Diffusive search for a stochastically-gated target with resetting
File(s)
Accepted version
Author(s)
Bressloff, Paul C
Type
Journal Article
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 its initial position x0 at a rate r. The gate switches between an open (absorbing) and closed (reflecting) 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 ρ0 that the gate is closed or reflecting. 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 ratio Δ(r) = T(r)/T(0), where T(r) is the MFPT at a resetting rate r, exhibits a non-monotonic dependence on ρ0 even though T(r) and T(0) increase monotonically with ρ0. In particular, the value of Δ(r) at the optimal resetting rate (when it exists) decreases with ρ0 up to some critical value, after which it increases and eventually approaches unity. 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.
Date Issued
2020-10-23
Date Acceptance
2020-09-14
Citation
Journal of Physics A: Mathematical and Theoretical, 2020, 53 (42)
ISSN
1751-8113
Publisher
IOP Publishing
Journal / Book Title
Journal of Physics A: Mathematical and Theoretical
Volume
53
Issue
42
Copyright Statement
Copyright © 2020 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/1751-8121/abb844
Identifier
http://dx.doi.org/10.1088/1751-8121/abb844
Publication Status
Published
Article Number
425001
Date Publish Online
2020-09-30