Multi-site enzymes as a mechanism for bistability in reaction networks

Here, we focus on a common class of enzymes that have multiple substrate-binding sites (multi-site enzymes), and analyse their capacity to generate bistable dynamics in the reaction systems that they are embedded in. Using mathematical techniques, we show that the inherent binding and catalysis reactions arising from multiple substrate-enzyme complexes creates a potential for bistable dynamics in a reaction system. We construct a generic model of an enzyme with n substrate binding sites and derive an analytical solution for the steady state concentration of all enzyme-substrate complexes. By studying these expressions, we obtain a mechanistic understanding for bistability and derive parameter combinations that guarantee bistability and show how changing specific enzyme kinetic parameters and enzyme levels can lead to bistability in reaction systems involving mjulti-site enzymes. Thus, the presented findings provide a biochemical and mathematical basis for predicting and engineering bistability in multi-site enzymes.