Diffusive search for a stochastically-gated target with resetting

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 ${\mathbb{R}}^d$, the dependence of the MFPT on the spatial dimension $d$ is significantly amplified in the presence of stochastic gating.

17 pages, 9 figures

References in corpus (4)

• First Passage Under Restart
• Diffusion with resetting in arbitrary spatial dimension
• Transport properties of random walks under stochastic non-instantaneous resetting
• First hitting times to intermittent targets

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