Diffusive search for a stochastically-gated target with resetting

TL;DR

This paper investigates how stochastic resetting and gating influence the mean first passage time for a diffusing particle to find a target, revealing complex interactions and optimization effects in various geometries.

Contribution

It introduces a detailed analysis of the combined effects of stochastic resetting and gating on search efficiency, highlighting non-trivial optimization behaviors.

Findings

MFPT increases with the closed fraction of the gate

Resetting can non-monotonically reduce MFPT depending on gating

Gating amplifies the dimension dependence of MFPT in spherical targets

Abstract

In this paper, we analyze the mean first passage time (MFPT) for a single Brownian particle to find a stochastically-gated target under the additional condition that the position of the particle is reset to a fixed position $\x_r$ at a rate $r$. The gate switches between an open and closed state according to a two-state Markov chain and can only be detected by the searcher in the open state. One possible example of such a target is a protein switching between different conformational states. As expected, the MFPT with or without resetting is an increasing function of the fraction of time $\rho_0$ that the gate is closed. However, the interplay between stochastic resetting and stochastic gating has non-trivial effects with regards the optimization of the search process under resetting. First, by considering the diffusive search for a gated target at one end of an interval, we show that the fractional change in the MFPT under resetting exhibits a non-monotonic dependence on $\rho_0$. In particular, the percentage reduction of the MFPT at the optimal resetting rate (when it exists) increases with $\rho_0$ up to some critical value, after which it decreases and eventually vanishes. Second, in the case of a spherical target in $\R^d$, the dependence of the MFPT on the spatial dimension $d$ is significantly amplified in the presence of stochastic gating.