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Reaction rates for mesoscopic reaction-diffusion kinetics.

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.

Authors+Show Affiliations

Department of Computer Science, University of California, Santa Barbara, California 93106-5070, Santa Barbara, USA.Department of Information Technology, Uppsala University, Box 337, SE-75105, Uppsala, Sweden.Department of Computer Science, University of California, Santa Barbara, California 93106-5070, Santa Barbara, USA.

Pub Type(s)

Journal Article
Research Support, N.I.H., Extramural
Research Support, U.S. Gov't, Non-P.H.S.

Language

eng

PubMed ID

25768640

Citation

Hellander, Stefan, et al. "Reaction Rates for Mesoscopic Reaction-diffusion Kinetics." Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol. 91, no. 2, 2015, p. 023312.
Hellander S, Hellander A, Petzold L. Reaction rates for mesoscopic reaction-diffusion kinetics. Phys Rev E Stat Nonlin Soft Matter Phys. 2015;91(2):023312.
Hellander, S., Hellander, A., & Petzold, L. (2015). Reaction rates for mesoscopic reaction-diffusion kinetics. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 91(2), p. 023312.
Hellander S, Hellander A, Petzold L. Reaction Rates for Mesoscopic Reaction-diffusion Kinetics. Phys Rev E Stat Nonlin Soft Matter Phys. 2015;91(2):023312. PubMed PMID: 25768640.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Reaction rates for mesoscopic reaction-diffusion kinetics. AU - Hellander,Stefan, AU - Hellander,Andreas, AU - Petzold,Linda, Y1 - 2015/02/23/ PY - 2014/11/01/received PY - 2015/3/14/entrez PY - 2015/3/15/pubmed PY - 2016/1/19/medline SP - 023312 EP - 023312 JF - Physical review. E, Statistical, nonlinear, and soft matter physics JO - Phys Rev E Stat Nonlin Soft Matter Phys VL - 91 IS - 2 N2 - 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. SN - 1550-2376 UR - https://www.unboundmedicine.com/medline/citation/25768640/Reaction_rates_for_mesoscopic_reaction_diffusion_kinetics_ L2 - https://www.ncbi.nlm.nih.gov/pmc/articles/pmid/25768640/ DB - PRIME DP - Unbound Medicine ER -