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

Abstract

Based on recently determined ionic channel properties, a simple theoretical model for the burst activity of the pancreatic β-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 tok _Ca, 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 Ca_i dissociation constantK _h. 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 varyingk _ca and that a given pattern may produce different levels of intracellular Ca²⁺ depending onK _h. 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.