My focus in this area is on the endocrine system. One interest is
insulin-secreting pancreatic beta-cells. These are the only cells in the body that secrete the key hormone insulin, and death or dysfunction of beta-cells leads to diabetes. I collaborate with mathematical and experimental labs on this project. Another project is the function and neuronal control of hormone-secreting cells in the pituitary gland. The 5 different types of cells here secrete different hormones that have a range of functions, controlling things like reproduction, parental behavior, growth, and stress. I direct a lab at FSU where experiments on this system are performed.
My main focus here is on the neural basis of bird song in the zebra finch. The male of this species learns its song by listening to a tutor, typically the bird's father. It first memorizes the song, and then goes through a period called subsong when it rehearses the song through trial and error. As an adult, it sings the same song throughout the rest of its life. In a collaboratino with Drs. Frank Johnson, Rick Hyson, and Wei Wu at FSU we study the neural mechanism for song production. The hope is that by understanding this in birds it will better help us understand human speech.
Analysis of Bursting Oscillations
Bursting oscillations, consisting of fast oscillations or
spikes followed by a period of quiescence, are prevalent
in excitable cells. The biophysical mechanisms driving these
oscillations vary from cell to cell, and I have been involved
in modeling these mechanisms in several bursting cells.
However, bursting oscillations can be studied from a
purely mathematical perspective, using techniques from
dynamical systems theory. For a number of years now I
have been involved in such studies. Most recently, I have worked with Dr. Joel Tabak at FSU and Dr. Martin Wechselberger on the "pseudo-plateau bursting" that occurs in pituitary cells. We use geometric singular perturbation theory in our analysis, and have related this bursting to structures called folded node singularities.