Theory and simulation of the influence of diffusion in enzyme-catalyzed reactions

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 theories all predict that the effective rate constant for substrate association is given by k(infinity) and the effective rate constant for substrate dissociation is given by k(d)k(infinity)/k(0), where k(d) is the rate constant for ES to form a geminate pair. Previous work has shown that k(infinity)/k(0) depends only weakly on interaction potential, hence favorable electrostatic interactions between enzyme and substrate, while enhancing the association rate constant k(infinity) significantly, will suppress the effective dissociation rate constant only marginally. By analogy, the release of product is also expected to be marginally affected by electrostatic interactions. Enzymes are thus found to enjoy all the benefits of electrostatic interactions but suffer very little from their side effects