The classical Michaelis-Menten (MM) equation, represents a non-cooperative kinetic response of enzymes with either a single or non-interacting multiple binding site(s). The mean catalytic rate of several monomeric enzymes, however, shows deviations from this classical behavior. This effect, termed as dynamic cooperativity, is believed to be associated with molecular mechanisms, stochastic reaction networks, that include enzymatic conformational fluctuations in product formation pathways.
In spite of the latter, however, the present understanding of dynamic cooperativity is confined to mean kinetic measures, obtained from deterministic rate equations, which can not account for fluctuations. Here, we consider a stochastic reaction network for a special class of monomeric enzyme, called mnemonical enzymes, which are known to exhibit both positive and negative (dynamic) cooperativity. We model their kinetics using the chemical master equation (CME) to show how the emergence of dynamic cooperativity, at the molecular level, is inextricably linked to the multiplicity of monomeric enzyme numbers, enzymatic conformational fluctuations and molecular memory. Our results show that dynamic cooperativity is a transient phenomenon, which emerges due to temporal correlations between enzymatic turnovers, and vanishes as these correlations decay and molecular memory fades.
Stochastic enzyme kinetics, enzyme cooperativity, mnemonical enzymes, chemical master equation, waiting time distributions.