Theoretical analysis of opening-up vesicles with single and two holes.

Cuplike lipid vesicles with a single hole and tubelike vesicles with two holes were theoretically analyzed by taking into account the line tension of membrane holes and the bending energy of membranes, using the area difference elasticity model. We numerically solved the Euler-Lagrange equation and the boundary conditions holding on the membrane edge to obtain axisymmetric vesicle shapes that minimize the total energy. The numerical results showed that when the line tension is very low, and for appropriate values of the relaxed area difference between the two monolayers of bilayer membranes, the model yields cup-, tube-, and funnel-shaped vesicles that closely resemble previously observed shapes of opening-up vesicles with additive guest molecules such as the protein talin and some detergents. This strongly suggests that these additive molecules greatly reduce the line tension of lipid membranes. The effect of the Gaussian bending modulus on the shape of the opening-up vesicles was also evaluated and the effect is greatest when the size of hole is small.