Search processes with stochastic resetting and partially absorbing targets

Abstract

We extend the theoretical framework used to study search processes with stochastic resetting to the case of partially absorbing targets. Instead of an absorption event occurring when the search particle reaches the boundary of a target, the particle can diffuse freely in and out of the target region and is absorbed at a rate κ when inside the target. In the context of cell biology, the target could represent a chemically reactive substrate within a cell or a region where a particle can be offloaded onto a nearby compartment. We apply this framework to a partially absorbing interval and to spherically symmetric targets in . In each case, we determine how the mean first passage time (MFPT) for absorption depends on κ, the resetting rate r, and the target geometry. For the given examples, we find that the MFPT is a monotonically decreasing function of κ, whereas it is a unimodal function of r with a unique minimum at an optimal resetting rate r opt. The variation of r opt with κ depends on the spatial dimension d, decreasing in sensitivity as d increases. For finite κ, r opt is a non-trivial function of the target size and distance between the target and the reset point. We also show how our results converge to those obtained previously for problems with totally absorbing targets and similar geometries when the absorption rate becomes infinite. Finally, we generalize the theory to take into account an extended chemical reaction scheme within a target.

First passage in the presence of stochastic resetting and a potential barrier

“…MFPT with resetting: We solve Eqn. (15,16) to find T r − = q − (x, 0) and T r + = q + (x, 0) as functions of r by using matching conditions Eqn. (A7), (A8) at x = x m and boundary conditions q − (x, s)| x=0 = 0, q + (x, s)| x=L = 0.…”

“…Noninstantaneous resetting has also been studied [10]. The idea of resetting has found applications in the problems of chemical reactions [11][12][13], biological processes [14][15][16], and magnetic phase transitions [17]. Resetting in the presence of space dependent potentials introduce interesting new features [18][19][20][21][22][23][24][25][26][27].…”

Stochastic resetting of a population of random walks with resetting-rate-dependent diffusivity

“…Anomalous diffusion with stochastic resetting has also been considered [15,16], notably in the context of record statistics [17]. The diffusion process with stochastic resetting also fostered further works on search strategies [18,19,20] and their optimality [21].…”

Diffusion processes with Gamma-distributed resetting and non-instantaneous returns

“…In the last years, resetting has been widely recognized as a simple yet effective mechanism to optimize diffusion and search processes. The effects of restart on stochastic dynamics have been considered in many branches of physics [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15], including quantum physics [16,17,18] and biophysics [19,20,21,22], but also in different fields such as computer science [23,24] and economics [25], to cite a few examples -see [26] for a review or [27] for a more recent introduction on the subject.…”