Diffusion-limited reactions in dynamic heterogeneous media

TL;DR

This paper develops a mathematical framework to understand how dynamic heterogeneities in cellular environments influence diffusion-limited reactions, revealing that disorder broadens reaction time distributions but can enhance individual reaction speed.

Contribution

It introduces a general approach to extend homogeneous diffusion results to heterogeneous media with dynamic disorder, providing new insights into reaction kinetics in living cells.

Findings

Dynamic heterogeneities broaden first-passage time distributions.

Disorder slows average reaction kinetics.

Dynamic disorder can facilitate faster individual reactions.

Abstract

Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid re-arrangements of the medium constantly change the effective diffusivity felt locally by a diffusing particle and thus impact the distribution of the first-passage time to a reaction event. Here, we investigate the effect of these dynamic spatio-temporal heterogeneities onto diffusion-limited reactions. We describe a general mathematical framework to translate many results for ordinary homogeneous Brownian motion to heterogeneous diffusion. In particular, we derive the probability density of the first-passage time to a reaction event and show how the dynamic disorder broadens the distribution and increases the likelihood of both short and long trajectories to reactive targets. While the disorder slows down reaction kinetics on average, its dynamic character is beneficial for a faster search and realization of an individual reaction event triggered by a single molecule.