The stochastic kinetics of chemical reaction networks can be 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 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:化学反应网络的随机动动学可以通过主方程描述化学反应网络的随机动动学,主方程可以提供由相互作用物种的矢量矢量组成的离散状态空间的概率分布的时间演变过程。由于总方程由于国家空间规模的组合爆炸而很难完全解决总方程,因此提出了若干分析近似。确定率方程(DRE)通过一个差别方程系统对系统进行宏观观察,该方程估计了每个物种的平均数量,但对于非线性互动,例如大规模运动动能学中的非线性动态,这种概率分布可能是不准确的。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组合组合总方程动态与DRE的人口动态结合起来,在微分数方程中进行介介介介,通过对化学反应网络的算法翻译,每个离散状态都代表了更不同的化学物种。我们从原始的系统向原始的系统解释其内在动态的网络,通过原始的系统向可扩展的系统解释的系统。