Revealing regions of multiple steady states in heterogeneous catalytic chemical reaction networks using Gröbner basis

Abstract

The Chemical Reaction Network Theory (CRNT) formalism classifies any CRN using a nonnegative index called deficiency. If the deficiency is equal to or greater than one, and the CRN fulfills some structural conditions, then it is possible to establish whether or not the set of Mass Action Kinetics Ordinary Differential Equations (MAK-ODEs) induced by the CRN can support Multiple Positive Steady States (MPSS) within each stoichiometric compatibility class. If MPSS exists the CRNT provides a set of kinetic constants for such steady states. Most of the heterogeneous catalytic CRNs are of deficiency one, thus the CRNT applies straightforwardly. Moreover, the balance of catalytic sites defines a stoichiometric compatibility class. In this contribution, CRNT is used along with Gröbner basis to derive analytical polynomial expressions depending on a measurable chemical species (e.g. the product of interest) and the catalytic site concentration. This methodology reveals the exact regions where MPSS are supported. Putative heterogeneous catalytic CRNs, such as Eley–Rideal and Langmuir–Hinshelwood, are analyzed using this methodology.