Translated Chemical Reaction Networks

TL;DR

This paper introduces a new method to analyze steady states in chemical reaction networks by linking their capacity for toric steady states to topological properties of translated networks, enhancing understanding of biochemical systems.

Contribution

The paper presents a novel approach connecting the existence of toric steady states to the topology of translated chemical reaction networks, expanding analytical tools in the field.

Findings

Method explicitly links steady states to network topology.

Application to biochemical examples demonstrates practical utility.

Provides new insights into the structure of steady states.

Abstract

Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems of polynomial ordinary differential equations. The steady states of these mass action systems have been analysed via a variety of techniques, including elementary flux mode analysis, algebraic techniques (e.g. Groebner bases), and deficiency theory. In this paper, we present a novel method for characterizing the steady states of mass action systems. Our method explicitly links a network's capacity to permit a particular class of steady states, called toric steady states, to topological properties of a related network called a translated chemical reaction network. These networks share their reaction stoichiometries with their source network but are permitted to have different complex stoichiometries and different network topologies. We apply the results to examples drawn from the biochemical literature.