Geometry and symmetry in biochemical reaction systems

Complex systems of intracellular biochemical reactions have a central role in regulating cell identities and functions. Biochemical reaction systems are typically studied using the language and tools of graph theory. However, graph representations only describe pairwise interactions between molecular species and so are not well suited to modelling complex sets of reactions that may involve numerous reactants and/or products. Here, we make use of a recently developed hypergraph theory of chemical reactions that naturally allows for higher-order interactions to explore the geometry and quantify functional redundancy in biochemical reactions systems. Our results constitute a general theory of automorphisms for oriented hypergraphs and describe the effect of automorphism group structure on hypergraph Laplacian spectra.

Automated summary

Intracellular biochemical reaction systems play a central role in regulating cell identities and functions. While traditionally studied using graph theory, the newly developed hypergraph theory of chemical reactions allows for higher-order interactions and provides insights into geometry and quantitative functional redundancy in these systems. The results contribute to a general theory of automorphisms for oriented hypergraphs and describe the impact of automorphism group structure on hypergraph Laplacian spectra.