Stability of uni- and multillamellar spherical vesicles.

Lipid molecules in water form uni- or multilamellar vesicles in polydisperse form. Herein, we present energetic considerations for their equilibrium morphological organization. Our formulation provides elemental energy diagrams, which explain the polydispersity and account for the structural diversity. These energy diagrams describe the ranges of core radius (r(c)) and number of lamellae (N) that result in the formation of stable vesicles under specific conditions, thus providing prescriptions for the design of vesicles tailored for specific properties, including stability, cargo capacity, and resistance to deformation by osmotic stress. We deduced key design criteria as follows: 1) designing highly stable unilamellar vesicles requires low bending rigidity lipids and dimensions exceeding a few hundred nm in radii; 2) very large unilamellar vesicles (r(c)>several tens of microns) are not stable for typical lipids; lipids with higher bending rigidity are required; 3) the distribution of the stable size of vesicles is proportional to the bending rigidity; 4) for the case of multilamellar vesicles, vesicles with more than a few hundred layers usually exhibit greater structural integrity than those with lower degrees of lamellarity, especially when the core radii are small (<100 nm); 5) for osmotically stressed vesicles, the energy contributed by even a small concentration gradient (>mM) is the most dominant factor in the free energy, suggesting active response by vesicles (e.g., poration) to release osmotic stress; and 6) vesicles with a core radius of a few hundred nm and more than hundred lamellae are more resistant to deformation by osmotic stress, thus making them more suited to applications involving osmotic pressure gradients, such as in drug delivery.