Hybrid Modeling and Simulation of Insulin Secretion Pathway in Pancreatic Islets

Insulin secreted by pancreatic islet β-cells is the principal regulating hormone of glucose metabolism. Disruption of insulin secretion may cause glucose to accumulate in the blood, and result in diabetes mellitus. Although deterministic models of the insulin secretion pathway are available, the stochastic aspect of the biological pathway has not been explored. As a first step in this direction, we present a hybrid model of the insulin secretion pathway, in which the delayed rectifying K⁺ channels are treated as stochastic events. Simulation results of our hybrid model demonstrate that our model not only can reproduce the bursts of electrical activity as the deterministic model does, but also can be used to predict the magnitude of the total number of the delayed rectifying K⁺ channels per cell needed in order to prevent the function of this pathway from disruption by stochastic effects. The coupling effect of multiple cells is also studied based on the hybrid model, which shows the synchronization behavior of the cells.