Reaction-diffusion master equation in the microscopic limit
Reaction-diffusion master equation in the microscopic limit
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DOI：
10.1103/physreve.85.042901
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发表时间：
2012-04-03
影响因子：
2.4
通讯作者：
Petzold, Linda
中科院分区：
文献类型：
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作者：
Hellander, Stefan;Hellander, Andreas;Petzold, Linda
反应扩散动力学的随机建模已成为生化反应网络研究的强大理论工具。两个经常使用的模型是粒子跟踪的Smoluchowski框架和驻留反应 - 扩散主方程（RDME）框架。随着网格尺寸从粗糙到细小，RDME最初变得更加准确。但是，最近的发展表明，随着晶格间距变得非常好，与Smoluchowski模型相比，它将变得越来越不准确。在这里，我们为为什么RDME崩溃给出了一个普遍而简单的论点。我们的分析表明，对体素大小的严格限制，没有局部RDME可以同意Smoluchowski模型，并让我们在两个和三个维度中量化此限制。在这个观点中，我们审查并讨论了最新的工作，其中已通过不同的方式修改了RDME，以便更好地同意非常小的体素尺寸的微观模型。
Stochastic modeling of reaction-diffusion kinetics has emerged as a powerful theoretical tool in the study of biochemical reaction networks. Two frequently employed models are the particle-tracking Smoluchowski framework and the on-lattice reaction-diffusion master equation (RDME) framework. As the mesh size goes from coarse to fine, the RDME initially becomes more accurate. However, recent developments have shown that it will become increasingly inaccurate compared to the Smoluchowski model as the lattice spacing becomes very fine. Here we give a general and simple argument for why the RDME breaks down. Our analysis reveals a hard limit on the voxel size for which no local RDME can agree with the Smoluchowski model and lets us quantify this limit in two and three dimensions. In this light we review and discuss recent work in which the RDME has been modified in different ways in order to better agree with the microscale model for very small voxel sizes.