Modified Donnan potentials for ion transport through biological ion channels

In the classical study of ion transport through charged membranes, Donnan potentials are used to approximate the difference between the applied electrostatic potential and the potential at the liquid/membrane interface. For very thin membranes (e.g., biological lipid bilayers), this discontinuous approximation of the potential is not sufficient. Here we derive a modification to the classic Donnan potential for ion transport through a biological ion channel embedded in a lipid bilayer. We also show how to derive the classic Donnan potential without the usual assumptions and estimate the amount of space charge at the liquid/membrane interface.