Stable and flexible system for glucose homeostasis

Pancreatic islets, controlling glucose homeostasis, consist of \alpha, \beta, and \delta\ cells. It has been observed that \alpha\ and \beta\ cells generate out-of-phase synchronization in the release of glucagon and insulin, counter-regulatory hormones for increasing and decreasing glucose levels, while \beta\ and \delta\ cells produce in-phase synchronization in the release of the insulin and somatostatin. Pieces of interactions between the islet cells have been observed for a long time, although their physiological role as a whole has not been explored yet. We model the synchronized hormone pulses of islets with coupled phase oscillators that incorporate the observed cellular interactions. The integrated model shows that the interaction from \beta\ to \delta\ cells, of which sign has controversial reports, should be positive to reproduce the in-phase synchronization between \beta\ and \delta\ cells. The model also suggests that \delta\ cells help the islet system flexibly respond to changes of glucose environment.