Author(s)

Takaaki Shirahata

Kagawa School of Pharmaceutical Sciences, Tokushima Bunri University, Sanuki, Japan.

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.

Mathematical Model, Computer Simulation, Ghostbursting, Ionic Conductance

Shirahata, T. (2016) The Relationship of Sodium and Potassium Conductances with Dynamic States of a Mathematical Model of Electrosensory Pyramidal Neurons. Applied Mathematics, 7, 819-823. doi: 10.4236/am.2016.79072.