Quantitative mechanistic models based on reaction networks with stochastic chemical kinetics can help elucidate fundamental biological process where random fluctuations are relevant, such as in single cells. The dynamics of such models is described by the master equation, which provides the time course evolution of the probability distribution across the discrete state space consisting of vectors of population levels of the interacting biochemical species. Since solving the master equation exactly is very difficult in general due to the combinatorial explosion of the state space size, several analytical approximations have been proposed. The deterministic rate equation (DRE) offers a macroscopic view of the system by means of a system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interactions such as in mass-action kinetics. Here we propose finite state expansion (FSE), an analytical method that mediates between the microscopic and the macroscopic interpretations of a chemical reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the population dynamics of the DRE. This is done via an algorithmic translation of a chemical reaction network into a target expanded one where each discrete state is represented as a further distinct chemical species. The translation produces a network with stochastically equivalent dynamics, but the DRE of the expanded network can be interpreted as a correction to the original ones. Through a publicly available software implementation of FSE, we demonstrate its effectiveness in models from systems biology which challenge state-of-the-art techniques due to the presence of intrinsic noise, multi-scale population dynamics, and multi-stability.
翻译:基于与随机波动相关的反应网络(如单细胞)的定量机械模型。这些模型的动态由主方程式描述,它提供了由相互作用生物化学物种的矢量组成的离散状态空间的概率分布的演化过程。由于精确地解决总方程非常困难,因为由于州空间规模的组合式爆炸,因此提出了若干分析近似值。多分流率方程式(DRE)通过一个差异方程式系统,对系统进行了宏观透视,该方程式估计了每种物种的平均数量,但对于非线性互动(如大规模行动动能学)而言,这种模型的动态可能并不准确。我们在这里建议了有限的状态扩展(FSE),这是一种分析方法,通过将所选择的离散状态空间的母方方程式动态与DRE的动态相混合,通过一个差异方程式变异性方程式系统进行宏观透析,通过对每个离异性方程式网络进行离异性变异性解释,从而将一个不同的化学变异的网络变成一个不同的化学动态网络。