Multiscale modeling of diffusion in a crowded environment

TL;DR

This paper introduces a multiscale modeling framework for diffusion in crowded biological environments, linking microscopic crowding effects to macroscopic diffusion and reaction rates, with implications for understanding cellular processes.

Contribution

It develops a novel multiscale approach that computes jump rates from local exit times and derives a space-dependent diffusion equation accounting for crowding effects.

Findings

Crowding molecules' shape and size significantly affect diffusion.

Molecular crowding can enhance or inhibit reactions depending on local obstacle density.

The model accurately captures the impact of crowding on diffusion and reaction rates.

Abstract

We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of biological systems, which becomes important in the low copy number regime. To model diffusion in the crowded cell environment efficiently, we compute the jump rates in this mesoscopic model from local first exit times, which account for the microscopic positions of the crowding molecules, while the diffusing molecules jump on a coarser Cartesian grid. We then extract a macroscopic description from the resulting jump rates, where the excluded volume effect is modeled by a diffusion equation with space dependent diffusion coefficient. The crowding molecules can be of arbitrary shape and size and numerical experiments demonstrate that those factors together with the size of the diffusing molecule play a crucial role on the magnitude of the decrease in diffusive motion. When correcting the reaction rates for the altered diffusion we can show that molecular crowding either enhances or inhibits chemical reactions depending on local fluctuations of the obstacle density.