Size and structure of spontaneously forming liposomes in lipid/PEG-lipid mixtures

The optimal size and structure of spontaneous liposomes formed from lipid/polymer-lipid mixtures was calculated using a molecular mean-field theory. The equilibrium properties of the aggregate are obtained by expanding the free energy of a symmetric planar bilayer up to fourth order in curvature and composition of lipid and polymer. The expansion coefficients are obtained from a molecular theory that explicitly accounts for the conformational degrees of freedom of the hydrophobic tails of the lipid and of the polymer chains. The polar headgroup interactions are treated using the opposing forces model. The onset of stability of the symmetric planar film is obtained from the expansion up to quadratic order. For unstable planar films the equilibrium size and structure of the spherical aggregates is obtained from the second- and fourth-order terms in curvature and composition of lipid and polymer. The driving force for the formation of spontaneous vesicles is the asymmetric distribution of polymers between the inner and outer monolayer. The composition asymmetry between the two monolayers in the aggregates is much larger for the polymer component than for the lipid, and it depends upon the size of the aggregate. The smaller the aggregate, the more asymmetric the distribution of polymer and lipid. The tendency of the polymer chains to be tethered on the outer surface of the aggregate is very strong, and it limits the range of polymer loading for which spherical liposomes are stable. A very small excess of polymer loading causes small spherical micelles to be the optimal aggregates. In these cases spontaneous liposomes can form as metastable aggregates, showing as a local minima in the free energy. Even for metastable aggregates the asymmetric distribution of polymers is very large. The elastic constants of the asymmetric bilayer in the spherical aggregate are found to be the same as those that are calculated from the planar symmetric film. Therefore, the stable structure of the aggregate is not needed to determine its mechanical properties. The range of stable liposomes is very narrow in the range of molecular weights studied, which include the experimental relevant domain of aggregates used in drug delivery. It is found that the stability of the spherical aggregates results from a very fine balance between the tendency of the polymer chains and lipid tails to pack in an asymmetric spherical aggregate and the tendency of the hydrophobic-water interface to keep the area per molecule fixed. The changes in free energy per molecules that are responsible for liposome formation are very small and are very sensitive to detailed molecular properties. The theoretical description of the aggregates requires a theory capable of incorporating these detailed molecular properties. The findings are discussed in the context of vesicle formation and liposome design for drug delivery.