Chaos in Biochemical Systems: The Peroxidase Reaction as a Case Study

Larter, Raima; Olsen, Lars Folke; Steinmetz, Curtis G.; Geest, Torben

doi:10.1142/9789814354745_0007

Cited by 19 publications

(18 citation statements)

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“…Complementing experimental studies of the PO reaction is a growing number of mechanistic models ,,,,− which seek to provide a mathematical accounting of its behavior. All of these schemes are rooted in the work of Yokota and Yamazaki, who, along with Fed'kina et al . − and Degn and Olsen, ,− were the first to attempt to capture the reaction mathematically.…”

Section: Computer Simulationsmentioning

confidence: 99%

“…In the former case, NADH and O 2 are supplied to a reactor in which products accumulate; in the latter, all reactants, including the enzyme, are fed into the reaction vessel, and products are removed via the overflow of excess liquid. In both circumstances, the PO reaction displays a rich variety of dynamic behaviors, including bistability, , periodic oscillations − (including mixed-mode oscillations (MMO's) − ), quasiperiodicity, , and at least two distinct forms of chaotic behavior. ,,, …”

Section: Introductionmentioning

confidence: 99%

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Routes to Chaos in the Peroxidase−Oxidase Reaction: Period-Doubling and Period-Adding

et al. 1997

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Previous investigations of the peroxidase−oxidase reaction indicate the existence of a period-doubling route to chaos at pH 5.2 and a period-adding route at pH 6.3. In the present study, we extend these results in two regards: (i) The reaction was studied at a series of intermediate pH values under otherwise identical conditions. The new experiments suggest that the transition from period-doubling to period-adding takes place at approximately pH 5.4 and is characterized by a loss of dynamical complexity. (ii) A detailed model (Bronnikova, T. V.; Fed'kina, V. R.; Schaffer, W. M.; Olsen, L. F. J. Phys. Chem. 1995, 99, 9309−9312) was shown capable of reproducing the principal experimental results. These include the shift from period-doubling to period-adding, the existence of narrow regions of period-doubling between adjacent mixed-mode oscillations in the period-adding regime and changes in cycle amplitude.

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Section: Computer Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Routes to Chaos in the Peroxidase−Oxidase Reaction: Period-Doubling and Period-Adding

et al. 1997

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“…BFSO is similar to the Urbanalator from which it differs by the inclusion of reactions that entail the conversion of ferric peroxidase (Per 3+ ) to ferrous peroxidase (Per 2+ ) and Per 2+ to oxyferrous peroxidase which is also called compound III (coIII). Both models, along with other related schemes − derive from the work of Yokota and Yamazaki 1 Elementary Steps in PO Reaction reaction R l constant 1.…”

Section: Introductionmentioning

confidence: 99%

Routes to Chaos in the Peroxidase−Oxidase Reaction. 2. The Fat Torus Scenario

Bronnikova¹,

Schaffer²,

Hauser³

et al. 1998

J. Phys. Chem. B

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Experimental studies [Hauser, M. J. B.; Olsen, L. F. J. Chem. Soc., Faraday Trans. 1996, 92, 2857−2863] of the peroxidase−oxidase (PO) reaction at pH values in excess of 5.4 suggest the existence of narrow regions of complex dynamics between adjacent mixed-mode oscillations (MMOs) that occur in period-adding sequences. Previously [Hauser, M. J. B.; Olsen, L. F.; Bronnikova, T. V.; Schaffer, W. M. J. Phys. Chem. B 1997, 101, 5075−5083], it was argued that both the period-adding sequences and the transitional regions between neighboring MMOs are predictable by a detailed model of the reaction called BFSO [Bronnikova, T. V.; Fed'kina, V. R.; Schaffer, W. M.; Olsen, L. F. J. Phys. Chem. 1995, 99, 9309−9312]. In the present paper, we study the transitional regions via computer simulation. Our investigations indicate that the motion therein may be periodic, quasiperiodic, or chaotic. In greater detail, we observe a quasiperiodic route to chaos whereby period-doubled cycles give rise to doubled tori that, in turn, undergo homoclinic bifurcations to chaos. Because the latter transitions are a consequence of progressive fattening of the tori, we propose calling this scenario the “fat torus” route to chaos, and the homoclinic bifurcations “fat torus” bifurcations (FTBs). The numerical results are qualitatively consistent with the experimental findings reported to date. FTBs and the resultant period-doubled, fractal tori may provide a criterion for discriminating among alternative models of the PO reaction.

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“…Some years after the discovery of oscillatory behavior in the peroxidase−oxidase (PO) reaction, the first hints of chaotic behavior were detected in this reaction, making it, along with the Belousov−Zhabotinskii reaction, one of the earliest examples of chemical chaos. Since that time, a number of groups have investigated the PO reaction, carrying out experimental studies and theoretical analyses in attempts to elucidate the mechanism by which oscillatory and chaotic behavior arise in this reaction (see ref for a recent review). Because the PO reaction involves a single enzyme and, yet, exhibits a whole range of complex dynamic behavior, including multistability, simple and complex oscillations, and chaotic behavior, it has become an important minimal case whose study has illuminated the possibilities for complex behavior in biology.…”

Section: Introductionmentioning

confidence: 99%

“…A recent flury of papers reporting new models 11,17,18 and new experimental observations 19 have served to focus attention on a subset of the steps comprising the so-called “detailed models” of the PO reaction . Early work on this reaction by Yamazaki (the discoverer of damped oscillatory behavior in the PO reaction) and co-workers led to a long list of reactions which were thought to occur in this system.…”

Section: Introductionmentioning

confidence: 99%

Further Refinements of the Peroxidase−Oxidase Oscillator Mechanism: Mixed-Mode Oscillations and Chaos

Larter

Hemkin

1996

J. Phys. Chem.

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A model of the peroxidase-oxidase (PO) reaction which explicitly includes the species 2,4-dichlorophenol (DCP) is proposed. Simulations with this model are run at different pH values, resulting in mixed-mode oscillations at pH ) 6.3, which go through period-doubling bifurcations into chaos, in agreement with recent experimental reports of studies at the higher pH. The dependence of features of these oscillations on NADH feedstream concentration and DCP initial concentration is also explored. Finally, comparison of detailed features of the simulated strange attractor to the recent experimental attractor reveals minor differences which may turn out to be important in elucidating the role of DCP in the mechanism which leads to chaos in the PO reaction.

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Chaos in Biochemical Systems: The Peroxidase Reaction as a Case Study

Cited by 19 publications

References 0 publications

Routes to Chaos in the Peroxidase−Oxidase Reaction: Period-Doubling and Period-Adding

Routes to Chaos in the Peroxidase−Oxidase Reaction: Period-Doubling and Period-Adding

Routes to Chaos in the Peroxidase−Oxidase Reaction. 2. The Fat Torus Scenario

Further Refinements of the Peroxidase−Oxidase Oscillator Mechanism: Mixed-Mode Oscillations and Chaos

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