TITLE:
Dynamic Behavior Induced by the Cooperation between Two Different Ionic Conductances in a Mathematical Model of Vibrissa Motoneurons
AUTHORS:
Takaaki Shirahata
KEYWORDS:
Mathematical Model, Numerical Simulation, Vibrissa, Ionic Conductance, Bistability
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.10,
June
15,
2016
ABSTRACT: A mathematical model of vibrissa
motoneurons (vMN), which has been developed by Harish and Golomb, can show
repetitive spiking in response to a transient external stimulation. The vMN
model is described by a system of nonlinear ordinary differential equations
based on the Hodgkin-Huxley scheme. The vMN model is regulated by various types
of ionic conductances, such as persistent sodium, transient sodium,
delayed-rectifier potassium, and slow ionic conductances (e.g., slowly
activating potassium afterhyperpolarization (AHP) conductance and h
conductance). In the present study, a numerical simulation analysis of the vMN
model was performed to investigate the effect of variations in the transient
sodium and the slow ionic conductance values on the response of the vMN model
to a transient external stimulation. Numerical simulations revealed that when
both the transient sodium and the AHP conductances are eliminated, the vMN
model shows a bistable behavior (i.e., a stimulation-triggered transition
between dynamic states). In contrast, none of the following induce the
transition alone: 1) elimination of the transient sodium conductance; 2)
elimination of the AHP conductance; 3) elimination of the h conductance; or 4)
elimination of both the transient sodium and the h conductances.