Membrane fusion: overcoming of the hydration barrier and local restructuring

The early stages of membrane fusion have been investigated theoretically. It has been shown that the hydration repulsion, operating between apposed membranes, is overcome locally under the action of out-of-plane thermal fluctuations of the bilayers. The fluctuations lead to the formation of close (less than 0.5 nm) contact between the membranes within a small area (approximately 10 nm2). Increasing hydration repulsion between apposed polar heads of lipid molecules in this area causes the rupture of interacting monolayers. The rupture results in monolayer fusion of the membranes, i.e. in the formation of a bridge connecting the monolayers, which is usually named the monolayer stalk. The influence of degree of hydration of the monolayers and their spontaneous curvature on conditions of monolayer fusion have been analysed. The proposed mechanism of early stages of fusion process can proceed without preliminary formation of tight dehydrated contact between the membranes and even without any dehydration.     

Stalk model of membrane fusion: solution of energy crisis.

Membrane fusion proceeds via formation of intermediate nonbilayer structures. The stalk model of fusion intermediate is commonly recognized to account for the major phenomenology of the fusion process. However, in its current form, the stalk model poses a challenge. On one hand, it is able to describe qualitatively the modulation of the fusion reaction by the lipid composition of the membranes. On the other, it predicts very large values of the stalk energy, so that the related energy barrier for fusion cannot be overcome by membranes within a biologically reasonable span of time. We suggest a new structure for the fusion stalk, which resolves the energy crisis of the model. Our approach is based on a combined deformation of the stalk membrane including bending of the membrane surface and tilt of the hydrocarbon chains of lipid molecules. We demonstrate that the energy of the fusion stalk is a few times smaller than those predicted previously and the stalks are feasible in real systems. We account quantitatively for the experimental results on dependence of the fusion reaction on the lipid composition of different membrane monolayers. We analyze the dependence of the stalk energy on the distance between the fusing membranes and provide the experimentally testable predictions for the structural features of the stalk intermediates.     

Model of membrane fusion: Continuous transition to fusion pore with regard of hydrophobic and hydration interactions

We consider the process of fusion of lipid membranes from the stage of stalk with minimal radius to the stage of fusion pore. We assume that stalk directly developed into the fusion pore, omitting the stage of hemifusion diaphragm. Energy of intermediate stages is calculated on the basis of the classical elasticity theory of liquid crystals adapted for lipid membranes. The trajectory of transition from stalk to pore is obtained with regard to hydrophobic and hydration interactions. Continuous change of orientation of lipids in distal monolayers occurs along the trajectory. The orientation changes from the direction along rotational axis of the system specific to stalk to the direction corresponding to the fusion pore. Dependence of energy of intermediate stages on the value of spontaneous curvature of distal monolayers of the fusing membranes is obtained. We demonstrate that the energy barrier of the stalk-to-pore transition decreases when distal monolayers have positive spontaneous curvature, which is in accordance with available experimental data.     

Lipid intermediates in membrane fusion: formation,structure, and decay of hemifusion diaphragm

Lipid bilayer fusion is thought to involve formation of a local hemifusion connection, referred to as a fusion stalk. The subsequent fusion stages leading to the opening of a fusion pore remain unknown. The earliest fusion pore could represent a bilayer connection between the membranes and could be formed directly from the stalk. Alternatively, fusion pore can form in a single bilayer, referred to as hemifusion diaphragm (HD), generated by stalk expansion. To analyze the plausibility of stalk expansion, we studied the pathway of hemifusion theoretically, using a recently developed elastic model. We show that the stalk has a tendency to expand into an HD for lipids with sufficiently negative spontaneous splay, (~)J(s)< 0. For different experimentally relevant membrane configurations we find two characteristic values of the spontaneous splay. (~)J*(s) and (~)J**(s), determining HD dimension. The HD is predicted to have a finite equilibrium radius provided that the spontaneous splay is in the range (~)J**(s)< (~)J(s)<(~)J*(s), and to expand infinitely for (~)J(s)<(~)J**(s). In the case of common lipids, which do not fuse spontaneously, an HD forms only under action of an external force pulling the diaphragm rim apart. We calculate the dependence of the HD radius on this force. To address the mechanism of fusion pore formation, we analyze the distribution of the lateral tension emerging in the HD due to the establishment of lateral equilibrium between the deformed and relaxed portions of lipid monolayers. We show that this tension concentrates along the HD rim and reaches high values sufficient to rupture the bilayer and form the fusion pore. Our analysis supports the hypothesis that transition from a hemifusion to a fusion pore involves radial expansion of the stalk.     

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.     

The gaussian curvature elastic modulus of N-monomethylated dioleoylphosphatidylethanolamine: relevance to membrane fusion and lipid phase behavior

The energy of intermediates in fusion of phospholipid bilayers is sensitive to kappa(m), the saddle splay (Gaussian curvature) elastic modulus of the lipid monolayers. The value kappa(m) is also important in understanding the stability of inverted cubic (Q(II)) and rhombohedral (R) phases relative to the lamellar (L(alpha)) and inverted hexagonal (H(II)) phases in phospholipids. However, kappa(m) cannot be measured directly. It was previously measured by observing changes in Q(II) phase lattice dimensions as a function of water content. Here we use observations of the phase behavior of N-mono-methylated dioleoylphosphatidylethanolamine (DOPE-Me) to determine kappa(m). At the temperature of the L(alpha)/Q(II) phase transition, T(Q), the partial energies of the two phases are equal, and we can express kappa(m) in terms of known lipid monolayer parameters: the spontaneous curvature of DOPE-Me, the monolayer bending modulus kappa(m), and the distance of the monolayer neutral surface from the bilayer midplane, delta. The calculated ratio kappa(m)/kappa(m) is -0.83 +/- 0.08 at T(Q) approximately 55 degrees C. The uncertainty is due primarily to uncertainty in the value of delta for the L(alpha) phase. This value of kappa(m)/kappa(m) is in accord with theoretical expectations, including recent estimates of the value required to rationalize observations of rhombohedral (R) phase stability in phospholipids. The value kappa(m) substantially affects the free energy of formation of fusion intermediates: more energy (tens of k(B)T) is required to form stalks and fusion pores (ILAs) than estimated solely on the basis of the bending elastic energy. In particular, ILAs are much higher in energy than previously estimated. This rationalizes the action of fusion-catalyzing proteins in stabilizing nascent fusion pores in biomembranes; a function inferred from recent experiments in viral systems. These results change predictions of earlier work on ILA and Q(II) phase stability and L(alpha)/Q(II) phase transition mechanisms. To our knowledge, this is the first determination of the saddle splay (Gaussian) modulus in a lipid system consisting only of phospholipids.     

Calculating Transition Energy Barriers and Characterizing Activation States for Steps of Fusion

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.     

Point-like protrusion as a prestalk intermediate in membrane fusion pathway

The widely accepted pathway of membrane fusion begins with the fusion stalk representing the initial intermediate of hemifusion. The lipid structures preceding hemifusion and their possible influence on fusion kinetics were not addressed. Here, we suggest the point-like protrusion as a prestalk fusion intermediate, which has energy lower than that of stalk and, therefore, does not limit the fusion rate. We demonstrate that by calculating the energy of the point-like protrusion, which depends on the lipid monolayer elastic parameters and the strength of the intermembrane hydration repulsion. The point-like protrusion completes the fusion-through-hemifusion model of membrane merger.     

Structural intermediates in influenza haemagglutinin-mediated fusion

Fusion pore formation in the haemagglutinin (HA)-mediated fusion is a culmination of a multistep process, which involves low-pH triggered refolding of HA and rearrangement of membrane lipid bilayers. This rearrangement was arrested or slowed down by either altering lipid composition of the membranes, or lowering the density of HA, and/ or temperature. The results suggest that fusion starts with the lateral assembly of activated HA into multimeric complexes surrounding future fusion sites. The next fusion stage involves hemifusion, i.e. merger of only contacting membrane monolayers. Lysophosphatidylcholine reversibly arrests fusion prior to this hemifusion stage. In the normal fusion pathway, hemifusion is transient and is not accompanied by any measurable transfer of lipid probes between the membranes. A temperature of 4degreeC stabilizes this `restricted hemifusion' intermediate. The restriction of lipid flow through the restricted hemifusion site is HA-dependent and can be released by partial cleaving of low pH-forms of HA with mild proteinase K treatment. Lipid effects indicate that fusion proceeds through two different lipid-involving intermediates, which are characterized by two opposite curvatures of the lipid monolayer. Hemifusion involves formation of a stalk, a local bent connection between the outer membrane monolayers. Fusion pore formation apparently involves bending of the inner membrane monolayers, which come together in hemifusion. To couple low pH-induced refolding of HA with lipid rearrangements, it is proposed that the extension of the alpha -helical coiled coil of HA pulls fusion peptides inserted into the HA-expressing membrane and locally bends the membrane into a saddle-like shape. Elastic energy drives self-assembly of these HA-containing membrane elements into a ring-like complex and causes the bulging of the host membrane into a dimple growing towards the target membrane. Bending stresses in the lipidic top of the dimple facilitate membrane fusion.     

Structural intermediates in influenza haemagglutinin-mediated fusion.

Fusion pore formation in the haemagglutinin (HA)-mediated fusion is a culmination of a multistep process, which involves low-pH triggered refolding of HA and rearrangement of membrane lipid bilayers. This rearrangement was arrested or slowed down by either altering lipid composition of the membranes, or lowering the density of HA, and/or temperature. The results suggest that fusion starts with the lateral assembly of activated HA into multimeric complexes surrounding future fusion sites. The next fusion stage involves hemifusion, i.e. merger of only contacting membrane monolayers. Lysophosphatidylcholine reversibly arrests fusion prior to this hemifusion stage. In the normal fusion pathway, hemifusion is transient and is not accompanied by any measurable transfer of lipid probes between the membranes. A temperature of 4 degrees C stabilizes this 'restricted hemifusion' intermediate. The restriction of lipid flow through the restricted hemifusion site is HA-dependent and can be released by partial cleaving of low pH-forms of HA with mild proteinase K treatment. Lipid effects indicate that fusion proceeds through two different lipid-involving intermediates, which are characterized by two opposite curvatures of the lipid monolayer. Hemifusion involves formation of a stalk, a local bent connection between the outer membrane monolayers. Fusion pore formation apparently involves bending of the inner membrane monolayers, which come together in hemifusion. To couple low pH-induced refolding of HA with lipid rearrangements, it is proposed that the extension of the alpha-helical coiled coil of HA pulls fusion peptides inserted into the HA-expressing membrane and locally bends the membrane into a saddle-like shape. Elastic energy drives self-assembly of these HA-containing membrane elements into a ring-like complex and causes the bulging of the host membrane into a dimple growing towards the target membrane. Bending stresses in the lipidic top of the dimple facilitate membrane fusion.     

Lipids in biological membrane fusion

The results reviewed suggest that membrane fusion in diverse biological fusion reactions involves formation of some specific intermediates: stalks and pores. Energy of these intermediates and, consequently, the rate and extent of fusion depend on the propensity of the corresponding monolayers of membranes to bend in the required directions.Proteins and peptides can control the bending energy of membrane monolayers in a number of ways. Monolayer lipid composition may be altered by different phospholipases [50, 85, 90], flipases and translocases [4, 50]. Proteins and peptides can change monolayer spontaneous curvature or hydrophobic void energy by direct interaction with membrane lipids [20, 32, 111]. Proteins may also provide some barriers for lipid diffusion in the plane of the monolayer [83, 141]. If diffusion of lipids at some specific membrane sites (e.g., in the vicinity of fusion protein) is somehow hindered, the energy of the bent fusion intermediates would reflect the elastic properties of these particular sites rather than the spontaneous curvature of the whole monolayers. Proteins may deform membranes while bringing them locally into close contact. The alteration of the geometric (external) curvature will certainly change the elastic energy of the initial state and, thus affect the energetic barriers of the formation of the intermediates [143]. In addition, the area and the energy of the stalk can be reduced by preliminary bending of the contacting membranes [111]. The possible effects of proteins and polymers on local elastic properties and local shapes of the membranes have been recently analyzed [22, 39, 45, 63]. These studies may provide a good basis for future development of theoretical models of protein-mediated fusion.     

Domain formation induced by the adsorption of charged proteins on mixed lipid membranes

Peripheral proteins can trigger the formation of domains in mixed fluid-like lipid membranes. We analyze the mechanism underlying this process for proteins that bind electrostatically onto a flat two-component membrane, composed of charged and neutral lipid species. Of particular interest are membranes in which the hydrocarbon lipid tails tend to segregate owing to nonideal chain mixing, but the (protein-free) lipid membrane is nevertheless stable due to the electrostatic repulsion between the charged lipid headgroups. The adsorption of charged, say basic, proteins onto a membrane containing anionic lipids induces local lipid demixing, whereby charged lipids migrate toward (or away from) the adsorption site, so as to minimize the electrostatic binding free energy. Apart from reducing lipid headgroup repulsion, this process creates a gradient in lipid composition around the adsorption zone, and hence a line energy whose magnitude depends on the protein's size and charge and the extent of lipid chain nonideality. Above a certain critical lipid nonideality, the line energy is large enough to induce domain formation, i.e., protein aggregation and, concomitantly, macroscopic lipid phase separation. We quantitatively analyze the thermodynamic stability of the dressed membrane based on nonlinear Poisson-Boltzmann theory, accounting for both the microscopic characteristics of the proteins and lipid composition modulations at and around the adsorption zone. Spinodal surfaces and critical points of the dressed membranes are calculated for several different model proteins of spherical and disk-like shapes. Among the models studied we find the most substantial protein-induced membrane destabilization for disk-like proteins whose charges are concentrated in the membrane-facing surface. If additional charges reside on the side faces of the proteins, direct protein-protein repulsion diminishes considerably the propensity for domain formation. Generally, a highly charged flat face of a macroion appears most efficient in inducing large compositional gradients, hence a large and unfavorable line energy and consequently lateral macroion aggregation and, concomitantly, macroscopic lipid phase separation.     

A novel phase of compressed bilayers that models the prestalk transition state of membrane fusion

The force model of protein-mediated membrane fusion hypothesizes that fusion is driven by mechanical forces exerted on the membranes, but many details are unknown. Here, we investigated by x-ray diffraction the consequence of applying compressive force on a stack of membranes against the hydration barrier. We found that as the osmotic pressure increased, the lamellar phase transformed first to a new phase of tetragonal lattice (T-phase) over a narrow range of relative humidity, and then to a phase of rhombohedral lattice. The unit cell structure changed from parallel bilayers to a bent configuration with a point contact between adjacent bilayers and then to the stalk hemifusion configuration. The T-phase is discussed as a possible transition state in the membrane merging pathway of fusion. We estimate the work required to form the T-phase and the subsequent hemifusion-stalk-resembling R-phase. The work for the formation of a stalk is compatible with the energy estimated to be released by several SNARE complexes.     

Short-chain alcohols promote an early stage of membrane hemifusion.

Hemifusion, the linkage of contacting lipid monolayers of two membranes before the opening of a fusion pore, is hypothesized to proceed through the formation of a stalk intermediate, a local and strongly bent connection between membranes. When the monolayers' propensity to bend does not support the stalk (e.g., as it is when lysophosphatidylcholine is added), hemifusion is inhibited. In contrast, short-chain alcohols, reported to affect monolayer bending in a manner similar to that of lysophosphatidylcholine, were here found to promote hemifusion between fluorescently labeled liposomes and planar lipid bilayers. Single hemifusion events were detected by fluorescence microscopy. Methanol or ethanol (1.2-1.6 w/w %) added to the same compartment of the planar bilayer chamber as liposomes caused a 5-50 times increase in the number of hemifusion events. Alcohol-induced hemifusion was inhibited by lysophosphatidylcholine. Promotion of membrane hemifusion by short-chain alcohol was also observed for cell-cell fusion mediated by influenza virus hemagglutinin (HA). Alcohol promoted a fusion stage subsequent to the low pH-dependent activation of HA. We propose that binding of short-chain alcohol to the surface of membranes promotes hemifusion by facilitating the transient breakage of the continuity of each of the contacting monolayers, which is required for their subsequent merger in the stalk intermediate.     

Contributions of Gaussian curvature and nonconstant lipid volume to protein deformation of lipid bilayers

An elastic model for membrane deformations induced by integral membrane proteins is presented. An earlier theory is extended to account for nonvanishing saddle splay modulus within lipid monolayers and perturbations to lipid volume proximal to the protein. Analytical results are derived for the deformation profile surrounding a single cylindrical protein inclusion, which compare favorably to coarse-grained simulations over a range of protein sizes. Numerical results for multi-protein systems indicate that membrane-mediated interactions between inclusions are strongly affected by Gaussian curvature and display nonpairwise additivity. Implications for the aggregation of proteins are discussed.     

HIV-1 fusion peptide decreases bending energy and promotes curved fusion intermediates

A crucial step in human immunodeficiency virus (HIV) infection is fusion between the viral envelope and the T-cell membrane, which must involve intermediate membrane states with high curvature. Our main result from diffuse x-ray scattering is that the bending modulus K(C) is greatly reduced upon addition of the HIV fusion peptide FP-23 to lipid bilayers. A smaller bending modulus reduces the free energy barriers required to achieve and pass through the highly curved intermediate states and thereby facilitates fusion and HIV infection. The reduction in K(C) is by a factor of 13 for the thicker, stiffer 1,2-sn-dierucoylphosphatidylcholine bilayers and by a factor of 3 for 1,2-sn-dioleoylphosphatidylcholine bilayers. The reduction in K(C) decays exponentially with concentration of FP-23, and the 1/e concentration is <1 mol % peptide/lipid, which is well within the physiological range for a fusion site. A secondary result is, when FP-23 is added to the samples which consist of stacks of membranes, that the distance between membranes increases and eventually becomes infinite at full hydration (unbinding); we attribute this both to electrostatic repulsion of the positively charged arginine in the FP-23 and to an increase in the repulsive fluctuation interaction brought about by the smaller K(C). Although this latter interaction works against membrane fusion, our results show that the energy that it requires of the fusion protein machinery to bring the HIV envelope membrane and the target T-cell membrane into close contact is negligible.     

The shape of lipid molecules and monolayer membrane fusion

The contact between two bilayer membranes results in their monolayer fusion comprising the formation of a trilaminar structure (a single bilayer connected to two bilayers over the whole perimeter) in the contact region. The time required for monolayer fusion was measured and irreversible electrical breakdown was studied for membranes of different compositions. A theoretical model of the monolayer fusion is suggested to explain the results. It assumes that the structural reorganization underlying the process involves the formation of a stalk between bilayers as a result of local bending of the interacting monolayers. This structural reorganization is similar to the hydrophilic pore formation in a bilayer under irreversible breakdown. However, the directions of the monolayer bending are different in the two processes and, therefore, the bending energies depend oppositely on the effective shape of lipid molecules. Theoretical predictions agree well with experimental data. The applicability of the suggested mechanism to biomembrane fusion is discussed.     

Quantification of phase transitions of lipid mixtures from bilayer to non-bilayer structures: Model,experimental validation and implication on membrane fusion

Lipid bilayers provide a solute-proof barrier that is widely used in living systems. It has long been recognized that the structural changes of lipids during the phase transition from bilayer to non-bilayer have striking similarities with those accompanying membrane fusion processes. In spite of this resemblance, the numerous quantitative studies on pure lipid bilayers are difficult to apply to real membranes. One reason is that in living matter, instead of pure lipids, lipid mixtures are involved and there is currently no model that establishes the connection between pure lipids and lipid mixtures. Here, we make this connection by showing how to obtain (i) the short-range repulsion between bilayers made of lipid mixtures and, (ii) the pressure at which transition from bilayer phase to non-bilayer phases occur. We validated our models by fitting the experimental data of several lipid mixtures to the theoretical data calculated based on our model. These results provide a useful tool to quantitatively predict the behavior of complex membranes at low hydration.     

pH Alters PEG-Mediated Fusion of Phosphatidylethanolamine-Containing Vesicles

Here, we examine the different mechanisms of poly(ethylene glycol)-mediated fusion of small unilamellar vesicles composed of dioleoylphosphatidylcholine/dioleoylphosphatidylethanolamine (DOPE)/sphingomyelin/cholesterol in a molar ratio of 35:30:15:20 at pH 7.4 versus pH 5. In doing so, we test the hypothesis that fusion of this lipid mixture should be influenced by differences in hydration of DOPE at these two pH values. An examination of the literature reveals that DOPE should be less hydrated at pH 5 (where influenza virus particles fuse with endosome membranes) than at pH 7.4 (where synaptic vesicles or HIV virus particles fuse with plasma membrane). Ensemble kinetic experiments revealed substantial differences in fusion of this plasma membrane mimetic system at these two pH values. The most dramatic difference was the observation of two intermediates at pH 5 but loss of one of these fusion intermediates at pH 7.4. Analysis of data collected at several temperatures also revealed that formation of the initial fusion intermediate (stalk) was favored at pH 7.4 due to increased activation entropy. Our observations support the hypothesis that the different negative intrinsic curvature of DOPE can account for different fusion paths and activation thermodynamics in steps of the fusion process at these two pH values. Finally, the effects of 2 mol % hexadecane on fusion at both pH values seemed to have similar origins for step 1 (promotion of acyl chain or hydrocarbon excursion into interbilayer space) and step 3 (reduction of interstice energy leading to expansion to a critical stalk radius). Different hexadecane effects on activation thermodynamics at these two pH values can also be related to altered DOPE hydration. The results support our kinetic model for fusion and offer insight into the critical role of phosphatidylethanolamine in fusion.     

Energetics of intermediates in membrane fusion: comparison of stalk and inverted micellar intermediate mechanisms.

To understand the mechanism of membrane fusion, we have to infer the sequence of structural transformations that occurs during the process. Here, it is shown how one can estimate the lipid composition-dependent free energies of intermediate structures of different geometries. One can then infer which fusion mechanism is the best explanation of observed behavior in different systems by selecting the mechanism that requires the least energy. The treatment involves no adjustable parameters. It includes contributions to the intermediate energy resulting from the presence of hydrophobic interstices within structures formed between apposed bilayers. Results of these calculations show that a modified form of the stalk mechanism proposed by others is a likely fusion mechanism in a wide range of lipid compositions, but a mechanism based on inverted micellar intermediates (IMIs) is not. This should be true even in the vicinity of the lamellar/inverted hexagonal phase transition, where IMI formation would be most facile. Another prediction of the calculations is that traces of apolar lipids (e.g., long-chain alkanes) in membranes should have a substantial influence on fusion rates in general. The same theoretical methods can be used to generate and refine mechanisms for protein-mediated fusion.