How to correct Goldman- Hodgkin-Katz ion channel models to include gating nonlinearity based on available Hodgkin_Huxley models

Abstract

To simulate the bioelectric response of cells to electric and magnetic fields, we should model the nonlinear behavior of membrane ion channels by mathematical equations. More than 19 types of ion channels have been identified and modeled by the Hodgkin_Huxley (HH) model. Nevertheless, the Hodgkin_Huxley model has a significant simulation problem. In other words, these models cannot produce the expected nonlinear physical response at high frequencies since they explicitly model gating nonlinearity and not adjustable concentration nonlinearity. In this study, we suggested a complete model representing two kinds of nonlinearity, gating and concentration nonlinearity, to produce the expected nonlinear physical response of different voltage-gated channels. We incorporated the gating nonlinearity into the permeability coefficient defined in the Goldman- Hodgkin-Katz model (GHK), expressing concentration nonlinearity, and eventually achieved a modified GHK model for a wide variety of channels. Also, we verified these results using response diagrams of these channels available on the Channelpedia website.