Geometry and symmetry in biochemical reaction systems

Raffaella Mulas,Rubén J Sánchez-García,Ben D Macarthur

doi:10.1007/s12064-021-00353-7

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.

Highlights

Many real-world complex systems can be modelled as graphs in which vertices represent system elements and edges pairwise interactions between those elements Newman (2018), Barabási (2016)
This approach allows powerful tools from graph theory to be used in the analysis of complex systems in numerous domains—from technological networks such as power grids, the internet and world-wideweb to biological networks such as food webs and molecular interaction networks, and social networks such as those that arise in online social media—and has been tremendously successful in discerning important structural and dynamical properties of the complex systems they represent Newman (2003)
Biochemical reaction systems often contain duplication which manifests as symmetry in their underlying hypergraphs

Summary

Introduction

Many real-world complex systems can be modelled as graphs in which vertices represent system elements and edges pairwise interactions between those elements Newman (2018), Barabási (2016). In oriented hypergraphs, every vertex has a sign for each hyperedge in which it is contained (Definition 3).

Results

Conclusion