First passage time statistics for two-channel diffusion

TL;DR

This paper rigorously analyzes the first passage time statistics for a two-channel diffusion process in 3D, revealing non-Poissonian behavior influenced by recognition and immobilization scenarios, with implications for cellular signaling.

Contribution

It provides the first rigorous results for two-channel Markov additive diffusion first passage times, highlighting non-trivial effects of recognition and immobilization on long-time behavior.

Findings

First passage times do not follow Poisson statistics at long times.

Recognition in only one mode affects first passage behavior.

Immobilization scenarios alter diffusion dynamics significantly.

Abstract

We present rigorous results for the mean first passage time and first passage time statistics for two-channel Markov additive diffusion in a 3-dimensional spherical domain. Inspired by biophysical examples we assume that the particle can only recognise the target in one of the modes, which is shown to effect a non-trivial first passage behaviour. We also address the scenario of intermittent immobilisation. In both cases we prove that despite the perfectly non-recurrent motion of two-channel Markov additive diffusion in 3 dimensions the first passage statistics at long times do not display Poisson-like behaviour if none of the phases has a vanishing diffusion coefficient. This stands in stark contrast to the standard (one-channel) Markov diffusion counterpart. We also discuss the relevance of our results in the context of cellular signalling.