Conformation of charged vesicles: the Debye-Hückel and the low-curvature limit

The shape as well as tension and pressure inside an uncharged vesicle are understood to be determined by the reduced volume of a vesicle. These parameters are important for a vesicle or a biological cell, since they can affect bio-physical processes such as osmosis and permeation, interaction with external agents such as bio-macromolecules as well as thermal fluctuations in a bilayer membrane of a vesicle. Charged membranes are ubiquitous in nature, most biological cell bio-membranes are charged, and therefore the knowledge of shape, tension and pressure of charged vesicles is critical. Additionally, the distribution of charges in the inner and outer leaflets is also important as it can affect the spatial interaction of a bilayer membrane with proteins and other micro and macromolecular species. This work addresses these issues in the low-charge and low-curvature limit. Our analysis indicates that despite a very strong two-way coupling between the charge and the curvature, the shapes of charged vesicles remain similar to that of uncharged vesicles at comparable reduced volumes, even for reasonable values of total charge. However, the tension and pressure values are higher, and are accurately estimated in our analysis. The charge distribution on the outer and inner leaflet which is strongly affected by the curvature is calculated. The value of spontaneous curvature due to charge redistribution is also estimated. The insensitivity of the shape to charges persists even when only the outer leaflet is charged instead of charged inner and outer leaflets.