THEORY AND SIMULATION OF THE INFLUENCE OF DIFFUSION IN ENZYME-CATALYZED REACTIONS

The Michaelis-Menten equation for the kinetics of a simple enzyme-cata lyzed reaction is based on the assumption that the two steps of the re action, (i) reversible formation of the enzyme-substrate complex (ES) by diffusional encounter and (ii) irreversible conversion of the subst rate 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 addr ess this question, three theoretical approaches to account for the inf luence of diffusion on the kinetics of enzyme-catalyzed reactions are discussed and tested on a model system. It is found that the restricti on 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 th at is of practical interest, the three theories all predict that the e ffective rate constant for substrate association is given by k(infinit y) 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 fo rm a geminate pair. Previous work has shown that k(infinity)/k(0) depe nds only weakly on interaction potential, hence favorable electrostati c interactions between enzyme and substrate, while enhancing the assoc iation rate constant k(infinity) significantly, will suppress the effe ctive dissociation rate constant only marginally. By analogy, the rele ase of product is also expected to be marginally affected by electrost atic interactions. Enzymes are thus found to enjoy all the benefits of electrostatic interactions but suffer very little from their side eff ects.