SUMMARYInfluenza A virus hemagglutinin (HA) changes conformation and drives membrane fusion of viral and endosomal membrane at low pH. Membrane fusion proceeds through an intermediate called hemifusion1,2. For viral fusion the hemifusion structures are not determined3. Here, influenza virus-like particles (VLP)4 carrying wild-type (WT) HA or HA hemifusion mutant G1S5 and liposome mixtures were studied at low pH by Volta phase plate (VPP) cryo-electron tomography (cET) which improves signal-to-noise ratio close to focus. We determined two distinct hemifusion structures: a hemifusion diaphragm (HD) and a novel structure termed lipidic junction. Liposomes with lipidic junctions were ruptured with membrane edges stabilized by HA. The rupture frequency and HD diameter were not affected by G1S mutation, but decreased when the cholesterol level in the liposomes was close to physiological concentrations. We propose that HA induces merger between the viral and a target membrane by one of two independent pathways: rupture-insertion pathway leading to lipidic junction and hemifusion-stalk pathway leading to fusion pore. The latter is relevant under the conditions of influenza virus infection of cells. Cholesterol concentration functions as a pathway switch due to its negative spontaneous curvature in the target bilayer as determined by continuum analysis.

In this paper, we demonstrate, through asymptotic expansions, the convergence of a phase field formulation to model surfaces minimizing the mean curvature energy with volume and surface area constraints. Under the assumption of the existence of a smooth limiting surface, it is shown that the interface of a phase field, which is a critical point of the elastic bending energy, converges to a critical point of the surface energy. Further, the elastic bending energy of the phase field converges to the surface energy and the Lagrange multipliers associated with the volume and surface area constraints remain uniformly bounded. This paper is a first step to analytically justify the numerical simulations performed by Du, Liu and Wang in 2004 to model equilibrium configurations of vesicle membranes.

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We use continuum mechanics to calculate an entire least energy pathway of membrane fusion, from stalk formation, to pore creation, and through fusion pore enlargement. The model assumes that each structure in the pathway is axially symmetric. The static continuum stalk structure agrees quantitatively with experimental stalk architecture. Calculations show that in a stalk, the distal monolayer is stretched and the stored stretching energy is significantly less than the tilt energy of an unstretched distal monolayer. The string method is used to determine the energy of the transition barriers that separate intermediate states and the dynamics of two bilayers as they pass through them. Hemifusion requires a small amount of energy independently of lipid composition, while direct transition from a stalk to a fusion pore without a hemifusion intermediate is highly improbable. Hemifusion diaphragm expansion is spontaneous for distal monolayers containing at least two lipid components, given sufficiently negative diaphragm spontaneous curvature. Conversely, diaphragms formed from single-component distal monolayers do not expand without the continual injection of energy. We identify a diaphragm radius, below which central pore expansion is spontaneous. For larger diaphragms, prior studies have shown that pore expansion is not axisymmetric, and here our calculations supply an upper bound for the energy of the barrier against pore formation. The major energy-requiring deformations in the steps of fusion are: widening of a hydrophobic fissure in bilayers for stalk formation, splay within the expanding hemifusion diaphragm, and fissure widening initiating pore formation in a hemifusion diaphragm.

Abstract. In this paper, we study the effects of the spontaneous curvature on the static deformation of a vesicle membrane under the elastic bending energy, with prescribed bulk volume and surface area. Generalizing the phase field models developed in our previous works, we deduce a new energy formula involving the spontaneous curvature effects. Several axis-symmetric configurations are obtained through numerical simulations. Some analysis on the effects of the spontaneous curvature on the vesicle membrane shapes are also provided.