The meaning of the Michaelis-Menten constant: Km describes a steady-state (original) (raw)
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The meaning of the Michaelis-Menten constant: Kmdescribes a steady-state
bioRxiv (Cold Spring Harbor Laboratory), 2019
Often, in vitro or in vivo enzyme-mediated catalytic events occur far from equilibrium and, therefore, substrate affinity measured as the inverse of ES D E+S dissociation equilibrium constant (K d) has a doubtful physiological meaning; in practice it is almost impossible to determine K d (except using stopped-flow or other sophisticated methodologies). The Michaelis-Menten constant (K m), the concentration of substrate ([S]) providing half of enzyme maximal activity, is not the (K d). In the simple E+S D ES → E+P or in more complex models describing S conversion into P, K m must be considered the constant defining the steady state at any substrate concentration. Enzyme kinetics is based on initial rate determination, i.e. in the linear part of the S to P conversion when the concentration of [ES] remains constant while steady state occurs. We also show that Systems Biology issues such as the time required to respond to a system perturbation, is more dependent on k 1 , the kinetic constant defining substrateenzyme association, than on K m. Whereas K m is instrumental for biochemical basic and applied approaches, in any physiological condition, an important parameter to be considered is the substrate association rate (k 1).
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.
Enzyme kinetics: the whole picture reveals hidden meanings
FEBS Journal, 2015
The methodology adopted by Michaelis and Menten in 1913 is still routinely used to characterize the catalytic power and selectivity of enzymes. These kinetic measurements must be performed soon after the purified enzyme is mixed with a large excess of substrate. Other time scales and solution compositions are no less physiologically relevant, but fall outside the range of applicability of the classical formalism. Here we show that the complete picture of an enzyme's mode of function is critically obscured by the limited scope of conventional kinetic analysis, even in the simplest case of a single active site without inhibition. This picture is now unveiled in a mathematically closed form that remains valid over the reaction time for all combinations of enzyme/substrate concentrations and rate constants. Algebraic simplicity is maintained in the new formalism when stationary reaction phases are considered. By achieving this century-old objective, the otherwise hidden role of the reversible binding step is revealed and atypical kinetic profiles are explained. Most singular kinetic behaviors are identified in a critical region of conditions that coincide with typical cell conditions. Because it is not covered by the Michaelis-Menten model, the critical region has been missed until now by low-and high-throughput screenings of new drugs. New possibilities are therefore raised for novel and once-promising inhibitors to therapeutically target enzymes.
On the status of the Michaelis-Menten equation and its implications for enzymology
Nature Precedings, 2008
The Michaelis-Menten equation (MME) is considered to be the fundamental equation describing the rates of enzyme-catalysed reactions, and thus the 'physicochemical key' to understanding all life processes. It is the basis of the current view of enzymes as generally proteinaceous macromolecules that bind the substrate reversibly at the active site, and convert it to the product in a relatively slow overall sequence of bonding changes ('turnover'). The manifested 'saturation kinetics', by which the rate of the enzymic reaction (essentially) increases linearly with the substrate concentration ([S]) at low [S] but reaches a plateau at high [S], is apparently modelled by the MME. However, it is argued herein that the apparent success of the MME is misleading, and that it is fundamentally flawed by its equilibrium-based derivation (as can be shown mathematically). Thus, the MME cannot be classed as a formal kinetic equation vis-a-vis the law of mass action, as it do...
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.
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 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.
Kinetic and Thermodynamic Aspects of Enzyme Control and Regulation †
The Journal of Physical Chemistry B, 2010
This paper develops concepts for assessing and quantifying the regulation of the rate of an enzyme-catalyzed reaction. We show how generic reversible rate equations can be recast in two ways, one making the distance from equilibrium explicit, thereby allowing the distinction between kinetic and thermodynamic control of reaction rate, as well as near-equilibrium and far-from-equilibrium reactions. Recasting in the second form separates mass action from rate capacity and quantifies the degree to which intrinsic mass action contributes to reaction rate and how regulation of an enzyme-catalyzed reaction either enhances or counteracts this mass-action behavior. The contribution of enzyme binding to regulation is analyzed in detail for a number of enzyme-kinetic rate laws, including cooperative reactions.