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Recent fluorescence spectroscopy measurements of single-enzyme kinetics haveshown that enzymatic turnovers form a renewal stochastic process in which theinverse of the mean waiting time between turnovers follows the Michaelis-Mentenequation. Under typical physiological conditions, however, tens to thousands ofenzymes react in catalyzing thousands to millions of substrates. We studyenzyme kinetics at these physiologically relevant conditions through a masterequation including stochasticity and molecular discreteness. From the exactsolution of the master equation we find that the waiting times are neitherindependent nor are they identically distributed, implying that enzymaticturnovers form a non-renewal stochastic process. The inverse of the meanwaiting time shows strong departures from the Michaelis-Menten equation. Thewaiting times between consecutive turnovers are anti-correlated, where shortintervals are more likely to be followed by long intervals and vice versa.Correlations persist beyond consecutive turnovers indicating that multi-scalefluctuations govern enzyme kinetics.

Non-renewal statistics in the catalytic activity of enzyme molecules at mesoscopic concentrations