Geometry and symmetry in biochemical reaction systems

TL;DR

This paper introduces a hypergraph-based framework to analyze the geometry and symmetry of biochemical reaction systems, capturing complex multi-molecular interactions beyond traditional pairwise graph models.

Contribution

It develops a general theory of automorphisms for oriented hypergraphs and links automorphism group structure to hypergraph Laplacian spectra, advancing the modeling of biochemical reactions.

Findings

Hypergraph automorphisms reveal symmetries in biochemical systems.

Automorphism group structure influences hypergraph Laplacian spectra.

The framework captures higher-order interactions in biochemical reactions.

Abstract

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.