A Model for Time Constant of Ionic Channels in Neurons

Time constant is a physical concept that one may deduce the speed of response or reaction of a system from it. Experimental findings confirm the dependency of the speed of opening-closing of ionic channels to the membrane voltage. In this paper with the reasoning of the voltage dependency of ionic channels and gates, a model for time constant of membrane voltage in neurons has been presented. At first, the presented model has been established as a theorem and then the theorem has been proved. According to the presented theorem, one can simulate different morphology and time course of action potential (AP) in neurons by tuning the model parameters. The validation of the presented theorem (model) has been shown by simulation examples of some kinds of neurons and cells APs. Regarding the generality of the presented theorem, our model not only can be applied in biomedical systems but also it may be used in any physical systems.