Minimal model for membrane oscillations in the pancreatic beta-cell

Following the experimental findings of Atwater et al. (In Biochemistry Biophysics of the Pancreatic-beta-Cell, George Thieme Verlag, New York, 100-107), we have formulated a mathematical model for ionic and electrical events that take place in pancreatic-beta-cells. Our formulation incorporates a Hodgkin-Huxley type gating mechanism for Ca2+ and K+ channels, in addition to Ca2+ gated K+-channels. Consistent with the experimental observations, our model generates spikes and bursts in beta-cell membrane potentials and gives the correct responses to additions of glucose, quinine, and tetraethylammonium ions. The response of the oscillations to ouabain and changing concentrations of external K+ can be incorporated into the present model, although a more complete treatment would require inclusion of the Na+/K+ pump.