Flexible Dynamics of Two Quorum Sensing Coupled Repressilators
  Genetic oscillators play important roles in cell life regulation. The regulatory efficiency usually depends strongly on the emergence of stable collective dynamic modes, which requires designing the interactions between genetic networks. We investigate the dynamics of two identical synthetic genetic repressilators coupled by an additional plasmid which implements quorum sensing (QS) in each network thereby supporting global coupling. In a basic genetic ring oscillator network in which three genes inhibit each other in unidirectional manner, QS stimulates the transcriptional activity of chosen genes providing for competition between inhibitory and stimulatory activities localized in those genes. The "promoter strength", the Hill cooperativity coefficient of transcription repression, and the coupling strength, i.e., parameters controlling the basic rates of genetic reactions, were chosen for extensive bifurcation analysis. The results are presented as a map of dynamic regimes. We found that the remarkable multistability of the anti-phase limit cycle and stable homogeneous and inhomogeneous steady states exists over broad ranges of control parameters. We studied the anti-phase limit cycle stability and the evolution of irregular oscillatory regimes in the parameter areas where the anti-phase cycle loses stability. In these regions we observed developing complex oscillations, collective chaos, and multistability between regular limit cycles and complex oscillations over uncommonly large intervals of coupling strength. QS-coupling stimulates the appearance of intrachaotic periodic windows with spatially symmetric and asymmetric partial limit cycles which, in turn, change the type of chaos from a simple anti-phase character into chaos composed of pieces of the trajectories having alternating polarity. Abstract truncated... 
Edward H. Hellen and Evgeny Volkov
physics.bio-ph nlin.AO q-bio.MN