  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.
