Chemical Reaction Network Decomposition Technique for Stability Analysis

TL;DR

This paper introduces a decomposition method for chemical reaction networks to analyze their stability, especially for large, complex, and non-weakly reversible networks, with applications to biochemical autocatalytic systems.

Contribution

It proposes a novel network decomposition technique that captures stability of complex networks by breaking them into simpler subnetworks, including complex balanced and low-dimensional parts.

Findings

Provides sufficient conditions for stability based on network decomposition.

Demonstrates applications to biochemical autocatalytic networks.

Applicable to networks with high dimension, deficiency, and complex structures.

Abstract

This paper develops the concept of decomposition for chemical reaction networks, based on which a network decomposition technique is proposed to capture the stability of large-scale networks characterized by a high number of species, high dimension, high deficiency, and/or non-weakly reversible structure. We present some sufficient conditions to capture the stability of a network (may possess any dimension, any deficiency, and/or any topological structure) when it can be decomposed into a complex balanced subnetwork and a few 1-dimensional subnetworks (and/or a few two-species subnetworks), especially in the case when there are shared species in different subnetworks. The results cover encouraging applications on autocatalytic networks with some frequently-encountered biochemical reactions examples of interest, such as the autophosphorylation of PAK1 and Aurora B kinase, autocatalytic cycles originating from metabolism, etc.