Information geometric bound on general chemical reaction networks

TL;DR

This paper introduces an information geometric method using the natural gradient to derive an upper bound on the reaction rates of chemical reaction networks, validated through numerical simulations and comparisons.

Contribution

It presents a novel information geometric approach to bound CRN dynamics, outperforming conventional methods and applicable to broader hypergraph-structured systems.

Findings

Faster convergence in certain CRNs using the proposed bound

The conventional approach cannot provide an upper bound

Potential applications in various fields with hypergraph structures

Abstract

We investigate the dynamics of chemical reaction networks (CRNs) with the goal of deriving an upper bound on their reaction rates. This task is challenging due to the nonlinear nature and discrete structure inherent in CRNs. To address this, we employ an information geometric approach, using the natural gradient, to develop a nonlinear system that yields an upper bound for CRN dynamics. We validate our approach through numerical simulations, demonstrating faster convergence in a specific class of CRNs. This class is characterized by the number of chemicals, the maximum value of stoichiometric coefficients of the chemical reactions, and the number of reactions. We also compare our method to a conventional approach, showing that the latter cannot provide an upper bound on reaction rates of CRNs. While our study focuses on CRNs, the ubiquity of hypergraphs in fields from natural sciences to engineering suggests that our method may find broader applications, including in information science.