论文标题
扩散搜索随机门控目标并重置
Diffusive search for a stochastically-gated target with resetting
论文作者
论文摘要
在本文中，我们分析了单个布朗粒子的平均第一个通道时间（MFPT），以在粒子的位置以$ r $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ r $重置为固定位置$ \ x_r $的额外条件下找到一个随机门控的目标。栅极根据两态马尔可夫链在开放状态和封闭状态之间开关，并且只能由搜索者以开放状态检测到。这种目标的一个可能例子是在不同构象状态之间切换蛋白质。如预期的那样，有或没有重置的MFPT是该门关闭的时间$ρ_0$的增加功能。但是，随机重置和随机门控之间的相互作用在重置下的搜索过程中具有非平凡的影响。首先，通过考虑间隔一端对封闭目标的扩散搜索，我们表明，重置下的MFPT的分数变化表现出对$ρ_0$的非单调依赖性。特别是，以最佳重置率（存在时）以$ρ_0$的增加到一定的临界值，MFPT的百分比降低了，此后降低并最终消失。其次，在$ \ r^d $中的球形目标的情况下，MFPT对空间尺寸$ d $的依赖在存在随机门控的情况下会大大放大。
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 $ρ_0$ 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 $ρ_0$. In particular, the percentage reduction of the MFPT at the optimal resetting rate (when it exists) increases with $ρ_0$ 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.
