Hepp Benjamin, Gupta Ankit, Khammash Mustafa
Department of Biosystems Science and Engineering (D-BSSE), ETH Zurich, Switzerland.
J Chem Phys. 2015 Jan 21;142(3):034118. doi: 10.1063/1.4905196.
The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate 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 sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such a partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any 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. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.
描述随机反应网络（SRN）状态的概率分布根据化学主方程（CME）演化。使用诸如随机模拟算法（SSA）等蒙特卡罗方法来估计其解是很常见的。在许多情况下，这些模拟可能需要耗费大量不切实际的计算时间。因此，已经开发了许多方法来近似底层随机过程的样本路径并估计CME的解。这类方法中一个突出的类别包括混合方法，该方法将物种集和反应集划分为离散和连续子集。这样的划分将动力学分离为离散部分和连续部分。模拟这样的随机过程在计算上可能比使用SSA模拟精确的离散随机过程要容易得多。此外，对于某些类别的网络，可以应用准稳态假设来近似快速子网络的动力学。然而，随着SRN的动力学演化，这些划分可能在模拟过程中需要进行调整。我们开发了一种混合方法，通过自动将反应和物种集划分为离散和连续组件，并对可识别的快速子网络应用准稳态假设来近似CME的解。我们的方法不需要任何用户干预，并且能够适应利用反应之间变化的时间尺度分离和/或组成物种拷贝数的变化幅度。我们通过考虑系统生物学中的例子来证明所提出方法的效率，并表明在显著更少的计算时间内可以实现与精确概率分布非常好的近似。对于具有振荡动力学的系统尤其如此，在感兴趣的时间段内系统动力学变化很大。
