Control of the dynamical behavior of the Repressilator by Quorum Sensing
We have investigated dynamics of synthetic genetic oscillators — repressilators — coupled through autoinducer diffusion. The model of the system with phase-repulsive coupling structure is under consideration. It has been shown that autoinducer production module added to the isolated repressilator cause the limit cycle to disappear through infinite period bifurcation for sufficiently large transcription rate. We have found hysteresis of limit cycle and stable steady
state the size of which is determined by ratio between mRNA and protein lifetimes.