Theory of the effect of extracellular potassium on oscillations in the pancreatic beta-cell.

Based on the observation that potassium ions are compartmentalized near the surface of pancreatic beta-cells in mouse islets (Perez-Armendariz, E.M., I. Atwater, and E. Rojas 1985, Biophys. J. 48:741-749), we present a theoretical treatment of the effect of external potassium on oscillations in the pancreatic beta-cell. Our model includes the effects of ionic diffusion, the Ca2+-activated K+ channel, voltage-gated K+ and Ca2+ channels, and some of the effects of glucose. It is described by four ordinary differential equations. Numerical integration of these equations allows us to examine the effect of glucose, external K+, quinine, and tetraethylammonium ion (TEA) on the oscillations in membrane potential, intracellular Ca2+, and compartmentalized K+. The results are in good agreement with experiment.