Mathematical models for insulin secretion in pancreatic β-cells

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Insulin secretion is one of the most characteristic features of β-cell physiology. As it plays a central role in glucose regulation, a number of experimental and theoretical studies have been performed since the discovery of the pancreatic β-cell. This review article aims to give an overview of the mathematical approaches to insulin secretion. Beginning with the bursting electrical activity in pancreatic β-cells, we describe effects of the gap-junction coupling between β-cells on the dynamics of insulin secretion. Then, implications of paracrine interactions among such islet cells as α-, β- and S-cells are discussed. Finally, we present mathematical models which incorporate effects of glycolysis and mitochondrial glucose metabolism on the control of insulin secretion.

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