Mesoscopic Modeling of Random Walk and Reactions in Crowded Media

TL;DR

This paper introduces a mesoscopic modeling framework for diffusion and reactions in crowded environments like living cells, using homogenization to connect microscopic details with macroscopic PDEs.

Contribution

It presents a novel homogenization-based approach to derive mesoscopic models from microscopic descriptions for crowded media.

Findings

The framework effectively captures diffusion in crowded environments.

Analytical solutions and numerical experiments validate the model.

The approach links microscopic details to macroscopic PDEs.

Abstract

We develop a mesoscopic modeling framework for diffusion in a crowded environment, particularly targeting applications in the modeling of living cells. Through homogenization techniques we effectively coarse-grain a detailed microscopic description into a previously developed internal state diffusive framework. The observables in the mesoscopic model correspond to solutions of macroscopic partial differential equations driven by stochastically varying diffusion fields in space and time. Analytical solutions and numerical experiments illustrate the framework.