Tuning an activator-repressor clock employing retroactivity

Activator-repressor systems have been shown to be capable of oscillations and are therefore an important clock motif in the field of Synthetic and Systems Biology. In this paper, we propose a method to regulate oscillatory behavior in such systems by the addition of DNA binding sites for the proteins involved in the clock network. We show that the retroactivity effect caused by this addition can effectively change the relative timescales among the protein dynamics and impact the behavior of the clock. We also employ root locus analysis to obtain a graphical interpretation of the results.