Strong current response to slow modulation: a metabolic case-study

TL;DR

This study investigates how a biochemical reaction network responds nonlinearly to slow periodic modulation, revealing resonance effects in current and fluctuations, with implications for metabolic and synthetic systems.

Contribution

The paper introduces an analytic formula for the nonlinear current response to slow periodic driving in a biochemical network, including stochastic effects and resonance phenomena.

Findings

Strong nonlinear response at low driving frequencies

Resonant effects observed in fluctuations and signal-to-noise ratio

Analytic and stochastic models elucidate the system's behavior

Abstract

We study the current response to periodic driving of a crucial biochemical reaction network, namely, substrate inhibition. We focus on the conversion rate of substrate into product under time-varying metabolic conditions, modeled by a periodic modulation of the product concentration. We find that the system exhibits a strong nonlinear response to small driving frequencies both for the mean time-averaged current and for the fluctuations. For the first, we obtain an analytic formula by coarse-graining the original model to a solvable one. The result is nonperturbative in the modulation amplitude and frequency. We then refine the picture by studying the stochastic dynamics of the full system using a large deviations approach, that allows to show the resonant effect at the level of the time-averaged variance and signal-to-noise ratio. Finally, we discuss how this nonequilibrium effect may play a role in metabolic and synthetic networks.