A network-based parametrization of positive steady states of power-law kinetic systems

Steady states are typically used to describe the long-term behaviors of chemical reaction networks (CRNs). In 2019, Johnston et al. developed a method of parametrizing positive steady states of a CRN by finding a dynamically equivalent generalized chemical reaction network (GCRN) to the original CRN. These GCRNs have two substructures: the stoichiometric network and the kinetic-order network. If each deficiency (i.e., measure of linear dependency of the reactions in a network) of these two substructures is zero and they are both weakly reversible (i.e., each reaction belongs to a directed cycle), then the positive steady state has a known parametrization. In 2023, Hernandez et al. proposed to decompose the CRN first into independent subnetworks before applying the parametrization of Johnston et al., as smaller subnetworks are easier to handle than the whole network. Although these approaches can be applied more generally, both of them considered mass-action systems as examples. In this work, however, we illustrate the usefulness of both approaches in more general systems that involve power-law kinetics. In particular, we apply the methods to an Earth’s pre-industrial carbon cycle model. More specifically, we solve its positive steady state symbolically, which allows an easy way to determine the generality of the concentration robustness property of the system.