Spontaneous formation of vesicles by weakly charged membranes

Abstract

The formation of vesicles by an amphiphilic bilayer at equilibrium due to spontaneous curvature and due to the difference in the charge densities in the two layers is analyzed. In the latter case, there is a decrease in the electrostaticenergy when the membrane forms a vesicle with the surface having the higher charge density placed on the outside, and this could compensate for the increase in the bending energy of the membrane. If the charge densities on the two surfaces are fixed, the decrease in the electrostaticenergy per vesicle is proportional to the radius of the vesicle in the Debye–Hückel approximation. If the charged molecules are permitted to flip from one surface to the other, there is an entropic increase in the free energy when there are different charge densities on the two sides, and the total decrease in the energy per vesicle is independent of the vesicle size. The distribution of vesicle radii is calculated by minimizing the total energy subject to the constraint that the area of membrane per unit volume is a constant. We find that it is possible to produce a narrow size distribution of vesicles which are much larger than the amphiphiles when the charge densities on the two sides are fixed, and there is a sharp transition from flat membranes to vesicles in this case. In the case of membranes with charges that are permitted to flip from one layer to the other and membranes stabilized by spontaneous curvature, the membrane area fraction that forms vesicles is small when the size of a vesicle is large compared to the size of an amphiphile.