Reaction cleaving and complex-balanced distributions for chemical reaction networks with general kinetics
Reaction networks have become a major modelling framework in the biological sciences from epidemiology and population biology to genetics and cellular biology. In recent years, much progress has been made on stochastic reaction networks (SRNs),modelled as continuous time Markov chains (CTMCs) and th...
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| Abstract | Reaction networks have become a major modelling framework in the biological sciences from epidemiology and population biology to genetics and cellular biology. In recent years, much progress has been made on stochastic reaction networks (SRNs),modelled as continuous time Markov chains (CTMCs) and their stationary distributions. We are interested in complex-balanced stationary distributions, where the probability flow out of a complex equals the flow into the complex. We characterise the existence and the form of complex-balanced distributions of SRNs with arbitrary transition functions through conditions on the cycles of the reaction graph (a digraph). Furthermore, we give a sufficient condition for the existence of a complex-balanced distribution and give precise conditions for when it is also necessary. The sufficient condition is also necessary for mass-action kinetics (and certain generalisations of that) or if the connected components of the digraph are cycles. Moreover, we state a deficiency theorem, a generalisation of the deficiency theorem for stochastic mass-action kinetics to arbitrary stochastic kinetics. The theorem gives the co-dimension of the parameter space for which a complex-balanced distribution exists. To achieve this, we construct an iterative procedure to decompose a strongly connected reaction graph into disjoint cycles, such that the corresponding SRN has equivalent dynamics and preserves complex-balancedness, provided the original SRN had so. This decomposition might have independent interest and might be applicable to edge-labelled digraphs in general. |
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| AbstractList | Reaction networks have become a major modelling framework in the biological sciences from epidemiology and population biology to genetics and cellular biology. In recent years, much progress has been made on stochastic reaction networks (SRNs),modelled as continuous time Markov chains (CTMCs) and their stationary distributions. We are interested in complex-balanced stationary distributions, where the probability flow out of a complex equals the flow into the complex. We characterise the existence and the form of complex-balanced distributions of SRNs with arbitrary transition functions through conditions on the cycles of the reaction graph (a digraph). Furthermore, we give a sufficient condition for the existence of a complex-balanced distribution and give precise conditions for when it is also necessary. The sufficient condition is also necessary for mass-action kinetics (and certain generalisations of that) or if the connected components of the digraph are cycles. Moreover, we state a deficiency theorem, a generalisation of the deficiency theorem for stochastic mass-action kinetics to arbitrary stochastic kinetics. The theorem gives the co-dimension of the parameter space for which a complex-balanced distribution exists. To achieve this, we construct an iterative procedure to decompose a strongly connected reaction graph into disjoint cycles, such that the corresponding SRN has equivalent dynamics and preserves complex-balancedness, provided the original SRN had so. This decomposition might have independent interest and might be applicable to edge-labelled digraphs in general. |
| ArticleNumber | e87 |
| Author | Xia, Panqiu Wiuf, Carsten Hoessly, Linard |
| Author_xml | – sequence: 1 givenname: Linard surname: Hoessly fullname: Hoessly, Linard – sequence: 2 givenname: Carsten orcidid: 0000-0002-1302-4445 surname: Wiuf fullname: Wiuf, Carsten – sequence: 3 givenname: Panqiu surname: Xia fullname: Xia, Panqiu |
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| Cites_doi | 10.1007/s00285-021-01620-3 10.1201/9781420010664 10.1007/s11538-010-9517-4 10.1016/j.cam.2008.10.029 10.1007/s11538-015-0102-8 10.1007/s11538-014-9947-5 10.1007/s11538-018-0458-7 10.1007/978-3-319-16895-1 10.1017/cbo9780511810633 10.24072/pci.mcb.100405 10.1137/19m1244494 10.1103/revmodphys.87.925 10.1137/17m1153315 10.1137/15m1029916 10.1007/s11538-016-0220-y 10.1017/apr.2022.20 10.3934/mbe.2019103 10.1016/j.jsc.2008.08.006 10.1007/978-3-030-03858-8 10.1007/b98868 10.48550/arxiv.1312.3043 10.1007/978-0-387-21822-9 10.1137/22m150469x 10.1098/rsif.2020.0243 10.1016/j.mbs.2018.03.002 10.1038/s42003-021-02117-x 10.1007/bf00251225 |
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| Title | Reaction cleaving and complex-balanced distributions for chemical reaction networks with general kinetics |
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