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