Reaction rates for a generalized reaction-diffusion master equation
- Univ. of California, Santa Barbara, CA (United States). Dept. of Computer Science
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules.
- Research Organization:
- Univ. of California, Santa Barbara, CA (United States)
- Sponsoring Organization:
- USDOE; National Science Foundation (NSF); National Institutes of Health (NIH); US Army Research Office (ARO)
- Grant/Contract Number:
- SC0008975; DMS-1001012; R01-GM113241-01; W911NF-09-D-0001; R01-EB014877-01
- OSTI ID:
- 1343615
- Alternate ID(s):
- OSTI ID: 1235628
- Journal Information:
- Physical Review E, Vol. 93, Issue 1; ISSN 2470-0045
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
A framework for discrete stochastic simulation on 3D moving boundary domains
|
journal | November 2016 |
Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning
|
journal | December 2017 |
Self-organised segregation of bacterial chromosomal origins
|
posted_content | August 2018 |
Self-organised segregation of bacterial chromosomal origins
|
journal | August 2019 |
Similar Records
Reaction rates for mesoscopic reaction-diffusion kinetics
A framework for discrete stochastic simulation on 3D moving boundary domains