An algebraic model for the kinetics of covalent enzyme inhibition at low substrate concentrations (original) (raw)

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