Origin, heterogeneity, and interconversion of noncanonical bistable switches from the positive feedback loops under dual signaling.

Designing new functional motifs with unique properties is an important objective in the realm of synthetic biology. We uncover emergent properties of positive feedback loops (PFLs) under dual input signaling using pseudo potential energy-based high-throughput bifurcation analysis. We show that under dual signaling a single PFL generates a variety of noncanonical bistable switches, with one or more bistable regions, due to fusion of multiple canonical bistable switches. Regulatory signs of the dual signaling must be coherent for mutual inhibition loop and incoherent for mutual activation loop of the PFL. Occurrence probabilities show that some of the noncanonical switches, such as isola and mushroom, are highly recurrent under random parameterization. Phase diagrams of the noncanonical switches reveal that feedback strengths of the PFL control the transition from one switch to another. Our calculations decipher the design principles of noncanonical bistable switches that originate from synthetically feasible simple PFL motifs under dual signaling.