TITLE:
The Relationship of Sodium and Potassium Conductances with Dynamic States of a Mathematical Model of Electrosensory Pyramidal Neurons
AUTHORS:
Takaaki Shirahata
KEYWORDS:
Mathematical Model, Computer Simulation, Ghostbursting, Ionic Conductance
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.9,
May
26,
2016
ABSTRACT: Electrosensory pyramidal neurons in weakly
electric fish can generate burst firing. Based on the Hodgkin-Huxley scheme, a
previous study has developed a mathematical model that reproduces this burst
firing. This model is called the ghostbursting model and is described by a
system of non-linear ordinary differential equations. Although the dynamic
state of this model is a quiescent state during low levels of electrical
stimulation, an increase in the level of electrical stimulation transforms the
dynamic state first into a repetitive spiking state and finally into a burst
firing state. The present study performed computer simulation analysis of the
ghostbursting model to evaluate the sensitivity of the three dynamic states of
the model (i.e., the quiescent, repetitive spiking, and burst firing states) to
variations in sodium and potassium conductance values of the model. The present
numerical simulation analysis revealed the sensitivity of the electrical
stimulation threshold required for eliciting the burst firing state to
variations in the values of four ionic conductances (i.e., somatic sodium,
dendritic sodium, somatic potassium, and dendritic potassium conductances) in
the ghostbursting model.