Design and Analysis of an Activator-Repressor Clock in E. Coli

We analyze a model for the activator-repressor oscillator motif proposed as a fundamental oscillating motif in the literature of biological rhythms. We show that incorporating the m-RNA dynamics in the model, we can obtain a much richer dynamical behavior with respect to the behaviors observed in the literature when only protein dynamics were modeled. The proposed analysis also leads to biochemical parameter relationships that guarantee stable oscillations. These relationships can be used as design guidelines for the construction of synthetic activator-repressor oscillators.