Interplay between Two Periodic Enzyme Reactions as a Source for Complex Oscillatory Behaviour

  • Olivier Decroly
Part of the NATO ASI Series book series (NSSA, volume 138)


A single autocatalytic enzyme reaction operating far from equilibrium has been recognized as a major mechanism responsible for instability leading to oscillatory behaviour in biochemistry. We analyse a biochemical system built as a sequence of two such positive feedback loops coupled in series, in order to investigate the new types of dynamical behaviour resulting from the interplay between two ‘biochemical oscillators’.


Periodic Orbit Bifurcation Diagram Chaotic Dynamic Biochemical System Behavioural Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    P. Collet and J.-P. Eckmann, “Iterated Maps on the Interval as Dynamical Systems”, Birkäuser Verlag, Basel and Boston (1980).Google Scholar
  2. [2]
    O. Decroly and A. Goldbeter, Proc. Natl. Acad. Sci. USA 79: 6917 (1982).PubMedCrossRefGoogle Scholar
  3. [3]
    O. Decroly and A. Goldbeter, Phys. Lett. 105A: 259 (1984).CrossRefGoogle Scholar
  4. [4]
    O. Decroly and A. Goldbeter, C.R. Acad. Sc. Paris Ser. II, 298: 779 (1984).Google Scholar
  5. [5]
    O. Decroly and A. Goldbeter, in “Fluctuations and Sensivity in Nonequilibrium Systems”, eds. W. Horsthemke and D.K. Kondepudi, Springer, Berlin-Heidelberg-New York-Tokyo, Proc. in Phys. 1:214 (1984).Google Scholar
  6. [6]
    O. Decroly and A. Goldbeter, J. theor. Biol. 113: 649 (1985).PubMedCrossRefGoogle Scholar
  7. [7]
    O. Decroly and A. Goldbeter, J. theor. Biol. (in press) (1986).Google Scholar
  8. [8]
    E.J. Doedel, “Proc. 10th Manitoba Conf. on Num. Maths and Comput. Winnipeg, Canada”, Cong. No. 30: 265.Google Scholar
  9. [9]
    M.J. Feigenbaum, J. Stat. Phys. 19: 25 (1978).CrossRefGoogle Scholar
  10. [10]
    G. Gerisch and U. Wick, Biochem. Biophys. Res. Commun. 65: 364 ( 1975 ].PubMedCrossRefGoogle Scholar
  11. [11]
    A. Goldbeter, in “Mathematical Models in Molecular and Cellular Biology”, p 248, ed. L.A. Segel, Cambridge University Press (1980).Google Scholar
  12. [12]
    A. Goldbeter and S.R. Caplan, Ann. Rev. Biophys. Bioeng. 5: 449 (1976).CrossRefGoogle Scholar
  13. [13]
    A. Goldbeter, J.-L. Martiel and O. Decroly, in “Dynamics of Biochemical System” p 173, ed. J. Ricard at A. Cornish-Bowden, Plenum Press, New York and London (1984).Google Scholar
  14. [14]
    A. Goldbeter and G. Nichols, Prog. Theor. Biol. 4: 56 (1976).Google Scholar
  15. [15]
    C. Grebogi, E. Ott and J.A. Yorke, Physica 7D: 181 (1983).Google Scholar
  16. [16]
    C. Grebogi, S.W. McDonald, E. Ott and J.A. Yorke, Phys. Lett. 99A: 415.Google Scholar
  17. [17]
    I. Gumowski and C. Mira, “Dynamique Chaotique”, ed. Cepadues, Toulouse (1980).Google Scholar
  18. [18]
    B.-L. Hao, Phys. Lett. 87A: 267 (1982).CrossRefGoogle Scholar
  19. [19]
    B. Hess and A. Boiteux, in “Regulatory Function of Biological Membranes”, p 148, ed. J. Jarnefelt, Elsevier, Amsterdam (1968).Google Scholar
  20. [20]
    Y.-X. Li, D.-F. Ding and J.-H. Xu, Comm. Theor. Phys. 3: 629 (1985).Google Scholar
  21. [21]
    E.N. Lorenz, J. Atm. Sc. 20: 130 (1963).CrossRefGoogle Scholar
  22. [22]
    M. Markus, D. Kuschmitz and B. Hess, FEBS Lett. 172: 235 (1984).PubMedCrossRefGoogle Scholar
  23. [23]
    J. Monod, J. Wyman and J.-P. Changeux, J. Mol. Biol. 12: 88–118 (1965).PubMedCrossRefGoogle Scholar
  24. [24]
    L.F. Olsen and H. Degn, Nature (London) 267: 177 (1977).CrossRefGoogle Scholar
  25. [25]
    E.K. Pye, Can. J. Bot. 47: 271 (1969).CrossRefGoogle Scholar
  26. [26]
    O.E. Rössler, Z. Naturforsch. 31a: 259 (1976).Google Scholar
  27. [27]
    O.E. Rössler, Bull. Math. Biol. 39: 275 (1977).PubMedGoogle Scholar
  28. [28]
    R. Shaw, Z. Naturforsch. 36a: 80 (1981).Google Scholar
  29. [29]
    S. Smale, Bull.Amer. Math. Soc. 73: 747 (1967).CrossRefGoogle Scholar
  30. [30]
    S. Takesue and K. Kaneko, Prog. Theor. Phys. 71: 35 (1984).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • Olivier Decroly
    • 1
  1. 1.Faculté des SciencesUniversité Libre de BruxellesBrusselsBelgium

Personalised recommendations