Effects of maximal sodium and potassium conductance on the stability of Hodgkin-Huxley model

Abstract

Hodgkin-Huxley (HH) equation is the first cell computing model in the world and pioneered the use of model to study electrophysiological problems. The model consists of four differential equations which are based on the experimental data of ion channels. Maximal conductance is an important characteristic of different channels. In this study, mathematical method is used to investigate the importance of maximal sodium conductance g - N a and maximal potassium conductance g - K. Applying stability theory, and taking g - N a and g - K as variables, we analyze the stability and bifurcations of the model. Bifurcations are found when the variables change, and bifurcation points and boundary are also calculated. There is only one bifurcation point when g - N a is the variable, while there are two points when g - K is variable. The (g - N a, g - K) plane is partitioned into two regions and the upper bifurcation boundary is similar to a line when both g - N a and g - K are variables. Numerical simulations illustrate the validity of the analysis. The results obtained could be helpful in studying relevant diseases caused by maximal conductance anomaly. © 2014 Yue Zhang et al.