Mathematical modelling of cyclic AMP-Ca2+ interactions in pancreatic islets.

A mathematical model is proposed to account for the interactions between Ca2+ and cyclic AMP in the process of glucose-induced insulin release. This model allows simulation of experimental findings such as the glucose-induced accumulation of cyclic AMP in islet cells, the calcium dependency of the latter accumulation, the time course of 45Ca net uptake by the islets exposed to glucose and/or a phosphodiesterase inhibitor, the stimulation of insulin release by glucose, the suppression of such a release at low extracellular Ca2+ concentration and its amplification by phosphodiesterase inhibitors, the restoration of a significant secretory response to glucose in islets deprived of Ca2+ but exposed to a phosphodiesterase inhibitor, and the usual relationship between 45Ca net uptake and insulin release. All these data refer to studies performed over a 90-min incubation. The model is not suitable, however, to simulate the rapid response of the islet cells during the first few minutes that follow a change in the environment of the islets.