Time Pattern Transitions in Biochemical Processes

  • Benno Hess
  • Mario Markus
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 22)


Historically, science has learned from the analysis of equilibrium states. The biochemist extracts reaction mechanisms from the study of isolated reactions under closed conditions. Thus, an enzyme-catalyzed reaction runs into equilibrium in a first-order approach whenever substrates or products are added. The rate laws describe the overall process fitting to the kinetics and the given chemical potential sets the direction of flux. The closed case is only a sophisticated approach of a simple experimental design. The open case is the case of nature: it means that all enzymes in a biological process are constantly, stochastically or periodically activated by substrates which are produced by the environment or by precursor enzymes and transformed so that they are picked up by other enzymes within a reaction sequence. Each enzyme in a sequence becomes an element in a multienzymic network.


Periodic Orbit Chaotic Attractor Chaotic State Input Flux Allosteric Enzyme 
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.
    B Hess: 8. Fritz Lipmann-Vorlesung, Hoppe-Seyler’s Z. Physiol. Chem. 364, 1 (1983)CrossRefGoogle Scholar
  2. 2.
    A. Boiteux, A. Goldbeter and B. Hess: Proc. Natl. Acad. Sci. USA 72 (10), 3829 (1975)ADSCrossRefGoogle Scholar
  3. 3.
    Th. Plesser, in: VII Int. Konf. über Nichtlineare Schwingungen ed. by G. Schmidt, Vol. 2, 273 ( Akademie-Verlag, Berlin, 1977 )Google Scholar
  4. 4.
    M. Markus and R. Schueller: 15th FEBS Meeting, Brussels, Abstract S-17/WE-194 (1983)Google Scholar
  5. 5.
    M. Markus, H. Becher and B. Hess: Hoppe-Seyler’s Z. Physiol. Chem. 364 (9), 1177 (1983)Google Scholar
  6. 6.
    J.G. Reich and E.E. Sel’kov: FEBS Letters 40, S119 (1974)CrossRefGoogle Scholar
  7. 7.
    A. Boiteux, M. Markus, Th. Plesser, B. Hess and M. Malcovati: Biochem. J. 211, 631 (1983)Google Scholar
  8. 8.
    D. Blangy, H. Buc and J. Monod: J. Mol. Biol. 31, 13 (1968)CrossRefGoogle Scholar
  9. 9.
    M. Markus, Th. Plesser, A. Boiteux, B. Hess and M. Malcovati: Biochem. J. 189, 421 (1980)Google Scholar
  10. 10.
    P. Schuster, K. Sigmund and R. Wolff: SIAM J. Appl. Math. C 37(1), 49 (1979)Google Scholar
  11. 11.
    N. Minorsky: Nonlinear Oscillations (R.E. Krieger Publ., Huntington, N.Y., 1974 )Google Scholar
  12. 12.
    P. Collet and J.-P. Eckmann: Iterated Maps on the Interval as Dynamic Systems ( Birkhäuser, Boston, 1980 )Google Scholar
  13. 13.
    S. Grossmann und S. Thomae, Zeitschrift für Naturforschung 32a, 1353 (1977)ADSGoogle Scholar
  14. 14.
    R. Shaw: Z. Naturforsch. 36a, 80 (1981)Google Scholar
  15. 15.
    M. Feigenbaum: J. Stat. Phys. 19, 25 (1978) and 21, 669 (1979)MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. 16.
    O. Decroly and A. Goldbeter: Proc. Nat. Acad. Sci. USA 79, 6917 (1982)MathSciNetADSzbMATHCrossRefGoogle Scholar
  17. 17.
    G. Benettin, L. Galgani and J.-M. Strelcyn: Phys. Rev. A14, 2338 (1976)ADSCrossRefGoogle Scholar
  18. 18.
    I. Shimada and T. Nagashima: Progr. Theor. Phys. 61, 1605 (1979)MathSciNetADSzbMATHCrossRefGoogle Scholar
  19. 19.
    E. Ott: Rev. Mod. Phys. 53(4), 655 (1981)Google Scholar
  20. 20.
    M. Prütter, Report Nr. 85, Forschungsschwerpunkt Dynamische Systeme, University of Bremen (1983)Google Scholar
  21. 21.
    J. Kaplan and J. Yorke: in Functional Differential Equations and Approximation of Fixed Points, ed. by H.O. Peitgen and H.O. Walther ( Springer, Berlin, Heidelberg, New York, 1979 )Google Scholar
  22. 22.
    J.D. Farmer: Physica 4D, 366 (1982)MathSciNetzbMATHGoogle Scholar
  23. 23.
    H. Mori: Progr. Theor. Phys. 63, 3 (1980)Google Scholar
  24. 24.
    H. Hayashi, S. Ishizuka, M. Ohta and K. Hirakawa: Physics Letters 88A, 435 (1982)Google Scholar
  25. 25.
    H. Hayashi, M. Nakao and K. Hirakawa: Physics Letters 88A, 265 (1982)CrossRefGoogle Scholar
  26. 26.
    B. Chance, B. Schoener and S. Elsaessar: J. Biol. Chem. 240, 3170 (1965)Google Scholar
  27. 27.
    B. Hess and A. Boiteux: in: Regulatory Functions of Biological Membranes, ed. by Johan Järnefelt (Biochim. Biophys. Acta Library, 1968) Vol. 11, 148Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Benno Hess
    • 1
  • Mario Markus
    • 1
  1. 1.Max-Planck-Institut für ErnährungsphysiologieDortmund 1Fed. Rep. of Germany

Personalised recommendations