Pernarowski 9704966 The investigator studies several problams related to the electrical activity of the pancreatic beta cell. Fast and slow subsystem bifurcations yielding different global behaviors in single cell, cell pair and continuum models of the islet are examined. The emphasis in the single cell analysis is to extend previous asymptotic procedures to models having more than one slow variable. For the cell pair analyses, the effect of phase differences in the slow variables and coupling conductance is examined using standard bifurcation and linearization techniques. One goal is to explain the prolongated active phase duration that is indirectly responsible for elevated insulin secretion. Lastly, a continuum model for the electrical activity in large collections (islets) of beta cells is examined using asymptotic, linearization and global monotone methods. The effect of heterogenity and coupling strength on fast subssystem bifurcations is studied in the context of a system of reaction diffusion equations used to model the islet behavior. The investigator studies mathematical models of the electrical and chemical behavior of the insulin secreting pancreatic beta cell. The salient feature of the study lies in the identification of electrical behaviors that lead to increased insulin secretion in both individual pancreatic cells and collections of such cells as they occur in the body. Knowledge of such behaviors facilitates an understanding of the cellular mechanisms that are most relevant in diabetic conditions. All mathematical analyses are motivated by experimental studies.
