Mass Action Law Conjugate Representation for General Chemical Mechanisms

TL;DR

This paper demonstrates that any chemical reaction rate law can be exactly represented using power-laws and can be transformed into a conjugate form resembling generalized Lotka-Volterra equations, simplifying network analysis.

Contribution

It introduces a novel exact conjugate representation of general chemical kinetics using power-laws and Lotka-Volterra form, extending beyond approximations.

Findings

Any rate law can be represented as a power-law exactly.

The conjugate form simplifies the structural analysis of reaction networks.

Provides a unique transformation for kinetic equations into Lotka-Volterra form.

Abstract

Power-law rates constitute a common approximation to the general analysis of the stability properties of complex reaction networks. We point out in this paper that this form for the rates does not need to be assumed as an approximation for general rate-laws. On the contrary, any functional form for a rate law can be represented exactly in terms of power-laws. Moreover, we can uniquely associate to any set of kinetic equations an equivalent 'conjugate' representation in terms of the well-known generalized Lotka-Volterra equations, standing for what we call per capita rates, which amounts to a great simplification in terms of the structural form of the mathematical representation of a reaction network.