A virial expansion for discrete charges buried in a membrane

Recent experiments (1,2) have shown that hydrophobic ions adsorbed to lipid membranes repel each other significantly at densities as low as one charge every few tens of square nanometers. This paper shows how to calculate the mutual repulsion of a population of such ions, assumed to be discrete but free to diffuse laterally in the plane of the membrane. The results fall between those for uniformly smeared charges (the "three-capacitor" model) and those for discrete charges immobilized on a periodic lattice.