Bistability in chemical reaction networks: Theory and application to the peroxidase–oxidase reaction

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Abstract
Starting with a comprehensive list of elementary steps in the mechanism of the peroxidase–oxidase (PO) reaction, we extract the part of the mechanism essential to the experimentally observed bistability. A general systematic method is used to sort out the mechanism. First the extreme currents are found and the structure of the current polytope is determined. Then conditions for the existence of multiple steady states are used to identify the dominant extreme currents that are essential for bistability. A clue to the cause of bistability came from applying stoichiometric network analysis to the much simpler classical substrate-inhibition enzyme mechanism. Three extreme currents are essential for bistability. These correspond to (i) a reversible flux of the inhibiting substrate, (ii) the catalytic cycle, and (iii) an inhibition pathway coupled to the catalytic cycle. The same three elements are found in the PO mechanism. Analysis of the model containing these elements shows that bistability requires less ferriperoxidase than compounds I and II taken together. The PO model can exhibit damped oscillations simultaneously with bistability, simulate experimentally observed phases in the kinetics of the closed system, and demonstrate that enzyme inhibition by the substrate oxygen exists.