Hu Jifeng, Kang Hye-Won, Othmer Hans G
School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA.
Bull Math Biol. 2014 Apr;76(4):854-94. doi: 10.1007/s11538-013-9849-y. Epub 2013 May 30.
Reaction and diffusion processes are used to model chemical and biological processes over a wide range of spatial and temporal scales. Several routes to the diffusion process at various levels of description in time and space are discussed and the master equation for spatially discretized systems involving reaction and diffusion is developed. We discuss an estimator for the appropriate compartment size for simulating reaction-diffusion systems and introduce a measure of fluctuations in a discretized system. We then describe a new computational algorithm for implementing a modified Gillespie method for compartmental systems in which reactions are aggregated into equivalence classes and computational cells are searched via an optimized tree structure. Finally, we discuss several examples that illustrate the issues that have to be addressed in general systems.
反应和扩散过程被用于在广泛的空间和时间尺度上对化学和生物过程进行建模。讨论了在时间和空间的不同描述层次上通向扩散过程的几种途径，并推导了涉及反应和扩散的空间离散系统的主方程。我们讨论了用于模拟反应扩散系统的合适隔室大小的估计器，并引入了离散系统中涨落的一种度量。然后，我们描述了一种新的计算算法，用于实现一种改进的 Gillespie 方法，用于隔室系统，其中反应被聚集到等价类中，并且通过优化的树结构搜索计算单元。最后，我们讨论了几个例子，这些例子说明了一般系统中必须解决的问题。
