Hasenauer J, Wolf V, Kazeroonian A, Theis F J
Institute of Computational Biology, Helmholtz Zentrum München, Ingolstädter Landstraße 1, 85764 , Neuherberg, Germany,
J Math Biol. 2014 Sep;69(3):687-735. doi: 10.1007/s00285-013-0711-5. Epub 2013 Aug 6.
The time-evolution of continuous-time discrete-state biochemical processes is governed by the Chemical Master Equation (CME), which describes the probability of the molecular counts of each chemical species. As the corresponding number of discrete states is, for most processes, large, a direct numerical simulation of the CME is in general infeasible. In this paper we introduce the method of conditional moments (MCM), a novel approximation method for the solution of the CME. The MCM employs a discrete stochastic description for low-copy number species and a moment-based description for medium/high-copy number species. The moments of the medium/high-copy number species are conditioned on the state of the low abundance species, which allows us to capture complex correlation structures arising, e.g., for multi-attractor and oscillatory systems. We prove that the MCM provides a generalization of previous approximations of the CME based on hybrid modeling and moment-based methods. Furthermore, it improves upon these existing methods, as we illustrate using a model for the dynamics of stochastic single-gene expression. This application example shows that due to the more general structure, the MCM allows for the approximation of multi-modal distributions.
连续时间离散状态生化过程的时间演化由化学主方程（CME）支配，该方程描述了每种化学物质分子数的概率。由于对于大多数过程而言，相应的离散状态数很大，因此对CME进行直接数值模拟通常是不可行的。在本文中，我们介绍了条件矩方法（MCM），这是一种求解CME的新型近似方法。MCM对低拷贝数物种采用离散随机描述，对中/高拷贝数物种采用基于矩的描述。中/高拷贝数物种的矩以低丰度物种的状态为条件，这使我们能够捕捉例如多吸引子和振荡系统中出现的复杂相关结构。我们证明，MCM是基于混合建模和基于矩的方法对CME先前近似的推广。此外，正如我们使用随机单基因表达动力学模型所说明的那样，它改进了这些现有方法。这个应用示例表明，由于结构更通用，MCM允许对多峰分布进行近似。
