Abstract
Considering the ATP-driven (SERCA) pump flux as function of glucose concentration and the calcium flux from the endoplasmic reticulum (ER) through the IP(3)R channel, the calcium-based phantom bursting model (PBM) of beta-cells (Bertram and Sherman in Bull Math Biol 66:1313, 2004) is theoretically extended to discuss the effects of glucose and inositol 1,4,5-trisphosphate (IP(3)) concentration on the membrane potential activities. When IP(3) concentration is fixed, it is found that there is a critical glucose concentration at which electrical bursting oscillations transfer into spiking, and the critical concentration of glucose is increased with the increasing of IP(3) concentration. To get the bursting oscillations in beta-cells, our theoretical results show that the stimulatory glucose concentration should be more than 10 mM, which is consistent with the normal physiological IP(3) level. When the stochastic opening and closing of IP(3)R channels are considered, it is shown that the membrane potential oscillation transfers from spiking to bursting with the channel number decreasing, and the average cytosolic free Ca(2+) concentration is increased with the increase of glucose concentration.
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