Independent Decompositions of Chemical Reaction Networks

TL;DR

This paper introduces a new necessary and sufficient condition for independent decompositions of chemical reaction networks, providing a systematic method to identify such decompositions and applying it to biological systems and virus models.

Contribution

It offers a novel step-by-step approach to determine independent decompositions in CRNs, enhancing analysis of large and complex systems.

Findings

A nontrivial independent decomposition exists for a yeast fermentation CRN.

Certain biological networks with feedback loops lack such decompositions.

Application to influenza models reveals steady state properties.

Abstract

A chemical reaction network (CRN) is composed of reactions that can be seen as interactions among entities called species, which exist within the system. Endowed with kinetics, CRN has a corresponding set of ordinary differential equations (ODEs). In Chemical Reaction Network Theory, we are interested with connections between the structure of the CRN and qualitative properties of the corresponding ODEs. One of the results in Decomposition Theory of CRNs is that the intersection of the sets of positive steady states of the subsystems is equal to the set of positive steady states of the whole system, if the decomposition is independent. Hence, computational approach using independent decompositions can be used as an efficient tool in studying large systems. In this work, we provide a necessary and sufficient condition for the existence of a nontrivial independent decomposition of a CRN, which leads to a novel step-by-step method to obtain such decomposition, if it exists. We also illustrate these results using real-life examples. In particular, we show that a CRN of a popular model of anaerobic yeast fermentation pathway has a nontrivial independent decomposition, while a particular biological system, which is a metabolic network with one positive feedforward and a negative feedback has none. Finally, we analyze properties of steady states of reaction networks of specific influenza virus models.