Reaction rates for mesoscopic reaction-diffusion kinetics

Stefan Hellander, Andreas Hellander, and Linda Petzold
Phys. Rev. E 91, 023312 – Published 23 February 2015

Abstract

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

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  • Received 1 November 2014

DOI:https://doi.org/10.1103/PhysRevE.91.023312

©2015 American Physical Society

Authors & Affiliations

Stefan Hellander

  • Department of Computer Science, University of California, Santa Barbara, California 93106-5070, Santa Barbara, USA

Andreas Hellander

  • Department of Information Technology, Uppsala University, Box 337, SE-75105, Uppsala, Sweden

Linda Petzold

  • Department of Computer Science, University of California, Santa Barbara, California 93106-5070, Santa Barbara, USA

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Issue

Vol. 91, Iss. 2 — February 2015

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