基于扩散的随机模拟算法在连续空间中的嵌入
A Diffusion-Based Embedding of the Stochastic Simulation Algorithm in Continuous Space
摘要：
各种模拟方法已经被用于对反应扩散动力学进行建模--包括基于微分方程（DE）、随机模拟算法（SSA）、布朗动力学（BD）、格林函数反应动力学（GFRD）及其变型的方法--每种方法都提供了关于它们可以建模的现象范围、它们的计算易处理性、以及将它们与实验测量相匹配的困难。在这里，我们开发了一个多尺度的方法相结合的高效的SSA样采样适合混合系统的方面较慢，但空间感知GFRD模型，假设与GFRD的反应发生在一个空间异构的环境，必须明确建模。我们的方法在两个主要方面扩展了SSA方法。首先，我们采样双分子缔合反应扩散运动与时间相关的反应倾向。其次，反应位置从描述单个反应物的空间概率密度的重叠扩散球内取样。我们展示了通过应用于Michaelis-Menten模型，与其他方法相比，提供空间异质生物化学有效模拟的方法。
英文摘要：
A variety of simulation methodologies have been used for modeling reaction-diffusion dynamics -- including approaches based on Differential Equations (DE), the Stochastic Simulation Algorithm (SSA), Brownian Dynamics (BD), Green's Function Reaction Dynamics (GFRD), and variations thereon -- each offering trade-offs with respect to the ranges of phenomena they can model, their computational tractability, and the difficulty of fitting them to experimental measurements. Here, we develop a multiscale approach combining efficient SSA-like sampling suitable for well-mixed systems with aspects of the slower but space-aware GFRD model, assuming as with GFRD that reactions occur in a spatially heterogeneous environment that must be explicitly modeled. Our method extends the SSA approach in two major ways. First, we sample bimolecular association reactions following diffusive motion with a time-dependent reaction propensity. Second, reaction locations are sampled from within overlapping diffusion spheres describing the spatial probability densities of individual reactants. We show the approach to provide efficient simulation of spatially heterogeneous biochemistry in comparison to alternative methods via application to a Michaelis-Menten model.
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