Reaction rates for mesoscopic reaction-diffusion kinetics.
Reaction rates for mesoscopic reaction-diffusion kinetics.
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介观反应扩散动力学的反应速率。
DOI：
10.1103/physreve.91.023312
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发表时间：
2015-02
期刊：
影响因子：
--
通讯作者：
Petzold L
中科院分区：
文献类型：
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作者：
Hellander S;Hellander A;Petzold L
介观反应扩散主方程（RDME）是系统生物学中常用的随机反应扩散动力学建模框架。RDME是从关于系统的底层物理特性的假设中派生出来的，如果这些假设不成立，它可能会为模型产生非物理的结果。在这种情况下，其他更全面的模型更适合，比如硬球布朗动力学（BD）。尽管RDME本身就是一个模型，而不是从任何特定的微尺度模型中推断出来的，但通过特定的介观反应速率选择来近似微尺度模型被证明是有用的。本文通过将RDME溶液的某些统计量与一种广泛使用的微观BD模型（具有Robin边界条件的Smoluchowski模型）在两个分子的反应半径处的溶液统计量相匹配，推导出了介观尺度相关的反应速率。我们还建立了网格分辨率范围的基本限制，该方法可以产生准确的结果，并在理论和数值示例中表明，当我们接近较低的基本限制时，介观动力学接近微观动力学。我们表明，对于低于基本下限的网格尺寸，结果不太准确。因此，下限决定了我们获得最准确结果的网格尺寸。
The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.