Paracrine regulation of glucagon secretion: the β/α/δ model

The regulation of glucagon secretion in the pancreatic α-cell is not well understood. It has been proposed that glucose suppresses glucagon secretion either directly through an intrinsic mechanism within the α-cell or indirectly through an extrinsic mechanism. Previously, we described a mathematical model for isolated pancreatic α-cells and used it to investigate possible intrinsic mechanisms of regulating glucagon secretion. We demonstrated that glucose can suppress glucagon secretion through both ATP-dependent potassium channels (K_ATP) and a store-operated current (SOC). We have now developed an islet model that combines previously published mathematical models of α- and β-cells with a new model of δ-cells and use it to explore the effects of insulin and somatostatin on glucagon secretion. We show that the model can reproduce experimental observations that the inhibitory effect of glucose remains even when paracrine modulators are no longer acting on the α-cell. We demonstrate how paracrine interactions can either synchronize α- and δ-cells to produce pulsatile oscillations in glucagon and somatostatin secretion or fail to do so. The model can also account for the paradoxical observation that glucagon can be out of phase with insulin, whereas α-cell calcium is in phase with insulin. We conclude that both paracrine interactions and the α-cell's intrinsic mechanisms are needed to explain the response of glucagon secretion to glucose.