On the coupling between membrane bending and stretching in lipid vesicles

ABSTRACT The formation of a lipid vesicle from a lamellar phase involves a cost in bending energy of 100–1000 times the thermal energy for values of the membrane bending rigidity k typical for phospholipid bilayers. The bending rigidity of a bilayer is however a strongly decreasing function of its thickness h , and the bilayer can thus reduce its bending energy by stretching (and thus thinning) the bilayer. In this paper, we construct a simple model to describe this mechanism for the coupling between bending and stretching and analyse its effect on the bending energy and thermal fluctuations of spherical lipid vesicles. We show that the bilayer thinning becomes significant for small vesicles, and for a vesicle with radius R 0 ∼ 15 nm there is a sizeable thinning of the bilayer compared to the planar state. We furthermore demonstrate how this thinning is associated with a significant decrease in free energy due to the thermally excited bending modes. We argue that this previously unexplored effect can explain the experimentally observed lower limit of achievable vesicle sizes, which eventually become unstable due to the thinning of the bilayer. We also sketch how this effect provides a potential generic mechanism for the strong curvature dependence of protein adsorption to lipid membranes. SIGNIFICANCE Theoretically, biological membranes are usually described as elastic sheets of constant area that deform by bending. In this study, we go beyond the constant-area assumption and show that lateral stretching of the membrane decreases the bending stiffness, which in turn significantly lowers the bending energy. For small vesicles in the 15 nm range, we show that this effect leads to a large enough bilayer stretching to cause vesicle rupture. The coupling between membrane bending and stretching also provides a generic mechanism for curvature sensing, caused by a significant increase in the exposed hydrophobic area. We argue that the sketched effect is physically relevant for all membrane remodelling processes where high membrane curvatures are involved, such as vesicle fusion and fission.