Trapping of a run-and-tumble particle in an inhomogeneous domain: the weak noise limit

TL;DR

This paper analyzes the escape dynamics of a one-dimensional run-and-tumble particle in an inhomogeneous environment using asymptotic methods, providing insights into metastability and first passage times in active matter systems.

Contribution

It introduces an asymptotic approach to compute mean first passage times for RTPs in spatially varying environments, advancing understanding of metastability in PDMPs.

Findings

Derived explicit formulas for MFPT in inhomogeneous potentials

Demonstrated the applicability of asymptotic methods to active matter models

Connected RTP escape dynamics to broader metastability frameworks

Abstract

A one-dimensional run-and-tumble particle (RTP) switches randomly between a left and right moving state of constant speed $v$. This type of motion arises in a wide range of applications in cell biology, including the unbiased growth and shrinkage of microtubules or cytonemes, the bidirectional motion of molecular motors, and the "run-and-tumble" motion of bacteria such as {\em E. coli}. RTPs are also of more general interest within the non-equilibrium statistical physics community, both at the single particle level and at the interacting population level, where it provides a simple example of active matter. In this paper we use asymptotic methods to calculate the mean first passage time (MFPT) for a one-dimensional RTP to escape an effective trapping potential generated by space-dependent switching rates. Such methods are part of a more general framework for studying metastability in so-called piecewise deterministic Markov processes (PDMPs), which include the RTP as a special case.