ArticleFrontiers in cell and developmental biology2023
The linear framework II: using graph theory to analyse the transient regime of Markov processes.
Article in Frontiers in cell and developmental biology, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
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7 citing papers in PubMed.
- Decoupling between activation time and steady-state level in input-output responses.PLoS computational biology · 2026Article
- Algebraic formulas for first-passage times of Markov processes in the linear framework.Bulletin of mathematical biology · 2025Article
- Decoupling between activation time and steady-state level in input-output responses.bioRxiv : the preprint server for biology · 2025Article
- Stochastic thermodynamics for biological functions.Quantitative biology (Beijing, China) · 2025Review
- A mathematical model clarifies the ABC Score formula used in enhancer-gene prediction.bioRxiv : the preprint server for biology · 2024Article
- The Hill function is the universal Hopfield barrier for sharpness of input-output responses.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- The Hill function is the universal Hopfield barrier for sharpness of input-output responses.bioRxiv : the preprint server for biology · 2024Article
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Abstract
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.
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