Recent advances in mathematical modeling and statistical analysis of exocytosis in endocrine cells

Most endocrine cells secrete hormones as a result of Ca²⁺-regulated exocytosis, i.e., fusion of the membranes of hormone-containing secretory granules with the cell membrane, which allows the hormone molecules to escape to the extracellular space. As in neurons, electrical activity and cell depolarization open voltage-sensitive Ca²⁺ channels, and the resulting Ca²⁺ influx elevate the intracellular Ca²⁺ concentration, which in turn causes exocytosis. Whereas the main molecular components involved in exocytosis are increasingly well understood, quantitative understanding of the dynamical aspects of exocytosis is still lacking. Due to the nontrivial spatiotemporal Ca²⁺ dynamics, which depends on the particular pattern of electrical activity as well as Ca²⁺ channel kinetics, exocytosis is dependent on the spatial arrangement of Ca²⁺ channels and secretory granules. For example, the creation of local Ca²⁺ microdomains, where the Ca²⁺ concentration reaches tens of µM, are believed to be important for triggering exocytosis. Spatiotemporal simulations of buffered Ca²⁺ diffusion have provided important insight into the interplay between electrical activity, Ca²⁺ channel kinetics, and the location of granules and Ca²⁺ channels. By confronting simulations with statistical time-to-event (or survival) regression analysis of single granule exocytosis monitored with TIRF microscopy, a direct connection between location and rate of exocytosis can be obtained at the local, single-granule level. To get insight into whole-cell secretion, simplifications of the full spatiotemporal dynamics have shown to be highly helpful. Here, we provide an overview of recent approaches and results for quantitative analysis of Ca²⁺ regulated exocytosis of hormone-containing granules.