Mathematical modelling of local calcium and regulated exocytosis during inhibition and stimulation of glucagon secretion from pancreatic alpha-cells

Abstract

The control of glucagon secretion from pancreatic alpha-cells is still unclear and, when defective, is involved in the development of diabetes. We propose a mathematical model of Ca2+ dynamics and exocytosis to understand better the intracellular mechanisms downstream of electrical activity that control glucagon secretion. The model exploits compartmental modelling of Ca2+ levels near open and closed high voltage-activated Ca2+ channels involved in exocytosis, in the sub-membrane Ca2+ compartment, in the bulk cytosol and in the endoplasmic reticulum. The model reproduces the effects of glucose, glucagon-like peptide 1 (GLP-1) and adrenaline, providing insight into the relative contributions of the various subcellular Ca2+ compartments in the control of glucagon secretion. Our results highlight that the number of open Ca2+ channels is a dominant factor in glucagon release, and clarify why cytosolic Ca2+ is a poor read-out of alpha-cell secretion. Glucagon secretion from pancreatic alpha-cells is dysregulated in diabetes. Despite decades of investigations of the control of glucagon release by glucose and hormones, the underlying mechanisms are still debated. Recently, mathematical models have been applied to investigate the modification of electrical activity in alpha-cells as a result of glucose application. However, recent studies have shown that paracrine effects such as inhibition of glucagon secretion by glucagon-like peptide 1 (GLP-1) or stimulation of release by adrenaline involve cAMP-mediated effects downstream of electrical activity. In particular, depending of the intracellular cAMP concentration, specific types of Ca2+ channels are inhibited or activated, which interacts with mobilization of secretory granules. To investigate these aspects of alpha-cell function theoretically, we carefully developed a mathematical model of Ca2+ levels near open or closed Ca2+ channels of various types, which was linked to a description of Ca2+ below the plasma membrane, in the bulk cytosol and in the endoplasmic reticulum. We investigated how the various subcellular Ca2+ compartments contribute to control of glucagon-exocytosis in response to glucose, GLP-1 or adrenaline. Our studies refine previous modelling studies of alpha-cell function, and provide deeper insight into the control of glucagon secretion.