Abstract
The long-term behavior of a chemical reaction network (CRN) is usually described by steady states. Recently, Hernandez et al. provided a method and a computational package for deriving positive steady states of CRNs via the concept of network decomposition. In particular, a given CRN is decomposed into stoichiometrically independent subnetworks; then, positive steady state parametrizations of these subnetworks are derived individually and merged to obtain a positive steady state parametrization of the given network. However, the framework applies to a fixed number of subnetworks. In this work, we establish a systematic approach to solving steady state parametrizations of CRNs that can be decomposed into \( n \) stoichiometrically independent and structurally identical subnetworks, where \( n \geq 2 \) is any positive integer. Specifically, we apply the method to the \( n \)-site processive phosphorylation/dephosphorylation model. That is, we compute the positive steady state parametrization for the case when \( n=2 \) via the concept of network decomposition using the result of parametrizing positive steady states of the network when \( n=1 \). Then, we generalize the parametrization for any positive integer \( n \geq 2 \) via the principle of mathematical induction.
