On the Electrical Activity and Glucose Response of Insulin-Secreting Cells

The β-cells of the mammalian pancreas exhibit electrical bursting activity in response to glucose (Fig. 1). A nonlinear differential equation model, developed by Chay and Keizer [8], describes several aspects of this bursting behavior for a representative cell (in a coupled, synchronized population). In this theory, the time scale of a burst is determined by the slow dynamics of intracellular free calcium, Ca, and the fast, spike generating, dynamics incorporates a calcium-activated K+ (K-Ca) channel as the site for slow feedback from Ca. We review how the structure of such models can be understood by using a singular perturbation dissection of the fast and slow subsystems of the model. We then outline how, under two different hypotheses for glucose action, an extended model leads to two different predictions for the time course of Ca. Finally we describe a further (stochastic) modification of the model to explore the question of why a single isolated β-cell does not burst, but electrically coupled cells in clusters do show bursting.