Biological Feedback Systems: A Computational Study of Oscillations and Homeostasis

In this talk, I will give an overview of my research as a graduate student, focusing on how temporal dynamics shape oscillations and robustness in biological feedback systems. First, I will discuss how delays in positive feedback can generate long-lasting transient oscillations. Using models of a toggle switch and a one-way switch, we show that delayed positive feedback can produce transient oscillations whose duration depends strongly on both the magnitude of the delay and the initial conditions. This provides a mechanism for oscillatory behavior distinct from the delayed negative feedback traditionally associated with oscillations.
I will then discuss a theoretical framework for dynamic homeostasis in biological systems with fast-slow dynamics. We show that even when fast variables exhibit large-amplitude oscillations, the temporal average of a slow variable can remain invariant to parameter changes. These results suggest that homeostasis need not correspond to a stable state at every timescale but can instead emerge through robust averaged dynamics. Together, these projects highlight how delays and multiple timescales can fundamentally shape the dynamics and robustness of biological feedback systems.