Theoretical studies on the electrical activity of pancreatic beta-cells as a function of glucose

The electrical activity of pancreatic beta-cells, which has been closely correlated both with intracellular Ca2+ concentration and insulin release, is characterized by a biphasic response to glucose and bursts of spiking action potentials. Recent voltage clamp and single channel patch clamp experiments have identified several transmembrane ionic channels that may play key roles in the electrophysiological behavior of beta-cells. There is a hypothesis that Ca2+-activated K+ channels are responsible for both the resting potential during low glucose concentration and the silent phase during bursting. The discovery of the ATP-inactivated K+ channel raises the possibility that the current for this latter K+ channel may dominate the resting potential, while the Ca2+-activated K+ current dominates the silent phase potential between bursts. The recent discovery that Ca2+-activated K+ channels are pH sensitive raises an interesting possibility for the biphasic electrical response. In this paper, numerical methods are presented for evaluating these hypotheses against experimental evidence.