Modeling and Analysis of Ion Permeation in Ach Membrane Channels

Abstract

This study is concerned with a transport process in the membrane ion channel, which is complicated by the presence of protein walls. The walls of actual biological channels have complicated shape geometries. These geometries pose a serious problem for calculation of electrical forces acting on an ion in the channel. Since proteins forming the channels have a low dielectric constant (2) compared to the water (80) in which ions move, the channel boundary plays a significant role in determining the electric forces. This interaction between ions and electric forces determines many of the properties of ion channel. In this respect, analytical solutions satisfying the Dirichlet boundary conditions for cylindrical and toroidal boundaries are presented. It appears that for realistic studies of ion transport in biological channels these geometries can describe the channel more accurately and the model system offers us the ability to reduce complex biological systems to the form that can be treated theoretically.