From diffusion in compartmentalized media to non-Gaussian random walks

TL;DR

This paper links diffusion in compartmentalized media with non-Gaussian Brownian motion, showing how microscopic barriers lead to exponential decay in positional density and affect long-term diffusion.

Contribution

It introduces a microscopic model with randomly placed barriers that explains non-Gaussian diffusion and transient confinement in heterogeneous media.

Findings

Exponential decay of positional probability density observed.

Significant decrease in long-time diffusion constant.

Transient confinement explained by the model.

Abstract

In this work we establish a link between two different phenomena that were studied in a large and growing number of biological, composite and soft media: the diffusion in compartmentalized environment and the Brownian yet non-Gaussian diffusion that exhibits linear growth of the mean square displacement joined by the exponential shape of the positional probability density. We explore a microscopic model that gives rise to transient confinement, similar to the one observed for hop-diffusion on top of a cellular membrane. The compartmentalization of the media is achieved by introducing randomly placed, identical barriers. Using this model of a heterogeneous medium we derive a general class of random walks with simple jump rules that are dictated by the geometry of the compartments. Exponential decay of positional probability density is observed and we also quantify the significant decrease of the long time diffusion constant. Our results suggest that the observed exponential decay is a general feature of the transient regime in compartmentalized media.