Effect of divalent counterions on asymmetrically charged lipid bilayers

We study an asymmetrically charged lipid bilayer in which the inner layer is negatively charged, while the outer one is neutral. In particular, we focus on the interplay between the asymmetrical charge distribution and counterion valency in determining the preferred curvature state of the bilayer. We show that, at low ionic strength, an entropic effect associated with counterion release tends to expand the inner layer-surprisingly, the excess charge of the bilayer opposes this. In the absence of multivalent ions, the entropic effect is dominant and gives rise to a tendency towards negative mean curvature. The presence of divalent counterions, however, counterbalances the entropic effect-they tend to shrink the inner layer, leading to positive mean curvature.