On facilitated computation of mesoscopic behavior of reaction‐diffusion systems

Various cellular and subcellular biological systems occur in the conditions where both reactions and diffusion take place. Since the concentration of species varies spatially, application of reaction‐diffusion master equation has served as an effective method to handle these complicated systems; yet solving these equation incurs a large CPU time penalty. Counter to the traditional technique of generating many sample paths, this article introduces a method which combines Grima's effective rate equation approach (Grima, J Chem Phys. 2010;133:3) with a linear operator formalism for diffusion to capture averaged species behaviors. The formulation also shows correct results at various choices of compartment sizes, which have been found to be an important factor that can affect accuracy of the final predictions (Erban, Chapman, Phys Biol. 2009;6:4). It is shown that the method presented allows the computation of the mesoscopic average of reaction‐diffusion systems at considerably accelerated rates (exceeding a thousand fold) over those based on sample path averages. © 2017 American Institute of Chemical Engineers AIChE J, 63: 5258–5266, 2017