Control of Metabolic Oscillations: Unpredictability, Critical Slowing Down, Optimal Stability and Hysteresis

  • Mario Markus
  • Benno Hess
Part of the NATO ASI Series book series (NSSA, volume 190)


Control analysis can be divided into three main areas. The first deals with systems in the steady state and is discussed in most of the contributions to the present volume. The second deals with time-dependent sensitivity coefficients of the first and second order (Larter et al., 1984; Edelson & Rabitz, 1985), sensitivity densities (Larter et al., 1983, 1984), as well as control and elasticity coefficients (Kohn et al., 1979; see also Chapter 25 by Acerenza in this book). The third is concerned with time-independent coefficients of time-dependent (oscillatory) processes, such as period sensitivities (Larter et al., 1984; Edelson & Rabitz, 1985) or control coefficients, as discussed by Acerenza in Chapter 25 of this book. We shall deal with this third area in the present contribution.


Pyruvate Kinase Chaotic Oscillation Maximum Lyapunov Exponent Control Coefficient Optimal Stability 
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. Acerenza, L., Sauro, H. M. & Kacser, H. (1989) J. Theor. Biol.,in pressGoogle Scholar
  2. Boiteux, A., Goldbeter, A. & Hess, B. (1975) Proc. Natl. Acad. Sci. USA 72, 3829–3833PubMedCrossRefGoogle Scholar
  3. Boiteux, A., Markus, M., Plesser, Th. Hess, B. & Malcovati, M. (1983) Biochem. J. 211, 631–640PubMedGoogle Scholar
  4. Burns, J. A., Cornish-Bowden, A., Groen, A.K., Heinrich, R., Kacser, H., Porteus, J. W., Rapoport, S. M., Rapoport, T. A., Stucki, J. W., Tager, J. M., Wanders, R. J. A. & Westerhoff, H. V. (1985) Trends Biochem. Sci. 10, 16CrossRefGoogle Scholar
  5. Decroly, O. & Goldbeter, A. (1982) Proc. Natl. Acad. Sci. USA 79, 6917–6921PubMedCrossRefGoogle Scholar
  6. Edelson, D. & Rabitz, H. (1985) in Oscillations and Travelling Waves in Chemical Systems (Field, R. J. & Burger, M., eds.), pp. 193–222, J. Wiley, New YorkGoogle Scholar
  7. Heinrichs, M. & Schneider, F. W. (1981) J. Chem. Phys. 85, 2112–2116CrossRefGoogle Scholar
  8. Hess, B. (1966) Studia Biophysica sl,s41-s63Google Scholar
  9. Hess, B. & Markus, M. (1984) in Synergetics — From Microscopic to Macroscopic Order (Frehland, E., ed.), pp. 6–16, Springer-Verlag, BerlinGoogle Scholar
  10. Hess, B. & Markus, M. (1985a) in Temporal Order (Rensing, L. & Jaeger, N.I., eds.), pp. 179–190, Springer-Verlag, BerlinGoogle Scholar
  11. Hess, B. & Markus, M. (19856) Ber. Bunsenges. Phys. Chem. 89,642–651Google Scholar
  12. Hess, B. & Markus, M. (1987) Trends Biochem. Sci. 12, 45–48CrossRefGoogle Scholar
  13. Kohn, M.C., Whitley, L.M. & Garfinkel, D. (1979) J. Theor. Biol. 76, 437–452PubMedCrossRefGoogle Scholar
  14. Lamer, R., Rabitz, H. & Kobayashi, M. (1983) J. Chem. Phys. 79, 692–707CrossRefGoogle Scholar
  15. Larter, R., Rabitz, H. & Kramer, M. (1984) J. Chem. Phys. 80, 4120–4128CrossRefGoogle Scholar
  16. L’vov, V.S., Predtechensky, A.A. & Chemikh, A.I. (1981) Soviet Physics JETP 53, 562–581Google Scholar
  17. Malraison, G., Atten, P., Bergé, P. & Dubois, M. (1983) J. Phys. Lett. 44, 897–902CrossRefGoogle Scholar
  18. Markus, M., Plesser, Th. Boiteux, A., Hess, B. & Malcovati, M. (1980) Biochem. J. 189, 421–433PubMedGoogle Scholar
  19. Markus, M. & Hess, B. (1984) Proc. Natl. Acad. Sci. USA 81, 4394–4398PubMedCrossRefGoogle Scholar
  20. Markus, M., Kuschmitz, D. & Hess, B. (1984) FEBS Lett. 172, 235–238PubMedCrossRefGoogle Scholar
  21. Markus, M. & Hess, B. (1985a) in Temporal Order (Rensing, L. & Jaeger, N.I., eds.), pp. 191–193, Springer-Verlag, BerlinGoogle Scholar
  22. Markus, M. & Hess, B. (1985b) Arch. Biol. Med. Exp. 18, 261–271PubMedGoogle Scholar
  23. Markus, M., Müller, S. C. & Hess, B. (1985a) Ber. Bunsenges. Phys. Chem. 89, 651–654CrossRefGoogle Scholar
  24. Markus, M., Kuschmitz, D. & Hess, B. (1985b)Biophys. Chem. 22,95–105Google Scholar
  25. Markus, M. & Hess, B. (1986) in Dynamics of Biochemical Systems (Damjanovich, S., Keleti, T. & Trion, L., eds.), pp. 11–25, Akadémiai Kiad6, BudapestGoogle Scholar
  26. Packard, N. H., Crutchfield, J. P., Fanner, J. D. & Shaw, R. S. (1980) Phys. Rev. Letts. 45, 712–716CrossRefGoogle Scholar
  27. Ricard, J. & Buc, J. (1988) Eur. J. Biochem. 176, 103–109PubMedCrossRefGoogle Scholar
  28. Schuster, H. G. (1984) Deterministic Chaos, Physik-Verlag, WeinheimGoogle Scholar
  29. Wolf, A., Swift, J. B., Swinney, H. L. & Vastano, J. A. (1985) Physica 16D, 285–317Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Mario Markus
    • 1
  • Benno Hess
    • 1
  1. 1.Max-Planck-Institut für ErnährungsphysiologieDortmund 1Federal Republic of Germany

Personalised recommendations