Reaction rates for mesoscopic reaction-diffusion kinetics

摘要: The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic kinetics in systems biology. RDME derived from assumptions about the underlying physical properties of system, and it may produce unphysical results for models where those fail. In that case, other more comprehensive are better suited, such as hard-sphere Brownian dynamics (BD). Although model its own right, not inferred any specific microscale model, proves useful attempt approximate by choice reaction rates. this paper we derive scale-dependent rates matching certain statistics solution widely used microscopic BD model: Smoluchowski with Robin boundary condition at radius two molecules. We also establish fundamental limits on range mesh resolutions which approach yields accurate show both theoretically numerical examples lower limit, dynamics. sizes below less accurate. Thus, limit determines size obtain most results.