Reconciling transport models across scales: the role of volume exclusion

TL;DR

This paper explores how volume exclusion impacts diffusive transport across biological and physical systems, proposing a random walk approach to reconcile models at different spatial scales while highlighting the limits of coarse-graining.

Contribution

It introduces a method to unify models of diffusion that include crowding effects across multiple spatial scales using a random walk framework.

Findings

Coarse-grained models can effectively incorporate volume exclusion effects.

Care must be taken when simplifying models to avoid losing essential crowding dynamics.

The approach helps bridge microscopic and macroscopic diffusion models.

Abstract

Diffusive transport is a universal phenomenon, throughout both biological and physical sciences, and models of diffusion are routinely used to interrogate diffusion-driven processes. However, most models neglect to take into account the role of volume exclusion, which can significantly alter diffusive transport, particularly within biological systems where the diffusing particles might occupy a significant fraction of the available space. In this work we use a random walk approach to provide a means to reconcile models that incorporate crowding effects on different spatial scales. Our work demonstrates that coarse-grained models incorporating simplified descriptions of excluded volume can be used in many circumstances, but that care must be taken in pushing the coarse-graining process too far.