Oscillations in delayed positive feedback systems.

Positive feedback loops exist in many biological circuits important for organismal function. In this work, we investigate how temporal delay affects the dynamics of two canonical positive feedback models. We consider models of a genetic toggle switch and a one-way switch with delay added to the feedback terms. We show that long-lasting transient oscillations exist in both models under general conditions and that the duration depends strongly on the magnitude of the delay and initial conditions. We then show the existence of long-lasting oscillations in specific biological examples: the Cdc2-Cyclin B/Wee1 system and a genetic regulatory network. Our results challenge fundamental assumptions underlying oscillatory behavior in biological systems. While generally delayed negative feedback systems are canonical in generating oscillations, we show that delayed positive feedback systems are a mechanism for generating oscillations as well.