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.