Understanding Multistationarity of Fully Open Reaction Networks

Shenghao  Yao; AmirHosein Sadeghimanesh; Matthew England

doi:10.1007/s11538-025-01537-8

Understanding Multistationarity of Fully Open Reaction Networks

Research Centre for Computational Science and Mathematical Modelling

Research output: Contribution to journal › Article › peer-review

Abstract

This work addresses multistationarity of fully open reaction networks equipped with mass action kinetics. We improve upon existing results relating existence of positive feedback loops in a reaction network and multistationarity; and we provide a novel deterministic operation to generate new non-multistationary networks. This is interesting because while there were many operations to create infinitely many new multistationary networks from a multistationary example, this is the first such operation for the non-multistationary counterpart.

Such tools for the generation of example networks have a use-case in the application of data science to reaction network theory. We demonstrate this by using new data, along with a novel graph representation of reaction networks that is unique up to a permutation on the name of species of the network, to train a graph attention neural network model to predict multistationarity of reaction networks. This is the first time machine learning tools are used for studying classification problems of reaction networks.

Original language	English
Article number	176
Number of pages	41
Journal	Bulletin of Mathematical Biology
Volume	87
DOIs	https://doi.org/10.1007/s11538-025-01537-8
Publication status	Published - 7 Nov 2025

Bibliographical note

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.
This version of the article has been accepted for publication, after peer review (when applicable) but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s11538-025-01537-8

Funding

The first author acknowledges funding from Coventry University for a summer research internship. The second and third authors acknowledge the support of UKRI EPSRC Grant EP/T015748/1, “Pushing Back the Doubly-Exponential Wall of Cylindrical Algebraic Decomposition (the DEWCAD Project).

Funders	Funder number
Coventry University
Engineering and Physical Sciences Research Council	EP/T015748/1

Keywords

Chemical Reaction Network
Multistationarity
Machine Learning
Graph Attention Network

Access to Document

10.1007/s11538-025-01537-8

Cite this

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abstract = " This work addresses multistationarity of fully open reaction networks equipped with mass action kinetics. We improve upon existing results relating existence of positive feedback loops in a reaction network and multistationarity; and we provide a novel deterministic operation to generate new non-multistationary networks. This is interesting because while there were many operations to create infinitely many new multistationary networks from a multistationary example, this is the first such operation for the non-multistationary counterpart. Such tools for the generation of example networks have a use-case in the application of data science to reaction network theory. We demonstrate this by using new data, along with a novel graph representation of reaction networks that is unique up to a permutation on the name of species of the network, to train a graph attention neural network model to predict multistationarity of reaction networks. This is the first time machine learning tools are used for studying classification problems of reaction networks.",

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N1 - Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders. This version of the article has been accepted for publication, after peer review (when applicable) but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s11538-025-01537-8

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N2 - This work addresses multistationarity of fully open reaction networks equipped with mass action kinetics. We improve upon existing results relating existence of positive feedback loops in a reaction network and multistationarity; and we provide a novel deterministic operation to generate new non-multistationary networks. This is interesting because while there were many operations to create infinitely many new multistationary networks from a multistationary example, this is the first such operation for the non-multistationary counterpart. Such tools for the generation of example networks have a use-case in the application of data science to reaction network theory. We demonstrate this by using new data, along with a novel graph representation of reaction networks that is unique up to a permutation on the name of species of the network, to train a graph attention neural network model to predict multistationarity of reaction networks. This is the first time machine learning tools are used for studying classification problems of reaction networks.

AB - This work addresses multistationarity of fully open reaction networks equipped with mass action kinetics. We improve upon existing results relating existence of positive feedback loops in a reaction network and multistationarity; and we provide a novel deterministic operation to generate new non-multistationary networks. This is interesting because while there were many operations to create infinitely many new multistationary networks from a multistationary example, this is the first such operation for the non-multistationary counterpart. Such tools for the generation of example networks have a use-case in the application of data science to reaction network theory. We demonstrate this by using new data, along with a novel graph representation of reaction networks that is unique up to a permutation on the name of species of the network, to train a graph attention neural network model to predict multistationarity of reaction networks. This is the first time machine learning tools are used for studying classification problems of reaction networks.

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Understanding Multistationarity of Fully Open Reaction Networks

Abstract

Bibliographical note

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Keywords

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Fingerprint

Designing Machine Learning Tools to Characterize Multi-stationarity of Fully Open Reaction Networks

Designing Machine Learning Tools to Characterize Multistationarity of Fully Open Reaction Networks

Using ML tools to predict number of solutions of parametric system of polynomial equations with the help of CRNs

Cite this

Understanding Multistationarity of Fully Open Reaction Networks

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Embargoed Document

Fingerprint

Activities

Designing Machine Learning Tools to Characterize Multi-stationarity of Fully Open Reaction Networks

Designing Machine Learning Tools to Characterize Multistationarity of Fully Open Reaction Networks

Using ML tools to predict number of solutions of parametric system of polynomial equations with the help of CRNs

Cite this