Memory, hysteresis, and kinetic cooperativity in stochastic mnemonic networks

Mnemonic networks are cyclic catalytic networks of monomeric enzymes that exhibit kinetic cooperativity as departures of the mean velocity from the hyperbolic, Michaelis-Menten-like response. In addition, such networks admit a hysteretic response when conformational fluctuations are slow compared to the catalytic rate. Here, we show how these fluctuation-driven effects emerge from the underlying stochasticity in the network. We use the chemical master equation to study the stochastic kinetics of mnemonic networks, which, in their minimal form, include a pair of conformers and triangular reaction pathways. We introduce statistical measures that are conditional on the turnovers to comprehensively analyze molecular fluctuations in the transient and stationary states of these networks. In the transient state, temporal correlations between enzyme turnovers lead to an inequivalence between number and temporal fluctuations, yielding a hysteretic response of the mean velocity to substrates. The transient relaxes to a stationary state with independent and identically distributed turnovers and equality between number and temporal fluctuations. This state is a non-equilibrium stationary state (NESS) when the Kolmogorov loop criterion is not satisfied, leading to the emergence of kinetic cooperativity. The symmetry of the number correlation functions allows us to distinguish between the absence of cooperativity in equilibrium and the accidental vanishing of cooperativity in a NESS. We conclude that memory and hysteresis are transient effects while kinetic cooperativity emerges as the macroscopic manifestation of the microscopic irreversibility of the NESS in a network with cyclic reaction pathways.