Glucose response to bursting-spiking pancreatic beta-cells by a barrier kinetic model

A mathematical model of the pancreatic beta-cell electrical activity was developed using a barrier kinetic model. Our model incorporates the glucose sensitive channel which is known to conduct K+ in the absence of glucose. The model also incorporates Cai sensitive K+ channels which are inhibited by intracellular H+ ions. It is described by three non-linear simultaneous differential equations. Numerical integration of these equations allowed us to examine the effect of glucose and of external Ca2+ ions on the electrical and cellular activity of the beta-cell. Our results show that the contribution of glucose-sensitive channel activity, if not completely inhibited, plays a very important role in determining the bursting periodicity. Our results also shows that even a small decrease in pHi is sufficient to change a bursting beta-cell to a spiking one. The voltage dependence of calcium sensitive K+ channels, however, affects little to the bursting mode of the electrical activity. Our simulation supports an incomplete selectivity of the voltage dependent calcium channel for calcium ions with low external [Ca2+]. It also supports the role of [Ca]i as an inhibitor of this channel when [Ca]i becomes unusually high.