Advertisement

Self-sustained oscillations in the Jacob-monod mode of gene regulation

  • Z. Grossman
  • I. Gumowski
Medicine And Biology
Part of the Lecture Notes in Computer Science book series (LNCS, volume 40)

Abstract

When pure delays are introduced into the Goodwin model of the Jacob-Monod mode of gene regulation, self-sustained stable periodic oscillations are found to exist in a wide parameter range, the parameters characterizing reaction rates, product synthesis, and transport times. Constant and concentration-dependent delays are both found to be primary causes of periodic oscillations.

Keywords

Periodic Solution Phase Plane Malonic Acid Variable Delay Transport Time 
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.

References

  1. 1).
    B.P. Belousov, Sb. Ref. Radiat. Med. (1958), Moscow (1959), p. 145.Google Scholar
  2. 2).
    A.M. Zhabotinskii, Dokl. Akad. Nauk SSSR 157 (1964), p. 392.Google Scholar
  3. 3).
    M. Herschkowitz-Kaufman, CR Acad. Sci. C. 270 (1970), p. 1049.Google Scholar
  4. 4).
    B. Hess and A. Boiteux, Annu. Rev. Biochemistry 40 (1971), p. 237.Google Scholar
  5. 5).
    E.E. Selkov, Eur. J. Biochem. 4 (1968), p. 79.Google Scholar
  6. 6).
    J. Higgins, R. Frenkel, E. Hulme, A. Lucas and G. Rangazas, "Biological and Biochemical Oscillators", Academic Press (1973), p. 127.Google Scholar
  7. 7).
    W.A. Knorre, Biochem. Biophys. Res. Commun. 31 (1968), p. 812.Google Scholar
  8. 8).
    B.C. Goodwin, Eur. J. Biochem. 10 (1969), p. 515.Google Scholar
  9. 9).
    W.A. Knorre, "Biological and Biochemical Oscillators", Academic Press (1973), p. 425.Google Scholar
  10. 10).
    B.C. Goodwin, "Temporal organization in cells", Academic Press (1963).Google Scholar
  11. 11).
    B.C. Goodwin, Adv. Enz. Regul. 3 (1965), p. 425.Google Scholar
  12. 12).
    J.S. Griffith, J. Theoret. Biol. 20 (1968), p. 202 and 209.Google Scholar
  13. 13).
    J. Tiwari, A. Fraser and R. Beckman, J. Theoret. Biol. 39 (1973), p. 679, and 45 (1974), p. 311.Google Scholar
  14. 14).
    J. Monod and M. Cohen-Bazire, CR Acad. Sci. 236 (1953), p. 417 and p. 530.Google Scholar
  15. 15).
    J. Monod and F. Jacob, Cold Spring Harbour Symp. Quant. Biol. 26 (1961), p. 389.Google Scholar
  16. 16).
    P. Rapp, Bio. Systems 5 (1975), No 112.Google Scholar
  17. 17).
    Correspondence Ninio-Lodish, Nature 255 (29 May 1975), p. 429.Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Z. Grossman
    • 1
  • I. Gumowski
    • 1
  1. 1.CERNGeneva 23Switzerland

Personalised recommendations