A simple model of genetic oscillations through regulated degradation

We present a simple model which aims at the description of the dynamics of cellular regulation through genetic circuits involving a feedback loop between a regulatory factor and a target that specifically triggers degradation of this regulator. In particular we study the possibility for this simple model to reproduce stable oscillations which have been recently observed experimentally. Our model takes the form of a time-delayed differential system and is inspired by the core circuit for the stress resistance p53 system. Depending on the protein degradation rates and the value of the delay we show that it is possible, in the presence of stress, to switch from a stable steady state to one of persistent oscillations (which die out when the stress disappears).