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.
