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We develop a detailed theoretical framework for various types oftranscription factor gene oscillators. We further demonstrate that one canbuild genetic-oscillators which are tunable and robust against perturbations inthe critical control parameters by coupling two or more independentGoodwin-Griffith oscillators through either -OR- or -AND- type logic. Most ofthe coupled oscillators constructed in the literature so far seem to be of -OR-type. When there are transient perturbations in one of the -OR- typecoupled-oscillators, then the overall period of the system remains constant(period-buffering) whereas in case of -AND- type coupling the overall period ofthe system moves towards the perturbed oscillator. Though there is aperiod-buffering, the amplitudes of oscillators coupled through -OR- type logicare more sensitive to perturbations in the parameters associated with thepromoter state dynamics than -AND- type. Further analysis shows that the periodof -AND- type coupled dual-feedback oscillators can be tuned without concedingon the amplitudes. Using these results we derive the basic design principlesgoverning the robust and tunable synthetic gene oscillators withoutcompromising on their amplitudes.

Theory on the Dynamics of Oscillatory Loops in the Transcription Factor Networks