Teardrop shapes minimize bending energy of fusion pores connecting planar bilayers

Abstract

A numerical gradient flow procedure was devised to characterize minimal energy shapes of fusion pores connecting two parallel planar bilayer membranes. Pore energy, composed of splay, tilt, and stretching, was obtained by modeling each bilayer as two monolayers and treating each monolayer of a bilayer membrane as a freely deformable surface described with a mean lipid orientation field. Voids between the two monolayers were prevented by a steric penalty formulation. Pore shapes were assumed to possess both axial and reflectional symmetry. For fixed pore radius and bilayer separation, the gradient flow procedure was applied to initially toroidal pore shapes. Using initially elliptical pore shapes yielded the same final shape. The resulting minimal pore shapes and energies were analyzed as a function of pore dimension and lipid composition. Previous studies either assumed or confined pore shapes, thereby tacitly supplying an unspecified amount of energy to maintain shape. The shapes derived in the present study were outputs of calculations and an externally provided energy was not supplied. Our procedure therefore yielded energy minima significantly lower than those reported in prior studies. The membrane of minimal energy pores bowed outward near the pore lumen, yielding a pore length that exceeded the distance between the two fusing membranes.

SNARE ‐mediated membrane fusion arrests at pore expansion to regulate the volume of an organelle

“…In order to characterize the tension required to expand such an early fusion pore, we calculated the line tension (see Materials and Methods), i.e., the force that the pore interface exerts against expansion, as a function of pore size (see Fig B and Materials and Methods). The early fusion pore features a gradual increase in line tension (λ) up to a radius (r) of 3 nm, which then converges to a constant value of ~24 pN, a number that is in agreement with estimations from elastic continuum models (Ryham et al , ). The estimated line tension of a fusion pore is thus about three times smaller than the line tension of a regular hole in a flat membrane, being ~74 pN within our model [~40 pN for POPC in atomistic simulations (West et al , )].…”

“…Fusion pore closure is opposed by an increase in bending stress (Ryham et al , ) and the unfavorable dehydration of lipid head groups (hydration repulsion) (Smirnova et al , ). The resulting, here‐predicted minimal pore size (~1.5 nm) should in principle allow free passage of small molecules, such as the fluorescent lumenal markers that we had used.…”

Palmitoylation Contributes to Membrane Curvature in Influenza A Virus Assembly and Hemagglutinin-Mediated Membrane Fusion

“…Consistently, it has been shown that the fusion peptide promotes negative spontaneous curvature of the outer monolayer of the fusion pore (55). This hypothesis is supported by a continuum analysis, which calculated that fusion pores with negative spontaneous curvature in both monolayers lower their total energy by expansion (56). However, in the virus fusion scenario where the viral envelope is already highly curved, the subsequent release of membrane bending energy upon membrane fusion may contribute to pore expansion without an additional requirement for negative curvature exerted by palmitoyl.…”

Free Energy Landscape of Rim-Pore Expansion in Membrane Fusion

“…The latter would, for example, occur in the presence of multiple (hemi)fusion events. Thus, the experimental observation of flickering fusion pores and subsequent opening/closing (1,2,9) may very well relate to rimpores as well as TFPs (9)(10)(11).…”

“…The free energy barrier of rim-pore nucleation has been estimated in molecular simulation studies (5)(6)(7)(8). In contrast to the toroidal fusion pore (TFP) (9)(10)(11)(12), however, little is known about the free energy landscape of subsequent rim-pore expansion, i.e., dilation of excess HD material, before TFP formation.…”