Dynamic Behavior Induced by the Cooperation between Two Different Ionic Conductances in a Mathematical Model of Vibrissa Motoneurons  

作　　者：Takaaki Shirahata Takaaki Shirahata(Institute of Neuroscience and Kagawa School of Pharmaceutical Sciences, Tokushima Bunri University, Sanuki, Japan)

机构地区：[1]Institute of Neuroscience and Kagawa School of Pharmaceutical Sciences, Tokushima Bunri University, Sanuki, Japan

出　　处：《Applied Mathematics》2016年第10期1043-1048,共6页应用数学（英文）

摘　　要：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.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.

关 键 词：Mathematical Model Numerical Simulation VIBRISSA Ionic Conductance BISTABILITY 

分 类 号：O17[理学—数学]