Maximal and minimal realizations of reaction kinetic systems: computation and properties

TL;DR

This paper investigates the optimization and properties of chemical reaction network realizations, providing methods to compute networks with maximal or minimal reactions and complexes, and analyzing their structural uniqueness and reversibility.

Contribution

It introduces a mixed integer programming approach for finding CRNs with extremal numbers of complexes and proves the uniqueness of maximal reaction realizations for fixed complexes.

Findings

Maximal reaction realizations are unique given fixed complexes.

A mixed integer programming method effectively computes minimal/maximal complexes.

Linear inequalities characterize reversible CRN realizations.

Abstract

This paper presents new results about the optimization based generation of chemical reaction networks (CRNs) of higher deficiency. Firstly, it is shown that the graph structure of the realization containing the maximal number of reactions is unique if the set of possible complexes is fixed. Secondly, a mixed integer programming based numerical procedure is given for computing a realization containing the minimal/maximal number of complexes. Moreover, the linear inequalities corresponding to full reversibility of the CRN realization are also described. The theoretical results are illustrated on meaningful examples.