Mathematical modeling of insulin secretion and the role of glucose-dependent mobilization, docking, priming and fusion of insulin granules.

In this paper we develop a new mathematical model of glucose-induced insulin secretion from pancreatic islet β-cells, and we use this model to investigate the rate limiting factors. We assume that insulin granules reside in different pools inside each β-cell, and that all β-cells respond homogeneously to glucose with the same recruitment thresholds. Consistent with recent experimental observations, our model also accounts for the fusion of newcomer granules that are not pre-docked at the plasma membrane. In response to a single step increase in glucose concentration, our model reproduces the characteristic biphasic insulin release observed in multiple experimental systems, including perfused pancreata and isolated islets of rodent or human origin. From our model analysis we note that first-phase insulin secretion depends on rapid depletion of the primed, release-ready granule pools, while the second phase relies on granule mobilization from the reserve. Moreover, newcomers have the potential to contribute significantly to the second phase. When the glucose protocol consists of multiple changes in sequence (a so-called glucose staircase), our model predicts insulin spikes of increasing height, as has been seen experimentally. This increase stems from the glucose-dependent increase in the fusion rate of insulin granules at the plasma membrane of single β-cells. In contrast, previous mathematical models reproduced the staircase experiment by assuming heterogeneous β-cell activation. In light of experimental data indicating limited heterogeneous activation for β-cells within intact islets, our findings suggest that a graded, dose-dependent cell response to glucose may contribute to insulin secretion patterns observed in multiple experiments, and thus regulate in vivo insulin release. In addition, the strength of insulin granule mobilization, priming and fusion are critical limiting factors in determining the total amount of insulin release.