TY - JOUR
T1 - A geometric understanding of how fast activating potassium channels promote bursting in pituitary cells
AU - Vo, Theodore
AU - Tabak, Joël
AU - Bertram, Richard
AU - Wechselberger, Martin
PY - 2014/4
Y1 - 2014/4
N2 - 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.
AB - 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.
KW - BK channel
KW - Bursting
KW - Dynamic clamp
KW - Geometric singular perturbation theory
KW - Mixed mode oscillations
UR - http://www.scopus.com/inward/record.url?scp=84896543938&partnerID=8YFLogxK
U2 - 10.1007/s10827-013-0470-8
DO - 10.1007/s10827-013-0470-8
M3 - Article
C2 - 23820858
AN - SCOPUS:84896543938
SN - 0929-5313
VL - 36
SP - 259
EP - 278
JO - Journal of Computational Neuroscience
JF - Journal of Computational Neuroscience
IS - 2
ER -