Repressilators and promotilators: loop dynamics in synthetic gene networks

Oscillators and switches are ubiquitous in gene regulatory networks. Understanding the dynamical properties of these systems is a necessity not only to reverse engineer their structure, but also to forward engineer novel structures in the context of the nascent field of "synthetic biology". In this work, we analyze two classes of cyclic gene networks. The first class corresponds to the "repressilator", which is to polemically equivalent to a class of negative gain networks. The second class corresponds to the "promotilator" which is topologically equivalent to a class of positive gain networks. We demonstrate that the repressilator can exhibit oscillatory behavior under conditions that we derive. We also demonstrate that the promotilator and its equivalent circuits belong to the class of strongly monotone systems, and as such, the behavior they can exhibit is convergence to stable equilibria.