Charge fluctuations on membrane surfaces in water

We generalize the predictions for attractions between overall neutral surfaces induced by charge fluctuations or correlations to nonuniform systems that include dielectric discontinuities, as is the case for mixed charged lipid membranes in an aqueous solution. We show that the induced interactions depend in a nontrivial way on the dielectric constants of membrane and water and show different scaling with distance depending on these properties. The generality of the calculations also allows us to predict under which dielectric conditions the interaction will change sign and become repulsive.