The effect of inactivation of calcium channels by intracellular Ca2+ ions in the bursting pancreatic beta-cells.

Based on recently determined ionic channel properties, a simple theoretical model for the burst activity of the pancreatic beta-cell is formulated in this paper. The model contains an inward voltage-activated Ca2+ current which is inactivated by intracellular calcium ions and an outward K+ current that is activated by the membrane potential. The probability of opening of the channel gates is represented by Boltzmann equations. Our model is applicable in a regime where an ATP-blockable K+ channel is inhibited. In this regime, glucose is treated as an activator for the rate of efflux of intracellular Ca2+ ions, and hence its effect is equated to kca, the efflux rate constant. In addition, intracellular H+ ion, which is a byproduct of the glycolytic metabolic process, is treated as a competitive inhibitor for Ca2+ ion. Since H+ is a competitive inhibitor (according to our assumption), its effect is equated to the strength of the Cai dissociation constant Kh. In the model, a Ca2+ binding site is assumed to exist in the inner membrane of the voltage-gated Ca2+ channel. The model predicts that a spike and burst electrical pattern can be generated by varying kca and that a given pattern may produce different levels of intracellular Ca2+ depending on Kh. In other words, it predicts that levels of [Ca2+]i can be separated from the electrical activity by controlling the concentration of glucose and pH appropriately. This may account for the experimental observation of Lebrun et al. (1985) that insulin secretion is not correlated to the burst of electrical activity.