Substrate inhibition as a problem of non-linear steady state kinetics with monomeric enzymes (original) (raw)
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An algebraic model for the kinetics of covalent enzyme inhibition at low substrate concentrations
This article describes an integrated rate equation for the time course of covalent enzyme inhibition under the conditions where the substrate concentration is significantly lower than the corresponding Michaelis constant, for example, in the Omnia assays of epidermal growth factor receptor (EGFR) kinase. The newly described method is applicable to experimental conditions where the enzyme concentration is significantly lower than the dissociation constant of the initially formed reversible enzyme–inhibitor complex (no ''tight binding''). A detailed comparison with the traditionally used rate equation for covalent inhibition is presented. The two methods produce approximately identical values of the first-order inactivation rate constant (k inact). However, the inhibition constant (K i), and therefore also the second-order inactiva-tion rate constant k inact /K i , is underestimated by the traditional method by up to an order of magnitude. Ó 2014 Published by Elsevier Inc. Covalent enzyme inhibition has both reversible and irreversible components. The reversible component is analogous to the equilibrium constant for simple reversible inhibitors (K i). In a subsequent step, characterized by the rate constant k inact , a covalent bond is formed irreversibly. Characterizing these two contributions to covalent inhibitor potency is essential to understand their biological impact as well as in the design of more effective drugs. In a recent article [1], we described a detailed kinetic analysis of covalent (irreversible) inhibition of the epidermal growth factor receptor (EGFR) 1 kinase under the special experimental conditions where the peptide substrate concentration, [S] 0 , is much lower than the corresponding Michaelis constant, K M,Pep. The mathematical model consisted of a system of simultaneous first-order ordinary differential equations (ODEs), which must be integrated numerically in order to compute the reaction time course. Two important advantages of ODE models in enzyme kinetics are that all conceivable molecular mechanisms can be treated and no simplifying assumptions are made regarding the experimental conditions. One important disadvantage is that the iterative numerical integration of ODE systems is a relatively tedious and time-consuming task that can be accomplished only by using highly specialized software packages such as DynaFit [2,3]. Here we describe a simple algebraic equation that can be used, instead of a full ODE system, to analyze covalent inhibition kinet-ics. This integrated rate equation is applicable under two simultaneously satisfied simplifying assumptions. First, as was the case in the previous article [1], we require that the substrate concentration must be much lower than the corresponding Michaelis constant. Second, the enzyme concentration must be much lower than the inhibition constant that characterizes the initially formed noncovalent enzyme–inhibitor complex. The second requirement is equivalent to saying that there is no ''tight binding'' [4–10]. Results obtained by using the newly presented method were compared with those obtained by using the conventionally applied kinetic model of covalent enzyme inhibition (see, e.g., chapter 9 in Ref. [11]). We show that ignoring what many casual observers would consider a ''minor'' nonlinearity in the no-inhibitor control can cause up to nearly one order of magnitude distortion in the best-fit values of K i and k inact /K i. Interestingly, the best-fit value of k inact obtained by the conventional mathematical model under low substrate concentrations (relative to the K M) shows only a minor distortion. Materials and methods Experimental The expression and purification of EGFR L858R/T790M double mutant, as well as the determination of active enzyme
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...
ACTA BIOCHIMICA POLONICA- …, 2000
A combined analysis of enzyme inhibition and activation is presented, based on a rapid equilibrium model assumption in which one molecule of enzyme binds one molecule of substrate (S) and/or one molecule of a modifier X. The modifier acts as activator (essential or non-essential), as inhibitor (total or partial), or has no effect on the reaction rate (v), depending on the values of the equilibrium constants, the rate constants of the limiting velocity steps, and the concentration of substrate ([S]). Different possibilities have been analyzed from an equation written to emphasize that v = ¦([X]) is, in general and at a fixed [S], a hyperbolic function. Formulas for S u (the value of [S], different from zero, at which v is unaffected by the modifier) and v su (v at that particular [S]) were deduced. In Lineweaver-Burk plots, the straight lines related to different [X] generally cross in a point (P) with coordinates (S u , v su). In certain cases, point P is located in the first quadrant which implies that X acts as activator, as inhibitor, or has no effect, depending on [S]. Furthermore, we discuss: (1) the apparent V max and K m displayed by the enzyme in different situations; (2) the degree of effect (inhibition or activation) observed at different concentrations of substrate and modifier; (3) the concept of K e , a parameter that depends on the concentration of substrate and helps to
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.
Extended monod kinetics for substrate inhibited systems
Bioprocess and Biosystems Engineering
The biochemical route is identified to be one of the simplest and cheapest means by which valuable chemicals are being synthesized. Microorganisms play a vital role in carrying out these processes. However, the kinetic studies relevant to this process is scarce. Most often inhibition effects due to either cells or substrates or products affect the performance of such processes. This paper deals with the study of various model equations for substrate inhibition kinetics. An attempt has been made to study the applicability of various model equations for substrate inhibited systems by fitting their experimental data and evaluating various parameters including the standard deviations in each case. Finally, a new model has been brought out which gives the best fit for almost all the systems.
Mathematical Modeling of Uncompetitive Inhibition of Bi-Substrate Enzymatic Reactions
2013
Currently, mathematical and computer modeling are widely used in different biological studies to predict or assess behavior of such a complex systems as a biological are. This study deals with mathematical and computer modeling of bi-substrate enzymatic reactions, which play an important role in different biochemical pathways. The main objective of this study is to represent the results from in silico investigation of bi-substrate enzymatic reactions in the presence of uncompetitive inhibitors, as well as to describe in details the inhibition effects. Four models of uncompetitive inhibition were designed using different software packages. Particularly, uncompetitive inhibitor to the first [ES1] and the second ([ES1S2]; [FS2]) enzyme-substrate complexes have been studied. The simulation, using the same kinetic parameters for all models allowed investigating the behavior of reactions as well as determined some interesting aspects concerning influence of different cases of uncompetitiv...
Biochemical Engineering Journal, 2014
Mathematical modeling of immobilized enzymes under different kinetics mechanism viz. simple Michaelis-Menten, uncompetitive substrate inhibition, total competitive product inhibition, total noncompetitive product inhibition and reversible Michaelis-Menten reaction are discussed. These five kinetic models are based on reaction diffusion equations containing non-linear terms related to Michaelis-Menten kinetics of the enzymatic reaction. Modified Adomian decomposition method is employed to derive the general analytical expressions of substrate and product concentration for all these five mechanisms for all possible values of the parameters ˚S (Thiele modulus for substrate), ˚P (Thiele modulus for product) and ˛ (dimensionless inhibition degree). Also we have presented the general analytical expressions for the mean integrated effectiveness factor for all values of parameters. Analytical results are compared with the numerical results and also with the limiting case results, which are found to be good in agreement.
Mechanistic and Kinetic Studies of Inhibition of Enzymes
Cell Biochemistry and Biophysics, 2000
A graphical method for analyzing enzyme data to obtain kinetic parameters, and to identify the types of inhibition and the enzyme mechanisms, is described. The method consists of plotting experimental data as v/(V o -v) vs 1/(I) at different substrate concentrations. I is the inhibitor concentration; V o and v are the rates of enzyme reaction attained by the system in the presence of a fixed amount of substrate, and in the absence and presence of inhibitor, respectively. Complete inhibition gives straight lines that go through the origin; partial inhibition gives straight lines that converge on the 1-I axis, at a point away from the origin. For competitive inhibition, the slopes of the lines increase with increasing substrate concentration; with noncompetitive inhibition, the slopes are independent of substrate concentration; with uncompetitive inhibition, the slopes of the lines decrease with increasing substrate concentrations. The kinetic parameters, K m , K i , K i ′, and β (degree of partiality) can best be determined from respective secondary plots of slope and intercept vs substrate concentration, for competitive and noncompetitive inhibition mechanism or slope and intercept vs reciprocal substrate concentration for uncompetitive inhibition mechanism. Functional consequencs of these analyses are represented in terms of specific enzyme-inhibitor systems.
International Journal of Engineering Research and Technology (IJERT), 2016
https://www.ijert.org/a-proposal-for-reversible-enzymatic-inhibition-applied-to-the-michaelis-menten-model-in-the-transient-state https://www.ijert.org/research/a-proposal-for-reversible-enzymatic-inhibition-applied-to-the-michaelis-menten-model-in-the-transient-state-IJERTV5IS040381.pdf Enzymatic processes that obey the classic Michaelis-Menten kinetic model were studied in the light of various proposals that aim to describe reversible inhibition. The proposed inhibition models were compared using a generic process in which the kinetic constants received unit values and the numeric value of the substrate concentration was greater than ten (10) times the numerical value of the enzyme concentration. For each proposed inhibition model, numerical solutions were obtained from a nonlinear system of ordinary differential equations, which produced the results shown in graph, revealing the variation in the enzyme and enzyme complexes and the variation in the substrate and reaction products. A model was developed in which the performance indicated a behavior pattern similar to that seen in the classic Michaelis-Menten model, in which the reaction complex is formed rapidly and, during the process, decays towards zero. In the proposed new model, the inhibitory effect starts at zero and, during the process, tends towards the initial nominal value of the enzyme concentration. Such responses were shown to be valid for distinct enzyme concentration values and process times, demonstrating robustness. The proposed model was applied to enzymatic hydrolysis, providing a fit with mass conservation regarding the product concentration responses upon completion of the process.
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.