] i ) is a key signal in the initiation of insulin secretion from the pancreatic -cell. This increase principally results from calcium influx through plasma membrane (PM) Ca 2ϩ channels, which open in response to secretagogues, primarily glucose. The metabolism of glucose through glycolysis and the tricarboxylic acid cycle leads to an increase in the cytoplasmic ATP-to-ADP (ATP/ADP) ratio. This causes closure of ATP-sensitive K ϩ (K ATP ) channels followed by depolarization of the -cell membrane to the threshold potential where Ca 2ϩ channels open, initiating Ca 2ϩ influx (4). These events underlie glucose-induced electrical activity that, in pancreatic islets, consists of Ca 2ϩ -dependent action potentials.There is extensive literature describing -cell electrical activity and its relationship to [Ca 2ϩ ] i in intact islets of Langerhans, isolated islet cells, and insulinoma cell lines. Most of the work has been carried out using mouse islets, with some studies using islets from rat, hamster, human, and other species.Mouse pancreatic -cells exhibit complex and cyclic spike-burst activity in response to a rise in extracellular glucose concentration. The bursts consist of a depolarized phase of Ca 2ϩ -carrying action potentials alternating with a silent phase of repolarization, resulting in oscillations in intracellular Ca 2ϩ , which can drive pulses of insulin secretion (28, 37).The only stimulus required for a complex cyclic spike-burst activity and corresponding [Ca 2ϩ ] i oscillations in islets and -cell clusters is elevation of glucose to levels above 5 and less than ϳ20 mM. Intermediate glucose concentrations induce two main types of oscillations in mouse pancreatic islets: fast, where the period ranges from 10 to 30 s, and slow, with periods of several minutes (37,54,83). Single mouse -cells can also respond to glucose stimulation with regular oscillations (37).We have previously studied slow and fast [Ca 2ϩ ] i oscillations in islets in response to a variety of conditions (70, 73; unpublished observations). We have also previously reported that a stable, transgenically derived murine insulinoma cell line (TC3-neo) responds to glucose with slow, large amplitude [Ca 2ϩ ] i oscillations but only in the presence of 10-20 mM tetraethylammonium (TEA), a blocker of K ϩ channels (74). We have utilized this cell line to characterize glucose-stimulated oscillatory activity (74).However, the precise interpretation of previous results is limited due to the numerous channels and pumps in -cells that work concurrently, and identification of physiologically slow variables that drive oscillations remains unclear. To clarify these complex experimental results, we used a mathematical modeling approach. Our goals, then, are twofold: to develop a model for -cell ion homeostasis, including the bursts and [Ca 2ϩ ] i oscillations that can simulate cellular behavior, and to explain on this basis the experimental data for single cells and islets.Several mathematical approaches in the literature have provid...