Abstract
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 antiphase limit cycle and stable homogeneous and inhomogeneous steady states exists over broad ranges of control parameters. We studied the antiphase limit cycle stability and the evolution of irregular oscillatory regimes in the parameter areas where the antiphase 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 antiphase character into chaos composed of pieces of the trajectories having alternating polarity. The very rich dynamics discovered in the system of two identical simple ring oscillators may serve as a possible background for biological phenotypic diversification, as well as a stimulator to search for similar coupling in oscillator arrays in other areas of nature, e.g., in neurobiology, ecology, climatology, etc.
Highlights
Synthetic genetic networks provide researchers with the opportunity of designing biologically based circuitry for accomplishing specific functions
We start with the demonstration of the general structure of the phase diagram for two coupled 4-dim repressilators [Eq (1)] with parameters similar to those used previously [20] in a study with nonreduced coupled 7-dim repressilators
The coupling strength is varied from 0 to 1.5 in order to show the entire structure of the system, values of Q > 1 are not accessible in the conventional biological system
Summary
Synthetic genetic networks provide researchers with the opportunity of designing biologically based circuitry for accomplishing specific functions. Networks displaying multistable dynamics provide a method for investigating possible mechanisms for biological diversity. In principle, such circuits can be incorporated into natural cellular machinery or used in an entirely synthetic environment. Oscillators are essential motifs for circuit design [1]. The repressilator is a synthetic genetic oscillator (GO) in the form of a ring of three genes sequentially inhibiting one another’s transcription. The GO has been inserted experimentally into E. coli [2] and extensively studied theoretically via deterministic and stochastic approaches [3,4,5]
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