Theory and Simulation of the Influence of Diffusion in Enzyme-Catalyzed Reactions

Abstract

The Michaelis−Menten equation for the kinetics of a simple enzyme-catalyzed reaction is based on the assumption that the two steps of the reaction, (i) reversible formation of the enzyme−substrate complex (ES) by diffusional encounter and (ii) irreversible conversion of the substrate in ES to product, are both described by ordinary rate equations. It is well-known that the rate coefficient, k(t), for enzyme−substrate binding is time dependent due to the influence of diffusion. Will the influence of diffusion lead to non-Michaelis−Menten kinetics? To address this question, three theoretical approaches to account for the influence of diffusion on the kinetics of enzyme-catalyzed reactions are discussed and tested on a model system. It is found that the restriction on the site for enzyme−substrate binding makes the time dependence of k(t) sufficiently weak so that deviation from the Michaelis−Menten equation is unlikely to be observed. Within the range of parameters that is of practical interest, the three t...