Structure and energy of fusion stalks: the role of membrane edges.

Fusion of lipid bilayers proceeds via a sequence of distinct structural transformations. Its early stage involves a localized, hemifused intermediate in which the proximal but not yet the distal monolayers are connected. Whereas the so-called stalk model most successfully accounts for the properties of the hemifused intermediate, there is still uncertainty about its microscopic structure and energy. We reanalyze fusion stalks using the theory of membrane elasticity. In our calculations, a short (cylindrical micelle-like) tether connects the two proximal monolayers of the hemifused membranes. The shape of the stalk and the length of the tether are calculated such as to minimize the overall free energy and to avoid the formation of voids within the hydrocarbon core. Our free energy expression is based on three internal degrees of freedom of a perturbed lipid layer: thickness, splay, and tilt deformations. Based on exactly the same model, we compare fusion stalks with and without the ability included to form sharp edges at the interfacial region between the hydrocarbon core and the polar environment. Requiring the interface to be smooth everywhere, our detailed calculations recover previous results: the stalk energies are far too high to account for the experimental observation of fusion intermediates. However, if we allow the interface to be nonsmooth, we find a remarkable reduction of the stalk free energy down to more realistic values. The corresponding structure of a nonsmooth stalk exhibits sharp edges at the transition regions between the bilayer and tether parts. In addition to that, a corner is formed at each of the two distal monolayers. We discuss the mechanism how membrane edges reduce the energy of fusion stalks.