期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 259, 期 -, 页码 536-567出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2013.12.023
关键词
Stochastic reaction-diffusion; First-Passage Kinetic Monte Carlo; Stochastic chemical kinetics; Cell biology; Fokker-Planck equation
资金
- NSF [DMS-0602204 EMSW21-RTG, DMS-0920886, DMS-1255408]
- Boston University
- CCS Summer Undergraduate Research Fellowship (SURF) program at UCSB
- UCSB Math
- Direct For Mathematical & Physical Scien [0956210] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1255408] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [0956210] Funding Source: National Science Foundation
Stochastic reaction-diffusion models are now a popular tool for studying physical systems in which both the explicit diffusion of molecules and noise in the chemical reaction process play important roles. The Smoluchowski diffusion-limited reaction model (SDLR) is one of several that have been used to study biological systems. Exact realizations of the underlying stochastic processes described by the SDLR model can be generated by the recently proposed First-Passage Kinetic Monte Carlo (FPKMC) method. This exactness relies on sampling analytical solutions to one and two-body diffusion equations in simplified protective domains. In this work we extend the FPKMC to allow for drift arising from fixed, background potentials. As the corresponding Fokker-Planck equations that describe the motion of each molecule can no longer be solved analytically, we develop a hybrid method that discretizes the protective domains. The discretization is chosen so that the drift-diffusion of each molecule within its protective domain is approximated by a continuous-time random walk on a lattice. New lattices are defined dynamically as the protective domains are updated, hence we will refer to our method as Dynamic Lattice FPKMC or DL-FPKMC. We focus primarily on the one-dimensional case in this manuscript, and demonstrate the numerical convergence and accuracy of our method in this case for both smooth and discontinuous potentials. We also present applications of our method, which illustrate the impact of drift on reaction kinetics. (C) 2013 Elsevier Inc. All rights reserved.
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