Rate enhancement of gated drift-diffusion process by optimal resetting

Abstract

“Gating” is a widely observed phenomenon in biochemistry that describes the transition between the activated (or open) and deactivated (or closed) states of an ion-channel, which makes transport through that channel highly selective. In general, gating is a mechanism that imposes an additional restriction on a transport, as the process ends only when the “gate” is open and continues otherwise. When diffusion occurs in the presence of a constant bias to a gated target, i.e., to a target that switches between an open and a closed state, the dynamics essentially slow down compared to ungated drift-diffusion, resulting in an increase in the mean completion time, ⟨TG⟩ > ⟨T⟩, where T denotes the random time of transport and G indicates gating. In this work, we utilize stochastic resetting as an external protocol to counterbalance the delay due to gating. We consider a particle in the positive semi-infinite space that undergoes drift-diffusion in the presence of a stochastically gated target at the origin and is moreover subjected to rate-limiting resetting dynamics. Calculating the minimal mean completion time ⟨Tr⋆G⟩ rendered by an optimal resetting rate r⋆ for this exactly solvable system, we construct a phase diagram that owns three distinct phases: (i) where resetting can make gated drift-diffusion faster even compared to the original ungated process, ⟨Tr⋆G⟩<⟨T⟩<⟨TG⟩, (ii) where resetting still expedites gated drift-diffusion but not beyond the original ungated process, ⟨T⟩≤⟨Tr⋆G⟩<⟨TG⟩, and (iii) where resetting fails to expedite gated drift-diffusion, ⟨T⟩<⟨TG⟩≤⟨Tr⋆G⟩. We also highlight various non-trivial behaviors of the completion time as the resetting rate, gating parameters, and geometry of the set-up are carefully ramified. Gated drift-diffusion aptly models various stochastic processes such as chemical reactions that exclusively take place in certain activated states of the reactants. Our work predicts the conditions under which stochastic resetting can act as a useful strategy to enhance the rate of such processes without compromising their selectivity.