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arXiv · 1503.07009

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

Emilie Blanc·Stefan Engblom·Andreas Hellander·Per Lötstedt
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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.

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Emilie Blanc, Stefan Engblom, Andreas Hellander, Per Lötstedt. 2015-03-24. Mesoscopic modeling of stochastic reaction-diffusion kinetics in the subdiffusive regime. https://doi.org/10.1137/15m1013110

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