Motif for controllable toggle switch in gene regulatory networks

Toggle switch as a common phenomenon in gene regulatory networks has been recognized important for biological functions. Despite much effort dedicated to understanding the toggle switch and designing synthetic biology circuit to achieve the biological function, we still lack a comprehensive understanding of the intrinsic dynamics behind such phenomenon and the minimum structure that is imperative for producing toggle switch. In this paper, we discover a minimum structure, a motif that enables a controllable toggle switch. In particular, the motif consists of a transformative double negative feedback loop (DNFL) that is regulated by an additional driver node. By enumerating all possible regulatory configurations from the driver node, we identify two types of motifs associated with the toggle switch that is captured by the existence of bistable states. The toggle switch is controllable in the sense that the gap between the bistable states is adjustable as determined by the regulatory strength from the driver nodes. We test the effect of the motifs in self-oscillating gene regulatory network (SON) with respect to the interplay between the motifs and the other genes, and find that the switching dynamics of the whole network can be successfully controlled insofar as the network contains a single motif. Our findings are important to uncover the underlying nonlinear dynamics of controllable toggle switch and can have implications in devising biology circuit in the field of synthetic biology.