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

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Algebraic Biology (AB 2008)

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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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Katsuhisa Horimoto Georg Regensburger Markus Rosenkranz Hiroshi Yoshida

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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. https://doi.org/10.1007/978-3-540-85101-1_5

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  • DOI: https://doi.org/10.1007/978-3-540-85101-1_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85100-4

  • Online ISBN: 978-3-540-85101-1

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