Nonlinear dynamics of the peroxidase-oxidase reaction: I. Bistability and bursting oscillations at low enzyme concentrations

Under CSTR or semibatch conditions, the horseradish peroxidase (HRP)-catalyzed peroxidase-oxidase (PO) reaction evidences a wide range of nonlinear dynamical behaviors. Many of these regimes have proved to be predictable by a detailed model of the reaction first proposed in 1995. This model, which we refer to as BFSO, can also account for experimentally observed bifurcation sequences in response to varying concentrations of phenolic modifiers and rates of hydrogen donor input. Among those findings for which the model cannot account is the observation of bistability and bursting at low enzyme concentrations. This deficiency is important not only because these phenomena are biologically important but also because their existence requires a topology which, for the experimental circumstances in question, appears to be inconsistent with the model as originally formulated. In the present paper, we show that this deficiency can be remedied by the inclusion of an additional reaction whereby NADH and superoxide anion react in the presence of hydrogen ion to produce WAD radicals and hydrogen peroxide. Comparison of the modified model's behavior with laboratory experiments suggests semiquantitative agreement between theory and observation. In particular, the model is able to reproduce experimentally observed responses to short-term perturbation by oxygen input suspension and the addition of hydrogen peroxide to the reaction mixture, as well as what was first described as autonomous switching between stable and oscillatory dynamics. Mathematically, addition of the new reaction makes possible the interaction of Hopf and hysteresis instabilities, as previously described in the Belousov-Zhabotinski reaction.