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Potvin-Trottier, L., Lord, N.D., Vinnicombe, G. and Paulsson, J. (2016) Synchronous Long-Term Oscillations in a Synthetic Gene Circuit. Nature, 538, 514-517.
https://doi.org/10.1038/nature19841

has been cited by the following article:

• TITLE: Hopf Bifurcation Analysis of the Repressilator Model

  AUTHORS: Anael Verdugo

  KEYWORDS: Hopf Bifurcation, Repressilator, Center Manifold Analysis

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.8 No.2, June 15, 2018

  ABSTRACT: The repressilator is a genetic network that exhibits oscillations. The net-work is formed of three genes, each of which represses each other cyclically, creating a negative feedback loop with nonlinear interactions. In this work we present a computational bifurcation analysis of the mathematical model of the repressilator. We show that the steady state undergoes a transition from stable to unstable giving rise to a stable limit-cycle in a Hopf bifurcation. The nonlinear analysis involves a center manifold reduction on the six-dimensional system, which yields closed form expressions for the frequency and amplitude of the oscillation born at the Hopf. A parameter study then shows how the dynamics of the system are influenced for different parameter values and their associated biological significance.