A calcium-based phantom bursting model for pancreatic islets

Richard Bertram, Arthur Sherman

Insulin-secreting β-cells, located within the pancreatic islets of Langerhans, are excitable cells that produce regular bursts of action potentials when stimulated by glucose. This system has been the focus of mathematical investigation for two decades, spawning an array of mathematical models. Recently, a new class of models has been introduced called ‘phantom bursters’ [Bertram et al. (2000) Biophys. J. 79, 2880-2892], which accounts for the wide range of burst frequencies exhibited by islets via the interaction of more than one slow process. Here, we describe one implementation of the phantom bursting mechanism in which intracellular Ca2+ controls the oscillations through both direct and indirect negative feedback pathways. We show how the model dynamics can be understood through an extension of the fast/slow analysis that is typically employed for bursting oscillations. From this perspective, the model makes use of multiple degrees of freedom to generate the full range of bursting oscillations exhibited by β-cells. The model also accounts for a wide range of experimental phenomena, including the ubiquitous triphasic response to the step elevation of glucose and responses to perturbations of internal Ca2+ stores. Although it is not presently a complete model of all β-cell properties, it demonstrates the design principles that we anticipate will underlie future progress in β-cell modeling.