Transients generate memory and break hyperbolicity in stochastic enzymatic networks

TL;DR

This paper reveals that stochastic transients in enzymatic networks cause memory effects and break hyperbolicity, but these effects diminish over time as the system reaches a classical steady state.

Contribution

It introduces a new analysis method linking transient dynamics to memory and hyperbolicity breakdown in stochastic enzyme networks, supported by experimental data.

Findings

Transient effects cause molecular memory in enzyme networks.

Memory effects vanish as the system approaches steady state.

Experimental data confirms the transient origin of memory effects.

Abstract

The hyperbolic dependence of catalytic rate on substrate concentration is a classical result in enzyme kinetics, quantified by the celebrated Michaelis-Menten equation. The ubiquity of this relation in diverse chemical and biological contexts has recently been rationalized by a graph-theoretic analysis of deterministic reaction networks. Experiments, however, have revealed that "molecular noise" - intrinsic stochasticity at the molecular scale - leads to significant deviations from classical results and to unexpected effects like "molecular memory", i.e., the breakdown of statistical independence between turnover events. Here we show, through a new method of analysis, that memory and non-hyperbolicity have a common source in an initial, and observably long, transient peculiar to stochastic reaction networks of multiple enzymes. Networks of single enzymes do not admit such transients. The transient yields, asymptotically, to a steady-state in which memory vanishes and hyperbolicity is recovered. We propose new statistical measures, defined in terms of turnover times, to distinguish between the transient and steady states and apply these to experimental data from a landmark experiment that first observed molecular memory in a single enzyme with multiple binding sites. Our study shows that catalysis at the molecular level with more than one enzyme always contains a non-classical regime and provides insight on how the classical limit is attained.