A Linear Programming Approach to Weak Reversibility and Linear Conjugacy of Chemical Reaction Networks

TL;DR

This paper introduces a linear programming method to identify weakly reversible chemical reaction networks that are linearly conjugate to a given network, enabling efficient structural analysis.

Contribution

It presents a novel mixed integer linear programming approach to determine weak reversibility and linear conjugacy in chemical reaction networks.

Findings

Method successfully identifies weakly reversible networks

Numerical examples demonstrate effectiveness

Approach is computationally efficient

Abstract

A numerically effective procedure for determining weakly reversible chemical reaction networks that are linearly conjugate to a known reaction network is proposed in this paper. The method is based on translating the structural and algebraic characteristics of weak reversibility to logical statements and solving the obtained set of linear (in)equalities in the framework of mixed integer linear programming. The unknowns in the problem are the reaction rate coefficients and the parameters of the linear conjugacy transformation. The efficacy of the approach is shown through numerical examples.