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The role of pancreatic β-cells is fundamental in the control endocrine system, maintaining the blood glucose homeostasis in a physiological regime, via the glucose-induced release of insulin. An increasing amount of detailed experimental evidences at the cellular and molecular biology levels have been collected on the key factors determining the insulin release by the pancreatic β-cells. The direct transposition of such experimental data into accurate mathematical descriptions might contribute to considerably clarify the impact of each cellular component on the global glucose metabolism. Under these perspectives, we model and computer-simulate the stimulus-secretion coupling in β-cells by describing four interacting cellular subsystems, consisting in the glucose transport and metabolism, the excitable electrophysiological behavior, the dynamics of the intracellular calcium ions, and the exocytosis of granules containing insulin. We explicit the molecular nature of each subsystem, expressing the mutual relationships and the feedbacks that determine the metabolic-electrophysiological behavior of an isolated β-cell. Finally, we discuss the simulation results of the behavior of isolated β-cells as well as of population of electrically coupled β-cells in Langerhans islets, under physiological and pathological conditions, including noninsulin dependent diabetes mellitus (NIDDM) and hyperinsulinemic hypoglycaemia (PHHI).