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The hyperbolic dependence of catalytic rate on substrate concentration is aclassical result in enzyme kinetics, quantified by the celebratedMichaelis-Menten equation. The ubiquity of this relation in diverse chemicaland biological contexts has recently been rationalized by a graph-theoreticanalysis of deterministic reaction networks. Experiments, however, haverevealed that "molecular noise" - intrinsic stochasticity at the molecularscale - leads to significant deviations from classical results and tounexpected effects like "molecular memory", i.e., the breakdown of statisticalindependence between turnover events. Here we show, through a new method ofanalysis, that memory and non-hyperbolicity have a common source in an initial,and observably long, transient peculiar to stochastic reaction networks ofmultiple enzymes. Networks of single enzymes do not admit such transients. Thetransient yields, asymptotically, to a steady-state in which memory vanishesand hyperbolicity is recovered. We propose new statistical measures, defined interms of turnover times, to distinguish between the transient and steady statesand apply these to experimental data from a landmark experiment that firstobserved molecular memory in a single enzyme with multiple binding sites. Ourstudy shows that catalysis at the molecular level with more than one enzymealways contains a non-classical regime and provides insight on how theclassical limit is attained.

Transients generate memory and break hyperbolicity in stochastic enzymatic networks