On the Reducible Character of Haldane-Radić Enzyme Kinetics to Conventional and Logistic Michaelis-Menten Models (original) (raw)
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Extending the kinetic solution of the classic Michaelis–Menten model of enzyme action
Journal of Mathematical Chemistry
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 of enzyme catalysis was undertaken by Briggs–Haldane (Biochem J 19:338, 1925). These authors proposed the steady-state treatment, since its applicability was constrained to this condition. The present work describes an extending solution of the Michaelis–Menten model without the need for such a steady-state restriction. We provide the first analysis of all of the individual reaction constants calculated analytically. Using this approach, it is possible to accurately predict the results under new experimental conditions and to characterize and optimize industrial processes in the fields of chemical and food engineering, pharmaceuticals and biotechnology.
A new approach to a century-old problem: Henri-Michaelis-Menten enzyme kinetics
AIP Conference Proceedings, 2012
A new approach to Henri-Michaelis-Menten (HMM) enzyme kinetics is presented. In the first part, a simplified but useful description that stresses the cyclic nature of the catalytic process is summarized. In particular, the timedependence of the substrate concentration is obtained in a simple way that dispenses the quasi-steady-state approximation. In the second part an exact one-dimensional formulation of HMM kinetics is presented. The whole problem is condensed in a second-order non-linear autonomous differential equation, and the exact solution of HMM kinetics is given as a set of Maclaurin series. From the same evolution equation, a number of approximate solutions, some known, some new, can be derived in a systematic way. The evolution equation obtained is also well suited for the numerical computation of the concentrations of all species as a function of time for any given combination of parameters.
Zenodo (CERN European Organization for Nuclear Research), 2022
For some time now, there has been growing interest in pre-steady-state (PSS) kinetic parameters for whatever reasons, the measurement of which needs high-tech equipment capable of transient timescale duration of assay. The proposition, however, is that all kinetic parameters, PSS and beyond, can be determined with appropriate PSS derivable equations and the usual Michaelis-Menten (MM) and Briggs-Haldane (BH) equations, respectively. The objectives of the research were: 1) To derive equations, for the determination of reverse rate constant when the substrate concentration, [S] « MM constant, KM, 2) determine by calculation, the reverse rate constant, forward rate constant, and consequently, show that it is possible to determine rate constant often seen to be masked within original MM cum BH mathematical formalism, and 3) validate corollaries from the derivation that justify procedural issue. Theoretical, experimental (Bernfeld method), and computational methods were explored. Pre-steady-state equations for the determination of kinetic parameters, the reverse rate constant, k-1, for the process ES E + S, the 2nd order rate constant, k1, and the rate, v1, for the formation of enzyme-substrate complex, ES, were derived. The derived originating equations with associated corollaries were validated and have been seen to be capable of reproducing experimental variables and kinetic parameters; rate constants that seemed masked in MM formalism were unmasked. Steady-state (SS) cum zero order kinetic parameters were » their PSS values. "Negative" catalytic efficiency (k-1/KM) was » "positive" catalytic efficiency, (kcat/KM), with lower [ET]. In conclusion, the equations for PSS kinetic parameters were derivable. Previously masked kinetic parameters in the MM/BB mathematical formalism can now be calculated using MM data; thus, all kinetic parameters can be determined regardless of the reaction pathway's state, PSS, and SS. PSS kinetic parameters were « SS/zero order values.
World Journal Of Advanced Research and Reviews, 2022
For some time now, there has been growing interest in pre-steady-state (PSS) kinetic parameters for whatever reasons, the measurement of which needs high-tech equipment capable of transient timescale duration of assay. The proposition, however, is that all kinetic parameters, PSS and beyond, can be determined with appropriate PSS derivable equations and the usual Michaelis-Menten (MM) and Briggs-Haldane (BH) equations, respectively. The objectives of the research were: 1) To derive equations, for the determination of reverse rate constant when the substrate concentration, [S] « MM constant, KM, 2) determine by calculation, the reverse rate constant, forward rate constant, and consequently, show that it is possible to determine rate constant often seen to be masked within original MM cum BH mathematical formalism, and 3) validate corollaries from the derivation that justify procedural issue. Theoretical, experimental (Bernfeld method), and computational methods were explored. Pre-steady-state equations for the determination of kinetic parameters, the reverse rate constant, k-1, for the process ES E + S, the 2nd order rate constant, k1, and the rate, v1, for the formation of enzyme-substrate complex, ES, were derived. The derived originating equations with associated corollaries were validated and have been seen to be capable of reproducing experimental variables and kinetic parameters; rate constants that seemed masked in MM formalism were unmasked. Steady-state (SS) cum zero order kinetic parameters were » their PSS values. "Negative" catalytic efficiency (k-1/KM) was » "positive" catalytic efficiency, (kcat/KM), with lower [ET]. In conclusion, the equations for PSS kinetic parameters were derivable. Previously masked kinetic parameters in the MM/BB mathematical formalism can now be calculated using MM data; thus, all kinetic parameters can be determined regardless of the reaction pathway's state, PSS, and SS. PSS kinetic parameters were « SS/zero order values.
Biochemical Journal, 1980
The possible graph shapes for one-site/two-state and substrate-modifier models are discussed. The two-state model is a version of the Monod-Wyman-Changeux model and gives a rate equation with 240 denominator terms. Discussion in terms of K and V effects is not possible. A simplified version of the mechanism can be shown to give v-versus-[S] curves that are either sigmoid or non-sigmoid. They may show substrate inhibition or no final maximum, and the double-reciprocal plots can be concave up or down. The corresponding binding model is determined by only two constants and gives a linear double-reciprocal plot. The substrate-modifier mechanism is a simple example of a mechanism where inclusion of catalytic steps leads to a genuine increase in degree of the rate equation. The v-versus-[S] curve can show such complexities as two maxima and a minimum, and the double-reciprocal plot can cross its asymptote twice, proving the rate equation to be 4:4. A simplified version is 3:3, and analysi...
17 Alternative Perspectives of Enzyme Kinetic Modeling
2012
The basis of enzyme kinetic modelling was established during the early 1900’s when the work of Leonor Michaelis and Maud Menten produced a pseudo-steady state equation linking enzymatic catalytic rate to substrate concentration (Michaelis & Menten, 1913). Building from the Michaelis-Menten equation, other equations used to describe the effects of modifiers of enzymatic activity were developed based on their effect on the catalytic parameters of the Michaelis-Menten equation. Initially, inhibitors affecting the substrate affinity were deemed competitive and inhibitors affecting the reaction rate were labelled non-competitive (McElroy 1947). These equations have persisted as the basis for inhibition studies and can be found in most basic textbooks dealing with the subject of enzyme inhibition. Here the functionality of the competitive and non-competitive equations are examined to support the development of a unified equation for enzymatic activity modulation. From this, a modular appr...
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 with the mathematical technique known as quasi-steady-state approximation. In the second part of the paper an exact one-dimensional formulation of HMM kinetics is considered. The whole problem is condensed in a single one-variable evolution equation that is a second-order non-linear autonomous differential equation, and the control parameters are reduced to three dimensionless quantities: enzyme efficiency, substrate reduced initial concentration, and enzyme reduced initial concentration. The exact solution of HMM kinetics is obtained as a set of Maclaurin series. From the same equation, a number of approximate solutions, some known, some new, are derived in a systematic way that allows a precise evaluation of the respective level of approximation and conditions of validity. The evolution equation obtained is also shown to be well suited for the numerical computation of the concentrations of all species as a function of time for any given combination of parameters.
A century of enzyme kinetic analysis, 1913 to 2013
FEBS Letters, 2013
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.
Journal of Mathematical Chemistry, 2007
This work presents an alternative analysis of the integrated rate equations corresponding to the simple Michaelis-Menten mechanism without product inhibition. The suggested new results are reached under a minimal set of assumptions and include, as a particular case, the classical integrated Michaelis-Menten equation. Experimental designs and a kinetic data analysis are suggested to the estimation of the maximum steady-state rate, V max , the Michaelis-Menten constant, K m , the initial enzyme * Corresponding author. 789 0259-9791/07/1100-0789/0 © 2006 Springer Science+Business Media, Inc. R. Varón et al. / Integrated form of the Michaelis-Menten Equation concentration, [E] 0 , and the catalytic constant, k 2 . The goodness of the analysis is tested with simulated time progress curves obtained by numerical integration.
A note on the kinetics of enzyme action: A decomposition that highlights thermodynamic effects
Michaelis and Menten's mechanism for enzymatic catalysis is remarkable both in its simplicity and its wide applicability. The extension for reversible processes, as done by Haldane, makes it even more relevant as most enzymes catalyze reactions that are reversible in nature and carry in vivo flux in both directions. Here, we decompose the reversible Michaelis-Menten equation into three terms, each with a clear physical meaning: catalytic capacity, substrate saturation and thermodynamic driving force. This decomposition facilitates a better understanding of enzyme kinetics and highlights the relationship between thermodynamics and kinetics, a relationship which is often neglected. We further demonstrate how our separable rate law can be understood from different points of view, shedding light on factors shaping enzyme catalysis.