A Steady-State Algebraic Model for the Time Course of Covalent Enzyme Inhibition

Abstract

This report describes an algebraic equation for the time course of irreversible enzyme inhibition following a two-step mechanism. In the first step, the enzyme and the inhibitor associate reversibly to form a non-covalent complex. In the second step, the noncovalent complex is irreversibly converted to the final covalent conjugate. Importantly, the algebraic derivation was performed under the<i> steady-state approximation</i>. Under the previously invoked <i>rapid-equilibrium approximation</i> [Kitz & Wilson (1962) <i>J. Biol. Chem.</i> <b>237</b>, 3245] it is by definition assumed that the rate constant for the reversible dissociation of the initial noncovalent complex is very much faster than the rate constant for the irreversible inactivation step. In contrast, the steady-state algebraic equation reported here removes any restrictions on the relative magnitude of microscopic rate constants. The resulting formula was used in heuristic simulations designed to test the performance of the standard rapid-equilibrium kinetic model. The results show that if the inactivation rate constant is significantly higher than the dissociation rate constant, the conventional “kobs” method for evaluating the potency of covalent inhibitors in drug discovery is incapable of correctly distinguishing between the two-step inhibition mechanism and a simpler one-step variant, even for inhibitors that have very high binding affinity in the reversible noncovalent step.