Simulation of spike-burst generation and Ca(2+) oscillation in pancreatic beta-cells

Based on the experimental evidence that Na(+)-Ca(2+) exchange participates in the regulation of intracellular Ca(2+) concentration in pancreatic beta-cells, we construct a mathematical model for the cyclic spike-bursts and oscillations of intracellular Ca(2+) concentration. In our model, an increase in ATP concentration by the stimulation of glucose metabolism leads to the closure of ATP-sensitive K(+) channels (K(ATP) channels) and gradual depolarization to the threshold of voltage-gated Ca(2+) channels. Spikes are generated by the alternate activation of voltage-gated Ca(2+) and K(+) channels, causing Ca(2+) entry. The accumulated Ca(2+) ions are extruded by Na(+)-Ca(2+) exchange and Ca(2+) active transport. An increase in Na(+) influx through Na(+)-Ca(2+) exchangers results in a rise in intracellular Na(+) concentration and the activation of Na(+)-K(+) active transport. The consumption of ATP during the process of Ca(2+) extrusion leads to the opening of K(ATP) channels and repolarization. The present model could reproduce the main experimental features of the spike-burst activity and Ca(2+) oscillations following changes in the extracellular glucose concentration. As the rate of ATP production increases, the spike-burst pattern changes from bursts with long silent phases to continuous spiking. Changes in the pattern of electrical activity produced by the alteration of extracellular Na(+) and K(+) concentrations and the addition of ouabain could be reproduced in the present model.