Applied Mathematics

Volume 7, Issue 9 (May 2016)

ISSN Print: 2152-7385   ISSN Online: 2152-7393

Google-based Impact Factor: 0.76  Citations  

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

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DOI: 10.4236/am.2016.79077    1,135 Downloads   1,455 Views   Citations
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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.

Cite this paper

Shirahata, T. (2016) Dynamics of a Pituitary Cell Model: Dependence on Long-Lasting External Stimulation and Potassium Conductance Kinetics. Applied Mathematics, 7, 861-866. doi: 10.4236/am.2016.79077.

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