Investigations and Analysis of Dynamical and Steady State Properties of Chemical Reaction Systems

In this paper, we investigate results from chemical reaction network theory and a list of techniques to test for the reaction-coordinates dynamical system to have a partial order induced by a positive orthant cone. A successful result from one of these tests guarantees mono-stationarity (and indeed convergence). We also investigate a recently published algorithmic and computational approach to determine whether a reaction network establishes mono- or multi-stationarity. We test new reactions that have not been previously introduced in the literature for mono- or multi-stationarity using this approach. This includes the two-site phosphorylation reaction network and a modified double phosphorylation reaction network that more accurately models the action of the enzymes of two distinct sites. We also use the enzymatic futile cycle as a running example to illustrate these results. We conclude the two-site phosphorylation reaction network is multi-stationary; while the original double phosphorylation reaction network is also multi-stationary, our modified version is mono-stationary