Access resistance of a single conducting membrane channel

We have considered the access resistance (AR) of a single conducting channel placed in a membrane bathed by an electrolyte. The classical expression for AR is due to Hall, who modeled the electrolyte as an ohmic conducting homogeneous medium. This approach is discussed in the present paper and it is shown that it is not valid in all cases, but depends on the ion concentration in solution and the ratio between solution and channel resistivities. To get a new expression for AR, we have combined the use of one-dimensional Nernst–Planck and Poisson (NPP) equations for the mouth of the channel and three-dimensional NPP equations for the outside solution. The influence of ion gradients and the channel itself on AR turns out to be considerable in diluted solutions (and also in the case of small channels in any solution). This influence is weaker in concentrated solutions, for which AR is well described by Hall's expression.