2023/03/24 by Praful Gagrani, V. M. Blanco, Gagrani, Praful +5 · 4 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #Gene Regulatory Network Analysis #Molecular Networks (q-bio.MN) #Origins and Evolution of Life #Protein Structure and Dynamics
paper · pdf · doi:10.48550/arxiv.2303.14238
openalex publication_date 2023/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.