Theoretical study of the effect of enzyme-enzyme interactions on steady-state enzyme kinetics

Equilibrium statistical mechanics is much concerned with problems involving intermolecularinteractions, either in lattices or in pure fluids or solutions. The possibility of enzyme-enzyme interactions suggests that the same problems might be studied profitably at steady state as well as at equilibrium. In the systems we consider, each of the identical enzyme molecules of the system undergoes steady-state stochastic cycling among states i equal 1,....,n. But the molecules do not cycle independently. Two neghboring molecules, in states i and j, interact with a free energy wij (a function of the distance r in the solution case). The instantaneous transition probabilities between states for a given molecule will depend on the instantaneous interactions between the molecule in question and its neighbors. The primary question of interest is how the enzyme flux is influenced by the interactions. The general problem is outlined here and some simple special cases are treated. The discussion will be continued in a following paper [Hill, T. L. (1977) Proc. Natl. Acad. Sci. USA 74, in press]