"Quorum sensing" generated multistability and chaos in a synthetic genetic oscillator

We model the dynamics of the synthetic genetic oscillator Repressilator equipped with quorum sensing. In addition to a circuit of 3 genes repressing each other in a unidirectional manner, the model includes a phase-repulsive type of the coupling module implemented as the production of a small diffusive molecule-autoinducer (AI). We show that the autoinducer (which stimulates the transcription of a target gene) is responsible for the disappearance of the limit cycle (LC) through the infinite period bifurcation and the formation of a stable steady state (SSS) for sufficiently large values of the transcription rate. We found conditions for hysteresis between the limit cycle and the stable steady state. The parameters' region of the hysteresis is determined by the mRNA to protein lifetime ratio and by the level of transcription-stimulating activity of the AI. In addition to hysteresis, increasing AI-dependent stimulation of transcription may lead to the complex dynamic behavior which is characterized by the appearance of several branches on the bifurcation continuation, containing different regular limit cycles, as well as a chaotic regime. The multistability which is manifested as the coexistence between the stable steady state, limit cycles, and chaos seems to be a novel type of the dynamics for the ring oscillator with the added quorum sensing positive feedback.