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Derivation of stationary distributions of biochemical reaction networks via structure transformation

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 d...

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Autores principales: Hong, Hyukpyo, Kim, Jinsu, Ali Al-Radhawi, M., Sontag, Eduardo D., Kim, Jae Kyoung
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8144570/
https://www.ncbi.nlm.nih.gov/pubmed/34031517
http://dx.doi.org/10.1038/s42003-021-02117-x
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author Hong, Hyukpyo
Kim, Jinsu
Ali Al-Radhawi, M.
Sontag, Eduardo D.
Kim, Jae Kyoung
author_facet Hong, Hyukpyo
Kim, Jinsu
Ali Al-Radhawi, M.
Sontag, Eduardo D.
Kim, Jae Kyoung
author_sort Hong, Hyukpyo
collection PubMed
description 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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spelling pubmed-81445702021-05-27 Derivation of stationary distributions of biochemical reaction networks via structure transformation Hong, Hyukpyo Kim, Jinsu Ali Al-Radhawi, M. Sontag, Eduardo D. Kim, Jae Kyoung Commun Biol Article 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. Nature Publishing Group UK 2021-05-24 /pmc/articles/PMC8144570/ /pubmed/34031517 http://dx.doi.org/10.1038/s42003-021-02117-x Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Hong, Hyukpyo
Kim, Jinsu
Ali Al-Radhawi, M.
Sontag, Eduardo D.
Kim, Jae Kyoung
Derivation of stationary distributions of biochemical reaction networks via structure transformation
title Derivation of stationary distributions of biochemical reaction networks via structure transformation
title_full Derivation of stationary distributions of biochemical reaction networks via structure transformation
title_fullStr Derivation of stationary distributions of biochemical reaction networks via structure transformation
title_full_unstemmed Derivation of stationary distributions of biochemical reaction networks via structure transformation
title_short Derivation of stationary distributions of biochemical reaction networks via structure transformation
title_sort derivation of stationary distributions of biochemical reaction networks via structure transformation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8144570/
https://www.ncbi.nlm.nih.gov/pubmed/34031517
http://dx.doi.org/10.1038/s42003-021-02117-x
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