Mathematical Analysis of Chemical Reaction Systems

TL;DR

This paper reviews the mathematical analysis of deterministic mass-action kinetic models in chemical reaction systems, highlighting how network properties influence solution behaviors.

Contribution

It provides a comprehensive explanation of how properties of chemical reaction networks affect the solutions of associated differential equations.

Findings

Mathematical properties are linked to network reversibility.

Feedback interactions influence system dynamics.

Deterministic models are based on coupled nonlinear differential equations.

Abstract

The use of mathematical methods for the analysis of chemical reaction systems has a very long history, and involves many types of models: deterministic versus stochastic, continuous versus discrete, and homogeneous versus spatially distributed. Here we focus on mathematical models based on deterministic mass-action kinetics. These models are systems of coupled nonlinear differential equations on the positive orthant. We explain how mathematical properties of the solutions of mass-action systems are strongly related to key properties of the networks of chemical reactions that generate them, such as specific versions of reversibility and feedback interactions.