Analysis of Mass-Action Systems by Split Network Translation

TL;DR

This paper introduces a novel network translation method for chemical reaction networks that enhances the analysis of steady states by leveraging structural properties like weak reversibility and deficiency reduction.

Contribution

It develops the concept of split network translation to extend network theory for mass-action systems and provides a computational approach using mixed-integer linear programming.

Findings

Enables characterization of steady states in mass-action systems.

Provides a computational tool for identifying weakly reversible split network translations.

Improves understanding of multistationarity and robustness in chemical networks.

Abstract

We introduce the notion of corresponding a chemical reaction network to a split network translation, and use this novel process to extend the scope of existing network-based theory for characterizing the steady state set of mass-action systems. In the process of network splitting, the reactions of a network are divided into subnetworks, called slices, in such a way that, when summed across the slices, the stoichiometry of each reaction sums to that of the original network. This can produce a network with more desirable structural properties, such as weak reversibility and a lower deficiency, which can then be used to establish steady state properties of the original mass-action system such as multistationarity and absolute concentration robustness. We also present a computational implementation utilizing mixed-integer linear programming for determining whether a given chemical reaction network has a weakly reversible split network translation.