Simulation of spike-burst generation and Ca2+ oscillation in pancreatic β-cells

Abstract

Based on the experimental evidence that Na+-Ca2+ exchange participates in the regulation of intracellular Ca2+ concentration in pancreatic β-cells, we construct a mathematical model for the cyclic spike- bursts and oscillations of intracellular Ca2+ 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 Ca2+ channels. Spikes are generated by the alternate activation of voltage-gated Ca2+ and K+ channels, causing Ca2+ entry. The accumulated Ca2+ ions are extruded by Na+Ca2+ exchange and Ca2+ active transport. An increase in Na+ influx through Na+-Ca2+ 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 Ca2+ 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 Ca2+ 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.