Validity conditions for stochastic chemical kinetics in diffusion-limited systems
Validity conditions for stochastic chemical kinetics in diffusion-limited systems
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DOI：
10.1063/1.4863990
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发表时间：
2014-02-07
影响因子：
4.4
通讯作者：
Seitaridou, Effrosyni
中科院分区：
文献类型：
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作者：
Gillespie, Daniel T.;Petzold, Linda R.;Seitaridou, Effrosyni
化学主方程 (CME) 和数学上等效的随机模拟算法 (SSA) 假设化学反应系统中的反应物分子在整个容纳体积中是“稀释的”和“充分混合的”。在这里，我们阐明了这两个条件的含义，并说明了为什么必须满足这两个条件才能使双分子反应以 CME 和 SSA 假定的方式物理发生。我们证明这些条件是密切相关的，因为当且仅当系统被稀释时，它才会保持良好的混合。我们探讨了这些有效性条件对于 CME 和 SSA 的反应扩散（或空间不均匀）扩展对包含体积不一定混合良好但可以划分为混合良好的立方子体积（体素）的系统的影响。我们证明，有效性条件以及确保体素之间扩散引起的分子跳跃概率的物理有效性所需的附加条件要求体素边缘长度具有严格的正下界。我们证明，如果体素边缘长度以尊重该下限的方式稳步减小，则反应扩散 CME 和 SSA 中双分子反应发生的平均速率将保持恒定，而扩散转移反应的平均速率将随着体素边缘长度的平方反比而增加。我们的结论是，尽管反应扩散 CME 和 SSA 本质上是近似的，并且不能通过将体素大小缩小到零来使其精确，但它们在许多实际情况下应该是有用的。 (C) 2014 AIP 出版有限责任公司。
The chemical master equation (CME) and the mathematically equivalent stochastic simulation algorithm (SSA) assume that the reactant molecules in a chemically reacting system are "dilute" and "well-mixed" throughout the containing volume. Here we clarify what those two conditions mean, and we show why their satisfaction is necessary in order for bimolecular reactions to physically occur in the manner assumed by the CME and the SSA. We prove that these conditions are closely connected, in that a system will stay well-mixed if and only if it is dilute. We explore the implications of these validity conditions for the reaction-diffusion (or spatially inhomogeneous) extensions of the CME and the SSA to systems whose containing volumes are not necessarily well-mixed, but can be partitioned into cubical subvolumes (voxels) that are. We show that the validity conditions, together with an additional condition that is needed to ensure the physical validity of the diffusion-induced jump probability rates of molecules between voxels, require the voxel edge length to have a strictly positive lower bound. We prove that if the voxel edge length is steadily decreased in a way that respects that lower bound, the average rate at which bimolecular reactions occur in the reaction-diffusion CME and SSA will remain constant, while the average rate of diffusive transfer reactions will increase as the inverse square of the voxel edge length. We conclude that even though the reaction-diffusion CME and SSA are inherently approximate, and cannot be made exact by shrinking the voxel size to zero, they should nevertheless be useful in many practical situations. (C) 2014 AIP Publishing LLC.