Skip to main content
SpringerLink
Log in

Routes to chaos in the peroxidase-oxidase reaction

  • Conference paper
  • First Online:
Book cover Transport and Structure

Part of the book series: Lecture Notes in Physics ((LNP,volume 532-532))

Abstract

We present an overview of the various types of dynamic behaviour observed in the peroxidase-oxidase reaction in homogeneous solution. These behaviours range from simple periodic oscillations over complex periodic oscillations to chaotic dynamics and quasiperiodicity.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Scheeline, A., Olson, D. L., Williksen, E. P., Horras, G. A., Klein, M. L., Larter, R. (1997): The Peroxidase-Oxidase Oscillator and its Constituent Chemistries. Chem. Rev. 97, 739–756

    Article  Google Scholar 

  2. Yamazaki, I., Yokota, K., Nakajima, R. (1965): Oscillatory Oxidations of Reduced Pyridine Nucleotide by Peroxidase. Biochem. Biophys. Res. Commun. 21, 301–310

    Article  Google Scholar 

  3. Degn, H. (1968): Bistability Caused by Substrate Inhibition of Peroxidase in an Open Reaction System. Nature 217, 1047–1050

    Article  ADS  Google Scholar 

  4. Nakamura, S., Yokota, K, Yamazaki, I (1969): Sustained Oscillations in a Lactoperoxidase, NADPH and O 2-System. Nature 222, 794

    Article  ADS  Google Scholar 

  5. Olsen, L. F., Degn, H. (1997): Chaos in an Enzyme Reaction. Nature 267, 177–178

    Article  ADS  Google Scholar 

  6. Hauck, T., Schneider, F. W. (1993): Mixed-Mode and Quasiperiodic Oscillations in the Peroxidase-Oxidase Reaction. J. Phys. Chem. 97, 391–397

    Article  Google Scholar 

  7. Kummer, U., Valeur, K. R., Baier, G., Wegmann, K., Olsen, L. F. (1996): Oscillations in the Peroxidase-Oxidase Reaction: a Comparison of Different Peroxidases. Biochim. Biophys. Acta 1289, 397–403

    Google Scholar 

  8. Olsen, L. F., Degn, H. (1978): Oscillatory Kinetics of the Peroxidase-Oxidase Reaction in an Open System. Experimental and Theoretical Studies. Biochim. Biophys. Acta 523, 321–334

    Google Scholar 

  9. Hauser, M. J. B., Olsen, L. F. (1996): Experimental Studies of the Mechanism of the Peroxidase-Oxidase Reaction. In Plant Peroxidases: Biochemistry and Physiology (Obinger, C., Burner, U., Ebermann, R., Penel, C., Greppin, H., eds.) (University of Geneva, Genva) pp. 82–87

    Google Scholar 

  10. Geest, T., Steinmetz, C. G., Larter, R., Olsen, L. F. (1992): Period-Doubling Bifurcations and Chaos in an Enzyme Reaction. J. Phys. Chem. 96, 5678–5680

    Article  Google Scholar 

  11. Hauser, M. J, B., Olsen, L. F. (1998): The Role of Naturally Occurring Phenols in Inducing Oscillations in the Peroxidase-Oxidase Reaction. Biochemistry 37, 2458–2469

    Article  Google Scholar 

  12. Kummer, U., Hauser, M. J. B., Wegmann, K., Olsen, L. F., Baier, G. (1997): Oscillations and Complex Dynamics in the Peroxidase-Oxidase Reaction Induced by Naturally Occurring Aromatic Substrates. J. Am. Chem. Soc. 119, 2084–2087

    Article  Google Scholar 

  13. Yamazaki, I., Yokota, K. (1973): Oxidation States of Peroxidase. Mol. Cell. Biochem. 2, 39–52

    Article  Google Scholar 

  14. Lvovich, V., Schelline, A. (1995): Complexation of Nicotinamide Adenine Dinucleotide with Ferric and Ferrous Ions. Arch. Biochem. Biophys. 320, 1–13

    Article  Google Scholar 

  15. Hauser, M. J. B., Olsen, L. F. (1996): Mixed-mode Oscillations and Homoclinic Chaos in an Enzyme Reaction. J. Chem. Soc. Faraday Trans. 92, 2857–2863

    Article  Google Scholar 

  16. Hauser, M. J. B., Olsen, L. F., Bronnikova, T. V., Schaffer, W. M., (1997): Routes to Chaos in the Peroxidase-Oxidase Reaction. 2. Period-Doubling and Period-Adding. J. Phys. Chem. B 101, 5075–5083

    Article  Google Scholar 

  17. Lazar, J. G., Ross, J. (1990): Changes in Mean Concentration, Phase Shifts, and Dissipation in a Forced Oscillatory Reaction. Science 247, 189–192

    Article  ADS  Google Scholar 

  18. Hauck, T., Schneider, F. W. (1994): Chaos in a Farey Sequence Through Period-Doubling in the Peroxidase-Oxidase Reaction. J. Phys. Chem. 98, 2072–2077

    Article  Google Scholar 

  19. Larter, L., Olsen, L. F., Steinmetz, C. G., Geest, T. (1993): Chaos in Biochemical Systems: The Peroxidase Reaction as a Case Study. In Chaos in Chemistry and Biochemistry (Field, R. J., Györgyi, L., eds.) (World Scientific, Singapore) pp. 175–224

    Google Scholar 

  20. Degn, H. (1969): Compound III Kinetics and Chemiluminescence in Oscillatory Oxidation Reactions Catalyzed by Horseradish Peroxidase. Biochim. Biophys. Acta 180, 271–290

    Article  Google Scholar 

  21. Fed’kina, V. R., Bronnikova, T. V., Ataullakhanov, F. I. (1981): Slow Oscillations in Peroxidase-Oxidase Reaction. Stud. Biophys. 82, 159–164

    Google Scholar 

  22. Aguda, B. D., Frisch, L.-L. H., Olsen, L. F. (1990): Experimental Evidence for the Coexistence of Oscillatory and Steady States in the Peroxidase-Oxidase Reaction. J. Am. Chem. Soc. 112, 6652–6656

    Article  Google Scholar 

  23. Li, T. Y., Yorke, J. A. (1975): Period Three Implies Chaos. Am. Math. Mon. 82, 985–992

    Article  MATH  MathSciNet  Google Scholar 

  24. Degn, H., Mayer, D. (1969): Theory of Oscillations in Peroxidase Catalyzed Oxidation Reactions in Open Systems. Biochim. Biophys. Acta 180, 291–300

    Article  Google Scholar 

  25. Olsen, L., F. (1983): An Enzyme Reaction with a Strange Attractor. Phys. Lett. 94A, 454–457

    ADS  Google Scholar 

  26. Fed’kina, V. R., Ataullakhanov, F. I., Bronnikova, T. V. (1984): Computer Simulations of Sustained Oscillations in Peroxidase-Oxidase Reaction. Biophys. Chem. 19, 259–264

    Article  Google Scholar 

  27. Aguda, B. D., Larter, R. (1991): Periodic-Chaotic Sequences in a Detailed Mechanism of the Peroxidase-Oxidase Reaction. J. Am. Chem. Soc. 113, 7913–7916

    Article  Google Scholar 

  28. Olson, D. L., Williksen, E. P., Scheeline, A. (1995): An Experimentally Based Model of the Peroxidase-NADH Biochemical Oscillator: An Enzyme-Mediated Chemical Switch. J. Am. Chem. Soc. 117, 2–15

    Article  Google Scholar 

  29. Yokota, K., Yamazaki, I. (1977): Analysis and Computer Simulation of Aerobic Oxidation of Reduced Nicotinamide Adenine Dinucleotide Catalyzed by Horseradish Peroxidase. Biochemistry 16 1913–1920

    Article  Google Scholar 

  30. Samples, M. S., Hung, Y.-F., Ross, J. (1992): Further Experimental Studies on the Horseradish Peroxidase-Oxidase Reaction. J. Phys. Chem. 96, 7338–7342

    Article  Google Scholar 

  31. Bronnikova, T. V., Schaffer, W. M., Olsen, L. F. (1996): Quasiperiodicity in a Detailed Model of the Peroxidase-Oxidase Reaction. J. Chem. Phys. 105, 10849–10859

    Article  ADS  Google Scholar 

  32. Lekebusch, A., Förster, A., Schneider, F. W. (1996): Chaos Control by Electric Current in an Enzymatic Reaction. Int. J. Neural Syst. 7, 393–397

    Article  Google Scholar 

  33. Lekebusch, A., Förster, A., Schneider, F. W. (1995): Chaos Control in an Enzymatic Reaction. J. Phys. Chem. 99, 681–686

    Article  Google Scholar 

  34. Steinmetz, C. G., Geest, T., Larter, R. (1993): Universality in the Peroxidase-Oxidase Reaction: Period Doublings, Chaos, Period Three, and Unstable Limit Cycles. J. Phys. Chem. 97, 5649–5653

    Article  Google Scholar 

  35. Argoul, F., Arnéodo, A., Richetti, P. (1987): Experimental Evidence for Homoclinic Chaos in the Belousov-Zhabotinskii Reaction. Phys. Lett. A 120, 269–275

    Article  ADS  Google Scholar 

  36. Argoul, F., Arnéodo, A., Richetti, P. (1991): Symbolic Dynamics in the Belousov-Zhabotinskii Reaction: From Rösslers Intuition to Experimental Evidence for Shil’nikov’s Homoclinic Chaos. In A Chaotic Hierarchy (Baier, G., Klein, M., eds.) (World Scientific, Singapore) pp. 79–118

    Google Scholar 

  37. Fed’kina, V. R., Bronnikova, T. V, Ataullakhanov, F. I. (1992): Structure of the Phasic Space of Models of the Peroxidase-Oxidase Reaction. Biophys 37, 781–789

    Google Scholar 

  38. Fed’kina, V. R., Bronnikova, T. V. (1994): Bistability and Birhythmicity in the Peroxidase-Oxidase Reaction. Biophysics 39, 597–605

    Google Scholar 

  39. Fed’kina, V. R., Bronnikova, T. V. (1995): Complex Oscillatory Regimes in the Peroxidase-Oxidase Reaction. Biophysics 40, 33–44

    Google Scholar 

  40. Bronnikova, T. V., Fed’kina, V. R., Schaffer, W. M., Olsen, L. F. (1995): Period-Doubling Bifurcations and Chaos in a Detailed Model of the Peroxidase-Oxidase Reaction. J. Phys. Chem. 99 9309–9312

    Article  Google Scholar 

  41. Larter, R., Hemkin, S. (1996): Further Refinement of the Peroxidase-Oxidase Oscillator Mechanism: Mixed-Mode Oscillations and Chaos. J. Phys. Chem. 100 18924–18930

    Article  Google Scholar 

  42. Bronnikova, T. V., Schaffer, W. M., Hauser, M. J. B., Olsen, L. F. (1998): Routes to Chaos in the Peroxidase-Oxidase Reaction. 2. The Fat Torus Scenario. J. Phys. Chem. B 102, 632–640

    Article  Google Scholar 

  43. Lekebusch, A., Schneider, F. W. (1997): Two Biochemical Oscillators Coupled by Mass Exchange. J. Phys. Chem. B 101, 9838–9843

    Article  Google Scholar 

  44. Epstein, I. R., Showalter, K. (1996): Nonlinear Chemical Dynamics: Oscillations, Patterns, and Chaos. J. Phys. Chem. 100, 13132–13147

    Article  Google Scholar 

  45. Goryatchev, A., Strizhak, P., Kapral, R. (1997): Slow Manifold Structure and the Emergence of Mixed-Mode Oscillations. J. Chem. Phys. 107, 2881–2889

    Article  ADS  Google Scholar 

  46. Cook, L., Larter, R., Shen, P., Geest, T. (1993): Kinetics of the Peroxidase-Oxidase Reaction with Immobilized Enzyme. J. Phys. Chem. 97, 9060–9063

    Article  Google Scholar 

  47. Ishikawa, T., Tamura, M., Yamazaki, I. (1980): A Kinetic Study on the Diffusion-coupled Reaction of a Basic Horseradish Peroxidase Adsorbed on a Carboxymethylcellulose Membrane. J. Biol. Chem. 255, 10764–10770

    Google Scholar 

  48. Elstner, E. F, Heupel, A. (1976): Formation of Hydrogen Peroxide by Isolated Cell Walls from Horseradish (Armoracia lapathifolia Gilib.). Planta 130, 175–180

    Article  Google Scholar 

  49. Møller, A. C., Hauser, M. J. B., Olsen, L. F. (1998): Oscillations in Peroxidase-Catalyzed Reactions and their Potential Function in Vivo. Biophys. Chem. 72, 63–72

    Article  Google Scholar 

  50. Goldbeter, A. (1996): Biochemical Oscillations and Cellular Rhythms. The Molecular Basis of Periodic and Chaotic Behaviour. Cambridge University Press, Cambridge

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Experimentelle Physik, Abteilung Biophysik, Otto-von-Guericke-Universität, Universitätsplatz 2, D-39106, Magdeburg, Germany

    Marcus J. B. Hauser

  2. Fysisk Biokemigruppen, Odense Universitet, Forskerparken 10, DK-5230, Odense M, Denmark

    Lars Folke Olsen

Authors
  1. Marcus J. B. Hauser
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lars Folke Olsen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Stefan C. Müller Jürgen Parisi Walter Zimmermann

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag

About this paper

Cite this paper

Hauser, M.J.B., Olsen, L.F. (1999). Routes to chaos in the peroxidase-oxidase reaction. In: Müller, S.C., Parisi, J., Zimmermann, W. (eds) Transport and Structure. Lecture Notes in Physics, vol 532-532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104230

Download citation

  • DOI: https://doi.org/10.1007/BFb0104230

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66632-5

  • Online ISBN: 978-3-540-48070-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation