Reaction rates for mesoscopic reaction-diffusion kinetics

Hellander, Stefan; Hellander, Andreas; Petzold, Linda

doi:10.1103/PhysRevE.91.023312

Reaction rates for mesoscopic reaction-diffusion kinetics

Journal Article · Mon Feb 23 00:00:00 EST 2015 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

DOI:https://doi.org/10.1103/PhysRevE.91.023312· OSTI ID:1343614

Hellander, Stefan ^[1]; Hellander, Andreas ^[2]; Petzold, Linda ^[3]

Univ. of California, Santa Barbara, CA (United States); DOE Office of Scientific and Technical Information (OSTI)
Uppsala Univ., Uppsala (Sweden)
Univ. of California, Santa Barbara, CA (United States)

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. Finally, 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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of California, Santa Barbara, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0008975

OSTI ID:: 1343614

Alternate ID(s):: OSTI ID: 1180098

Journal Information:: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics Journal Issue: 2 Vol. 91; ISSN 1539-3755; ISSN PLEEE8

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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