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

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.