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

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 Poincare-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 2007is thereby generalized. The rigorous method is illustrated over the basic enzymatic reaction.

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