TITLE:
Dynamics of a Pituitary Cell Model: Dependence on Long-Lasting External Stimulation and Potassium Conductance Kinetics
AUTHORS:
Takaaki Shirahata
KEYWORDS:
Mathematical Model, Computer Simulation, Pituitary Cells, Pseudo-Plateau Bursting
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.9,
May
26,
2016
ABSTRACT: Stern et al. have developed a mathematical
model describing pseudo-plateau bursting of pituitary cells. This model is
formulated based on the Hodgkin-Huxley scheme and described by a system of
nonlinear ordinary differential equations. In the present study, computer
simulation analysis of this model was performed to evaluate the correlation
between the dynamic states of the model and two system parameters: long-lasting
external stimulation (Iapp) and the time constant of delayed-rectifier
potassium conductance activation (τn). Computer simulation results revealed
that the model showed four different dynamic states: a hyperpolarized steady
state, a depolarized steady state, a repetitive spiking state, and a bursting
state. An increase in Iapp changed the dynamic states from the hyperpolarized
steady state to bursting state to depolarized steady state when τn was fixed at
smaller values, whereas it changed the dynamic states from the hyperpolarized
steady state to bursting state to repetitive spiking state when τn was fixed at
larger values. An increase in τn 1) did not change the dynamic states when Iapp
was fixed at a very small value, 2) changed the dynamic states from the
depolarized steady state to repetitive spiking state when Iapp was fixed at a
very large value, and 3) changed the dynamic states from the depolarized steady
state to bursting state to repetitive spiking state when Iapp was fixed at an
intermediate value.