{
  "id": "2009.02739",
  "version": "v1",
  "published": "2020-09-06T13:59:03.000Z",
  "updated": "2020-09-06T13:59:03.000Z",
  "title": "Diffusive search for a stochastically-gated target with resetting",
  "authors": [
    "Paul C Bressloff"
  ],
  "comment": "17 pages, 9 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-06T13:59:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastically-gated target",
      "diffusive search",
      "mean first passage time",
      "single brownian particle",
      "two-state markov chain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}