Diffusive flux into a stochastically gated tube

TL;DR

This paper derives an explicit formula for diffusive flux into a stochastically gated tube, extending previous models to broader geometries and diffusivity conditions, and validates it through simulations.

Contribution

It provides a new flux estimate formula valid for non-narrow tubes and differing diffusivities, with proofs and extensive simulation validation.

Findings

The flux estimate is exact in certain regimes.

The estimate remains accurate across broad parameter ranges.

The results differ from prior models on gated diffusion.

Abstract

Diffusion-influenced reactions in the presence of gates which randomly open and close have been studied for decades in a variety of biophysical and biochemical scenarios. The diffusive flux from a large bulk reservoir to the end of a narrow tube with a stochastically gated entrance has been previously estimated. In this paper, we extend this gated flux estimate to be valid if (i) the tube is not necessarily narrow and/or (ii) the diffusivity differs in the tube versus the bulk. Extension (i) is challenging because it entails a nontrivial three-dimensional geometry. Extension (ii) is challenging because it introduces multiplicative noise. We derive an explicit flux estimate formula and prove that it is exact in certain parameter regimes. We further use stochastic simulations to show that the estimate remains accurate across a very broad range of parameters. Our results differ from prior work on extensions (i) and (ii).