diabetic subjects. A better equation is needed in order to give an accurate estimation of GFR in type 2 diabetic patients in China.
How Hot Precursor Modify Island Nucleation: A Rate-Equation Model
Morales-Cifuentes, Josue; Einstein, T. L.; Pimpinelli, Alberto
2015-03-01
We describe the analysis, based on rate equations, of the hot precursor model mentioned in the previous talk. Two key parameters are the competing times of ballistic monomers decaying into thermalized monomers vs. being captured by an island, which naturally define a ``thermalization'' scale for the system. We interpret the energies and dimmensionless parameters used in the model, and provide both an implicit analytic solution and a convenient asymptotic approximation. Further analysis reveals novel scaling regimes and nonmonotonic crossovers between them. To test our model, we applied it to experiments on parahexaphenyl (6P) on sputtered mica. With the resulting parameters, the curves derived from our analytic treatment account very well for the data at the 4 different temperatures. The fit shows that the high-flux regime corresponds not to ALA (attachment-limited aggregation) or HMA (hot monomer aggregation) but rather to an intermediate scaling regime related to DLA (diffusion-limited aggregation). We hope this work stimulates further experimental investigations. Work at UMD supported by NSF CHE 13-05892.
Rate equation modelling of erbium luminescence dynamics in erbium-doped silicon-rich-silicon-oxide
Shah, Miraj, E-mail: m.shah@ee.ucl.ac.uk [Department of Electronic and Electrical Engineering, UCL, Torrington Place, London WC1E 7JE (United Kingdom); Wojdak, Maciej; Kenyon, Anthony J. [Department of Electronic and Electrical Engineering, UCL, Torrington Place, London WC1E 7JE (United Kingdom); Halsall, Matthew P.; Li, Hang; Crowe, Iain F. [Photon Science Institute and School of Electrical and Electronic Engineering, University of Manchester, Sackville St Building, Manchester M13 9PL (United Kingdom)
2012-12-15
Erbium doped silicon-rich silica offers broad band and very efficient excitation of erbium photoluminescence (PL) due to a sensitization effect attributed to silicon nanocrystals (Si-nc), which grow during thermal treatment. PL decay lifetime measurements of sensitised Er{sup 3+} ions are usually reported to be stretched or multi exponential, very different to those that are directly excited, which usually show a single exponential decay component. In this paper, we report on SiO{sub 2} thin films doped with Si-nc's and erbium. Time resolved PL measurements reveal two distinct 1.54 {mu}m Er decay components; a fast microsecond component, and a relatively long lifetime component (10 ms). We also study the structural properties of these samples through TEM measurements, and reveal the formation of Er clusters. We propose that these Er clusters are responsible for the fast {mu}s decay component, and we develop rate equation models that reproduce the experimental transient observations, and can explain some of the reported transient behaviour in previously published literature.
Halász, Adám M; Lai, Hong-Jian; McCabe Pryor, Meghan; Radhakrishnan, Krishnan; Edwards, Jeremy S
2013-01-01
True steady states are a rare occurrence in living organisms, yet their knowledge is essential for quasi-steady-state approximations, multistability analysis, and other important tools in the investigation of chemical reaction networks (CRN) used to describe molecular processes on the cellular level. Here, we present an approach that can provide closed form steady-state solutions to complex systems, resulting from CRN with binary reactions and mass-action rate laws. We map the nonlinear algebraic problem of finding steady states onto a linear problem in a higher-dimensional space. We show that the linearized version of the steady-state equations obeys the linear conservation laws of the original CRN. We identify two classes of problems for which complete, minimally parameterized solutions may be obtained using only the machinery of linear systems and a judicious choice of the variables used as free parameters. We exemplify our method, providing explicit formulae, on CRN describing signal initiation of two important types of RTK receptor-ligand systems, VEGF and EGF-ErbB1.
The rate equation based optical model for phosphor-converted white light-emitting diodes
Du, Kang; Li, Haokai; Guo, Keqin; Wang, Heng; Li, Dacheng; Zhang, Wending; Mei, Ting; Chua, Soo Jin
2017-03-01
An optical model based on the rate equation was developed to calculate the emission spectrum of a phosphor-converted white light-emitting diode (pc-WLED) taking into consideration the phosphor weight percentage, film thickness, and optical properties of phosphor, viz. absorption spectrum, quantum efficiency spectrum and fluorescent emission spectrum. Films containing a mixture of phosphor and silicone elastomer encapsulant were investigated using this model. A linear relationship was found between the peak absorption coefficient and the phosphor weight percentage with slopes of 66.76 ± 0.52 mm‑1 and 29.66 ± 2.05 mm‑1 for a red phosphor CaAlSiN3:Eu2+ and a yellow phosphor Y3Al5O12:Ce3+, respectively. With these parameters, the model predicted emission spectra which are in good agreement with measurement, thus verifying the validity of the model. The model correctly predicts redshift and spectral width reduction of the emission peak for increasing phosphor weight percentage or film thickness, as expected from the phenomenon of photon reabsorption by the phosphors. This model does not require the use of Monte Carlo simulation and Mie theory.
Lewis, Teresa V; Harrison, Donald L; Gildon, Brooke L; Carter, Sandra M; Turman, Martin A
2016-06-01
To determine if significant correlations exist between glomerular filtration rate (GFR) prediction equation values, derived by using the original Schwartz equation and the Chronic Kidney Disease in Children (CKiD) bedside equation with a 24-hour urine creatinine clearance (Clcr ) value normalized to a body surface area of 1.73 m(2) in overweight and obese children. Prospective analysis (20 patients) and retrospective analysis (43 patients). Pediatric inpatient ward and pediatric nephrology clinic at a comprehensive academic medical center. Sixty-three pediatric patients (aged 5-17 years), of whom 27 were overweight (body mass index [BMI] at the 85th percentile or higher) and 36 were not overweight (BMI lower than the 85th percentile [controls]) between 2007 and 2012. Data from the overweight patients were compared with nonoverweight controls. GFR values were calculated by using the original Schwartz equation and the CKiD bedside equation. Each patient's 24-hour urine Clcr value normalized to a body surface area of 1.73 m(2) served as the index value. A Pearson correlation coefficient model was used to determine association between the 24-hour urine Clcr value (index value) with the Schwartz and CKiD GFR estimations. Significant correlation was found to exist between the Schwartz and CKiD bedside GFR estimations relative to the 24-hour urine Clcr in the control subjects (r = 0.85, pSchwartz and CKiD bedside GFR values with the 24-hour urine Clcr value in overweight subjects (r = 0.86, pSchwartz equation estimated average GFR 21.75 ml/minute/1.73 m(2) higher than 24-hour urine Clcr (pSchwartz and CKiD bedside estimations of GFR correlated with 24-hour urine Clcr values in both overweight and nonoverweight children. Compared with the Schwartz equation, which tended to overestimate renal function, the CKiD bedside equation appeared to approximate 24-hour urine Clcr more closely in overweight children with kidney disorder. © 2016 Pharmacotherapy Publications, Inc.
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.
Mao, You-An; Zhong, Ke-Jun; Wei, Wan-Zhi; Wei, Xin-Liang; Lu, Hong-Bing
2005-02-01
The effect of N'-nitrosonornicotine (NNN), one of the tobacco-specific nitrosamines, on the catalytic activity of glutamate dehydrogenase (GLDH) in the alpha-ketoglutarate amination, using reduced nicotinamide adenine dinucleotide as coenzyme, was studied by a chronoamperometric method. The maximum reaction rate of the enzyme-catalyzed reaction and the Michaelis-Menten constant, or the apparent Michaelis-Menten constant, were determined in the absence and presence of NNN. NNN remarkably inhibited the bio-catalysis activity of GLDH, and was a reversible competitive inhibitior with K(i), estimated as 199 micromol l(-1) at 25 degrees C and pH 8.0.
The Effect of Saquinavir on the Rate of Metabolism of Midazolam
2013-01-31
Hensyl, 1990). Saquinavir and Midazolam 8 Ki The inhibition constant for Michaelis - Menten kinetics which describes the ability of a drug to inhibit...Redacted] PREFACE This study was conducted to provide information regarding the kinetic interaction between midazolam and saquinavir. Midazolam is a...the catalysis of a second drug (Fabre et. al., 1988). Km The Michaelis constant that describes the affinity of an enzyme to a particular substrate
Gaeuman, D.; Andrews, E.D.; Kraus, A.; Smith, W.
2009-01-01
Bed load samples from four locations in the Trinity River of northern California are analyzed to evaluate the performance of the Wilcock-Crowe bed load transport equations for predicting fractional bed load transport rates. Bed surface particles become smaller and the fraction of sand on the bed increases with distance downstream from Lewiston Dam. The dimensionless reference shear stress for the mean bed particle size (t*rm) is largest near the dam, but varies relatively little between the more downstream locations. The relation between t*rm and the reference shear stresses for other size fractions is constant across all locations. Total bed load transport rates predicted with the Wilcock-Crowe equations are within a factor of 2 of sampled transport rates for 68% of all samples. The Wilcock-Crowe equations nonetheless consistently under-predict the transport of particles larger than 128 mm, frequently by more than an order of magnitude. Accurate prediction of the transport rates of the largest particles is important for models in which the evolution of the surface grain size distribution determines subsequent bed load transport rates. Values of term estimated from bed load samples are up to 50% larger than those predicted with the Wilcock-Crowe equations, and sampled bed load transport approximates equal mobility across a wider range of grain sizes than is implied by the equations. Modifications to theWilcock-Crowe equation for determining t*rm and the hiding function used to scale term to other grain size fractions are proposed to achieve the best fit to observed bed load transport in the Trinity River. Copyright 2009 by the American eophysical Union.
Mann, Sarah L; Selby, Edward A; Bates, Marsha E; Contrada, Richard J
2015-10-01
High frequency heart rate variability (HRV) is a measure of neurocardiac communication thought to reflect predominantly parasympathetic cardiac regulation. Low HRV has been associated empirically with clinical and subclinical levels of anxiety and depression and, more recently, high levels of HRV have been associated with better performance on some measures of executive functioning (EF). These findings have offered support for theories proposing HRV as an index measure of a broad, self-regulatory capacity underlying aspects of emotion regulation and executive control. This study sought to test that proposition by using a structural equation modeling approach to examine the relationships of HRV to negative affect (NA) and EF in a large sample of U.S. adults ages 30s-80s. HRV was modeled as a predictor of an NA factor (self-reported trait anxiety and depression symptoms) and an EF factor (performance on three neuropsychological tests tapping facets of executive abilities). Alternative models also were tested to determine the utility of HRV for predicting NA and EF, with and without statistical control of demographic and health-related covariates. In the initial structural model, HRV showed a significant positive relationship to EF and a nonsignificant relationship to NA. In a covariate-adjusted model, HRV's associations with both constructs were nonsignificant. Age emerged as the only significant predictor of NA and EF in the final model, showing inverse relationships to both. Findings may reflect population and methodological differences from prior research; they also suggest refinements to the interpretations of earlier findings and theoretical claims regarding HRV.
陆靖; 范康年
1999-01-01
A dynamical theory of spectroscopy with femtosecond pulse excitation is developed in Liouville space. By using density matrix formalism, the transient rate equation that can be reduced to the classical KHD expression in CW case is obtained. This theory is applied to the Raman excitation profile of IBr and the results are in agreement with the experiments.
New, G.H.C.; Orkney, K.E.; Nock, M.J.W.
1976-09-01
New theoretical results connected with the stability of multiple pulsing in a passively mode-locked quasicontinuous laser in the rate equation approximation are presented. Together with earlier results, these allow the number of pulses per cavity transit to be predicted and a qualitative estimate made of the pulse duration for any combination of parameters. The results are illustrated by computer evolutions.
Ye XS
2014-09-01
Full Text Available Xiaoshuang Ye,1 Lu Wei,1 Xiaohua Pei,1 Bei Zhu,1 Jianqing Wu,2 Weihong Zhao1 1Division of Nephrology, Department of Geriatrics, The First Affiliated Hospital of Nanjing Medical University, Nanjing, Jiangsu, People’s Republic of China; 2Division of Respiration, Department of Geriatrics, The First Affiliated Hospital of Nanjing Medical University, Nanjing, Jiangsu, People’s Republic of China Background: No conventional creatinine- or cystatin C-based glomerular filtration rate (GFR estimation equation performed consistently outstandingly in elderly Chinese in our previous studies. This research aimed to further evaluate the performance of some recently proposed estimation equations based on creatinine and cystatin C, alone or combined, in this specific population. Materials and methods: The equations were validated in a population totaling 419 participants (median age 68 [range 60–94] years. The estimated GFR (eGFR calculated separately by ten equations was compared with the reference GFR (rGFR measured by the 99mTc-DTPA renal dynamic imaging method. Results: Median serum creatinine, cystatin C, and rGFR levels were 0.93 mg/L, 1.13 mg/L, and 74.20 mL/min/1.73 m2, respectively. The Chinese population-developed creatinine- and cystatin C-based (Cscr-cys equation yielded the least median absolute difference (8.81 vs range 9.53–16.32, P<0.05, vs the Chronic Kidney Disease Epidemiology Collaboration serum creatinine equation, the highest proportion of eGFR within 15% and 30% of rGFR (P15 and P30, 55.13 and 85.44, P<0.05 and P<0.01, vs the Chronic Kidney Disease Epidemiology Collaboration serum creatinine equation, and the lowest root mean square error (14.87 vs range 15.30–22.45 in the whole cohort. A substantial agreement of diagnostic consistency between eGFR and rGFR (with a kappa 0.61–0.80 was also observed with the Cscr-cys equation. Moreover, measures of performance in the Cscr-cys equation were consistent across normal to mildly
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...
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
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
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
Zhiren Jin
2008-02-01
Full Text Available We prove growth rate estimates and existence of solutions to Dirichlet problems for prescribed mean curvature equation on unbounded domains inside the complement of a cone or a parabola like region in $mathbb{R}^n$ ($ngeq 2$. The existence results are proved using a modified Perron's method by which a subsolution is a solution to the minimal surface equation, while the role played by a supersolution is replaced by estimates on the uniform $C^{0}$ bounds on the liftings of subfunctions on compact sets.
Wei, Ruiying; Guo, Boling; Li, Yin
2017-09-01
The Cauchy problem for the three-dimensional compressible magneto-micropolar fluid equations is considered. Existence of global-in-time smooth solutions is established under the condition that the initial data are small perturbations of some given constant state. Moreover, we obtain the time decay rates of the higher-order spatial derivatives of the solution by combining the Lp-Lq estimates for the linearized equations and the Fourier splitting method, if the initial perturbation is small in H3-norm and bounded in L1-norm.
Trapp, O
2006-01-01
A unified equation to evaluate elution profiles of reversible as well as irreversible (pseudo-) first-order reactions in dynamic chromatography and on-column reaction chromatography has been derived. Rate constants k1 and k(-1) and Gibbs activation energies are directly obtained from the chromatographic parameters (retention times tR(A) and tR(B) of the interconverting or reacting species A and B, the peak widths at half-height wA and wB, and the relative plateau height h(p)), the initial amounts A0 and B0 of the reacting species, and the equilibrium constant K(A/B). The calculation of rate constants requires only a few iterative steps without the need of performing a computationally extensive simulation of elution profiles. The unified equation was validated by comparison with a data set of 125,000 simulated elution profiles to confirm the quality of this equation by statistical means and to predict the minimal experimental requirements. Surprisingly, the recovery rate from a defined data set is on average 35% higher using the unified equation compared to the evaluation by iterative computer simulation.
Orskov, Bjarne; Strandgaard, Svend; Ørskov, Bjarne;
2010-01-01
(CKD-EPI) equation, the Cockcroft-Gault equation adjusted for body surface area and the MDRD equation with cystatin C. Performance was evaluated by mean bias, precision and accuracy. RESULTS: The MDRD equation with cystatin C had 97% of GFR estimates within 30% of measured GFR (accuracy). Both the CKD......-EPI and Cockcroft-Gault equations had an accuracy of 90% whereas the MDRD equation had an accuracy of 83%. This difference of accuracy was especially marked with GFR >60 ml/min/1.73 m(2). CONCLUSION: For estimating GFR in ADPKD patients the MDRD equation with cystatin C incorporated had the best performance...
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.
Yu-Wei Chen; Han-Hsiang Chen; Tsang-En Wang; Ching-Wei Chang; Chen-Wang Chang; Chih-Jen Wu
2011-01-01
AIM: To evaluate the difference between the performance of the (CKD-EPI) and Modification of Diet in Renal Disease (MDRD) equations in cirrhotic patients. METHODS: From Jan 2004 to Oct 2008, 4127 cirrhotic patients were reviewed. Patients with incomplete data with respect to renal function were excluded; thus, a total of 3791 patients were included in the study. The glomerular filtration rate (GFR) was estimated by the 4-variable MDRD (MDRD-4), 6-variable MDRD (MDRD-6), and CKD-EPI equations. RESULTS: When serum creatinine was 0.7-6.8 mg/dL and 0.6-5.3 mg/dL in men and women, respectively, a significantly lower GFR was estimated by the MDRD-6 than by the CKD-EPI. Similar GFRs were calculated by both equations when creatinine was > 6.9 mg/dL and > 5.4 mg/dL in men and women, respectively. In predicting in-hospital mortality, estimated GFR obtained by the MDRD-6 showed better accuracy [81.72%; 95% confidence interval (CI), 0.94-0.95] than that obtained by the MDRD-4 (80.22%; 95%CI, 0.96-0.97), CKD-EPI (79.93%; 95%CI, 0.96-0.96), and creatinine (77.50%; 95%CI, 2.27-2.63). CONCLUSION: GFR calculated by the 6-variable MDRD equation may be closer to the true GFR than that calculated by the CKD-EPI equation.
Schmuck, Markus; Kalliadasis, Serafim
2013-01-01
We study phase field equations based on the diffuse-interface approximation of general homogeneous free energy densities showing different local minima of possible equilibrium configurations in perforated/porous domains. The study of such free energies in homogeneous environments found a broad interest over the last decades and hence is now widely accepted and applied in both science and engineering. Here, we focus on strongly heterogeneous materials with perforations such as porous media. To the best of our knowledge, we present a general formal derivation of upscaled phase field equations for arbitrary free energy densities and give a rigorous justification by error estimates for a broad class of polynomial free energies. The error between the effective macroscopic solution of the new upscaled formulation and the solution of the microscopic phase field problem is of order $\\epsilon^1/2$ for a material given characteristic heterogeneity $\\epsilon$. Our new, effective, and reliable macroscopic porous media fo...
The Blow-Up Rate for Strongly Perturbed Semilinear Wave Equations in the Conformal Case
Hamza, M. A., E-mail: ma.hamza@fst.rnu.tn; Saidi, O., E-mail: saidi.omar@hotmail.fr [Université de Tunis El Manar, Faculté des Sciences de Tunis, LR03ES04 Èquations aux dérivées partielles et applications (Tunisia)
2015-12-15
We consider in this work some class of strongly perturbed for the semilinear wave equation with conformal power nonlinearity. We obtain an optimal estimate for a radial blow-up solution and we have also obtained two less stronger estimates. These results are achieved in three-steps argument by the construction of a Lyapunov functional in similarity variables and the Pohozaev identity derived by multiplying (1.14) by y∂{sub y}w.
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.
Determinants of the ZAR/USD exchange rate and policy implications: A simultaneous-equation model
Yu Hsing
2016-12-01
Full Text Available This paper examines the determinants of the South African rand/US dollar (ZAR/USD exchange rate based on demand and supply analysis. Applying the EGARCH method, the paper finds that the ZAR/USD exchange rate is positively associated with the South African government bond yield, US real GDP, the US stock price and the South African inflation rate and negatively influenced by the 10-year US government bond yield, South African real GDP, the South African stock price, and the US inflation rate. The adoption of a free floating exchange rate regime has reduced the value of the rand vs. the US dollar.
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.
Salhoumi, A.; Galenko, P. K.
2017-04-01
Rapidly moving solid-liquid interface is treated analytically and numerically. Derivation and qualitative analysis of interface propagation kinetics is presented. Quantitative predictions of solutions, which follow from the Kinetic Rate Theory and the solution of Gibbs-Thomson-type equation, are compared with Molecular Dynamics simulation data (MD-data) on crystallization and melting of fcc-lattice of nickel. It is shown in the approximation of a linear behavior of the interface velocity versus undercooling that the Gibbs-Thomson-type equation and kinetic rate theory describe MD-data well enough, in the range of small growth velocity and within the range of relatively small undercooling, with a relative error for the obtained values of kinetic coefficient of the order 1.1%. Within the small-and long range of undercooling, in nonlinear behavior of the interface velocity versus undercooling, the kinetic rate theory disagrees sharply with MD-data, qualitatively and quantitatively, unlike to the Gibbs-Thomson-type equation which is in a good agreement with MD-data within the whole range of undercooling and crystal growth velocity.
Crossvalidation of two heart rate-based equations for predicting VO2max in white and black men.
Esco, Michael R; Olson, Michele S; Williford, Henry N; Mugu, Emmanuel M; Bloomquist, Barbara E; McHugh, Aindrea N
2012-07-01
The purpose of this investigation was to crossvalidate 2 equations that use the ratio of maximal heart rate (HRmax) to resting HR (HRrest) for predicting maximal oxygen consumption (VO2max) in white and black men. One hundred and nine white (n = 51) and black (n = 58) men completed a maximal exercise test on a treadmill to determine VO2max. The HRrest and HRmax were used to predict VO2max via the HRindex and HRratio equations. Validity statistics were done to compare the criterion versus predicted VO2max values across the entire cohort and within each race separately. For the entire group, VO2max was significantly overestimated with the HRindex equation, but the HRratio equation yielded no significant difference compared with the criterion. In addition, there were no significant differences shown between VO2max and either HR-based prediction equation for the white subgroup. However, both equations significantly overestimated VO2max in the black group. Furthermore, large standard error of estimates (ranging from 6.92 to 7.90 ml·kg(-1)·min(-1)), total errors (ranging from 8.30 to 8.62 ml·kg(-1)·min(-1)), and limits of agreement (ranging from upper limits of 16.65 to lower limits of -18.25 ml·kg(-1)·min(-1)) were revealed when comparing the predicted to criterion VO2max for both the groups. Considering the results of this investigation, the HRratio and HRindex methods appear to crossvalidate and prove useful for estimating the mean VO2max in white men as a group but not for an age-matched group of black men. However, because of inflated values for error, caution should be exercised when using these methods to predict individual VO2max.
Kim, Daewook; Kim, Dojin; Hong, Keum-Shik; Jung, Il Hyo
2014-01-01
The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku'' + M(|A (1/2) u|(2))Au + g(u') = 0 under suitable assumptions on K, A, M(·), and g(·). Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations in order to verify the analytical results are given.
QUASI-SURE CONVERGENCE RATE OF EULER SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS
Wenliang HUANG; Xicheng ZHANG
2014-01-01
Let Xt(x) be the solution of stochastic differential equations with smooth and bounded derivatives coefficients. Let Xnt (x) be the Euler discretization scheme of SDEs with step 2-n . In this note, we prove that for any R>0 and γ∈(0, 1/2), sup t∈[0,1],|x|6R|X nt (x,ω)-Xt (x,ω)|6ξR,γ(ω)2-nγ, n>1, q.e., whereξR,γ(ω) is quasi-everywhere finite.
Zhensheng GAO; Zhong TAN; Guochun WU
2014-01-01
In this paper, we are concerned with the global existence and convergence rates of the smooth solutions for the compressible magnetohydrodynamic equations without heat conductivity, which is a hyperbolic-parabolic system. The global solutions are obtained by combining the local existence and a priori estimates if H3-norm of the initial perturbation around a constant states is small enough and its L1-norm is bounded. A priori decay-in-time estimates on the pressure, velocity and magnetic field are used to get the uniform bound of entropy. Moreover, the optimal convergence rates are also obtained.
LI Hai-xia; XU Guo-bin; WANG Xue-jing; ZHANG Xu-chu; YANG Jian-mei
2010-01-01
Background The equations for estimating glomerular filtration rate (GFR) based on creatinine have been found to have limitations and have not been generalizable across all populations. Equations based on cystatin C provide an alternative method to estimate GFR. Whether the equation based on cystatin C alone or combined creatinine would improve GFR estimates has not been validated among Chinese patients with chronic kidney disease (CKD) and diabetes. The aim of this study was to compare the performance of the modification of diet in renal disease (MDRD) equation based on creatinine with the five cystatin C-based formulae for estimation of GFR in patients with CKD and diabetes. Methods A total of 166 patients with CKD and 91 patients with type 2 diabetes were enrolled in this study. Cystatin C was measured by using the particle-enhanced immunonephelometric method and estimated formulae proposed by five different investigator teams (Stevens, Ma, Rule, Macisaac and Perkins). The plasma clearance of ~(99m)Tc-DTPA was determined as measured GFR (mGFR).Results For CKD patients, the bias and accuracy for the Ma and Macisaac equations were superior compared with the MDRD, and the mean results for the Ma formula were closer to mGFR than the other equations in CKD stages 2-5. The differences between Macisaac and mGFR in CKD stages 2-4 were significantly less than those in CKD stage 1 or 5.Stevens and Rule's formulae revealed a similar bias and accuracy compared with the MDRD equation. The MDRD formula had a higher accuracy in CKD stages 3-5 as compared with the results in other stages. For diabetic patients, the mean results between Macisaac and mGFR were closer than those of other equations in mGFR≥90 ml.min~(-1).1.73 m~(-2) stage, in GFR 60-89 ml·min~(-1)·1.73 m~(-2) stage, the MDRD formula showed the smallest difference compared with other equations. All equations overestimated GFR in the cases with GFR <60 mi.min~(-1)·1.73 m~(-2) stages. The MDRD formula had a
Yin, Jun-Jie; Hyde, James S.
Rate equations describing the time dependence of population differences of the five allowed transitions in an 14N 15N spin-label pair problem are set up. Included in the formulation are the three Heisenberg exchange rate constants and different nitrogen nuclear spin-lattice relaxation rates, electron spin-lattice relaxation rates, and populations for the 14N and 15N moieties. Using matrix algebra, stationary and time-dependent solutions are obtained in a unified theoretical framework. The calculations apply to stationary and pulse electron-electron double resonance and to saturation-recovery ESR. Particular emphasis is placed on short pulse initial excitation, where the transverse relaxation processes are sufficiently slow that only the population difference of the irradiated transition departs significantly from Boltzmann equilibrium during the excitation.
Jahan, F; Chowdhury, M N U; Mahbub, T; Arafat, S M; Jahan, S; Hossain, M; Khan, M F
2013-08-01
To ensure that potential kidney donors in Bangladesh have no renal impairment, it is extremely important to have accurate methods for evaluating the glomerular filtration rate (GFR). We evaluated the performance of serum creatinine based GFR in healthy adult potential kidney donors in Bangladesh to compare GFR determined by DTPA with that determined by various prediction equations. In this study GFR in 61 healthy adult potential kidney donors were measured with 99mTc-diethylenetriamine penta-acetic acid (DTPA) renogram. We also estimated GFR using a four variable equation modification of diet in renal disease (MDRD), Cockcroft-Gault creatinine clearance (CGCrCl), Cockcroft-Gault glomerular filtration rate (CG-GFR). The mean age of study population was 34.31 +/- 9.46 years and out of them 65.6% was male. In this study mean mGFR was 85.4 +/- 14.8. Correlation of estimated GFR calculated by CG-CrCl, CG-GFR and MDRD were done with measured GFR DTPA using quartile. Kappa values were also estimated which was found to be 0.104 for (p = 0.151), 0.336 for (p = 0.001) and 0.125 for (p = 0.091) respectively. This indicates there is no association between estimated GFR calculated by CG-CrCl, CG-GFR, MDRD with measured GFR DTPA. These results show poor performance of these equations in evaluation of renal function among healthy population and also raise question regarding validity of these equations for assessment of renal function in chronic kidney disease in our population.
Gasperini, P; Gasperini, Paolo; Lolli, Barbara
2005-01-01
We analyzed the correlations among the parameters of the Reasenberg and Jones (1989) formula describing the aftershock rate after a mainshock as a function of time and magnitude, on the basis of parameter estimates made in previous works for New Zealand, Italy and California. For all of three datasets we found that the magnitude-independent productivity a is significantly correlated with the b-value of the Gutenberg-Richter law and, in some cases, with parameters p and c of the modified Omori's law. We argued that the correlation between a and b can be ascribed to an inappropriate definition of the coefficient of mainshock magnitude as the correlation becomes insignificant if the latter is assumed to be $\\alpha\\simeq$ 2/3b rather than b. This interpretation well agrees with the results of direct a estimates we made, by an epidemic type model (ETAS), from the data of some large Italian sequences. We also verified that assuming $\\alpha$ about 2/3 of the average b value estimated from Italian sequences occurred ...
Development of wide-range constitutive equations for calculations of high-rate deformation of metals
Preston D.
2011-01-01
Full Text Available For development of models of strength and compressibility of metals in wide range of pressures (up to several megabar and strain rates ~ 1÷108 s−1, the method of dynamic tests is used. Since direct measurement of strength is impossible under complicated intensive high-rate loading, a formal model is created at first, and then it is updated basing on comparison with many experiments, which are sensitive to shear strength. Elastic-plastic, viscous-elastic-plastic and relaxation integral models became nowadays most commonly used. The basic unsolved problems in simulation of high-rate deformation of metals are mentioned in the paper.
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
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
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.
Manipulating single enzymes by an external harmonic force
Lomholt, Michael A; Urbakh, Michael; Metzler, Ralf
2007-01-01
We study a Michaelis-Menten reaction for a single two-state enzyme molecule, whose transition rates between the two conformations are modulated by an harmonically oscillating external force. In particular, we obtain a range of optimal driving frequencies for changing the conformation of the enzyme...
KINETICS OF QUERCETIN NITRATIO N BY HORSERADISH PEROXIDASE
Andrija Šmelcerović
2013-03-01
Full Text Available In this study we investigated the kinetics of the nitration of quercetin by horseradish peroxidase. Quercetin nitration reaction was followed by recording the spectral changes over the time at 380 nm. The reaction rate increases with increasing of the quercetin concentration and follows the Michaelis-Menten type kinetics. Kinetic parameters of the studied enzymatic reaction were determined.
Constitutive equations of basalt filament tows under quasi-static and high strain rate tension
Zhu Lvtao; Sun Baozhong [College of Textiles, Donghua University, Shanghai 201620 (China); Hu, Hong [Institute of Textiles and Clothing, Hong Kong Polytechnic University, Hung Hom Kowloon (Hong Kong); Gu Bohong, E-mail: gubh@dhu.edu.cn [College of Textiles, Donghua University, Shanghai 201620 (China); Department of Textile Engineering, Zhongyuan Institute of Technology, Zhengzhou, Henan Province 450007 (China)
2010-05-25
The tensile properties of basalt filament tows were tested at quasi-static (0.001 s{sup -1}) and high strain rates (up to 3000 s{sup -1}) with MTS materials tester (MTS 810.23) and split Hopkinson tension bar (SHTB), respectively. Experimental results showed that the mechanical properties of the basalt filament tows were rather sensitive to strain rate. Specifically, the stiffness and failure stress of the basalt filament tows increased distinctly as the strain rate increased, while the failure strain decreased. From scanning electronic microscope (SEM) photographs of the fracture surface, it is indicated that the basalt filament tows failed in a more brittle mode and the fracture surface got more regular as the strain rate increases. The strength distributions of the basalt filament tows have been evaluated by a single Weibull distribution function. The curve predicted from the single Weibull distribution function was in good agreement with the experimental data points.
Respiration Rate Predictive Equation and Effective Heat Stress Relief Ways for Hanwoo Steers
Gutierrez, Winson-Montanez; Oh, Taek-Kuen; Kim, Dong-Hyeok; Lee, Jin-Ju; Kim, Suk; Min, Wong; Lee, Seung-Joo; Kim, Byeong-Woo; Chang, Hong-Hee; Chikushi, Jiro
2012-01-01
Normalizing respiration rate in heat–stress challenged cattle during summer season is very important. In this study, we investigated the contribution of different thermal factors such as skin temperature, dew–point temperature, solar radiation, dry–bulb temperature and wind speed on its influence to the respiration rate dynamics of 45 Hanwoo steers in 2010. Secondly, the heat insulation efficiencies of the three kinds of roofing materials such as sandwich panel (SP), master panel (MP), and fi...
The 220-age equation does not predict maximum heart rate in children and adolescents
Verschuren, Olaf; Maltais, Desiree B.; Takken, Tim
Our primary purpose was to provide maximum heart rate (HR(max)) values for ambulatory children with cerebral palsy (CP). The secondary purpose was to determine the effects of age, sex, ambulatory ability, height, and weight on HR(max). In 362 ambulatory children and adolescents with CP (213 males
The 220-age equation does not predict maximum heart rate in children and adolescents
Verschuren, Olaf; Maltais, Desiree B.; Takken, Tim
2011-01-01
Our primary purpose was to provide maximum heart rate (HR(max)) values for ambulatory children with cerebral palsy (CP). The secondary purpose was to determine the effects of age, sex, ambulatory ability, height, and weight on HR(max). In 362 ambulatory children and adolescents with CP (213 males an
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.
Pauwels, Valentijn R. N.; Verhoest, Niko E. C.; de Troch, FrançOis P.
2002-12-01
In hydrology the slow, subsurface component of the discharge is usually referred to as base flow. One method to model base flow is the conceptual approach, in which the complex physical reality is simplified using hypotheses and assumptions, and the various physical processes are described mathematically. The purpose of this paper is to develop and validate a conceptual method, based on hydraulic theory, to calculate the base flow of a catchment, under observed precipitation rates. The governing groundwater equation, the Boussinesq equation, valid for a unit width sloping aquifer, is linearized and solved for a temporally variable recharge rate. The solution allows the calculation of the transient water table profile in and the outflow from an aquifer under temporally variable recharge rates. When a catchment is considered a metahillslope, the solution can be used, when coupled to a routing model, to calculate the catchment base flow. The model is applied to the Zwalm catchment and four subcatchments in Belgium. The results suggest that it is possible to model base flow at the catchment scale, using a Boussinesq-based metahillslope model. The results further indicate that it is sufficient to use a relatively simple formulation of the infiltration, overland flow, and base flow processes to obtain reasonable estimates of the total catchment discharge.
Optimal decay rate of vibrating beam equations controlled by combined boundary feedback forces
于景元; 李胜家; 王耀庭; 粱展东
1999-01-01
The optimal decay rate problem is considered for boundary control system modeling by a flexible structure consisting of a Eular-Bernoulli beam. Controls are a bending moment in proportion to angular velocity and a shear force in proportion to velocity. A sensitivity asymptotic analysis of the system’ s eigenvalues and eigenfunctions is set up. It is proved that, for every 0
Local Lyapunov exponents sublimiting growth rates of linear random differential equations
Siegert, Wolfgang
2009-01-01
Establishing a new concept of local Lyapunov exponents the author brings together two separate theories, namely Lyapunov exponents and the theory of large deviations. Specifically, a linear differential system is considered which is controlled by a stochastic process that during a suitable noise-intensity-dependent time is trapped near one of its so-called metastable states. The local Lyapunov exponent is then introduced as the exponential growth rate of the linear system on this time scale. Unlike classical Lyapunov exponents, which involve a limit as time increases to infinity in a fixed system, here the system itself changes as the noise intensity converges, too.
How "Hot Precursors" Modify Island Nucleation: A Rate-Equation Model
Morales-Cifuentes, Josue R.; Einstein, T. L.; Pimpinelli, A.
2014-12-01
We propose a novel island nucleation and growth model explicitly including transient (ballistic) mobility of the monomers deposited at rate F , assumed to be in a hot precursor state before thermalizing. In limiting regimes, corresponding to fast (diffusive) and slow (ballistic) thermalization, the island density N obeys scaling N ∝Fα . In between is found a rich, complex behavior, with various distinctive scaling regimes, characterized by effective exponents αeff and activation energies that we compute exactly. Application to N (F ,T ) of recent organic-molecule deposition experiments yields an excellent fit.
Rate equation approach to understanding the ion-catalyzed formation of peptides
Dubrovskii, V. G.; Sibirev, N. V.; Eliseev, I. E.; Vyazmin, S. Yu; Boitsov, V. M.; Natochin, Yu. V.; Dubina, M. V.
2013-06-01
The salt-induced peptide formation is important for assessing and approaching schemes of molecular evolution. Here, we present experimental data and an exactly solvable kinetic model describing the linear polymerization of L-glutamic amino acid in water solutions with different concentrations of KCl and NaCl. The length distributions of peptides are well fitted by the model. Strikingly, we find that KCl considerably enhances the peptide yield, while NaCl does not show any catalytic effect in most cases under our experimental conditions. The greater catalytic effect of potassium ions is entirely interpreted by one and single parameter, the polymerization rate constant that depends on the concentration of a given salt in the reaction mixture. We deduce numeric estimates for the rate constant at different concentrations of the ions and show that it is always larger for KCl. This leads to an exponential increase of the potassium- to sodium-catalyzed peptide concentration ratio with length. Our results show that the ion-catalyzed peptides have a higher probability to emerge in excess potassium rather than in sodium-rich water solutions.
Geomorphic Flux From Himalayan Flashflood Equates to 1000 yrs Average Erosion Rate
Sinclair, Hugh; Mudd, Simon; LeDivellec, Tom; Dallas, Kirsten; Andy, Hein
2016-04-01
Extreme flood events are increasingly reported from the western Himalaya; we use geomorphic analyses to reconstruct both the spatial distribution and approximate the recurrence interval for these events. During the summer of 2010, an enhanced monsoon resulted in extensive flooding of the Indus Valley of Pakistan. An unusual aspect of this event was the intense precipitation in the arid upper reaches of the Indus River in Ladakh. On August 5th, a mesoscale convective system caused intense, short-lived precipitation, with estimates of 75-100 mm falling in approximately 30 minutes. The short-lived convective nature of the rainfall meant TRMM data was unable to locate the main event. However, a geomorphic reconstruction of river discharge and hillslope activity demonstrates that the precipitation was limited to a 3 to 6 km wide band on the southward facing slopes of the Ladakh Range, and that this can be traced approximately 120 km along the strike of the range. In addition to mapping out the extent of the event, we also reconstruct the total flux mobilised on selected hillslopes by debris flows; this was achieved by measuring width/depth ratios across a range of scales, and then assigning a stream order to the debris flows which are then mapped over selected sub-catchments. This process provided a volume of mass flux which was then compared to background erosion rates derived from detrital cosmogenic 10Be measurements. This comparison reveals that the Ladakh event mobilised the equivalent of 800-1200 yrs of the mean background erosion rate in these catchments. Repeat 10Be measurements from the same catchments before and after the event record a reduction in concentrations which are explored in terms of the scale of debris flows principally responsible for the flux. Two years after the Ladakh event, another major flood event occurred in Uttarakhand, resulting in >5700 deaths. Initial investigations of the erosion of dated moraines and the deposition of new terraces
Gheissari, Alaleh; Roomizadeh, Peyman; Kelishadi, Roya; Abedini, Amin; Haghjooy-Javanmard, Shaghayegh; Abtahi, Seyed-Hossein; Mehdikhani, Bahareh
2014-09-01
To determine the performance of the updated Schwartz, combined Schwartz and Grubb glomerular filtration rate (GFR) equations in a relatively large number of healthy children with no known renal disease, we studied 712 students aged between seven and 18 years from the Isfahan province of Iran by random cluster sampling between 2009 and 2010. Blood investigations included blood urea nitrogen, creatinine and cystatin C. For each participant, GFR was calculated based on the three equations. We used Bland-Altman plots and weighted kappa statistics to compare the performance of the study equations. The mean age of the children was 12.2 ± 2.4 years. A high concordance in estimating GFR (mean difference: 0 ± 12.7 mL/min/1.73 m 2 ) and a very good agreement in defining chronic kidney disease (CKD) and non-CKD individuals (weighted kappa: 0.85; 95% confidence intervals: 0.69-1) were observed between the updated Schwartz and the combined Schwartz equations. Poor agreement was observed between the Grubb equation and two Schwartz equations in estimating GFR and defining CKD. There was no systematic deviation between the updated Schwartz and the combined Schwartz equations in children with normal renal function. The Grubb equation was highly inconsistent with both Schwartz equations in this population. We conclude that the updated Schwartz equation is simpler and more accessible than the combined Schwartz equation in daily clinical practice and CKD screening programs.
Alaleh Gheissari
2014-01-01
Full Text Available To determine the performance of the updated Schwartz, combined Schwartz and Grubb glomerular filtration rate (GFR equations in a relatively large number of healthy children with no known renal disease, we studied 712 students aged between seven and 18 years from the Isfahan province of Iran by random cluster sampling between 2009 and 2010. Blood investigations included blood urea nitrogen, creatinine and cystatin C. For each participant, GFR was calculated based on the three equations. We used Bland-Altman plots and weighted kappa statistics to compare the performance of the study equations. The mean age of the children was 12.2 ± 2.4 years. A high concordance in estimating GFR (mean difference: 0 ± 12.7 mL/min/1.73 m 2 and a very good agreement in defining chronic kidney disease (CKD and non-CKD individuals (weighted kappa: 0.85; 95% confidence intervals: 0.69-1 were observed between the updated Schwartz and the combined Schwartz equations. Poor agreement was observed between the Grubb equation and two Schwartz equations in estimating GFR and defining CKD. There was no systematic deviation between the updated Schwartz and the combined Schwartz equations in children with normal renal function. The Grubb equation was highly inconsistent with both Schwartz equations in this population. We conclude that the updated Schwartz equation is simpler and more accessible than the combined Schwartz equation in daily clinical practice and CKD screening programs.
Geicimara Guimarães
2011-01-01
Full Text Available
The objective of this study was to evaluate levels of sucrose on microbial growth. Roll tubes were filled with 15.6 mL of buffer Chen, 1 mL of inocula (rumen fluid from fistulated steer at pasture, 1 mL of Trypticase or hydrolyzed casein (1 g L^{-1} as final concentration and 2.4 mL of sucrose solutions (0.00 g L^{-1}, 0.37 g L^{-1}, 0.75 g L^{-1}, 1.5 g L^{-1}, 3.0 g L^{-1}, 6.0 g L^{-1}, 12.0 g L^{-1}, and 24.0 g L^{-1}, in triplicate. The pH was 5.56 at 0 h and 4.6 after 6 h, and 5.83 in 0 g L^{-1} and 4.18 above 1.5 g L^{-1} of sucrose. The optical density (OD-600 nm and microbial protein (MP-595 nm tended to stabilize after 12 h and 6 g L^{-1} of sucrose, with no interaction between them. The OD (6 h to 24 h mean values was curvilinear (hyperbolic, as a function of sucrose concentration, followed the saturation kinetics of Michaelis-Menten, which is typical of enzymes systems, and was described by the following Lineweaver-Burk equation: 1/OD = 0.508*(1/sucrose + 1.15, R² = 0.99. The theoretical maximum microbial growth (1/a = k_{max} was 0.87 OD and the concentration of sucrose to reach half of k_{max} (b/a = K_{s} was 0.44 g L^{-1} of sucrose. The microbial growth was affected by incubation time, substrate concentration, and culture medium acidification.
KEY-WORDS: Lineweaver-Burk; Michaelis-Menten; p
Bhattacharya, Samyadeb; Misra, Avijit; Mukhopadhyay, Chiranjib; Pati, Arun Kumar
2017-01-01
An exact canonical master equation of the Lindblad form is derived for a central spin interacting uniformly with a sea of completely unpolarized spins. The Kraus operators for the dynamical map are also derived. The non-Markovianity of the dynamics in terms of the divisibility breaking of the dynamical map and the increase of the trace distance fidelity between quantum states is shown. Moreover, it is observed that the irreversible entropy production rate is always negative (for a fixed initial state) whenever the dynamics exhibits non-Markovian behavior. In continuation with the study of witnessing non-Markovianity, it is shown that the positive rate of change of the purity of the central qubit is a faithful indicator of the non-Markovian information backflow. Given the experimental feasibility of measuring the purity of a quantum state, a possibility of experimental demonstration of non-Markovianity and the negative irreversible entropy production rate is addressed. This gives the present work considerable practical importance for detecting the non-Markovianity and the negative irreversible entropy production rate.
Domanskyi, Sergii; Schilling, Joshua E.; Gorshkov, Vyacheslav; Libert, Sergiy; Privman, Vladimir
2016-09-01
We develop a theoretical approach that uses physiochemical kinetics modelling to describe cell population dynamics upon progression of viral infection in cell culture, which results in cell apoptosis (programmed cell death) and necrosis (direct cell death). Several model parameters necessary for computer simulation were determined by reviewing and analyzing available published experimental data. By comparing experimental data to computer modelling results, we identify the parameters that are the most sensitive to the measured system properties and allow for the best data fitting. Our model allows extraction of parameters from experimental data and also has predictive power. Using the model we describe interesting time-dependent quantities that were not directly measured in the experiment and identify correlations among the fitted parameter values. Numerical simulation of viral infection progression is done by a rate-equation approach resulting in a system of "stiff" equations, which are solved by using a novel variant of the stochastic ensemble modelling approach. The latter was originally developed for coupled chemical reactions.
Dong, B; Ding, G H; Lei, X L
2015-05-27
A general theoretical formulation for the effect of a strong on-site Coulomb interaction on the time-dependent electron transport through a quantum dot under the influence of arbitrary time-varying bias voltages and/or external fields is presented, based on slave bosons and the Keldysh nonequilibrium Green's function (GF) techniques. To avoid the difficulties of computing double-time GFs, we generalize the propagation scheme recently developed by Croy and Saalmann to combine the auxiliary-mode expansion with the celebrated Lacroix's decoupling approximation in dealing with the second-order correlated GFs and then establish a closed set of coupled equations of motion, called second-order quantum rate equations (SOQREs), for an exact description of transient dynamics of electron correlated tunneling. We verify that the stationary solution of our SOQREs is able to correctly describe the Kondo effect on a qualitative level. Moreover, a comparison with other methods, such as the second-order von Neumann approach and Hubbard-I approximation, is performed. As illustrations, we investigate the transient current behaviors in response to a step voltage pulse and a harmonic driving voltage, and linear admittance as well, in the cotunneling regime.
Ziegler, Felix; Albers, Jan [Technische Univ. Berlin (Germany). Inst. fuer Energietechnik
2009-04-15
The method of characteristic equations can be used to describe the performance of absorption chillers in a wide rage of part load conditions as a linear function of a characteristic temperature difference ({delta}{delta}t). This temperature difference combines the external temperatures of hot, chilled and cooling water into one parameter. Normally the achieved part load characteristic is a linear function of {delta}{delta}t provided that the heat transfer coefficients and thus the external flow rates are constant. Nevertheless, this assumption is often not fullfilled under practical conditions. Therefore the classical method has been improved in order to account for variable temperature and flow conditions. Despite of some simplifications the results are in good accordance with measurements. (orig.)
Huthmacher, Klaus [Department of Physics and OPTIMAS Research Center, University of Kaiserslautern (Germany); Molberg, Andreas K. [Department of Chemistry and OPTIMAS Research Center, University of Kaiserslautern (Germany); Rethfeld, Bärbel [Department of Physics and OPTIMAS Research Center, University of Kaiserslautern (Germany); Gulley, Jeremy R., E-mail: jgulley@kennesaw.edu [Department of Physics, Kennesaw State University, Kennesaw, GA 30144 (United States)
2016-10-01
A split-step numerical method for calculating ultrafast free-electron dynamics in dielectrics is introduced. The two split steps, independently programmed in C++11 and FORTRAN 2003, are interfaced via the presented open source wrapper. The first step solves a deterministic extended multi-rate equation for the ionization, electron–phonon collisions, and single photon absorption by free-carriers. The second step is stochastic and models electron–electron collisions using Monte-Carlo techniques. This combination of deterministic and stochastic approaches is a unique and efficient method of calculating the nonlinear dynamics of 3D materials exposed to high intensity ultrashort pulses. Results from simulations solving the proposed model demonstrate how electron–electron scattering relaxes the non-equilibrium electron distribution on the femtosecond time scale.
CHARACTERIZATIONS ON THE THIXOTROPY-LOOP TESTS USING UCM MODEL WITH A RATE-TYPE KINETIC EQUATION
Shu-xin Huang; Chuan-jing Lu
2006-01-01
The theoretical characterizations on the triangular-form thixotropy-loop tests of an LDPE melt (PE-FSB23D022/Q200) were conducted in the present paper by using a new thixotropy model, which is constituted by the upper convected Maxwell model and a rate-type kinetic equation. The new thixotropic Maxwell model can partially describe well three reported thixotropy-loop experiments by comparison with the previous calculations of the variant form of the thixotropy-type Huang model. It is noted that the stress deviations between the experiments and the predictions of the new thixotropic Maxwell model are much slighter than those deviations obtained by using the variant Huang model at the same condition, although both models include five parameters. The constitution of the new thixotropic Maxwell model is more reasonable than that of the variant Huang model.
Huthmacher, Klaus; Molberg, Andreas K.; Rethfeld, Bärbel; Gulley, Jeremy R.
2016-10-01
A split-step numerical method for calculating ultrafast free-electron dynamics in dielectrics is introduced. The two split steps, independently programmed in C++11 and FORTRAN 2003, are interfaced via the presented open source wrapper. The first step solves a deterministic extended multi-rate equation for the ionization, electron-phonon collisions, and single photon absorption by free-carriers. The second step is stochastic and models electron-electron collisions using Monte-Carlo techniques. This combination of deterministic and stochastic approaches is a unique and efficient method of calculating the nonlinear dynamics of 3D materials exposed to high intensity ultrashort pulses. Results from simulations solving the proposed model demonstrate how electron-electron scattering relaxes the non-equilibrium electron distribution on the femtosecond time scale.
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.
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
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.
Pan, Wenxiao; Daily, Michael D.; Baker, Nathan A.
2015-12-01
We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to an acetylcholinesterase monomer. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) boundary condition, is considered on the reactive boundaries. This new boundary condition treatment allows for the analysis of enzymes with "imperfect" reaction rates. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.
Illg, Christian; Haag, Michael; Teeny, Nicolas; Wirth, Jens; Fähnle, Manfred
2016-03-01
Scatterings of electrons at quasiparticles or photons are very important for many topics in solid-state physics, e.g., spintronics, magnonics or photonics, and therefore a correct numerical treatment of these scatterings is very important. For a quantum-mechanical description of these scatterings, Fermi's golden rule is used to calculate the transition rate from an initial state to a final state in a first-order time-dependent perturbation theory. One can calculate the total transition rate from all initial states to all final states with Boltzmann rate equations involving Brillouin zone integrations. The numerical treatment of these integrations on a finite grid is often done via a replacement of the Dirac delta distribution by a Gaussian. The Dirac delta distribution appears in Fermi's golden rule where it describes the energy conservation among the interacting particles. Since the Dirac delta distribution is a not a function it is not clear from a mathematical point of view that this procedure is justified. We show with physical and mathematical arguments that this numerical procedure is in general correct, and we comment on critical points.
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.
Gian Paolo Beretta
2008-08-01
Full Text Available A rate equation for a discrete probability distribution is discussed as a route to describe smooth relaxation towards the maximum entropy distribution compatible at all times with one or more linear constraints. The resulting dynamics follows the path of steepest entropy ascent compatible with the constraints. The rate equation is consistent with the Onsager theorem of reciprocity and the fluctuation-dissipation theorem. The mathematical formalism was originally developed to obtain a quantum theoretical unification of mechanics and thermodinamics. It is presented here in a general, non-quantal formulation as a part of an effort to develop tools for the phenomenological treatment of non-equilibrium problems with applications in engineering, biology, sociology, and economics. The rate equation is also extended to include the case of assigned time-dependences of the constraints and the entropy, such as for modeling non-equilibrium energy and entropy exchanges.
Beretta, Gian P.
2008-09-01
A rate equation for a discrete probability distribution is discussed as a route to describe smooth relaxation towards the maximum entropy distribution compatible at all times with one or more linear constraints. The resulting dynamics follows the path of steepest entropy ascent compatible with the constraints. The rate equation is consistent with the Onsager theorem of reciprocity and the fluctuation-dissipation theorem. The mathematical formalism was originally developed to obtain a quantum theoretical unification of mechanics and thermodinamics. It is presented here in a general, non-quantal formulation as a part of an effort to develop tools for the phenomenological treatment of non-equilibrium problems with applications in engineering, biology, sociology, and economics. The rate equation is also extended to include the case of assigned time-dependences of the constraints and the entropy, such as for modeling non-equilibrium energy and entropy exchanges.
Fach, S; Sitzenfrei, R; Rauch, W
2009-01-01
It is state of the art to evaluate and optimise sewer systems with urban drainage models. Since spill flow data is essential in the calibration process of conceptual models it is important to enhance the quality of such data. A wide spread approach is to calculate the spill flow volume by using standard weir equations together with measured water levels. However, these equations are only applicable to combined sewer overflow (CSO) structures, whose weir constructions correspond with the standard weir layout. The objective of this work is to outline an alternative approach to obtain spill flow discharge data based on measurements with a sonic depth finder. The idea is to determine the relation between water level and rate of spill flow by running a detailed 3D computational fluid dynamics (CFD) model. Two real world CSO structures have been chosen due to their complex structure, especially with respect to the weir construction. In a first step the simulation results were analysed to identify flow conditions for discrete steady states. It will be shown that the flow conditions in the CSO structure change after the spill flow pipe acts as a controlled outflow and therefore the spill flow discharge cannot be described with a standard weir equation. In a second step the CFD results will be used to derive rating curves which can be easily applied in everyday practice. Therefore the rating curves are developed on basis of the standard weir equation and the equation for orifice-type outlets. Because the intersection of both equations is not known, the coefficients of discharge are regressed from CFD simulation results. Furthermore, the regression of the CFD simulation results are compared with the one of the standard weir equation by using historic water levels and hydrographs generated with a hydrodynamic model. The uncertainties resulting of the wide spread use of the standard weir equation are demonstrated.
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.
Winckler, N; Shevelko, V P; Al-Turany, M; Kollegger, T; Stöhlker, Th
2017-01-01
A detailed description of a recently developed BREIT computer code (Balance Rate Equations of Ion Transportation) for calculating charge-state fractions of ion beams passing through matter is presented. The code is based on the analytical solutions of the differential balance equations for the charge-state fractions as a function of the target thickness and can be used for calculating the ion evolutions in gaseous, solid and plasma targets. The BREIT code is available on-line and requires the charge-changing cross sections and initial conditions in the input file. The eigenvalue decomposition method, applied to obtain the analytical solutions of the rate equations, is described in the paper. Calculations of non-equilibrium and equilibrium charge-state fractions, performed by the BREIT code, are compared with experimental data and results of other codes for ion beams in gaseous and solid targets. Ability and limitations of the BREIT code are discussed in detail.
Winckler, N.; Rybalchenko, A.; Shevelko, V. P.; Al-Turany, M.; Kollegger, T.; Stöhlker, Th.
2017-02-01
A detailed description of a recently developed BREIT computer code (Balance Rate Equations of Ion Transportation) for calculating charge-state fractions of ion beams passing through matter is presented. The code is based on the analytical solutions of the differential balance equations for the charge-state fractions as a function of the target thickness and can be used for calculating the ion evolutions in gaseous, solid and plasma targets. The BREIT code is available on-line and requires the charge-changing cross sections and initial conditions in the input file. The eigenvalue decomposition method, applied to obtain the analytical solutions of the rate equations, is described in the paper. Calculations of non-equilibrium and equilibrium charge-state fractions, performed by the BREIT code, are compared with experimental data and results of other codes for ion beams in gaseous and solid targets. Ability and limitations of the BREIT code are discussed in detail.
Liu X
2013-10-01
Full Text Available Xun Liu,1,2,* Huijuan Ma,1,* Hui Huang,3 Cheng Wang,1 Hua Tang,1 Ming Li,1 Yanni Wang,1 Tanqi Lou1 1Division of Nephrology, Department of Internal Medicine, The Third Affiliated Hospital of Sun Yat-sen University, 2College of Biology Engineering, South China University of Technology, 3Department of Cardiology, Sun Yat-sen Memorial Hospital of Sun Yat-sen University, Guangzhou, People's Republic of China*These authors contributed equally to the paperBackground: We aimed to evaluate the performance of the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI creatinine–cystatin C equation in a cohort of elderly Chinese participants.Materials and methods: Glomerular filtration rate (GFR was measured in 431 elderly Chinese participants by the technetium-99m diethylene-triamine-penta-acetic acid (99mTc-DTPA renal dynamic imaging method, and was calibrated equally to the dual plasma sample 99mTc-DTPA-GFR. Performance of the CKD-EPI creatinine–cystatin C equation was compared with the Cockroft–Gault equation, the re-expressed 4-variable Modification of Diet in Renal Disease (MDRD equation, and the CKD-EPI creatinine equation.Results: Although the bias of the CKD-EPI creatinine–cystatin C equation was greater than with the other equations (median difference, 5.7 mL/minute/1.73 m2 versus a range from 0.4–2.5 mL/minute/1.73 m2; P<0.001 for all, the precision was improved with the CKD-EPI creatinine–cystatin C equation (interquartile range for the difference, 19.5 mL/minute/1.73 m2 versus a range from 23.0–23.6 mL/minute/1.73 m2; P<0.001 for all comparisons, leading to slight improvement in accuracy (median absolute difference, 10.5 mL/minute/1.73 m2 versus 12.2 and 11.4 mL/minute/1.73 m2 for the Cockcroft–Gault equation and the re-expressed 4-variable MDRD equation, P=0.04 for both; 11.6 mL/minute/1.73 m2 for the CKD-EPI creatinine equation, P=0.11, as the optimal scores of performance (6.0 versus a range from 1.0–2.0 for the other
Koyama, Kohei; Kikuzawa, Kihachiro; 小山, 耕平
2009-01-01
Allometric scalings and a logistic equation assume that whole-plant photosynthetic rate under resource-unlimited conditions is proportional to leaf area. We tested this proportionality for the herb Helianthus tuberosus. During growth, we repeatedly measured the percentage of leaves with high, medium, and low photosynthetic capacity to estimate the whole-plant sum of photosynthetic capacity. We found that the whole-plant sum of the light-saturated photosynthetic rate of leaves is proportional ...
Koyama, Kohei; Kikuzawa, Kihachiro
2009-05-01
Allometric scalings and a logistic equation assume that whole-plant photosynthetic rate under resource-unlimited conditions is proportional to leaf area. We tested this proportionality for the herb Helianthus tuberosus. During growth, we repeatedly measured the percentage of leaves with high, medium, and low photosynthetic capacity to estimate the whole-plant sum of photosynthetic capacity. We found that the whole-plant sum of the light-saturated photosynthetic rate of leaves is proportional to the whole-plant leaf area, disregarding the dynamics of the leaf population. We also found that the daily photosynthesis of each leaf appeared as a linear function of the light-saturated photosynthetic rate of that leaf, as predicted by the optimization theory. Using those results, we expressed whole-plant photosynthetic rate as a product of the light-saturated whole-plant photosynthetic rate and an efficiency index that reflects resource limitation as in the logistic equation. This efficiency decreased with increasing leaf area, reflecting light limitation. Therefore, realized whole-plant photosynthetic rate is not proportional to leaf area. These "diminishing returns" are well explained by a simple saturating curve, such as the logistic equation.
Selistre, Luciano; Rabilloud, Muriel; Cochat, Pierre; de Souza, Vandréa; Iwaz, Jean; Lemoine, Sandrine; Beyerle, Françoise; Poli-de-Figueiredo, Carlos E; Dubourg, Laurence
2016-03-01
Estimating kidney glomerular filtration rate (GFR) is of utmost importance in many clinical conditions. However, very few studies have evaluated the performance of GFR estimating equations over all ages and degrees of kidney impairment. We evaluated the reliability of two major equations for GFR estimation, the CKD-EPI and Schwartz equations, with urinary clearance of inulin as gold standard. The study included 10,610 participants referred to the Renal and Metabolic Function Exploration Unit of Edouard Herriot Hospital (Lyon, France). GFR was measured by urinary inulin clearance (only first measurement kept for analysis) then estimated with isotope dilution mass spectrometry (IDMS)-traceable CKD-EPI and Schwartz equations. The participants' ages ranged from 3 to 90 y, and the measured GFRs from 3 to 160 ml/min/1.73 m2. A linear mixed-effects model was used to model the bias (mean ratio of estimated GFR to measured GFR). Equation reliability was also assessed using precision (interquartile range [IQR] of the ratio) and accuracy (percentage of estimated GFRs within the 10% [P10] and 30% [P30] limits above and below the measured GFR). In the whole sample, the mean ratio with the CKD-EPI equation was significantly higher than that with the Schwartz equation (1.17 [95% CI 1.16; 1.18] versus 1.08 [95% CI 1.07; 1.09], p Schwartz equation were closer to 1 than the mean ratios with the CKD-EPI equation whatever the age class (1.02 [95% CI 1.01; 1.03] versus 1.15 [95% CI 1.13; 1.16], p Schwartz equation had a better precision and was also more accurate than the CKD-EPI equation at GFR values under 60 ml/min/1.73 m2 (IQR: 0.32 [95% CI 0.28; 0.33] versus 0.40 [95% CI 0.36; 0.44]; P30: 81.4 [95% CI 78.1; 84.7] versus 63.8 [95% CI 59.7; 68.0]) and also at GFR values of 60-89 ml/min/1.73 m2. In all patients aged ≥65 y, the CKD-EPI equation performed better than the Schwartz equation (IQR: 0.33 [95% CI 0.31; 0.34] versus 0.40 [95% CI 0.38; 0.41]; P30: 77.6 [95% CI 75.7; 79
Gaubert, Stéphane
2012-01-01
We give a formula for the Lipschitz constant in Thompson's part metric of any order-preserving flow on the interior of a (possibly infinite dimensional) closed convex pointed cone. This provides an explicit form of a characterization of Nussbaum concerning non order-preserving flows. As an application of this formula, we show that the flow of the generalized Riccati equation arising in stochastic linear quadratic control is a local contraction on the cone of positive definite matrices and characterize its Lipschitz constant by a matrix inequality. We also show that the same flow is no longer a contraction in other natural Finsler metrics on this cone, including the standard invariant Riemannian metric. This is motivated by a series of contraction properties concerning the standard Riccati equation, established by Bougerol, Liverani, Wojtowski, Lawson, Lee and Lim: we show that some of these properties do, and that some other do not, carry over to the generalized Riccati equation.
Gugushvili, S.; Spreij, P.
2016-01-01
We consider the problem of non-parametric estimation of the deterministic dispersion coefficient of a linear stochastic differential equation based on discrete time observations on its solution. We take a Bayesian approach to the problem and under suitable regularity assumptions derive the posteror
1989-12-01
and f,+ respectively from equation (39). 3.1.4 (I-hC) Matriz This section of the program simultaneously loads the C-matrix, mul- tiplies it by the time...and others. Numerical Analysis. Boston : Prindle, Weber and Schmidt, 1981. 14. Kieffer, L.J. "A Compilation of Electron Collision Cross Section Data
Dattner, I.; Klaassen, C.A.J.
2015-01-01
Many processes in biology, chemistry, physics, medicine, and engineering are modeled by a system of differential equations. Such a system is usually characterized via unknown parameters and estimating their ‘true’ value is thus required. In this paper we focus on the quite common systems for which t
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...
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.
Farazdaghi, Hadi
2011-02-01
Photosynthesis is the origin of oxygenic life on the planet, and its models are the core of all models of plant biology, agriculture, environmental quality and global climate change. A theory is presented here, based on single process biochemical reactions of Rubisco, recognizing that: In the light, Rubisco activase helps separate Rubisco from the stored ribulose-1,5-bisphosphate (RuBP), activates Rubisco with carbamylation and addition of Mg²(+), and then produces two products, in two steps: (Step 1) Reaction of Rubisco with RuBP produces a Rubisco-enediol complex, which is the carboxylase-oxygenase enzyme (Enco) and (Step 2) Enco captures CO₂ and/or O₂ and produces intermediate products leading to production and release of 3-phosphoglycerate (PGA) and Rubisco. PGA interactively controls (1) the carboxylation-oxygenation, (2) electron transport, and (3) triosephosphate pathway of the Calvin-Benson cycle that leads to the release of glucose and regeneration of RuBP. Initially, the total enzyme participates in the two steps of the reaction transitionally and its rate follows Michaelis-Menten kinetics. But, for a continuous steady state, Rubisco must be divided into two concurrently active segments for the two steps. This causes a deviation of the steady state from the transitional rate. Kinetic models are developed that integrate the transitional and the steady state reactions. They are tested and successfully validated with verifiable experimental data. The single-process theory is compared to the widely used two-process theory of Farquhar et al. (1980. Planta 149, 78-90), which assumes that the carboxylation rate is either Rubisco-limited at low CO₂ levels such as CO₂ compensation point, or RuBP regeneration-limited at high CO₂. Since the photosynthesis rate cannot increase beyond the two-process theory's Rubisco limit at the CO₂ compensation point, net photosynthesis cannot increase above zero in daylight, and since there is always respiration at
无
2002-01-01
A set of microphysics equations is scaled based on the convective length and velocity scales. Comparisons are made among the dynamical transport and various microphysical processes. From the scaling analysis, it becomes apparent which parameterized microphysical processes present off-scaled influences in the integration of the set of microphysics equations. The variabilities of the parameterized microphysical processes are also studied using the approach of a controlled parameter space. Given macroscopic dynamic and thermodynamic conditions in different regions of convective storms, it is possible to analyze and compare vertical profiles of these processes. Bulk diabatic heating profiles for a cumulus convective updraft and downdraft are also derived from this analysis. From the two different angles, the scale analysis and the controlled-parameter space approach can both provide an insight into and an understanding of microphysics parameterizations.
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.
Smagin, V. V.
1997-04-01
We consider a weakly solvable parabolic problem in a separable Hilbert space. We seek approximations to the exact solution by projective and projective-difference methods. In this connection the discretization of the problem with respect to the spatial variables is carried out by the semidiscrete method of Galerkin, and with respect to time by the implicit method of Euler. In this paper we establish a coercive mean-square error estimate for the approximate solutions. We illustrate the effectiveness of these estimates with parabolic equations of second order with Dirichlet or Neumann boundary conditions in projective subspaces of finite element type.
Manipulating single enzymes by an external harmonic force
Lomholt, Michael A; Urbakh, Michael; Metzler, Ralf
2007-01-01
We study a Michaelis-Menten reaction for a single two-state enzyme molecule, whose transition rates between the two conformations are modulated by an harmonically oscillating external force. In particular, we obtain a range of optimal driving frequencies for changing the conformation of the enzyme......, thereby controlling the enzymatic activity (i.e., product formation). This analysis demonstrates that it is, in principle, possible to obtain information about particular rates within the kinetic scheme....
Yao, Chung-Tay; Lai, Ching-Long; Hsieh, Hsiu-Shan; Chi, Chin-Wen; Yin, Shih-Jiun
2010-09-01
Alcohol dehydrogenase (ADH) catalyzes oxidation of ingested ethanol to acetaldehyde, the first step in hepatic metabolism. The purpose of this study was to establish an ex vivo rat liver perfusion system under defined and verified steady states with respect to the metabolites and the metabolic rates, and to quantitatively correlate the observed rates with simulations based on the kinetic mechanism-based rate equations of rat liver ADH. Class I ADH1 was isolated from male Sprague-Dawley rats and characterized by steady-state kinetics in the Krebs-Ringer perfusion buffer with supplements. Nonrecirculating liver perfusion with constant input of ethanol at near physiological hepatic blood flow rate was performed in situ. Ethanol and the related metabolites acetaldehyde, acetate, lactate, and pyruvate in perfusates were determined. Results of the initial velocity, product, and dead-end inhibition studies showed that rat ADH1 conformed to the Theorell-Chance Ordered Bi Bi mechanism. Steady-state metabolism of ethanol in the perfused liver maintained up to 3h as evidenced by the steady-state levels of ethanol and metabolites in the effluent, and the steady-state ethanol disappearance rates and acetate production rates. The changes of the metabolic rates were qualitatively and in general quantitatively correlated to the results from simulations with the kinetic rate equations of ADH1 under a wide range of ethanol, in the presence of competitive inhibitor 4-methylpyrazole and of uncompetitive inhibitor isobutyramide. Preliminary flux control analysis estimated that apparent C(ADH)(J) in the perfused liver may approximate 0.7 at constant infusion with 1-2 mM ethanol, suggesting that ADH plays a major but not the exclusive role in governing hepatic ethanol metabolism. The reported steady-state rat liver perfusion system may potentially be applicable to other drug or drug-ethanol interaction studies.
Rogers, G; Oosthuyse, T
2000-02-01
The standard equation used to calculate mean arterial pressure (MAP) assumes that diastole persists for 2/3 and systole for 1/3 of each cardiac cycle. This ratio is altered when heart rate increases, and therefore we investigated the efficacy of predicting MAP during exercise using non-invasive indirect methods. Eight subjects exercised on a cycle ergometer for 3 minute intervals to elicit heart rates between 100-110, 120-130, 140-150, 160-170, and 180-190 beats/min. In the last minute of each 3 min interval an ECG recording was taken and systolic (SP) and diastolic (DP) blood pressure was measured by manual auscultation. MAP was calculated for each heart rate interval by: MAP=DP+1/3(SP-DP) (method A), and MAP= DP + Fs(SP- DP) (method B), where Fs is the fraction of the cardiac cycle comprising systole, measured from the ECG. Fs increased from 0.35+/-0.049 at rest to 0.47+/-0.039 at a heart rate of 180-190 beats/min. MAP measured by method B was consistently greater than MAP calculated by method A at all heart rates greater than resting heart rate (pequation (method A) to derive MAP during exercise (measured as the percentage difference between method A and B) increased linearly with heart rate (r=0.98). The standard MAP equation should not be applied during exercise, as it does not account for the change in the systolic: diastolic period ratio as heart rate increases.
Karimzadeh, Iman; Khalili, Hossein
2016-06-06
Serum cystatin C (Cys C) has a number of advantages over serum creatinine in the evaluation of kidney function. Apart from Cys C level itself, several formulas have also been introduced in different clinical settings for the estimation of glomerular filtration rate (GFR) based upon serum Cys C level. The aim of the present study was to compare a serum Cys C-based equation with Cockcroft-Gault serum creatinine-based formula, both used in the calculation of GFR, in patients receiving amphotericin B. Fifty four adult patients with no history of acute or chronic kidney injury having been planned to receive conventional amphotericin B for an anticipated duration of at least 1 week for any indication were recruited. At three time points during amphotericin B treatment, including days 0, 7, and 14, serum cystatin C as well as creatinine levels were measured. GFR at the above time points was estimated by both creatinine (Cockcroft-Gault) and serum Cys C based equations. There was significant correlation between creatinine-based and Cys C-based GFR values at days 0 (R = 0.606, P = 0.001) and 7 (R = 0.714, P creatinine-and a cystatin C-based glomerular filtration rate equation in patients receiving amphotericin B.
Kuster, Nils; Cristol, Jean-Paul; Cavalier, Etienne; Bargnoux, Anne-Sophie; Halimi, Jean-Michel; Froissart, Marc; Piéroni, Laurence; Delanaye, Pierre
2014-01-20
The National Kidney Disease Education Program group demonstrated that MDRD equation is sensitive to creatinine measurement error, particularly at higher glomerular filtration rates. Thus, MDRD-based eGFR above 60 mL/min/1.73 m² should not be reported numerically. However, little is known about the impact of analytical error on CKD-EPI-based estimates. This study aimed at assessing the impact of analytical characteristics (bias and imprecision) of 12 enzymatic and 4 compensated Jaffe previously characterized creatinine assays on MDRD and CKD-EPI eGFR. In a simulation study, the impact of analytical error was assessed on a hospital population of 24084 patients. Ability using each assay to correctly classify patients according to chronic kidney disease (CKD) stages was evaluated. For eGFR between 60 and 90 mL/min/1.73 m², both equations were sensitive to analytical error. Compensated Jaffe assays displayed high bias in this range and led to poorer sensitivity/specificity for classification according to CKD stages than enzymatic assays. As compared to MDRD equation, CKD-EPI equation decreases impact of analytical error in creatinine measurement above 90 mL/min/1.73 m². Compensated Jaffe creatinine assays lead to important errors in eGFR and should be avoided. Accurate enzymatic assays allow estimation of eGFR until 90 mL/min/1.73 m² with MDRD and 120 mL/min/1.73 m² with CKD-EPI equation.
Amrah Javaid
2015-01-01
Full Text Available To compare the measured glomerular filtration rate (rGFR using [99mTc] diethylene triamine pentacetic acid (DTPA clearance or estimated GFR (eGFR by the Modification of Diet in Renal Disease (MDRD equation in cancer patients with raised serum creatinine level, we studied 100 cancer patients; 50 patients with normal serum creatinine (control group and 50 patients with abnormal serum creatinine (study group. History of patients, including site of cancer, chemotherapy regime and dose of chemotherapy, was recorded. The rGFR and eGFR were increased in the study group as compared with the control group, but the GFR recorded by the MDRD formula or DTPA revealed similar values. It is therefore concluded that the MDRD equation may be recommended for eGFR estimation even with abnormal creatinine, without the need for exposure to radiation.
Cabrerizo-García, José Luis; Díez-Manglano, Jesús; García-Arilla, Ernesto; Revillo-Pinilla, Paz; Ramón-Puertas, José; Sebastián-Royo, Mariano
2015-01-06
The Modification of Diet in Renal Disease (MDRD) equation is recommended by most scientific societies to calculate the estimated glomerular filtration rate (GFR). Recently the group Chronic Kidney Disease Epidemiology Collaboration (CKP-EPI) has published a new, more precise and accurate equation. We have analyzed its behavior in a group of polypathological patients (PP) and compared it with the classic MDRD-4.version Multicenter, observational, descriptive and transversal study. We calculated GFR by MDRD-4 and CKD-EPI in 425 PP. Each stage was assigned according to the GFR: 1:>90; 2: 60-89; 3: 30-59; 4: 15-29; and 5 renal insufficiency, especially in older women. Copyright © 2013 Elsevier España, S.L.U. All rights reserved.
Jia-fu Feng
Full Text Available OBJECTIVE: To establish equations for the estimation of glomerular filtration rates (eGFRs based on serum creatinine (SCr and/or serum cystatin C (SCysC in Chinese patients with chronic kidney disease (CKD, and to compare the new equations with both the reference GFR (rGFR and the literature equations to evaluate their applicability. METHODS: The 788 Chinese CKD patients were randomly divided into two groups, the training group and the testing group, to establish new eGFR-formulas based on serum CysC and to validate the established formulas, respectively. (99mTc-DTPA clearance (as the rGFR, serum Cr, and serum CysC were determined for all patients, and GFR was calculated using the Cockcroft-Gault equation (eGFR1, the MDRD formula (eGFR2, the CKD-EPI formulas (eGFR3, eGFR4, and the Chinese eGFR Investigation Collaboration formulas (eGFR5, eGFR6. The accuracy of each eGFR was compared with the rGFR. RESULTS: The training and testing groups' mean GFRs were 50.84±31.36 mL/min/1.73 m(2 and 54.16±29.45 mL/min/1.73 m(2, respectively. The two newly developed eGFR formulas were fitted using iterative computation: [Formula: see text] and [Formula: see text]. Significant correlation was observed between each eGFR and the rGFR. However, proportional errors and constant errors were observed between rGFR and eGFR1, eGFR2, eGFR4, eGFR5 or eGFR6, and constant errors were observed between eGFR3 and rGFR, as revealed by the Passing & Bablok plot analysis. The Bland-Altman analysis illustrated that the 95% limits of agreement of all equations exceeded the previously accepted limits of <60 mL/min •1.73 m(2, except the equations of eGFR7 and eGFR8. CONCLUSION: The newly developed formulas, eGFR7 and eGFR8, provide precise and accurate GFR estimation using serum CysC detection alone or in combination with serum Cr detection. Differences in detection methods should be carefully considered when choosing literature eGFR equations to avoid misdiagnosis and
Sousa Jr R.
2004-01-01
Full Text Available Partial hydrolysis of whey proteins by enzymes immobilized on an inert support can either change or evidence functional properties of the produced peptides, thereby increasing their applications. The hydrolysis of sweet cheese whey proteins by alcalase, which is multipoint-immobilized on agarose gel, is studied here. A Michaelis-Menten model that takes into account competitive inhibition by the product was fitted to experimental data. The influence of pH on the kinetic parameters in the range 6.0 to 11.0 was assessed, at 50ºC. Initial reaction-rate assays in a pHstat at different concentrations of substrate were used to estimate kinetic and Michaelis-Menten parameters, k and K M. Experimental data from long-term batch assays were used to quantify the inhibition parameter, K I. The fitting of the model to the experimental data was accurate in the entire pH range.
Hydrolysis of Toxic Natural Glucosides Catalyzed by Cyclodextrin Dicyanohydrins
Bjerre, Jeannette; Nielsen, Erik Holm; Bols, Mikael
2008-01-01
The hydrolysis of toxic 7-hydroxycoumarin glucosides and other aryl and alkyl glucosides, catalyzed by modified a- and ß-cyclodextrin dicyanohydrins, was investigated using different UV, redox, or HPAEC detection assays. The catalyzed reactions all followed Michaelis-Menten kinetics, and an impre......The hydrolysis of toxic 7-hydroxycoumarin glucosides and other aryl and alkyl glucosides, catalyzed by modified a- and ß-cyclodextrin dicyanohydrins, was investigated using different UV, redox, or HPAEC detection assays. The catalyzed reactions all followed Michaelis-Menten kinetics......, and an impressive rate increase of up to 7569 (kcat/kuncat) was found for the hydroxycoumarin glucoside substrate 4-MUGP. Good and moderate degrees of catalysis (kcat/kuncat) of up to 1259 were found for the natural glucosides phloridzin and skimmin. By using a newly developed catechol detection UV-assay, a weak...
Pratt, D. T.; Radhakrishnan, K.
1986-01-01
The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent.
Calcite Dissolution in Deionized Water from 50℃ to 250℃ at I0 MPa:Rate Equation and Reaction Order
GONG Qingjie; DENG Jun; WANG Qingfei; YANG Liqiang; SHE Min
2008-01-01
Carbonate minerals and water (or geofiuids) reactions are important for modeling of geochemical processes and have received considerable attention over the past decades. The calcite dissolution rates from 50℃ to 250℃ at 10 Mpa in deionized water with a flow rate varying from 0.2 to 5 mL/min were experimentally measured in a continuous flow column pressure vessel reactor. The dissolution began near the equilibrium with clceq > 0.3 and finally reached the equilibrium at 100℃-250℃, so the corresponding solubility was also determined as 1.87, 2.02, 2.02 and 1.88×10-4"mol/L at 100℃, 150℃, 200~C and 2500C respectively, which was first increasing and then switching to decreasing with temperature and the maximum value might occur between 150℃ and 200℃. The experimental dissolution rate not only increased with temperature, but also had a rapid increase between 150℃ and 200℃ at a constant flow rate of 4 mL/min. The measured dissolution rates can be described using rate equations of R = k(1-c/c) or R = kc. In these equations the reaction order n changed with temperature, which indicates that n was a variable rather than a constant, and the activation energy was 13.4 kJ/mol calculated with R = k(1-c/c) or 18.0 kJ/mol with R = kc, which is a little lower than the surface controlled values. The varied reaction order and lower activation energy indicates that calcite dissolution in this study is a complex interplay of diffusion controlled and surface controlled processes.
Estimating glomerular filtration rate equation and medical laboratory%估算肾小球滤过率的建立与医学检验
潘柏申
2014-01-01
Estimating glomerular filtration rate is very useful in the management of chronic kidney disease.The clinical laboratories should understand these eGFR equations.%估算肾小球滤过率在慢性肾脏疾病的诊断治疗中有着重要临床意义。了解这些eGFR公式的发展和临床应用过程，可以得到一些有价值的启示。（中华检验医学杂志，2014，37：401-403）
Optical Density bioscreen measurements of P. aeruginosa to perform a Maximum Likelihood estimation of the model parameters and subsequently obtain a smoothing estimate for the model state variables by means of a nonlinear smoothing algorithm based on the extended Kalman filter, using an implementation....... aeruginosa we observe a growth pattern far from Monod growth. Therefore a reformulation of the growth expression is necessary. Without any pre-knowledge about the functional dependence between the growth rate and the substrate content and with only limited experimental resources necessary, the proposed...... described by Kristensen et. al [2]. The resulting time series allows us graphically to inspect the functional dependence of the growth rate on the substrate content. From the method described above we find three new plausible expressions for μ(S). Therefore we apply the likelihood-ratio test to compare...
Kinetic Modeling of Enzymatic Hydrolysis of Coconut Oil with Lipase%脂肪酶水解椰子油动力学研究
武林贺; 白新鹏; 吴谦; 徐小梦; 马若影; 李雪
2016-01-01
A kinetic study on hydrolysis for the production of derivatives catalyzed by Lipase was investigated. The effects of substrate concentration,enzyme concentration,temperature and time on the hydrolysis rate of co-conut oil by lipase were analyzed. Based on this,the Michaelis constant(km) and maximum rate(Vm) were de-duced by Lineweaver-Burk plotting and Wilkinson statistical method. Results showed that,under the optimal conditions of enzyme concentration 1%and temperature 50℃,the km and Vm were 1.273 9 [mg/(g·mL)] and 0.969 6 [mg/(g·mL·min)] respectively. The Michaelis-Menten equation was:v= 0.969 6[S]1.273 9+[S] . The model-pre-dicted values were consistent with the actually measured values from confirmation tests. Though the simulation of Michaelis-Menten equation to the hydrolysis process,goodness of fit were greater than 0.99,it found that ap-plication of Michaelis-Menten equation in hydrolysis process was reasonable. It can provide research foundation for the fat digestion process.%为了探究脂肪酶水解椰子油的动力学过程，在研究了底物质量浓度、酶添加量、酶解温度及酶解时间对脂肪酶水解椰子油反应速率影响的基础上，本试验采用Lineweaver-Burk法和Wilkinson统计法两种方法对酶解过程进行拟合，计算酶解过程的动力学常数km和Vm，并求解脂肪酶水解椰子油动力学方程。结果表明：在酶添加量为1%、温度为50℃的条件下，动力学常数km为1.2739[mg/（g·mL）]，Vm为0.9696[mg/（g·mL·min）]，米氏方程为：v=0.9696[S]1.2739+[S]。经过试验验证得出米氏方程的拟合度大于0.99，说明方程的预测值与测定值基本吻合，米氏方程适合脂肪酶水解椰子油动力学研究，为油脂酶解过程提供理论模型。
New types of experimental data shape the use of enzyme kinetics for dynamic network modeling.
Tummler, Katja; Lubitz, Timo; Schelker, Max; Klipp, Edda
2014-01-01
Since the publication of Leonor Michaelis and Maude Menten's paper on the reaction kinetics of the enzyme invertase in 1913, molecular biology has evolved tremendously. New measurement techniques allow in vivo characterization of the whole genome, proteome or transcriptome of cells, whereas the classical enzyme essay only allows determination of the two Michaelis-Menten parameters V and K(m). Nevertheless, Michaelis-Menten kinetics are still commonly used, not only in the in vitro context of enzyme characterization but also as a rate law for enzymatic reactions in larger biochemical reaction networks. In this review, we give an overview of the historical development of kinetic rate laws originating from Michaelis-Menten kinetics over the past 100 years. Furthermore, we briefly summarize the experimental techniques used for the characterization of enzymes, and discuss web resources that systematically store kinetic parameters and related information. Finally, describe the novel opportunities that arise from using these data in dynamic mathematical modeling. In this framework, traditional in vitro approaches may be combined with modern genome-scale measurements to foster thorough understanding of the underlying complex mechanisms.
Trapp, Oliver; Bremer, Sabrina; Weber, Sven K
2009-11-01
An extension of the unified equation of chromatography to directly access reaction rate constants k(1) of first-order reaction in on-column chromatography is presented. This extended equation reflects different response factors in the detection of the reaction educt and product which arise from structural changes by elimination or addition, e.g., under pseudo-first-order reaction conditions. The reaction rate constants k(1) and Gibbs activation energies DeltaG(double dagger) of first-order reactions taking place in a chromatographic system can be directly calculated from the chromatographic parameters, i.e., retention times of the educt E and product P (t(R)(A) and t(R)(B)), peak widths at half height (w(A) and w(B)), the relative plateau height (h(p)) of the conversion profile, and the individual response factors f(A) and f(B). The evaluation of on-column reaction gas chromatographic experiments is exemplified by the evaluation of elution profiles obtained by ring-closing metathesis reaction of N,N-diallytrifluoroacetamide in presence of Grubbs second-generation catalyst, dissolved in polydimethylsiloxane (GE SE 30).
Phenomenological analysis of ATP dependence of motor proteins.
Yunxin Zhang
Full Text Available In this study, through phenomenological comparison of the velocity-force data of processive motor proteins, including conventional kinesin, cytoplasmic dynein and myosin V, I found that, the ratio between motor velocities of two different ATP concentrations is almost invariant for any substall, superstall or negative external loads. Therefore, the velocity of motors can be well approximated by a Michaelis-Menten like formula V = [ATP]k(FL([ATP] + K(M, with L the step size, and k(F the external load F dependent rate of one mechanochemical cycle of motor motion in saturated ATP solution. The difference of Michaelis-Menten constant K(M for substall, superstall and negative external load indicates, the configurations at which ATP molecule can bind to motor heads for these three cases might be different, though the expression of k(F as a function of F might be unchanged for any external load F. Verifications of this Michaelis-Menten like formula has also been done by fitting to the recent experimental data.
Phenomenological analysis of ATP dependence of motor protein
Zhang, Yunxin
2011-01-01
In this study, through phenomenological comparison of the velocity-force data of processive motor proteins, including conventional kinesin, cytoplasmic dynein and myosin V, we found that, the ratio between motor velocities of two different ATP concentrations is almost invariant for any substall, superstall or negative external loads. Therefore, the velocity of motor can be well approximated by a Michaelis-Menten like formula $V=\\atp k(F)L/(\\atp +K_M)$, with $L$ the step size, and $k(F)$ the external load $F$ dependent rate of one mechanochemical cycle of motor motion in saturated ATP solution. The difference of Michaelis-Menten constant $K_M$ for substall, superstall and negative external load indicates, the ATP molecule affinity of motor head for these three cases are different, though the expression of $k(F)$ as a function of $F$ might be unchanged for any external load $F$. Verifications of this Michaelis-Menten like formula has also been done by fitting to the recent experimental data.
Fischer, H Felix; Tritt, Karin; Klapp, Burghard F; Fliege, Herbert
2011-12-01
A wide range of questionnaires for measuring depression are available. Item Response Theory models can help to evaluate the questionnaires exceeding the boundaries of Classical Test Theory and provide an opportunity to equate the questionnaires. In this study after checking for unidimensionality, a General Partial Credit Model was applied to data from two different depression scales [Patient Health Questionnaire (PHQ-9) and ICD-10-Symptom Rating (ISR)] obtained in clinical settings from a consecutive sample, including 4517 observations from a total of 2999 inpatients and outpatients of a psychosomatic clinic. The precision of each questionnaire was compared and the model was used to transform scores based on the assumed underlying latent trait. Both instruments were constructed to measure the same construct and their estimates of depression severity are highly correlated. Our analysis showed that the predicted scores provided by the conversion tables are similar to the observed scores in a validation sample. The PHQ-9 and ISR depression scales measure depression severity across a broad range with similar precision. While the PHQ-9 shows advantages in measuring low or high depression severity, the ISR is more parsimonious and also suitable for clinical purposes. Furthermore, the equation tables derived in this study enhance the comparability of studies using either one of the instruments, but due to substantial statistical spread the comparison of individual scores is imprecise.
Simulation of Enzyme Catalysis in Calcium Alginate Beads
Ameel M. R. Al-Mayah
2012-01-01
Full Text Available A general mathematical model for a fixed bed immobilized enzyme reactor was developed to simulate the process of diffusion and reaction inside the biocatalyst particle. The modeling and simulation of starch hydrolysis using immobilized α-amylase were used as a model for this study. Corn starch hydrolysis was carried out at a constant pH of 5.5 and temperature of . The substrate flow rate was ranging from 0.2 to 5.0 mL/min, substrate initial concentrations 1 to 100 g/L. α-amylase was immobilized on to calcium alginate hydrogel beads of 2 mm average diameter. In this work Michaelis-Menten kinetics have been considered. The effect of substrate flow rate (i.e., residence time and initial concentration on intraparticle diffusion have been taken into consideration. The performance of the system is found to be affected by the substrate flow rate and initial concentrations. The reaction is controlled by the reaction rate. The model equation was a nonlinear second order differential equation simulated based on the experimental data for steady state condition. The simulation was achieved numerically using FINITE ELEMENTS in MATLAB software package. The simulated results give satisfactory results for substrate and product concentration profiles within the biocatalyst bead.
Fu, Houqiang; Lu, Zhijian; Zhao, Yuji [School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287 (United States)
2016-06-15
We study the low efficiency droop characteristics of semipolar InGaN light-emitting diodes (LEDs) using modified rate equation incoporating the phase-space filling (PSF) effect where the results on c-plane LEDs are also obtained and compared. Internal quantum efficiency (IQE) of LEDs was simulated using a modified ABC model with different PSF filling (n{sub 0}), Shockley-Read-Hall (A), radiative (B), Auger (C) coefficients and different active layer thickness (d), where the PSF effect showed a strong impact on the simulated LED efficiency results. A weaker PSF effect was found for low-droop semipolar LEDs possibly due to small quantum confined Stark effect, short carrier lifetime, and small average carrier density. A very good agreement between experimental data and the theoretical modeling was obtained for low-droop semipolar LEDs with weak PSF effect. These results suggest the low droop performance may be explained by different mechanisms for semipolar LEDs.
Rolland, J; Simonnet, E
2015-01-01
In this paper we compute and analyse the transition rates and duration of reactive trajectories of the stochastic 1-D Allen-Cahn equations for both the Freidlin-Wentzell regime (weak noise or temperature limit) and finite-amplitude white noise, as well as for small and large domain. We demonstrate that extremely rare reactive trajectories corresponding to direct transitions between two metastable states are efficiently computed using an algorithm called adaptive multilevel splitting. This algorithm is dedicated to the computation of rare events and is able to provide ensembles of reactive trajectories in a very efficient way. In the small noise limit, our numerical results are in agreement with large-deviation predictions such as instanton-like solutions, mean first passages and escape probabilities. We show that the duration of reactive trajectories follows a Gumbel distribution like for one degree of freedom systems. Moreover, the mean duration growths logarithmically with the inverse temperature. The prefa...
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
Jin, Jian; Ma, Haile; Qu, Wenjuan; Wang, Kai; Zhou, Cunshan; He, Ronghai; Luo, Lin; Owusu, John
2015-11-01
The effects of multi-frequency power ultrasound (MPU) pretreatment on the kinetics and thermodynamics of corn gluten meal (CGM) were investigated in this research. The apparent constant (KM), apparent break-down rate constant (kA), reaction rate constants (k), energy of activation (Ea), enthalpy of activation (ΔH), entropy of activation (ΔS) and Gibbs free energy of activation (ΔG) were determined by means of the Michaelis-Menten equation, first-order kinetics model, Arrhenius equation and transition state theory, respectively. The results showed that MPU pretreatment can accelerate the enzymolysis of CGM under different enzymolysis conditions, viz. substrate concentration, enzyme concentration, pH, and temperature. Kinetics analysis revealed that MPU pretreatment decreased the KM value by 26.1% and increased the kA value by 7.3%, indicating ultrasound pretreatment increased the affinity between enzyme and substrate. In addition, the values of k for ultrasound pretreatment were increased by 84.8%, 41.9%, 28.9%, and 18.8% at the temperature of 293, 303, 313 and 323 K, respectively. For the thermodynamic parameters, ultrasound decreased Ea, ΔH and ΔS by 23.0%, 24.3% and 25.3%, respectively, but ultrasound had little change in ΔG value in the temperature range of 293-323 K. In conclusion, MPU pretreatment could remarkably enhance the enzymolysis of CGM, and this method can be applied to protein proteolysis industry to produce peptides.
Fan, Niannian; Zhong, Deyu; Wu, Baosheng; Foufoula-Georgiou, Efi; Guala, Michele
2014-03-01
Bed load transport is a highly complex process. The probability density function (PDF) of particle velocities results from the local particle momentum variability in response to fluid drag and interactions with the bed. Starting from the forces exerted on a single particle under low transport rates (i.e., rolling and sliding regimes), we derive here the nonlinear stochastic Langevin equation (LE) to describe the dynamics of a single particle, accounting for both the deterministic and the stochastic components of such forces. Then, the Fokker-Planck equation (FPE), which describes the evolution of the PDF of the ensemble particle velocities, is derived from the LE. We show that the theoretical PDFs of both streamwise and cross-stream velocities obtained by solving the FPE under equilibrium conditions have exponential form (PDFs of both positive and negative velocities decay exponentially), consistent with the experimental data by Roseberry et al. Moreover, we theoretically show how the exponential-like PDF of an ensemble of particle velocities results from the forces exerted on a single particle. We also show that the simulated particle motions using the proposed Langevin model exhibit an emergent nonlinear relationship between hop distances and travel times (power law with exponent 5/3), in agreement with the experimental data, providing a statistical description of the particles' random motion in the context of a stochastic transport process. Finally, our study emphasizes that the motion of individual particles, described by the LE, and the behavior of the ensemble, described by the FPE, are connected within a statistical mechanics framework.
Near-Critical Phenomena in Intracellular Metabolite Pools
Elf, Johan; Paulsson, Johan; Berg, Otto G.; Ehrenberg, Måns
2003-01-01
The supply and consumption of metabolites in living cells are catalyzed by enzymes. Here we consider two of the simplest schemes where one substrate is eliminated through Michaelis-Menten kinetics, and where two types of substrates are joined together by an enzyme. It is demonstrated how steady-state substrate concentrations can change ultrasensitively in response to changes in their supply rates and how this is coupled to slow relaxation back to steady state after a perturbation. In the one-substrate system, such near-critical behavior occurs when the supply rate approaches the maximal elimination rate, and in the two-substrate system it occurs when the rates of substrate supply are almost balanced. As systems that operate near criticality tend to display large random fluctuations, we also carried out a stochastic analysis using analytical approximations of master equations and compared the results with molecular-level Monte Carlo simulations. It was found that the significance of random fluctuations was directly coupled to the steady-state sensitivity and that the two substrates can fluctuate greatly because they are anticorrelated in such a way that the product formation rate displays only small variation. Basic relations are highlighted and biological implications are discussed. PMID:12524272
Maximum hydrogen production from genetically modified microalgae biomass
Vargas, Jose; Kava, Vanessa; Ordonez, Juan
A transient mathematical model for managing microalgae derived H2 production as a source of renewable energy is developed for a well stirred photobioreactor, PBR. The model allows for the determination of microalgae and H2 mass fractions produced by the PBR in time. A Michaelis-Menten expression is proposed for modeling the rate of H2 production, which introduces an expression to calculate the resulting effect on H2 production rate after genetically modifying the microalgae. The indirect biophotolysis process was used. Therefore, an opportunity was found to optimize the aerobic to anaerobic stages time ratio of the cycle for maximum H2 production rate, i.e., the process rhythm. A system thermodynamic optimization is conducted with the model equations to find accurately the optimal system operating rhythm for maximum H2 production rate, and how wild and genetically modified species compare to each other. The maxima found are sharp, showing up to a ~60% variation in hydrogen production rate within 2 days around the optimal rhythm, which highlights the importance of system operation in such condition. Therefore, the model is expected to be useful for design, control and optimization of H2 production. Brazilian National Council of Scientific and Technological Development, CNPq (project 482336/2012-9).
Seagrass productivity: the effect of light on carbon uptake
Williams, S.L.; McRoy, C.P.
1982-08-01
Productivity, as estimated by /sup 14/C uptake, was determined as a function of irradiance for six North American seagrasses (Thalassia testudinum Banks ex. Koenig, Syringodium filiforme Kuetz, Halodule wrightii Aschers., Halophila engelmanni Aschers., Phyllospadix scouleri Hook and Ruppia maritima L.s.l.) from temperature, subtropical and tropical environments. Light versus productivity curves were typical of those of aquatic plants. Seagrasses achieved high rates of uptake (up to 17.31 mg C (g dry)-1 h-1) and exhibited high saturation irradiances (greater than or equal to 40% surface irradiance). Within each environment half-saturation and saturation irradiances were similar, indicating no competition for light in the production systems of the various species. Between environments maximum productivity and saturation irradiances changed as a function of the differing irradiance. When rates were normalized for ambient irradiance, there were no differences in maximum rates, except for plants from Texas. In the subtropics and tropics where several species co-exist in the same seagrass bed, two types of responses occurred, corresponding to climax versus colonizer species. The difference in the responses appeared in the initial and maximum rates and in sensitivity to high irradiance. Productivity of seagrasses can be estimated, with certain limitations, from light measurements using the equations of Michaelis-Menten and Steele. (Refs. 35).
Davis, Rebecca Anne
2008-03-01
The increase in waste disposal and energy costs has provided an incentive to convert carbohydrate-rich food waste streams into fuel. For example, dining halls and restaurants discard foods that require tipping fees for removal. An effective use of food waste may be the enzymatic hydrolysis of the waste to simple sugars and fermentation of the sugars to ethanol. As these wastes have complex compositions which may change day-to-day, experiments were carried out to test fermentability of two different types of food waste at 27 degrees C using Saccharomyces cerevisiae yeast (ATCC4124) and Genencor's STARGEN enzyme in batch simultaneous saccharification and fermentation (SSF) experiments. A mathematical model of SSF based on experimentally matched rate equations for enzyme hydrolysis and yeast fermentation was developed in Matlab Simulink. Using Simulink parameter estimation 1.1.3, parameters for hydrolysis and fermentation were estimated through modified Michaelis-Menten and Monod-type equations with the aim of predicting changes in the levels of ethanol and glycerol from different initial concentrations of glucose, fructose, maltose, and starch. The model predictions and experimental observations agree reasonably well for the two food waste streams and a third validation dataset. The approach of using Simulink as a dynamic visual model for SSF represents a simple method which can be applied to a variety of biological pathways and may be very useful for systems approaches in metabolic engineering in the future.
Davis, Rebecca Anne
The increase in waste disposal and energy costs has provided an incentive to convert carbohydrate-rich food waste streams into fuel. For example, dining halls and restaurants discard foods that require tipping fees for removal. An effective use of food waste may be the enzymatic hydrolysis of the waste to simple sugars and fermentation of the sugars to ethanol. As these wastes have complex compositions which may change day-to-day, experiments were carried out to test fermentability of two different types of food waste at 27° C using Saccharomyces cerevisiae yeast (ATCC4124) and Genencor's STARGEN™ enzyme in batch simultaneous saccharification and fermentation (SSF) experiments. A mathematical model of SSF based on experimentally matched rate equations for enzyme hydrolysis and yeast fermentation was developed in Matlab Simulink®. Using Simulink® parameter estimation 1.1.3, parameters for hydrolysis and fermentation were estimated through modified Michaelis-Menten and Monod-type equations with the aim of predicting changes in the levels of ethanol and glycerol from different initial concentrations of glucose, fructose, maltose, and starch. The model predictions and experimental observations agree reasonably well for the two food waste streams and a third validation dataset. The approach of using Simulink® as a dynamic visual model for SSF represents a simple method which can be applied to a variety of biological pathways and may be very useful for systems approaches in metabolic engineering in the future.
Quantifying the relative contributions of different solute carriers to aggregate substrate transport
Taslimifar, Mehdi; Oparija, Lalita; Verrey, Francois; Kurtcuoglu, Vartan; Olgac, Ufuk; Makrides, Victoria
2017-01-01
Determining the contributions of different transporter species to overall cellular transport is fundamental for understanding the physiological regulation of solutes. We calculated the relative activities of Solute Carrier (SLC) transporters using the Michaelis-Menten equation and global fitting to estimate the normalized maximum transport rate for each transporter (Vmax). Data input were the normalized measured uptake of the essential neutral amino acid (AA) L-leucine (Leu) from concentration-dependence assays performed using Xenopus laevis oocytes. Our methodology was verified by calculating Leu and L-phenylalanine (Phe) data in the presence of competitive substrates and/or inhibitors. Among 9 potentially expressed endogenous X. laevis oocyte Leu transporter species, activities of only the uniporters SLC43A2/LAT4 (and/or SLC43A1/LAT3) and the sodium symporter SLC6A19/B0AT1 were required to account for total uptake. Furthermore, Leu and Phe uptake by heterologously expressed human SLC6A14/ATB0,+ and SLC43A2/LAT4 was accurately calculated. This versatile systems biology approach is useful for analyses where the kinetics of each active protein species can be represented by the Hill equation. Furthermore, its applicable even in the absence of protein expression data. It could potentially be applied, for example, to quantify drug transporter activities in target cells to improve specificity. PMID:28091567
Korla, Kalyani; Vadlakonda, Lakshmipathi; Mitra, Chanchal K
2015-01-01
In the present work, we have kinetically simulated two mitochondrial shuttles, malate-aspartate shuttle (used for transferring reducing equivalents) and citrate-pyruvate shuttle (used for transferring carbon skeletons). However, the functions of these shuttles are not limited to the points mentioned above, and they can be used in different arrangements to meet different cellular requirements. Both the shuttles are intricately associated with Krebs cycle through the metabolites involved. The study of this system of shuttles and Krebs cycle explores the response of the system in different metabolic environments. Here, we have simulated these subsets individually and then combined them to study the interactions among them and to bring out the dynamics of these pathways in focus. Four antiports and a pyruvate pump were modelled along with the metabolic reactions on both sides of the inner mitochondrial membrane. Michaelis-Menten approach was extended for deriving rate equations of every component of the system. Kinetic simulation was carried out using ordinary differential equation solver in GNU Octave. It was observed that all the components attained steady state, sooner or later, depending on the system conditions. Progress curves and phase plots were plotted to understand the steady state behaviour of the metabolites involved. A comparative analysis between experimental and simulated data show fair agreement thus validating the usefulness and applicability of the model.
Goharrizi, A. Zandi; Alahyarizadeh, Gh.
2016-08-01
The use of semiconductor lasers is beneficial in long-distance communications. Practical communication systems based on these lasers need high ambient temperature, with temperature changes between 40∘C and 85∘C. The study of the temperature-dependent response of these lasers is important to improve them. This study investigates the effect of temperature on InGaN-based vertical cavity surface emitting lasers (VCSEL). The active region in this structure includes a single quantum well (SQW). The rate equations of carriers and densities are numerically solved. The time variations of carrier density, photon density and output power (N, S and P) at 25∘C and the current injection of 0.04 A are obtained. Values obtained for threshold current and output power include 7 mA and 44 mW, respectively. The effect of temperature on the time variations of N, S and P from 10∘C to 35∘C is studied. Results show that these parameters decrease and the threshold current increases with an increase in temperature. Furthermore, the investigation of the effect of injection current on N, S and P shows that raising the injection current can increase these parameters. Moreover, an increase in the injection current reduces the time response.
Measurement of mouse liver glutathione S-transferase activity by the integrated method
廖飞; 李甲初; 康格非; 曾昭淳; 左渝萍
2003-01-01
Objective: The integrated method was investigated to measure Vm/Km of mouse liver glutathione S-transferase (GST) activity on GSH and 7-Cl-4-nitrobenzofurazozan. Methods: Presetting concentration of one substrate twenty-fold above the others and taking maximum product absorbance Am as parameter while Km as constant, Vm/Km was obtained by nonlinear fitting of GST reaction curve to the integrated Michaelis-Menten equation ln [Am/(Am-Ai)]+Ai/(ε×Km)=(Vm/Km)×ti (1). Results: Vm/Km for GST showed slight dependence on initial substrate concentration and data range, but it was resistant to background absorbance, error in reaction origin and small deviation in presetting Km. Vm/Km was proportional to the amount of GST with upper limit higher than that by initial rate. There was close correlation between Vm/Km and initial rate of the same GST. Consistent results were obtained by this integrated method and classical initial rate method for the measurement of mouse liver GST. Conclusion: With the concentration of one substrate twenty-fold above the others, this integrated method was reliable to measure the activity of enzyme on two substrates, and substrate concentration of the lower one close to its apparent Km was able to be used.
Rolland, Joran; Bouchet, Freddy; Simonnet, Eric
2016-01-01
In this article we compute and analyse the transition rates and duration of reactive trajectories of the stochastic 1-D Allen-Cahn equations for both the Freidlin-Wentzell regime (weak noise or temperature limit) and finite-amplitude white noise, as well as for small and large domain. We demonstrate that extremely rare reactive trajectories corresponding to direct transitions between two metastable states are efficiently computed using an algorithm called adaptive multilevel splitting. This algorithm is dedicated to the computation of rare events and is able to provide ensembles of reactive trajectories in a very efficient way. In the small noise limit, our numerical results are in agreement with large-deviation predictions such as instanton-like solutions, mean first passages and escape probabilities. We show that the duration of reactive trajectories follows a Gumbel distribution like for one degree of freedom systems. Moreover, the mean duration growths logarithmically with the inverse temperature. The prefactor given by the potential curvature grows exponentially with size. The main novelty of our work is that we also perform an analysis of reactive trajectories for large noises and large domains. In this case, we show that the position of the reactive front is essentially a random walk. This time, the mean duration grows linearly with the inverse temperature and quadratically with the size. Using a phenomenological description of the system, we are able to calculate the transition rate, although the dynamics is described by neither Freidlin-Wentzell or Eyring-Kramers type of results. Numerical results confirm our analysis.
CKD-EPI方程估算肾小球滤过率的评价%Assessment of CKD-EPI equation for estimating glomerular filtration rate
王宏斌; 夏先考; 吴建华
2011-01-01
Objective To compare the applicability of CKD-EPI equation with MDRD equation in predicting glomerular filtration rate(GFR)in patients with chronic kidney disease(CKD) and healthy controls, and the relative risk factor of the decrease of GFR was analyzed by CKD-EPI equation. Methods GFR of 91 cases of hospitalized patients with CKD and 198 cases of healthy controls were estimated by CKD-FPI and MDRD equation respectively[denoted as GFR( CKD-EPI) and GFR( MDRD) ]. Correlation and consistency between GFR (CKD-FPI) and GFR ( MDRD) were analyzed by Person correlation analysis and Bland-Altman analytic process. CKD stage of subj ects was assessed according to GFR( MDRD) . Scr, GFR( MDRD) and GFR(CKDEPI) of each stage were compared. Correlation between GFR(CKD-FPI) and other items were also analyzed. Results There was no significant difference of age,Scr,GFR(MDRD)and GFR(CKDEPI) between male an female group(P＜O. 05). There was fine correlation between GFR ( MDRD) and GFR( CKD-FPI) [GFR( MDRD) = 0. 944×GFR( CKD-FPI) +0. 612 , r2 = 0. 960 ( P＜O. 001) ]. BlandAltman analytic process indicated that there was fine consistency between GFR( MDRD) and GFR(CKD-EPI). All subjects were classified into 5 CKD stages according to GFR(MDRD). Compared with GFR( MDRD) ,.mean of GFR(CKD-EPI) in CKD Ⅰ、 Ⅱ、Ⅲ stage increased 0. 15,7. 34 and l. 60 mL. min-1 . (1. 73 m2 )-1 respectively, mean of GFR(CKD-FPI) in CKD Ⅳ、Ⅴ stage decreased 0. 25 and 0. 41 mL. min-1 ( 1. 73 m2) -1 respectively. GFR ( CKD-EPI) was negatively correlative to age , systolic blood pressure ( SBP) , diastolic blood pressure( DBP) ,serum creatinine( Scr) , serum uric acid( SUA) , fasting blood glucose( FBG) , urine protein( UP) and urine protein-to-creatinine ratio( UP/Ucr) , was positively correlative to total cholesterol( TC) and urine uric acid ( P＜O. 05) , but was not correlative to gender and triglyceride(P＞O. 05). Conclusion The application of CKD-FPI equation to estimate GFR could reduce
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.
Physiological Response of Plants Grown on Porous Ceramic Tubes
Tsao, David; Okos, Martin
1997-01-01
This research involves the manipulation of the root-zone water potential for the purposes of discriminating the rate limiting step in the inorganic nutrient uptake mechanism utilized by higher plants. This reaction sequence includes the pathways controlled by the root-zone conditions such as water tension and gradient concentrations. Furthermore, plant based control mechanisms dictated by various protein productions are differentiated as well. For the nutrients limited by the environmental availability, the kinetics were modeled using convection and diffusion equations. Alternatively, for the nutrients dependent upon enzyme manipulations, the uptakes are modeled using Michaelis-Menten kinetics. In order to differentiate between these various mechanistic steps, an experimental apparatus known as the Porous Ceramic Tube - Nutrient Delivery System (PCT-NDS) was used. Manipulation of the applied suction pressure circulating a nutrient solution through this system imposes a change in the matric component of the water potential. This compensates for the different osmotic components of water potential dictated by nutrient concentration. By maintaining this control over the root-zone conditions, the rate limiting steps in the uptake of the essential nutrients into tomato plants (Lycopersicon esculentum cv. Cherry Elite) were differentiated. Results showed that the uptake of some nutrients were mass transfer limited while others were limited by the enzyme kinetics. Each of these were adequately modeled with calculations and discussions of the parameter estimations provided.
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
Heim, Lale; Schaal, Susanne
2014-01-01
As a consequence of the 1994 Rwandan genocide, prevalences of mental disorders are elevated in Rwanda. More knowledge about determinants of mental stress can help to improve mental health services and treatment in the east-central African country. The present study aimed to investigate actual rates of mental stress (posttraumatic stress disorder, syndromal depression and syndromal anxiety) in Rwanda and to examine if gender, persecution during the genocide, readiness to reconcile as well as importance given to religiosity and quality of religiosity are predictors of mental stress. The study comprised a community sample of N = 200 Rwandans from Rwanda's capital Kigali, who experienced the Rwandan genocide. By conducting structured interviews, ten local Master level psychologists examined types of potentially lifetime traumatic events, symptoms of posttraumatic stress disorder (PTSD), depression and anxiety, readiness to reconcile and religiosity. Applying non-recursive structural equation modeling (SEM), the associations between gender, persecution, readiness to reconcile, religiosity and mental stress were investigated. Respondents had experienced an average number of 11.38 types of potentially lifetime traumatic events. Of the total sample, 11% met diagnostic criteria for PTSD, 19% presented with syndromal depression and 23% with syndromal anxiety. Female sex, persecution and readiness to reconcile were significant predictors of mental stress. Twofold association was found between centrality of religion (which captures the importance given to religiosity) and mental stress, showing, that higher mental stress provokes a higher centrality and that higher centrality reduces mental stress. The variables positive and negative religious functioning (which determine the quality of religiosity) respectively had an indirect negative and positive effect on mental stress. Study results provide evidence that rates of mental stress are still elevated in Rwanda and that
汪秀英; 黄蕾蕾; 宋慧; 丁伟洁; 陈茂杰; 卓朗
2011-01-01
Objective To investigate the features of each glomerular filtration rate (GFR) equation in calculating the estimated glomerular filtration rate (eGFR) among mass samples, and to provide guidance to the appropriate equation selections of in the estimation of eGFR. Methods The mass samples were based on the physical examination data in recent years in Xuzhou. Simplified MDRD equation, modified MDRD equation, racial coefficient equation and Ruijin equation were designated to compare differences in statistic indexes and evaluate each equation via dynamic diagrammatic trends. Results Of the four equations, the means of eGFR by simplified MDRD equation were approximate to those by modified MDRD equation, with those by Ruijin equation at the nadir and those by racial coefficient equation at the peak.The standardized rate of reduced renal function was 0.53％, 0.45％, 0.62％ and 0. 17％, respectively. The standardized rate of chronic kidney disease (CKD) was 11.71％, 11.66％, 11.81％ and 11.46％, respectively. Conclusion The CKD in population study consists in hematuria and proteinuria, with little bias between different equations. Simplified MDRD equation or modified MDRD equation is still preferable in the study of the prevalence of CKD until new biochemical indicator is adopted to substitute serum creatinine so as to facilitate horizontal and vertical comparisons among relevant studies.%目的 通过使用不同的肾小球滤过率(GFR)公式估计人群的估计GFR(eGFR),了解不同公式的特征,指导正确选用公式有效估计eGFR.方法 本研究使用徐州地区近年来健康体检者的资料,比较简化MDRD公式、国内改良MDRD公式、种族系数公式和瑞金方程,比较各种统计指标之间的差异,通过图表的动态变化来判断各公式的价值.结果 简化MDRD公式的eGFR值与国内改良MDRD公式接近,瑞金方程最低,种族系数公式最高.肾功能下降标化患病率依次为0.53%、0.45%、0.62%、0.17%,慢
Kinetics of the intestinal uptake of zinc acexamate in normal and zinc-depleted rats.
Torres-Molina, F; Martínez-Coscollá, A; Gisbert, S; Quintana, E; Sendrós, S; Peris-Ribera, J E; Plá-Delfina, J M
1990-10-01
The uptake of zinc as acexamic acid salt in the small intestine of the anaesthetized rat was shown to be a two-phase process in normal animals. The first phase is rapid mucosal binding which satisfies the Freundlich isotherm equation and which involves about 30 per cent of the initially perfused zinc. The second phase was characterized as an apparent absorption step which obeys Michaelis-Menten and first-order combined kinetics, with the following parameters: Vm = 6.51 mg h-1; Km = 2.96 mg; ka = 0.306 h-1. In largely non-saturated conditions, an apparent global rate constant of about 2.50 h-1 was calculated. No significant interference due to endogenous zinc excretion into the small intestine was observed during the absorption period. In zinc-deficient animals, the two phases were not so well characterized. Binding was non-linear and apparent absorption efficiency was much greater at high zinc concentrations, so no evidence of saturable kinetics was found, thus confirming the hypothesis of a homeostatic zinc regulation mechanism.
Savic, Sasa; Vojinovic, Katarina; Milenkovic, Sanja; Smelcerovic, Andrija; Lamshoeft, Marc; Petronijevic, Zivomir
2013-12-15
Flavonoid oxidation is important issue in food processing and quality. The kinetic mechanism of enzymatic oxidation of rutin by horseradish peroxidase (HRP) was studied. Rutin oxidation reaction was followed by recording of spectral changes over the time at 360 nm. The studied oxidation is mostly enzymatic and less part non-enzymatic. The reaction with HRP has a higher rate compared with the reaction without of HRP, whereby is part of non-enzymatic reaction about 10% of the total reaction. Kinetic parameters were determined from graphics of linear Michaelis-Menten equation, and it was found that investigated reactions of rutin oxidation by HRP take place in a ping-pong kinetic mechanism. High resolution HPLC-MS analysis of the mixture of oxidized products of rutin revealed the presence of rutin dimer. Because of widely distribution of rutin as well as presence of peroxidases and hydrogen peroxide in fresh foods identification of this enzymatic modification product can be beneficial for foods quality and safety.
Zoe Rogers
2016-09-01
Full Text Available N-acetyltransferase 2 (NAT2 catalyzes the acetylation of isoniazid to N-acetylisoniazid. NAT2 polymorphism explains 88% of isoniazid clearance variability in adults. We examined the effects of clinical and genetic factors on Michaelis-Menten reaction kinetic constants of maximum velocity (Vmax and affinity (Km in children 0–10 years old. We measured the rates of isoniazid elimination and N-acetylisoniazid production in the blood of 30 children. Since maturation effects could be non-linear, we utilized a pharmacometric approach and the artificial intelligence method, multivariate adaptive regression splines (MARS, to identify factors predicting NAT2 Vmax and Km by examining clinical, genetic, and laboratory factors in toto. Isoniazid concentration predicted both Vmax and Km and superseded the contribution of NAT2 genotype. Age non-linearly modified the NAT2 genotype contribution until maturation at ≥5.3 years. Thus, enzyme efficiency was constrained by substrate concentration, genes, and age. Since MARS output is in the form of basis functions and equations, it allows multiscale systems modeling from the level of cellular chemical reactions to whole body physiological parameters, by automatic selection of significant predictors by the algorithm.
The interplay of intrinsic and extrinsic bounded noises in biomolecular networks.
Giulio Caravagna
Full Text Available After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a biomolecular network. The influence of intrinsic and extrinsic noises on biomolecular networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: (i the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, (ii a model of enzymatic futile cycle and (iii a genetic toggle switch. In (ii and (iii we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possible functional role of bounded noises.
Vitamin D-regulated calcium transport in Caco-2 cells: unique in vitro model.
Giuliano, A R; Wood, R J
1991-02-01
The human colon adenocarcinoma cell line Caco-2 is the only intestinal cell line to differentiate spontaneously in culture exhibiting structural and biochemical characteristics of mature enterocytes and to possess a vitamin D receptor in the fully differentiated state. Transepithelial calcium transport was characterized in differentiated Caco-2 cells grown on permeable filters supports to assess the potential utility of this cell line as an in vitro model to study 1,25-dihydroxyvitamin D3 [1,25(OH)2D3]-induced calcium transport. Calcium transport was increased in a dose-dependent manner by 1,25(OH)2D3. Total calcium transport at different calcium concentrations could be fitted to a modified Michaelis-Menten equation containing a linear transport component. The maximum rate of saturable calcium transport was increased by 4.3-fold (P less than 0.005) in cells treated with 10(-8) M 1,25(OH)2D3. This treatment also increased the apparent buffer calcium concentration that results in half-maximal velocity from 0.4 to 1.3 mM but had no significant effect on nonsaturable calcium transport. Caco-2 cells grown on permeable filter supports provide a unique in vitro human cell culture model to study the mechanism of vitamin D-regulated transepithelial intestinal calcium transport.
Gao, Lijuan; Sun, Jing; Guan, Kai; Shen, Tingting; Wang, Xikui
2017-05-01
Diatomite modified sodium alginate (Si/SA) immobilized Delftia sp. A2(2011) (STT01) was applied to degrade amoxicillin. The immobilized pellets provided a direct and visual probe for the degradation process due to their intrinsic bright colour. The results demonstrated that 100% of amoxicillin and 68.5% of CODcr removal were achieved after 72 h, comparing with the cases of sodium alginate (SA) system (81.2%, 46.9%) and the free cells system (60.5%, 35.5%). The degradation kinetics was in good agreement with Michaelis-Menten equation. The maximum rate (Vm ) and Michaelis constant (Km ) were calculated as 9.09 mg L-1 h-1 and 228 mg L-1, respectively. The results further revealed that diatomite not only acted as immobilization support to improve the mechanical strength and lifetime of the pellets but also as absorbent to promote the treatment efficiency. Therefore, both enzymatic catalysis and chemisorption were responsible for the removal of amoxicillin.