Bending rigidity of mixed phospholipid bilayers and the equilibrium radius of corresponding vesicles

In spite of the large mean bending moduli observed for phospholipid bilayers, stable vesicle phases were recently observed for dilute solutions of charged phospholipids. A correspondingly large negative Gaussian bending modulus associated with charged membranes results in an overall curvature energy that is so low that entropic stabilization is possible. The mean bending modulus determines the membrane persistence length and therefore it is reasonable that there is a correlation between the membrane rigidity and the size of the lipid vesicles. Here we show that in mixtures of the anionic phospholipid dioleoylphosphatidylglycerol and the zwitterionic phospholipid dioleoylphosphatidylcholine the radius of vesicles produced by repetitive freeze-thaw cycles is considerably smaller than expected from the rigidities of the corresponding pure lipid bilayers. Self-consistent field calculations indicate that the changes in the equilibrium radius of mixed bilayers can be attributed to the dependences of the mean bending modulus k(c) on lipid mixing and the average surface charge density