Homeostasis-Bifurcation Singularities and Hepatic Lipid Dynamic

Homeostasis-Bifurcation Singularities and Hepatic Lipid Dynamic

###### Mathematical Biology Seminar

#### William Duncan (Duke University, Mathematics)

**Friday, December 6, 2019 -1:30pm to 2:30pm**

In this talk I will discuss two separate projects. The projects lie on opposite ends of the math-biology spectrum with the first being math inspired by biology and the second being a biological modeling project. The first project studies the interaction of homeostasis and bifurcation. Homeostasis can be studied by restricting one’s attention to homeostasis points—points at which a component of a dynamical system has a vanishing derivative with respect to a parameter. In a feed-forward network, if a node has a homeostasis point, downstream nodes will inherit it. This is the case except when the downstream node has a bifurcation point coinciding with the homeostasis point. At these homeostasis-bifurcation points, the downstream node often exhibits complex behavior as the input parameter is varied. In the case of steady state bifurcation, this includes multiple homeostatic plateaus separated by hysteretic switches, which are observed in glycolysis. In the case of Hopf Bifurcation, the downstream node often has homeostatic limit cycles, which are observed in circadian rhythms. The second project is work done during an internship in the quantitative systems pharmacology group at Pfizer. I will discuss the role of mathematical modeling at Pfizer and my work on a model for hepatic lipid dynamics. The model is being developed to better understand how to treat non-alcoholic fatty liver disease, which affects 30% of adults in the U.S..