Bifurcations and multistability in an inducible three-gene switch network

Control of transcription presides over a vast array of biological processes, manifesting through gene regulatory circuits that exhibit multistability. Existing theoretical models of these circuits, however, typically vary parameters such as dissociation constants, transcription rates, and degradation rates without referring to how these parameters are biologically controlled. We investigate an extension of the bistable switch to three genes, which permits richer dynamics including tristability and beyond. Importantly, our model incorporates the underlying role of effector molecules, which can alter the concentrations of the active transcription factors that control regulation, thus allowing evaluation of bifurcations in dynamic phase space as a function of inducer concentrations. We then study how the conditions required for multistability evolve under various interpretations of the regulatory circuit mechanics, the underlying activity of inducers, and perturbations, and proceed to investigate how the three-gene switch may facilitate robust multistability in the face of downstream feedback. In this way, we determine key parameters and regulatory features that drive phenotypic decisions. From a gene network design perspective, our model presents an experimentally tunable structure for encoding multistable behavior.