The first passage problem for diffusion through a cylindrical pore with sticky walls

TL;DR

This paper derives the first passage time distribution for diffusive particles in a cylindrical pore with sticky walls, revealing insights into how binding events influence transport times, with implications for cellular transport mechanisms.

Contribution

It introduces a diagrammatic expansion method to analytically compute first passage time statistics for diffusion with sticky boundary conditions.

Findings

Derived explicit first passage time distribution

Linked model to nucleocytoplasmic transport

Provided analytical framework for sticky boundary diffusion

Abstract

We calculate the first passage time distribution for diffusion through a cylindrical pore with sticky walls. A particle diffusively explores the interior of the pore through a series of binding and unbinding events with the cylinder wall. Through a diagrammatic expansion we obtain first passage time statistics for the particle's exit from the pore. Connections between the model and nucleocytoplasmic transport in cells are discussed.