Various cellular and subcellular biological systems occur in the conditions where both reactions and diffusion take place. Since the concentration of species varies spatially, application of reaction-diffusion master equation has served as an effective method to handle these complicated systems; yet solving these equation incurs a large CPU time penalty. Counter to the traditional technique of generating many sample paths, this article introduces a method which combines Grima's effective rate equation approach (Grima, J Chem Phys. 2010;133:3) with a linear operator formalism for diffusion to capture averaged species behaviors. The formulation also shows correct results at various choices of compartment sizes, which have been found to be an important factor that can affect accuracy of the final predictions (Erban, Chapman, Phys Biol. 2009;6:4). It is shown that the method presented allows the computation of the mesoscopic average of reaction-diffusion systems at considerably accelerated rates (exceeding a thousand fold) over those based on sample path averages. © 2017 American Institute of Chemical Engineers AIChE J, 2017

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关于反应扩散系统介观行为的便利计算

在反应和扩散均发生的条件下，会发生各种细胞和亚细胞生物系统。由于物质的浓度在空间上变化，因此反应扩散主方程的应用已成为处理这些复杂系统的有效方法。但是解决这些方程式会导致大量的CPU时间损失。与生成许多样本路径的传统技术相反，本文介绍了一种结合Grima有效速率方程法的方法（Grima，J Chem Phys。2010; 133：3），使用线性算子形式表示进行扩散，以捕获平均物种行为。该制剂还在隔室尺寸的各种选择上显示出正确的结果，已发现这是可以影响最终预测的准确性的重要因素（Erban，Chapman，Phys Biol。2009 ; 6：4）。结果表明，与基于样本路径平均值的方法相比，所提出的方法可以以相当大的加速速率（超过一千倍）计算反应扩散系统的介观平均值。©2017美国化学工程师学会AIChE J，2017