The role of large-conductance Calcium-activated K⁺ (BK) channels in shaping bursting oscillations of a somatotroph cell model

We study a recently proposed somatotroph model that exhibits plateau bursting, a form of electrical activity that is typical for this cell type. We focus on the influence of the large conductance (BK-type) Ca2+-activated K+ current on the oscillations and duration of the active phase. The model involves two different time scales, but a standard bifurcation analysis of the fast time limit does not completely explain the behaviour of the model, which is subtly different from classical models for plateau bursting. In particular, the nullclines and velocities of the fast variables play an important role in shaping the bursting oscillations. We determine numerically how the fraction of open BK channels controls the amplitude of the fast oscillations during the active phase. Furthermore, we show how manifolds of the fast subsystem are involved in the termination of the active phase.