Compound bursting in an electrical coupling model with three different time scales

Abstract

Synchronization of bursting activities in pancreatic islets when pancreatic β-cells are coupled together by gap junctions plays an important role in the insulin secretion. A minimal and generic phantom bursting model proposed by Bertram et al is employed to produce compound bursting synchronization with anti-phase spikes of two electrical coupling pancreatic β-cells, where the membrane exhibits a transition between a burst episode composed of a long burst and several short bursts and a relatively long rest state with large amplitude on both sides but small at the middle. Two different fast/slow analyses for the moderate and the slower slow variables in three-dimensional spaces are combined to highlight better how these two slow variables with different time scales commonly or separately result in complex dynamics of the compound bursting of the two electrical coupling β-cells. Especially for the compound bursting synchronization with anti-phase spikes, more is stressed on how varying coupling strengths lead to a change of the number of the short bursts within the burst episode of different compound bursting.