Chaos in the peroxidase-oxidase reaction : The DOP model revisited

Christophe LETELLIER
Lars Olsen Folke

Biochemical reaction systems, whether taking place \textitin vitro or \textitin vivo, have traditionally been considered to operate at or near a steady-state. Now we know that this is not the case, and that biochemical, and more generally biological, systems have natural dynamic behaviors that include oscillations, quasiperiodcity and chaos. A herald of simple (bio)chemical systems NOT showing steady-state behavior is the peroxidase-oxidase (PO) reaction. This experimental reaction system exhibits a wealth of dynamic behaviors starting from bistability to oscillations to quasiperiodicity and chaos. Chaos was first observed in the PO reaction [1] almost simultaneously with the first observation of chaos in the Belousov-Zhabotinskii reaction [2][. Both studies were inspired by Otto R\"ossler’s seminal paper [3], presenting the first example of chaos in a simple chemical reaction model. In the early PO experiments the parameter region in which chaos occurred was situated between regular periodic oscillations and bursting oscillations. Shortly after the discovery of chaos in the PO reaction a simple 4-variable model of the reaction was proposed [4]. This model, sometimes referred to as the DOP model, contains two positive feed-back loops. It could reproduce the simple and bursting oscillations observed experimentally, but in-between these two extremes only periodic mixed-mode oscillations were found.

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talk given by Lars Olsen

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

[2] R. A. Schmitz, K. R. Graziani & J. L. Hudson, Experimental-evidence of chaotic states in Belousov-Zhabotinskii reaction, Journal of Chemical Physics, 67, 3040-3044, 1977.

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

[4] L. F. Olsen & H. Degn, Oscillatory kinetics of the peroxidase-oxidase reaction in an open system : Experimental and theoretical studies, Biochimica et Biophysica Acta, 523, 321-334, 1978.


talk given by Lars Olsen
PDF · 7.5 Mo
945 - 05/12/23

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