Section: Mathematical & Computational Biology
Topic:
Biophysics and computational biology,
Cell biology,
Systems biology
Reaction cleaving and complex-balanced distributions for chemical reaction networks with general kinetics
Corresponding author(s): Wiuf, Carsten (wiuf@math.ku.dk)
10.24072/pcjournal.614 - Peer Community Journal, Volume 5 (2025), article no. e87
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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.
Type: Research article
Hoessly, Linard 1; Wiuf, Carsten 2; Xia, Panqiu 3
CC-BY 4.0
@article{10_24072_pcjournal_614,
author = {Hoessly, Linard and Wiuf, Carsten and Xia, Panqiu},
title = {Reaction cleaving and complex-balanced distributions for chemical reaction networks with general kinetics},
journal = {Peer Community Journal},
eid = {e87},
publisher = {Peer Community In},
volume = {5},
year = {2025},
doi = {10.24072/pcjournal.614},
language = {en},
url = {https://peercommunityjournal.org/articles/10.24072/pcjournal.614/}
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TY - JOUR AU - Hoessly, Linard AU - Wiuf, Carsten AU - Xia, Panqiu TI - Reaction cleaving and complex-balanced distributions for chemical reaction networks with general kinetics JO - Peer Community Journal PY - 2025 VL - 5 PB - Peer Community In UR - https://peercommunityjournal.org/articles/10.24072/pcjournal.614/ DO - 10.24072/pcjournal.614 LA - en ID - 10_24072_pcjournal_614 ER -
%0 Journal Article %A Hoessly, Linard %A Wiuf, Carsten %A Xia, Panqiu %T Reaction cleaving and complex-balanced distributions for chemical reaction networks with general kinetics %J Peer Community Journal %D 2025 %V 5 %I Peer Community In %U https://peercommunityjournal.org/articles/10.24072/pcjournal.614/ %R 10.24072/pcjournal.614 %G en %F 10_24072_pcjournal_614
Hoessly, L.; Wiuf, C.; Xia, P. Reaction cleaving and complex-balanced distributions for chemical reaction networks with general kinetics. Peer Community Journal, Volume 5 (2025), article no. e87. https://doi.org/10.24072/pcjournal.614
PCI peer reviews and recommendation, and links to data, scripts, code and supplementary information: 10.24072/pci.mcb.100405
Conflict of interest of the recommender and peer reviewers:
The recommender in charge of the evaluation of the article and the reviewers declared that they have no conflict of interest (as defined in the code of conduct of PCI) with the authors or with the content of the article.
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