Enzyme Inhibition and Activation: A General Theory (original) (raw)
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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
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.
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.
Enzyme kinetics: Partial and complete competitive inhibition
Biochemical Education, 1997
A graphical method for analysing enzyme data to obtain kinetic parameters, to identify the types of inhibition and the enzyme mechanisms is described. The method consists of plotting experimental data as v/(< !v) versus 1/(I) at di!erent substrate concentrations. I is the inhibitor concentration; <
Enzyme kinetics: partial and complete uncompetitive inhibition
Biochemical education, 2000
A graphical method for analysing enzyme data to obtain kinetic parameters, to identify the types of inhibition and the enzyme mechanisms is described. The method consists of plotting experimental data as v/(V(0)-v) versus 1/(I) at different substrate concentrations. I is the inhibitor concentration; V(0) and v are the initial 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 pass through the origin while partial inhibition gives straight lines that converge on the 1/I-axis at a point away from the origin. With uncompetitive inhibition the slopes of the lines decrease with increasing substrate concentration. The kinetic parameters K(m), K'(i) and beta (degree of partiality) can best be determined from respective secondary plots of slope and intercept versus reciprocal of substrate concentration.
Substrate inhibition as a problem of non-linear steady state kinetics with monomeric enzymes
Journal of Molecular Catalysis, 1980
Starting horn the clas.sical model of substrate inhibition by an ES2 comples, as developed by Haldane in 1930, new concepts including our own are presented. Most of the models iuckde ar, enzyme isomer&&ion skp, are ofcyclicnature,uldcan de~benon-llnearklnetics~~outanyasumpt.ionofsubunitinterar&ions. TheinitialrakequationsofaJl'Jle modelsare veq-sixnikr. Hovzever, one model is based OE tbennodynamic principles, in order to understand t%e induced-fit theory. AlI the models reported so far in the literature, can be cksif~ecl according to three concepts: classical substrate inhibition, slow transition model, thermodynamics of induced-fit model.
A qualitative approach to enzyme inhibition
Biochemistry and Molecular Biology Education, 2009
Most general biochemistry textbooks present enzyme inhibition by showing how the basic Michaelis-Menten parameters K(m) and V(max) are affected mathematically by a particular type of inhibitor. This approach, while mathematically rigorous, does not lend itself to understanding how inhibition patterns are used to determine the kinetic aspects of an enzyme. The discussion here describes a qualitative approach to teaching enzyme inhibition that allows for a physical or mechanistic understanding. This qualitative approach to enzyme inhibition starts by recognizing that the two fundamental kinetic parameters of an enzyme catalyzed reaction are V(max) and V(max) /K(m) , which correspond to the apparent rates of reaction at very high and very low concentrations of substrate, respectively. It just so happens that the reciprocals of V(max) and V(max) /K(m) correspond to the y-intercept and slope of the Lineweaver-Burk plot, respectively. Thus, an inhibitor that affects the y-intercept binds to the enzyme at very high substrate concentrations, and thus binds to the enzyme-substrate complex, while an inhibitor that affects the slope binds to the enzyme at very low substrate concentrations, and thus binds only to free enzyme. These simple precepts can be used to interpret the basic inhibition patterns, competitive, uncompetitive and noncompetitive, and more importantly, derive mechanistic information, especially in multisubstrate reactions. The application of these principles is illustrated by using an example from cancer chemotherapy, the inhibition of thymidylate synthase by 5-fluorouracil and leucovorin.
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...
Analytical aspects of enzyme reversible inhibition
Talanta, 2014
A simple graphical method for the determination of reversible inhibition type, inhibition constant (K i ) and estimation of fifty percent of inhibition I 50 of an enzyme reaction is described. The method consists of plotting experimental data as "degree of inhibition" versus the inhibitor concentration at two or more concentrations of substrate. Diagnosis of inhibition type is based on determination of I 50 and the observation of the shift of the inhibition curves. Relationship between I 50 and inhibition constant K i was discussed. A simplified hyperbolae equation of degree of inhibition showing kinetic orders of 1 and zero at low and high concentrations of inhibitors respectively is proposed. The relative error of inhibitor concentration increased drastically when degree of inhibition reached values of 90%. Examples of published inhibition reports as well as an experimental example of amperometric biosensor based on tyrosinase inhibition by benzoic acid were in agreement with the proposed theoretical approach.