Pulses and chaos: Dynamical response in a simple genetic oscillator

We investigate the dynamical behaviour of the genetic feedback loop present in the signalling network of the transcription factor NF-kappa B. This transcription factor is one of the most important regulators in mammalian cells, involved in a large number of cellular responses. We find that when the external stimulus is constant, the concentration of NF-kappa B inside the cell nucleus is either stationary or shows spiky oscillations. If the external stimulus is time dependent, the response can be more intricate. Here, we consider the response to pulsed and periodic stimuli. In the latter case the response can be chaotic with the NF-kappa B concentration converging to a strange attractor. The corresponding bifurcation diagram is also presented.