Simulating mesoscopic reaction-diffusion systems using the Gillespie algorithm
Simulating mesoscopic reaction-diffusion systems using the Gillespie algorithm
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DOI：
10.1103/physreve.71.041103
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发表时间：
2005-04-01
影响因子：
2.4
通讯作者：
Bernstein, D
中科院分区：
文献类型：
--
作者：
Bernstein, D
我们研究了Gillesbie算法在模拟细胞和微腔等介观体积中的空间非均匀反应扩散系统的应用。该方法包括将腔体离散成几个元素，并通过分子在相邻元素之间的运动来模拟化学物种的扩散。这些转变以一系列反应的形式表示，这些反应加入到化学体系中。这些扩散反应速率的推导是通过与非均匀网格上热方程的有限体积离散化相比较的。允许每个物种的扩散系数在空间上是不均匀的，包括不连续的。所得到的系统用快速直接法用吉列斯皮算法求解。我们证明，在适当的极限下，该方法再现了纯扩散系统的热方程和描述立方自催化反应的非线性反应速率方程的精确解。
We examine an application of the Gillespie algorithm to simulating spatially inhomogeneous reaction-diffusion systems in mesoscopic volumes such as cells and microchambers. The method involves discretizing the chamber into elements and modeling the diffusion of chemical species by the movement of molecules between neighboring elements. These transitions are expressed in the form of a set of reactions which are added to the chemical system. The derivation of the rates of these diffusion reactions is by comparison with a finite volume discretization of the heat equation on an unevenly spaced grid. The diffusion coefficient of each species is allowed to be inhomogeneous in space, including discontinuities. The resulting system is solved by the Gillespie algorithm using the fast direct method. We show that in an appropriate limit the method reproduces exact solutions of the heat equation for a purely diffusive system and the nonlinear reaction-rate equation describing the cubic autocatalytic reaction.