ArticleCommunications biology2021
Derivation of stationary distributions of biochemical reaction networks via structure transformation.
Article in Communications biology, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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6 citing papers in PubMed.
- Toward single-cell control: noise-robust perfect adaptation in biomolecular systems.Nature communications · 2025Article
- Topological criterion for robust perfect adaptation of reaction fluxes in biological networks.iScience · 2025Article
- Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them.Entropy (Basel, Switzerland) · 2024Article
- A framework for deriving analytic steady states of biochemical reaction networks.PLoS computational biology · 2023Article
- Systematic inference identifies a major source of heterogeneity in cell signaling dynamics: The rate-limiting step number.Science advances · 2022Article
- Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities.PLoS computational biology · 2021Article
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Authors and funding
5 authors.
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Abstract
Long-term behaviors of biochemical reaction networks (BRNs) are described by steady states in deterministic models and stationary distributions in stochastic models. Unlike deterministic steady states, stationary distributions capturing inherent fluctuations of reactions are extremely difficult to derive analytically due to the curse of dimensionality. Here, we develop a method to derive analytic stationary distributions from deterministic steady states by transforming BRNs to have a special dynamic property, called complex balancing. Specifically, we merge nodes and edges of BRNs to match in- and out-flows of each node. This allows us to derive the stationary distributions of a large class of BRNs, including autophosphorylation networks of EGFR, PAK1, and Aurora B kinase and a genetic toggle switch. This reveals the unique properties of their stochastic dynamics such as robustness, sensitivity, and multi-modality. Importantly, we provide a user-friendly computational package, CASTANET, that automatically derives symbolic expressions of the stationary distributions of BRNs to understand their long-term stochasticity.
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