Applying a Rigorous Quasi-Steady State Approximation Method for Proving the Absence of Oscillations in Models of Genetic Circuits

  • François Boulier
  • Marc Lefranc
  • François Lemaire
  • Pierre-Emmanuel Morant
Conference paper

DOI: 10.1007/978-3-540-85101-1_5

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5147)
Cite this paper as:
Boulier F., Lefranc M., Lemaire F., Morant PE. (2008) Applying a Rigorous Quasi-Steady State Approximation Method for Proving the Absence of Oscillations in Models of Genetic Circuits. In: Horimoto K., Regensburger G., Rosenkranz M., Yoshida H. (eds) Algebraic Biology. AB 2008. Lecture Notes in Computer Science, vol 5147. Springer, Berlin, Heidelberg

Abstract

In this paper, we apply a rigorous quasi-steady state approximation method on a family of models describing a gene regulated by a polymer of its own protein. We study the absence of oscillations for this family of models and prove that Poincaré-Andronov-Hopf bifurcations arise if and only if the number of polymerizations is greater than 8. A result presented in a former paper at Algebraic Biology 2007 is thereby generalized. The rigorous method is illustrated over the basic enzymatic reaction.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • François Boulier
    • 1
  • Marc Lefranc
    • 2
  • François Lemaire
    • 1
  • Pierre-Emmanuel Morant
    • 2
  1. 1.LIFLUniversity Lille IVilleneuve d’AscqFrance
  2. 2.PHLAMUniversity Lille IVilleneuve d’AscqFrance

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