1983 A 4D model for the peroxidase-oxidase reaction

Christophe LETELLIER

The peroxidase-oxidase reaction involves an organic substance, commonly the reduced nicotinamide adenine dinucleotide NADH, is oxidised with molecular oxygen according to

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Lars Folke Olsen

Damped oscillations were first seen in 1965 [1] The nonlinear behavior of the peroxidase-oxidase reaction was studied using structurally different peroxidases. [2] : this study leads to the conclusion that the mechanisms responsible for oscillatory kinetics may vary from one peroxidase to the other. Soon after the simple model for chaotic chemical reaction proposed by Otto E. Rössler [3], chaos was experimentally observed in this reaction by Lars F. Olsen and Hans Degn (Fig. 1) [4]

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Fig. Experimental concentration of the oxygen in the peroxidase-oxidase reaction investigated by Olsen & Degn.

After a first model proposed in 1978 [5], Olsen proposed in 1983 a simplified model [6]. This is a four-dimensional system

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where x corresponds to [O2], y to [NADH], z and w to intermediate products.

For the well chosen parameter values

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this model produces a time series for the evolution of the oxygen concentration [O2] (Fig. 2) which is very similar to the one measured in the experimental reaction (Fig. 1).

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Fig. 2. Numerical time series of the oxygen concentration produced by the model proposed by Olsen.

When k1 = 1.35, a chaotic attractor characterized by a foliated smooth "quasi-unimodal" map (Fig. 3).

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Fig. 3. Chaotic behavior produced by the 4D model proposed by Olsen.

[1] I.Yamazaki, K.Yokota & R.Nakajima, Oscillatory oxidations of reduced pyridine nucleotide by peroxidase, Biochemical and Biophysical Research Communications, 21 (6), 21, 582-586, 1965.

[2] U. Kummer, K. R. Valeur, G. Baier, K. Wegmann & L. F. Olsen, Oscillations in the peroxidase-oxidase reaction : a comparison of different peroxidases, Biochimica et Biophysica Acta, 1289 (3), 397-403, 1996.

[3] O. E. Rössler, Chaotic behavior in simple reaction system, Zeitschrift für Naturforschung A, 31, 259-264, 1976.

[4] L. F. Olsen & H. Degn, Chaos in an enzyme reaction, Nature, 267, 177-178, 1977.

[5] L. F. Olsen \& H. Degn, Oscillatory kinetics of the peroxidase-oxidase reaction in an open system, Biochimica et Biophysica Acta, 523, 321-334, 1978.

[6] L. F. Olsen, An enzyme reaction with a strange attractor, Physics Letters A, \bf 94 (9), 454-457, 1983.

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