Mesoscopic modeling of stochastic reaction-diffusion kinetics in the subdiffusive regime
For researchers studying stochastic reaction-diffusion kinetics in living cells, this work provides a computational framework for subdiffusive chemical processes, though it is an incremental extension of an existing model.
The paper extends a mesoscopic model of subdiffusion into a reaction-subdiffusion computational framework, revealing two possible reaction models and deriving basic dynamic properties. Through analysis and numerical experiments, it estimates macroscopic effects of reactions under subdiffusive mixing, showing ordinary, anomalous, and ordinary behavior over different time intervals.
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.