Year: 2025
Type: article
Abstract: A common scenario in a variety of biological systems is that multiple particles are searching in parallel for an immobile target located in a bounded domain, and the fastest among them that arrives to the target first triggers a given desirable or detrimental process. The statistics of such extreme events—the first-passage to the target—is well-understood by now through a series of theoretical analyses, but exclusively under the assumption that all N particles start , i.e., all are introduced into the domain instantly, by δ -function-like pulses. However, in many practically important situations this is not the case: to start their search, the particles often have to enter first into a bounded domain, e.g., a cell or its nucleus, penetrating through gated channels or nuclear pores. This entrance process has a random duration so that the particles appear in the domain sequentially and with a time delay. Here we focus on the effect of such an extended-in-time injection of multiple particles on the fastest first-passage time (fFPT) and its statistics. We derive the full probability density function H N ( t ) of the fFPT with an arbitrary time-dependent injection intensity of N particles. Under rather general assumptions on the survival probability of a single particle and on the injection intensity, we derive the large- N asymptotic formula for the mean fFPT, which is quite different from that obtained for the instantaneous δ -pulse injection. The extended injection is also shown to considerably slow down the convergence of H N ( t ) to its large- N limit—the Gumbel distribution—so that the latter may be inapplicable in the most relevant settings with few tens to few thousands of particles.
Source: Physical Review Research
Authors: Denis S. Grebenkov, Ralf Metzler, Gleb Oshanin
Language: English
Subfield: Molecular Biology
Domain: Life Sciences
Open Access status: gold
Estimated APC paid: $2,625
Awards: G5418811136, G860973739
OpenAlex ID: W4411151141