How far is complex balancing from detailed balancing?

TL;DR

This paper explores the algebraic conditions that determine when kinetic systems in chemistry and biology are complex balanced or detailed balanced, clarifying their relationship using tools from computational algebra.

Contribution

It clarifies the algebraic relationship between conditions for complex and detailed balancing in kinetic systems, extending foundational work by Horn, Jackson, and Feinberg.

Findings

Established algebraic conditions for complex and detailed balancing

Clarified the relationship between these conditions in kinetic systems

Extended the theoretical framework for analyzing reaction equilibria

Abstract

The aim of this article is to build on the use of tools from computational algebra initiated in Craciun, Dickenstein, Shiu, Sturmfels (JSC, 2009), for the study of general kinetic systems, which have a wide range of applications in chemistry and biology. We clarify the relation between the algebraic conditions that must be satisfied by the reaction constants in general (mass action) kinetics systems for the existence of detailed or complex balancing equilibria. The main properties of these systems have been set by Horn, Jackson and Feinberg.