Transitions and thermodynamics on species graphs of chemical reaction networks.

Abstract

Chemical reaction network (CRN) theory is widely utilized to model and analyze a wide range of biochemical phenomena. Structural transformations and reductions serve as essential tools to better understand how topological properties of a CRN are related with specific functions. In this context, graph-based representations of CRNs have been explored; however, their connections to concentration dynamics and thermodynamics remain elusive. In this study, we propose a natural transformation from the classical complex-reaction graph to a species-transition graph, leveraging the conservation laws of the stoichiometric matrix. By introducing transition matrices on the species graph, the concentration dynamics of CRNs are reinterpreted as the differences between the physically observable inflow and outflow of species. This approach enables the formal lumping of multiple reactions into fewer interactions, which we demonstrate using a realistic metabolic model of E. coli. Additionally, we define species-specific thermodynamic quantities on the species graphs and establish bounds relating them to conventional reactionwise quantities. The specieswise bounds of conventional driving forces and entropy production rates can outperform the bounds determined by reactionwise flux fluctuations, as illustrated through numerical simulations with the Brusselator model. The proposed framework unifies graph-based representations of CRNs with concentration dynamics and thermodynamic principles, offering novel insights and computational advantages for analyzing complex biochemical networks.