Current fluctuations in presence of time-periodic metabolic conditions*

We address 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, modelled by a periodic modulation of the product concentration. Coarse-graining the original model to a minimal solvable one by means of a projection technique, we study the leading behavior of the time averaged current and its fluctuations using a large deviations approach. We show that there exist different regimes, depending on the kinetic rates, in which positive and negative amplitude resonant effects take place, and we provide interpretations for the role that these nonequilibrium effects can play in the metabolic network.