- Mathematical and Computational Neuroscience
- Mathematical Physiology
- Dynamical Systems
Current Research Interests
Activity of Pancreatic Beta-Cells
Pancreatic Beta-cells are the only cells in the body that secrete insulin, a hormone that is necessary for the uptake of glucose by other cells. Defects in beta-cell functioning lead to diabetes, which can result in death if not treated. The release of insulin is controlled by many physiological variables, including the cell's electrical activity, calcium, and nucleotide concentrations. I work in the development and analysis of mathematical models of beta-cell activity. This work is done in collaboration with Artie Sherman at the National Institutes of Health and Les Satin at the University of Michigan Medical School.
Hypothalamic Control of Hormone Secretion
The hypothalamus is the region of the brain that regulates the level and timing of hormone release from endocrine glands. One such gland, the pituitary, is located near the hypothalamus, and secretions from this gland regulate secretions from other glands. For this reason, the pituitary is sometimes called the master gland. The hypothalamus sends both stimulatory and inhibitory input to the pituitary, providing neural regulation to secretion from gonadotrophs, somatotrophs, corticotrophs, melanotrophs, and lactotrophs. With Joel Tabak and and Arturo Gonzalez-Iglesias I run a laboratory that studies this system using in vivo and in vitro techniques, as well as using mathematical modeling to design and interpret experiments.
Bursting Oscillations in Excitable Cells
In nerve cells, information is transmitted through electrical impulses. Electrical impulses also cause muscles to contract and endocrine cells to secrete hormones. Quite often, impulses are generated as high-frequency bursts, followed by periods of quiescence. This is particularly true in endocrine cells such as pancreatic beta-cells and anterior pituitary cells. I am interested both in the dynamics of bursting (a mathematical topic) and in the mechanisms by which different cells generate periodic bursts of impulses (a biological topic).
Neural Basis of Bird Song
The male zebra finch learns its song from its father and sings this song throughout adulthood. This is similar to the way that humans learn speach. In this project, done in collaboration with Frank Johnson, Wei Wu, and Rick Hyson, we use a combination of approaches in different labs to understand the neural basis of birdsong in the male zebra finch. We study behavioral aspects, and develop statistical tools to quantify the data. We also study mechanistic aspects through brain slice electrophysiology. Mathematical models are developed to interpret both the behavioral and the electrophysiological data.