The Journal of Physical Chemistry B. 105: 310-321 (2001).

Under CSTR or semi-batch conditions, the horseradish peroxidase (HRP) catalyzed peroxidase-oxidase (PO) reaction (Figure 1) evidences a wide range of nonlinear dynamical behaviors [od77 od78, gslo92, sgl93, hs94, hobs97]. Many of these regimes have proved to be predictable by a detailed model (Table 1) of the reaction first proposed in 1995 [bfso95]. 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 [afo90] (Figure 2) and bursting [od77, afo90] at (Figure 3) low enzyme concentrations. This deficiency is important, not only because the phenomena in question 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 remediated by the inclusion of an additional reaction, R₁₄ [Table 1 (continuation)], whereby NADH and superoxide anion react in the presence of hydrogen ion to produce NAD radicals and hydrogen peroxide. Comparison of the modified model's behavior with laboratory experiments suggests semi-quantitative agreement between theory and observation. In particular, the model is able to reproduce both experimentally observed responses to short-term perturbation by oxygen input suspension and the addition of hydrogen peroxide to reaction mixture (Figure 4) as well as as "autonomous" switching between stable and oscillatory dynamics (Figure 5), i.e., bursting. Mathematically, addition of the new reaction, makes possible the interaction of Hopf and hysteresis instabilities as previously described in the Belousov-Zhabotinskii reaction. The result (Figure 6) is coexisting attractors (fixed point with periodic orbit or torus) and heteroclinic connections.

References.

[afo90] Aguda, B. D.; Frisch, L. L. H.; Olsen, L. F. J. Am. Chem. Soc. 1990, 112, 6652-6656.

[bfso95] Bronnikova, T. V.; Fed'kina, V. R.; Schaffer, W. M.; Olsen, L. F. J. Phys. Chem. 1995, 99, 9309-9312.

[gslo92] Geest, T.; Steinmetz, C. G.; Larter, R.; Olsen, L. F. J. Phys. Chem. 1992 , 96, 5678-5680.

[hobs97] Hauser, M. J. B.; Olsen, L. F.; Bronnikova, T. V.; Schaffer, W. M. J. Phys. Chem B. 1997, 101, 5075-5083.

[hs94] Hauck, T.; Schneider, F. W. J. Chem. Phys. 1994, 98, 2072-2080.

[od77] Olsen, L.F.; Degn, H. Nature 1977, 267, 177-178.

[od78] Olsen, L. F.; Degn, H. Biochim. Biophys. Acta 1978, 523, 321-334.

[sgl93] Steinmetz, C. G.; Geest, T.; Larter, R. J. Phys. Chem. 1993, 97, 5649-5653.