Transitions and Thermodynamics on Species Graphs of Chemical Reaction Networks

TL;DR

This paper introduces a new graph-based framework for analyzing the dynamics and thermodynamics of chemical reaction networks, applicable to both reversible and irreversible systems, validated through numerical simulations.

Contribution

It develops a novel approach to represent CRN dynamics on species graphs with thermodynamic-like quantities, bridging structure and behavior analysis.

Findings

Thermodynamic quantities can be defined on species graphs for CRNs.

The framework applies to both reversible and irreversible CRNs.

Numerical validation with the Brusselator system supports the methodology.

Abstract

Chemical reaction networks (CRNs) exhibit complex dynamics governed by their underlying network structure. In this paper, we propose a novel approach to study the dynamics of CRNs by representing them on species graphs (S-graphs). By scaling concentrations by conservation laws, we obtain a graph representation of transitions compatible with the S-graph, which allows us to treat the dynamics in CRNs as transitions between chemicals. We also define thermodynamic-like quantities on the S-graph from the introduced transitions and investigate their properties, including the relationship between specieswise forces, activities, and conventional thermodynamic quantities. Remarkably, we demonstrate that this formulation can be developed for a class of irreversible CRNs, while for reversible CRNs, it is related to conventional thermodynamic quantities associated with reactions. The behavior of these specieswise quantities is numerically validated using an oscillating system (Brusselator). Our work provides a novel methodology for studying dynamics on S-graphs, paving the way for a deeper understanding of the intricate interplay between the structure and dynamics of chemical reaction networks.