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.     

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.     

Inner but Not Outer Membrane Leaflets Control the Transition from Glycosylphosphatidylinositol-anchored Influenza Hemagglutinin-induced Hemifusion to Full Fusion

Cells that express wild-type influenza hemagglutinin (HA) fully fuse to RBCs, while cells that express the HA-ectodomain anchored to membranes by glycosylphosphatidylinositol, rather than by a transmembrane domain, only hemifuse to RBCs. Amphipaths were inserted into inner and outer membrane leaflets to determine the contribution of each leaflet in the transition from hemifusion to fusion. When inserted into outer leaflets, amphipaths did not promote the transition, independent of whether the agent induces monolayers to bend outward (conferring positive spontaneous monolayer curvature) or inward (negative curvature). In contrast, when incorporated into inner leaflets, positive curvature agents led to full fusion. This suggests that fusion is completed when a lipidic fusion pore with net positive curvature is formed by the inner leaflets that compose a hemifusion diaphragm. Suboptimal fusion conditions were established for RBCs bound to cells expressing wild-type HA so that lipid but not aqueous dye spread was observed. While this is the same pattern of dye spread as in stable hemifusion, for this “stunted” fusion, lower concentrations of amphipaths in inner leaflets were required to promote transfer of aqueous dyes. Also, these amphipaths induced larger pores for stunted fusion than they generated within a stable hemifusion diaphragm. Therefore, spontaneous curvature of inner leaflets can affect formation and enlargement of fusion pores induced by HA. We propose that after the HA-ectodomain induces hemifusion, the transmembrane domain causes pore formation by conferring positive spontaneous curvature to leaflets of the hemifusion diaphragm.     

Initiation and dynamics of hemifusion in lipid bilayers

One approach to the understanding of fusion in cells and model membranes involves stalk formation and expansion of the hemifusion diaphragm. We predict theoretically the initiation of hemifusion by stalk expansion and the dynamics of mesoscopic hemifusion diaphragm expansion in the light of recent experiments and theory that suggested that hemifusion is driven by intramembrane tension far from the fusion zone. Our predictions include a square-root scaling of the hemifusion zone size on time as well as an estimate of the minimal tension for initiation of hemifusion. Whereas a minimal amount of pressure is evidently needed for stalk formation, it is not necessarily required for stalk expansion. The energy required for tension-induced fusion is much smaller than that required for pressure-driven fusion.     

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.     

Membrane fusion: stalk model revisited.

Membrane fusion is believed to proceed via intermediate structures called stalks. Mathematical analysis of the stalk provided the elastic energy involved in this structure and predicted the possible evolution of the overall process, but the energies predicted by the original model were suspiciously high. This was due to an erroneous assumption, i.e., that the stalk has a figure of revolution of a circular arc. Here we abandon this assumption and calculate the correct shape of the stalk. We find that it can be made completely stress free and, hence, its energy, instead of being positive and high can become negative, thus facilitating the fusion process. Based on our new calculations, the energies of hemifusion, of complete fusion, and of the pore in a bilayer were analyzed. Implications for membrane fusion and lipid phase transitions are discussed.     

New phases of phospholipids and implications to the membrane fusion problem

Membrane fusion is a ubiquitous process in eukaryotic cells. When two membranes fuse, lipid must undergo molecular rearrangements at the point of merging. To understand how lipid structure transitions occur, scientists studied the phase transition of lipid between the lamellar (L(alpha)) phase and the inverted hexagonal (H(II)) phase, based on the idea that lipid must undergo a similar rearrangement as in fusion. However, previous investigations on the system of dioleoylphosphatidylcholine (DOPC) and dioleoylphosphatidylethanolamine (DOPE) did not reveal intermediate phases between the L(alpha) and H(II) phases. Recently, we found a rhombohedral phase of diphytanoylphosphatidylcholine between its L(alpha) and H(II) phases using substrate-supported samples. Here we report the observation of two new phases in the DOPC-DOPE system: a rhombohedral phase and a distorted hexagonal phase. The rhombohedral phase confirms the stalk hypothesis for the L(alpha)-H(II) transition, but the phase of stable stalks exists only for a certain range of spontaneous curvature. The distorted hexagonal phase exists only in a lipid mixture. It implies that lipids may demix to adjust its local spontaneous curvature in order to achieve energy minimum under stress.     

Persistent voids: a new structural metric for membrane fusion

MOTIVATION: Membrane fusion constitutes a key stage in cellular processes such as synaptic neurotransmission and infection by enveloped viruses. Current experimental assays for fusion have thus far been unable to resolve early fusion events in fine structural detail. We have previously used molecular dynamics simulations to develop mechanistic models of fusion by small lipid vesicles. Here, we introduce a novel structural measurement of vesicle topology and fusion geometry: persistent voids. RESULTS: Persistent voids calculations enable systematic measurement of structural changes in vesicle fusion by assessing fusion stalk widths. They also constitute a generally applicable technique for assessing lipid topological change. We use persistent voids to compute dynamic relationships between hemifusion neck widening and formation of a full fusion pore in our simulation data. We predict that a tightly coordinated process of hemifusion neck expansion and pore formation is responsible for the rapid vesicle fusion mechanism, while isolated enlargement of the hemifusion diaphragm leads to the formation of a metastable hemifused intermediate. These findings suggest that rapid fusion between small vesicles proceeds via a small hemifusion diaphragm rather than a fully expanded one. AVAILABILITY: Software available upon request pending public release. SUPPLEMENTARY INFORMATION: Supplementary data are available on Bioinformatics online.     

Lipid flip-flop vs. lateral diffusion in the relaxation of hemifusion diaphragms

Molecular dynamics simulations of a solvent-free coarse-grained lipid model are used to characterize the mechanisms by which lipid-bilayer hemifusion diaphragm (HD) intermediates relax, across a range of global compositions of negative intrinsic curvature (NIC) lipids and neutral-curvature lipids. At low concentrations of NIC lipids, rapid fission produces a double bilayer end state through a lateral diffusion-based mechanism enabled by spontaneous rim-pore defects. At moderately higher NIC lipid concentrations, rim pores are absent and stable leaflet three-junctions persist, revealing an HD relaxation mechanism entirely reliant on lipid flip-flop, and end states that are either stable fusion pores or stable HD's. These fusogenic systems exhibit dynamics highly dependent on NIC lipid concentration via an underlying sensitivity of flip-flop rates for neutral lipids on NIC lipid concentration. This work illustrates that HD dynamics may be altered through regulation of lipid composition in the immediate three-junction region. This work further highlights the potential role of flippases in biological fusion and the importance of lipid composition on fusion dynamics.     

On the theory of membrane fusion. The stalk mechanism

Based on literary data, conditions necessary for membrane fusion are discussed. It is proposed that fusion mechanisms should be classified according to the primary act involving a change in the membrane structure. Two principal fusion mechanisms are identified: the stalk mechanism, starting with the appearance of a stalk between approaching membranes, and the adhesion mechanism which involves bilayer reorganization as a result of a tight junction of the membranes. The origin and evolution of the monolayer and bilayer stalks between membranes are analysed. Using the expression for the elastic energy of the stalk it was possible to find the value of the spontaneous curvature of its membrane, Ks, at which the existence of a stalk is in principle possible. It is shown that, within the framework of the stalk mechanism, there exists a possibility of either the formation of a stalk of a finite radius, or complete fusion. The Ks values have been determined at which one of the variants occur. The energy barrier of the hydrophobic interaction and the elastic energy barrier, which have to be overcome by the membranes to form the stalk are analysed. The theoretical analysis of the stalk formation mechanism is supported by experimental data. It has been shown by freeze-fracture electron microscopy that the addition of Ca+2, Mg+2, Mn+2 or Cd+2 to suspensions of egg phosphatidylcholine and cardiolipin (1:1 or 3:1) leads to the formation of numerous intramembrane particles (imp's) and crater-like (stalk) structures.     

Field theoretic study of bilayer membrane fusion: II. Mechanism of a stalk-hole complex

We use self-consistent field theory to determine structural and energetic properties of intermediates and transition states involved in bilayer membrane fusion. In particular, we extend our original calculations from those of the standard hemifusion mechanism, which was studied in detail in the first article of this series, to consider a possible alternative to it. This mechanism involves non-axial stalk expansion, in contrast to the axially symmetric evolution postulated in the classical mechanism. Elongation of the initial stalk facilitates the nucleation of holes and leads to destabilization of the fusing membranes via the formation of a stalk-hole complex. We study properties of this complex in detail, and show how transient leakage during fusion, previously predicted and recently observed in experiment, should vary with lipid architecture and tension. We also show that the barrier to fusion in the alternative mechanism is lower than that of the standard mechanism by a few k(B)T over most of the relevant region of system parameters, so that this alternative mechanism is a viable alternative to the standard pathway. We emphasize that any mechanism, such as this alternative one, which affects, even modestly, the line tension of a hole in a membrane, affects greatly the ability of that membrane to undergo fusion.     

Calculation of free energy barriers to the fusion of small vesicles

The fusion of small vesicles, either with a planar bilayer or with one another, is studied using a microscopic model in which the bilayers are composed of hexagonal- and lamellar-forming amphiphiles. The free energy of the system is obtained within the self-consistent field approximation. We find that the free energy barrier to form the initial stalk is hardly affected by the radius of the vesicle, but that the barrier to expand the hemifusion diaphragm and form a fusion pore decreases rapidly as the radius decreases. As a consequence, once the initial barrier to stalk formation is overcome, one which we estimate at 13 k_BT for biological membranes, fusion involving small vesicles should proceed with little or no further input of energy.     

The influenza haemagglutinin-induced fusion cascade: effects of target membrane permeability changes.

To define the stages in influenza haemagglutinin (HA)-mediated fusion the kinetics of fusion between cell pairs consisting of single influenza HA-expressing cells and single erythrocytes (RBC) which had been labelled with both a fluorescent lipid (Dil) in the membrane and a fluorescent solute (calcein) in the aqueous space have been monitored. It is shown that release of solute from the target cell occurs, following the formation of the hemi-fusion diaphragm. These results are discussed in terms of a model in which fusion peptide insertion into the target membrane induces lipid stalks, which results in the formation of a hemifusion diaphragm and a fusion pore. Bilayer expansion due to overproduction of these stalks can give rise to collateral damage of target membranes.     

Direct simulation of protein-mediated vesicle fusion: lung surfactant protein B

We simulated spontaneous fusion of small unilamellar vesicles mediated by lung surfactant protein B (SP-B) using the MARTINI force field. An SP-B monomer triggers fusion events by anchoring two vesicles and facilitating the formation of a lipid bridge between the proximal leaflets. Once a lipid bridge is formed, fusion proceeds via a previously described stalk - hemifusion diaphragm - pore-opening pathway. In the absence of protein, fusion of vesicles was not observed in either unbiased simulations or upon application of a restraining potential to maintain the vesicles in close proximity. The shape of SP-B appears to enable it to bind to two vesicles at once, forcing their proximity, and to facilitate the initial transfer of lipids to form a high-energy hemifusion intermediate. Our results may provide insight into more general mechanisms of protein-mediated membrane fusion, and a possible role of SP-B in the secretory pathway and transfer of lung surfactant to the gas exchange interface.     

Effects of Spontaneous Bilayer Curvature on Influenza Virus–mediated Fusion Pores

Cells expressing the hemagglutinin protein of influenza virus were fused to planar bilayer membranes containing the fluorescent lipid probes octadecylrhodamine (R18) or indocarbocyanine (DiI) to investigate whether spontaneous curvature of each monolayer of a target membrane affects the growth of fusion pores. R18 and DiI lowered the transition temperatures for formation of an inverted hexagonal phase, indicating that these probes facilitate the formation of negative curvature structures. The probes are known to translocate from one monolayer of a bilayer membrane to the other in a voltage-dependent manner. The spontaneous curvature of the cis monolayer (facing the cells) or the trans monolayer could therefore be made more negative through control of the polarity of voltage across the planar membrane. Electrical admittance measurements showed that the open times of flickering fusion pores were shorter when probes were in trans monolayers and longer when in cis monolayers compared with times when probe was symmetrically distributed. Open times were the same for probe symmetrically distributed as when probes were not present. Thus, open times were a function of the asymmetry of the spontaneous curvature between the trans and cis monolayers. Enriching the cis monolayer with a negative curvature probe reduced the probability that a small pore would fully enlarge, whereas enriching the trans monolayer promoted enlargement. Lysophosphatidylcholine has positive spontaneous curvature and does not translocate. When lysophosphatidylcholine was placed in trans leaflets of planar membranes, closing of fusion pores was rare. The effects of the negative and positive spontaneous curvature probes do not support the hypothesis that a flickering pore closes from an open state within a hemifusion diaphragm (essentially a “flat” structure). Rather, such effects support the hypothesis that the membrane surrounding the open pore forms a three-dimensional hourglass shape from which the pore flickers shut.     

High Cholesterol Obviates a Prolonged Hemifusion Intermediate in Fast SNARE-Mediated Membrane Fusion

Cholesterol is essential for exocytosis in secretory cells, but the exact molecular mechanism by which it facilitates exocytosis is largely unknown. Distinguishing contributions from the lateral organization and dynamics of membrane proteins to vesicle docking and fusion and the promotion of fusion pores by negative intrinsic spontaneous curvature and other mechanical effects of cholesterol have been elusive. To shed more light on this process, we examined the effect of cholesterol on SNARE-mediated membrane fusion in a single-vesicle assay that is capable of resolving docking and elementary steps of fusion with millisecond time resolution. The effect of cholesterol on fusion pore formation between synaptobrevin-2 (VAMP-2)-containing proteoliposomes and acceptor t-SNARE complex-containing planar supported bilayers was examined using both membrane and content fluorescent markers. This approach revealed that increasing cholesterol in either the t-SNARE or the v-SNARE membrane favors a mechanism of direct fusion pore opening, whereas low cholesterol favors a mechanism leading to a long-lived (>5 s) hemifusion state. The amount of cholesterol in the target membrane had no significant effect on docking of synaptobrevin vesicles. Comparative studies with α-tocopherol (vitamin E) show that the negative intrinsic spontaneous curvature of cholesterol and its presumed promotion of a very short-lived (<50 ms) lipid stalk intermediate is the main factor that favors rapid fusion pore opening at high cholesterol. This study also shows that this single-vesicle fusion assay can distinguish between hemifusion and full fusion with only a single lipid dye, thereby freeing up a fluorescence channel for the simultaneous measurement of another parameter in fast time-resolved fusion assays.     

Multi-step formation of a hemifusion diaphragm for vesicle fusion revealed by all-atom molecular dynamics simulations

Membrane fusion is essential for intracellular trafficking and virus infection, but the molecular mechanisms underlying the fusion process remain poorly understood. In this study, we employed all-atom molecular dynamics simulations to investigate the membrane fusion mechanism using vesicle models which were pre-bound by inter-vesicle Ca^2 +-lipid clusters to approximate Ca^2 +-catalyzed fusion. Our results show that the formation of the hemifusion diaphragm for vesicle fusion is a multi-step event. This result contrasts with the assumptions made in most continuum models. The neighboring hemifused states are separated by an energy barrier on the energy landscape. The hemifusion diaphragm is much thinner than the planar lipid bilayers. The thinning of the hemifusion diaphragm during its formation results in the opening of a fusion pore for vesicle fusion. This work provides new insights into the formation of the hemifusion diaphragm and thus increases understanding of the molecular mechanism of membrane fusion. This article is part of a Special Issue entitled: Membrane Structure and Function: Relevance in the Cell's Physiology, Pathology and Therapy.     

The influenza haemagglutinin-induced fusion cascade: effects of target membrane permeability changes

To define the stages in influenza haemagglutinin (HA)-mediated fusion the kinetics of fusion between cell pairs consisting of single influenza HA-expressing cells and single erythrocytes (RBC) which had been labelled with both a fluorescent lipid (DiI) in the membrane and a fluorescent solute (calcein) in the aqueous space have been monitored. It is shown that release of solute from the target cell occurs, following the formation of the hemi-fusion diaphragm. These results are discussed in terms of a model in which fusion peptide insertion into the target membrane induces lipid stalks, which results in the formation of a hemifusion diaphragm and a fusion pore. Bilayer expansion due to overproduction of these stalks can give rise to collateral damage of target membranes.     

Energetics of vesicle fusion intermediates: comparison of calculations with observed effects of osmotic and curvature stresses

We reported previously the effects of both osmotic and curvature stress on fusion between poly(ethylene glycol)-aggregated vesicles. In this article, we analyze the energetics of fusion of vesicles of different curvature, paying particular attention to the effects of osmotic stress on small, highly curved vesicles of 26 nm diameter, composed of lipids with negative intrinsic curvature. Our calculations show that high positive curvature of the outer monolayer "charges" these vesicles with excess bending energy, which then releases during stalk expansion (increase of the stalk radius, r(s)) and thus "drives" fusion. Calculations based on the known mechanical properties of lipid assemblies suggest that the free energy of "void" formation as well as membrane-bending free energy dominate the evolution of a stalk to an extended transmembrane contact. The free-energy profile of stalk expansion (free energy versus r(s)) clearly shows the presence of two metastable intermediates (intermediate 1 at r(s) approximately 0 - 1.0 nm and intermediate 2 at r(s) approximately 2.5 - 3.0 nm). Applying osmotic gradients of +/-5 atm, when assuming a fixed trans-bilayer lipid mass distribution, did not significantly change the free-energy profile. However, inclusion in the model of an additional degree of freedom, the ability of lipids to move into and out of the "void", made the free-energy profile strongly dependent on the osmotic gradient. Vesicle expansion increased the energy barrier between intermediates by approximately 4 kT and the absolute value of the barrier by approximately 7 kT, whereas compression decreased it by nearly the same extent. Since these calculations, which are based on the stalk hypothesis, correctly predict the effects of both membrane curvature and osmotic stress, they support the stalk hypothesis for the mechanism of membrane fusion and suggest that both forms of stress alter the final stages, rather than the initial step, of the fusion process, as previously suggested.     

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.