9404521 Pernarowski Several projects related to the bursting electrical activity of the pancreatic beta cell are studied by the investigator. Analog and biophysical models for single cell bursting electrical activity are used to model the behavior of discrete clusters (islets) of N coupled cells. For the analog cluster model, the steady state analysis for large N is examined in the context of a mapping problem to ascertain the effect that coupling has on the solution behavior. Also, continuum limits that describe islet electrical activity are examined. These models are parabolic partial differential equations that contain a small parameter. Asymptotic analyses are used to examine the existence and stability of steady states, travelling waves and spiral waves. The investigator studies the difference between the electrical behavior of single beta cells and clusters of beta cells through the use of mathematical models. These studies are important because the beta cell is the only insulin secreting cell in the body and the electrical behavior of such clusters has been strongly correlated to insulin release rate.
