多尺度随机反应网络的自适应混合模拟
Adaptive Hybrid Simulations for Multiscale Stochastic Reaction Networks
摘要：
描述随机反应网络状态的概率分布根据化学主方程（CME）演化。通常使用蒙特卡罗方法（例如随机模拟算法（SSA））来估计其解。在许多情况下，这些模拟可能需要不切实际的计算时间。因此，已经开发了许多方法来近似化学主方程下的随机过程。突出的策略是混合模型，认为一些反应通道的发射是连续的，并应用准静态假设来近似快速子网络的动态。然而，由于随机反应网络的动态随时间变化，这些近似可能必须在模拟期间进行调整。我们开发了一种方法，通过自动划分的反应动力学到离散/连续的组件和应用可识别的快速子网络的准静态假设近似的解决方案的CME。我们的方法不需要用户干预，它适合利用反应之间的时间间隔和/或组成物种的拷贝数的变化幅度。我们证明了所提出的方法的效率，考虑从系统生物学的例子，并显示出非常好的近似的确切的概率分布，可以实现在显着更少的计算时间。
英文摘要：
The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases these simulations can take an impractical amount of computational time. Therefore many methods have been developed that approximate the Stochastic Process underlying the Chemical Master Equation. Prominent strategies are Hybrid Models that regard the firing of some reaction channels as being continuous and applying the quasi-stationary assumption to approximate the dynamics of fast subnetworks. However as the dynamics of a Stochastic Reaction Network changes with time these approximations might have to be adapted during the simulation. We develop a method that approximates the solution of a CME by automatically partitioning the reaction dynamics into discrete/continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from Systems Biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time.
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