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
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5147)


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.


Genetic Circuit System Page General Mass Action Steady Point Nonzero Arbitrary Constant 
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© 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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