The linear framework II: using graph theory to analyse the transient regime of Markov processes.
The linear framework II: using graph theory to analyse the transient regime of Markov processes.
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DOI：
10.3389/fcell.2023.1233808
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发表时间：
2023
影响因子：
5.5
通讯作者：
中科院分区：
文献类型：
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线性框架使用有限的有向图和标记的边缘来模拟生物分子系统。图形顶点表示化学物质或分子状态，边缘表示反应或转变，边缘标签表示速率，也描述了系统如何与环境相互作用。本文是最近对该框架的回顾的续集，该框架侧重于图论方法如何将稳态作为边标记的有理代数函数提供洞察力。在这里，我们关注于对应于连续时间马尔可夫过程的系统的暂态状态。在这种情况下，图指定了过程的无穷小生成器。我们展示了第一次穿越时间分布的矩，以及相关的量，如分裂概率和条件第一次穿越时间，也可以表示为标签的有理代数函数。这种能力是及时的，因为新的实验方法终于可以进入瞬态动态状态，并揭示在达到稳态之前发生的计算和信息处理。我们通过实例说明了概念、方法和公式，并展示了如何使用结果来阐明文献中的先前发现。
The linear framework uses finite, directed graphs with labelled edges to model biomolecular systems. Graph vertices represent chemical species or molecular states, edges represent reactions or transitions and edge labels represent rates that also describe how the system is interacting with its environment. The present paper is a sequel to a recent review of the framework that focussed on how graph-theoretic methods give insight into steady states as rational algebraic functions of the edge labels. Here, we focus on the transient regime for systems that correspond to continuous-time Markov processes. In this case, the graph specifies the infinitesimal generator of the process. We show how the moments of the first-passage time distribution, and related quantities, such as splitting probabilities and conditional first-passage times, can also be expressed as rational algebraic functions of the labels. This capability is timely, as new experimental methods are finally giving access to the transient dynamic regime and revealing the computations and information processing that occur before a steady state is reached. We illustrate the concepts, methods and formulas through examples and show how the results may be used to illuminate previous findings in the literature.