Common Complexes of Decompositions and Complex Balanced Equilibria of Chemical Reaction Networks

TL;DR

This paper investigates how decomposing chemical reaction networks into subnetworks affects their complex balanced equilibria, introducing criteria based on common complexes and incidence independence, and generalizing the Defficiency Zero Theorem for certain power law kinetic systems.

Contribution

It develops a framework to analyze incidence independence in network decompositions using common complexes and extends the Defficiency Zero Theorem to specific power law kinetic systems.

Findings

Identified decomposition classes characterized by common complexes.

Established a criterion for incidence independence in decompositions.

Provided a sufficient condition for complex balancing in power law kinetic systems.

Abstract

A decomposition of a chemical reaction network (CRN) is produced by partitioning its set of reactions. The partition induces networks, called subnetworks, that are "smaller" than the given CRN which, at this point, can be called parent network. A complex is called a common complex if it occurs in at least two subnetworks in a decomposition. A decomposition is said to be incidence independent if the image of the incidence map of the parent network is the direct sum of the images of the subnetworks' incidence maps. It has been recently discovered that the complex balanced equilibria of the parent network and its subnetworks are fundamentally connected in an incidence independent decomposition. In this paper, we utilized the set of common complexes and a developed criterion to investigate decomposition's incidence independence properties. A framework was also developed to analyze decomposition classes with similar structure and incidence independence properties. We identified decomposition classes that can be characterized by their sets of common complexes and studied their incidence independence. Some of these decomposition classes occur in some biological and chemical models. Finally, a sufficient condition was obtained for the complex balancing of some power law kinetic (PLK) systems with incidence independent and complex balanced decompositions. This condition led to a generalization of the Defficiency Zero Theorem for some PLK systems.