Mesoscopic modeling of stochastic reaction-diffusion kinetics in the subdiffusive regime

TL;DR

This paper develops a mesoscopic computational framework for reaction-diffusion processes under subdiffusion, revealing models that capture the transition from ordinary to anomalous behavior over time.

Contribution

It extends existing subdiffusion models into a consistent reaction-diffusion framework and analyzes their dynamic properties and macroscopic implications.

Findings

Models exhibit ordinary behavior at short and long times.

Intermediate times show anomalous subdiffusive behavior.

Numerical experiments confirm the theoretical predictions.

Abstract

Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model of subdiffusion into an accurate and consistent reaction-subdiffusion computational framework. Two different possible models of chemical reaction are revealed and some basic dynamic properties are derived. In certain cases those mesoscopic models have a direct interpretation at the macroscopic level as fractional partial differential equations in a bounded time interval. Through analysis and numerical experiments we estimate the macroscopic effects of reactions under subdiffusive mixing. The models display properties observed also in experiments: for a short time interval the behavior of the diffusion and the reaction is ordinary, in an intermediate interval the behavior is anomalous, and at long times the behavior is ordinary again.