Mathematical Biology Seminar - Bhargav Karamched

Bhargav Karamched, Department of Mathematics, Florida State University Oscillations in Delayed Positive Feedback Systems Positive feedback loops exist in many biological circuits important for organismal function. In this talk , I will discuss how temporal delay affects the dynamics of two canonical positive feedback models: the genetic toggle switch and a one-way switch. I will demonstrate 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. This phenomenon occurs in specific biological examples as well: the Cdc2-Cyclin B/Wee1 system and a genetic regulatory network. This result challenges fundamental assumptions underlying oscillatory behavior in biological systems. While generally delayed negative feedback systems are canonical in generating oscillations, this work shows that delayed positive feedback systems are a mechanism for generating oscillations as we...