A geometric understanding of how fast activating potassium channels promote bursting in pituitary cells

Abstract

The electrical activity of endocrine pituitary cells is mediated by a plethora of ionic currents and establishing the role of a single channel type is difficult. Experimental observations have shown however that fast-activating voltage- and calcium-dependent potassium (BK) current tends to promote bursting in pituitary cells. This burst promoting effect requires fast activation of the BK current, otherwise it is inhibitory to bursting. In this work, we analyze a pituitary cell model in order to answer the question of why the BK activation must be fast to promote bursting. We also examine how the interplay between the activation rate and conductance of the BK current shapes the bursting activity. We use the multiple timescale structure of the model to our advantage and employ geometric singular perturbation theory to demonstrate the origin of the bursting behaviour. In particular, we show that the bursting can arise from either canard dynamics or slow passage through a dynamic Hopf bifurcation. We then compare our theoretical predictions with experimental data using the dynamic clamp technique and find that the data is consistent with a burst mechanism due to a slow passage through a Hopf.

Dynamics of a Pituitary Cell Model: Dependence on Long-Lasting External Stimulation and Potassium Conductance Kinetics

“…For example, variations in the time constant of dendritic delayed-rectifier potassium conductance inactivation induces the transition between the repetitive spiking and bursting states [5]. Variations in the time constant of BK conductance activation induce the transition between the repetitive spiking and bursting states [6]. Similarly to these two cases, the present study demonstrated that variations in the time constant were involved in the transition between the repetitive spiking and bursting states.…”

“…For example, changes in the time constant of dendritic delayed-rectifier potassium conductance inactivation induce a nonlinear effect on the dynamic states of the ghostbursting model [5]. In a mathematical model that has been derived based on pituitary lactotroph cell data, bursting dynamics appears when the time constant of fast-activating voltage-and calcium-dependent potassium (BK) conductance activation is fixed at a smaller value, whereas spiking dynamics appears when the time constant is fixed at a larger value [6]. In addition, it is implied that changes in the time constant of delayed-rectifier potassium conductance activation play an important role in modulating the dynamic states of the Stern model [4].…”

Large conductance Ca2+‐activated K+ (BK) channels promote secretagogue‐induced transition from spiking to bursting in murine anterior pituitary corticotrophs

“…; Vo et al . ). Pseudo‐plateau bursting has been proposed to increase intracellular Ca 2+ to a greater extent than spiking alone which is thought to be important in driving hormone secretion in endocrine cells (Van Goor et al .…”

“…; Vo et al . ) yet display predominantly spontaneous single spike activity but can transition to pseudo‐plateau bursting when stimulated (Kuryshev et al . ; Van Goor et al .…”

Mixed-mode oscillations in pyramidal neurons under antiepileptic drug conditions

“…Recently, Wechselberger et al reported that a class of three-dimensional canards, called type-I folded nodes, produces small-amplitude oscillations in MMOs [60]. Afterwards, several studies applied canard theory to the CB model of neurons to predict the number of STOs per spike in MMOs [61–65]. However, further research has yet to explore how the mathematical results of such studies relate to the neuronal electrophysiological mechanisms.…”