Transients and Cooperativity: A SLOW TRANSITION MODEL FOR RELATING TRANSIENTS AND COOPERATIVE KINETICS OF ENZYMES

Abstract

A model is proposed to account for the occurrence of both slow transient kinetics and cooperativity in a monomeric, single-site enzyme. This slow transition model incorporates one reaction of the enzyme, in addition to normal catalytic steps, which is slower than other steps in the mechanism and is influenced by substrate. The slow reaction step may be an isomerization (conformation change), a dissociation-association, or binding of another ligand (modifier). Analysis of steady state kinetics and simulation studies for the slow isomerization mechanism have demonstrated that both positive and negative cooperativity can occur with either bursts or lags of enzyme activity. Examination of various combinations of rate constants have illustrated the dependence of cooperativity of the system on changes in certain rate constants. For example, a necessary condition for cooperativity in this model requires that both the binding and the isomerization steps of the mechanism be in a steady state but not at equilibrium. Modifiers could potentially shift the extent or type of cooperativity. The combination of slow transitions with homotropic, sitesite interaction could generate several types of complex, cooperative kinetics. Whenever a transient is observed in a progress curve the contribution of the slow transition model to cooperativity of the kinetics should be assessed. The results of binding studies, initial (pre-transition) velocity measurements, and the effects of factors (e.g. pH, temperature, modifiers) on the half-time of the transient should be capable of determining the extent of the contribution of the slow transition to cooperativity. A table of 10 enzymes which show both transients and cooperativity suggests that these phenomena do occur together and may be related mechanistically through the slow transition mechanism. Thus, in those cases in which a slow transition occurs, the transition may be responsible for nonlinear, double reciprocal plots of the steady state kinetics without requiring interactions between more than one site.