论文标题
与非质量动力学的复杂平衡反应网络的过渡图分解
Transition graph decomposition for complex balanced reaction networks with non-mass-action kinetics
论文作者
论文摘要
反应网络是广泛使用的模型来描述生化过程。生物大分子计数中的随机波动由于人口较小而引起了后果。这使得有必要偏爱随机，离散的人群，连续的时间模型。固定分布提供了固定机制上模型行为的快照，因此，在模型参数方面找到了它们的表达。本文的目的是描述原始模型的固定分布（其状态空间可能是无限的）何时与截断为有限状态的有限亚集的工艺的固定分布完全一致，直至归一化常数。我们确定的状态的有限子集称为副本，并受到反应网络模型的模块化拓扑的启发。通过这样的选择，我们证明了对反应网络随机模型的复杂平衡概念的新图形表征。该论文的结果适用于常用的质量动力学，但不限于它，实际上是为了进行更一般的环境。
Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor stochastic, discrete population, continuous time models. The stationary distributions provide snapshots of the model behavior at the stationary regime, and as such finding their expression in terms of the model parameters is of great interest. The aim of the present paper is to describe when the stationary distributions of the original model, whose state space is potentially infinite, coincide exactly with the stationary distributions of the process truncated to finite subsets of states, up to a normalizing constant. The finite subsets of states we identify are called copies and are inspired by the modular topology of reaction network models. With such a choice we prove a novel graphical characterization of the concept of complex balancing for stochastic models of reaction networks. The results of the paper hold for the commonly used mass-action kinetics but are not restricted to it, and are in fact stated for more general setting.
