Polyhedral geometry and combinatorics of an autocatalytic ecosystem

Developing a mathematical understanding of autocatalysis in reaction networks has both theoretical and practical implications. We review definitions of autocatalytic networks and prove some properties for minimal autocatalytic subnetworks (MASs). We show that it is possible to classify MASs in equiv...

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Bibliographic Details
Published inarXiv.org
Main Authors Gagrani, Praful, Blanco, Victor, Smith, Eric, Baum, David
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 10.11.2023
Subjects
Algorithms
Autocatalysis
Chemical reactions
Clusters
Combinatorial analysis
Granulation
Mathematical analysis
Networks
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Summary:Developing a mathematical understanding of autocatalysis in reaction networks has both theoretical and practical implications. We review definitions of autocatalytic networks and prove some properties for minimal autocatalytic subnetworks (MASs). We show that it is possible to classify MASs in equivalence classes, and develop mathematical results about their behavior. We also provide linear-programming algorithms to exhaustively enumerate them and a scheme to visualize their polyhedral geometry and combinatorics. We then define cluster chemical reaction networks, a framework for coarse-graining real chemical reactions with positive integer conservation laws. We find that the size of the list of minimal autocatalytic subnetworks in a maximally connected cluster chemical reaction network with one conservation law grows exponentially in the number of species. We end our discussion with open questions concerning an ecosystem of autocatalytic subnetworks and multidisciplinary opportunities for future investigation.
ISSN:2331-8422