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.     

Elastic curvature constants of lipid monolayers and bilayers

Bending elasticity is an important property of lipid vesicles, non-lamellar lipid phases and biological membranes. Experimental values of the mean curvature moduli, k(c), of lipid bilayers and of the monolayer leaflets of inverted hexagonal (H(II)) phases of lipids are tabulated here for easy reference. Experimental estimates of the Gaussian curvature modulus, k (c), are also included. Consideration is given to the relation between the bending moduli of bilayers and the constituent monolayer leaflets. Useful mathematical relations involving the bending moduli and spontaneous curvature are summarized.     

Electrostatic free energy and spontaneous curvature of spherical charged layered membrane

A biophysical model for the equilibrium curvature of a composite membrane element is derived taking into account the mechanical bilayer properties and the adjacent charged protein layers. The minimum of the total free energy density with respect to the curvature of such a membrane curved was estimated from the sum of the electrostatic free energy density of the charges of the membrane and the elastic surface energy density due to bending the lipid bilayer membrane. It was shown that the equilibrium curvature, i.e. the spontaneous curvature, of such a charged composite sandwich-like membrane depends inversely on the bending stiffness of the lipid membrane itself and directly on the charge amount inside and outside the membrane to the second power. Furthermore the geometric and electrostatic structure of the protein layers and the physico-chemical environment conditions are involved. Corresponding to the model developed a "standard RBC" membrane element has a negative spontaneous curvature, accounting for a discocyte RBC shape. The shape change from a discocyte to a more stomatocytic shape (increase in the negative spontaneous curvature) after reducing the charges in the glycocalyx is also explained within this model.     

Lipid phase transitions in membranes involving intrinsic periodic curvature

A conformation of the lipid bilayer of membranes is proposed, with periodic curvature corresponding to the minimal surface structure of cubic lipid phases. Evidence is given indicating that activities of lipid synthesis/modification enzymes embedded in the membrane are controlled by the lateral "packing-pressure", so that the lipid bilayer is close to a transition from the lamellar (L alpha) type of conformation to this periodically curved conformation. Such a phase transition mechanism is assumed to be involved in numerous cooperative membrane functions.     

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.     

The phase behavior of cationic lipid-DNA complexes

We present a theoretical analysis of the phase behavior of solutions containing DNA, cationic lipids, and nonionic (helper) lipids. Our model allows for five possible structures, treated as incompressible macroscopic phases: two lipid-DNA composite (lipoplex) phases, namely, the lamellar (L(alpha)(C)) and hexagonal (H(II)(C)) complexes; two binary (cationic/neutral) lipid phases, that is, the bilayer (L(alpha)) and inverse-hexagonal (H(II)) structures, and uncomplexed DNA. The free energy of the four lipid-containing phases is expressed as a sum of composition-dependent electrostatic, elastic, and mixing terms. The electrostatic free energies of all phases are calculated based on Poisson-Boltzmann theory. The phase diagram of the system is evaluated by minimizing the total free energy of the three-component mixture with respect to all the compositional degrees of freedom. We show that the phase behavior, in particular the preferred lipid-DNA complex geometry, is governed by a subtle interplay between the electrostatic, elastic, and mixing terms, which depend, in turn, on the lipid composition and lipid/DNA ratio. Detailed calculations are presented for three prototypical systems, exhibiting markedly different phase behaviors. The simplest mixture corresponds to a rigid planar membrane as the lipid source, in which case, only lamellar complexes appear in solution. When the membranes are "soft" (i.e., low bending modulus) the system exhibits the formation of both lamellar and hexagonal complexes, sometimes coexisting with each other, and with pure lipid or DNA phases. The last system corresponds to a lipid mixture involving helper lipids with strong propensity toward the inverse-hexagonal phase. Here, again, the phase diagram is rather complex, revealing a multitude of phase transitions and coexistences. Lamellar and hexagonal complexes appear, sometimes together, in different regions of the phase diagram.     

How cholesterol is distributed between monolayers in asymmetric lipid membranes

The distribution of cholesterol in asymmetric lipid bilayers was studied by extensive coarse-grained molecular dynamics simulations. The effects of the lipid head group charge, acyl chain saturation, spontaneous membrane curvature and surface tension of the membrane were investigated. Four asymmetric bilayers containing DOPC, DOPS, DSPC or DSPS lipids were simulated on a time scale extended to tens of microseconds. We show that cholesterol strongly prefers anionic lipids to neutral and saturated lipid tails to unsaturated with a distribution ratio of ~0.7 in neutral/anionic bilayers and of ~0.4 in unsaturated/saturated bilayers. Multiple flip-flop transitions of cholesterol were observed directly, and their mean times ranged from 80 to 250?ns. It was shown that the distribution of cholesterol in the asymmetric membrane depends not only on the type of lipid, but also on the local membrane curvature and the surface tension. The membrane curvature enhances the influence of the lipid head groups on cholesterol distribution, while non-optimal surface tension caused by different areas per lipid in different monolayers increases the effect of the lipid tail saturation. It was clearly seen that the monolayers of asymmetric bilayers are interdependent. Mean distances from the bilayer center to cholesterol molecules depend not only on the type of the lipid in the considered monolayer but also on the composition of the opposite monolayer.     

The role of spontaneous lipid curvature in the interaction of interfacially active peptides with membranes

Research on antimicrobial peptides is in part driven by urgent medical needs such as the steady increase in pathogens being resistant to antibiotics. Despite the wealth of information compelling structure–function relationships are still scarce and thus the interfacial activity model has been proposed to bridge this gap. This model also applies to other interfacially active (membrane active) peptides such as cytolytic, cell penetrating or antitumor peptides. One parameter that is strongly linked to interfacial activity is the spontaneous lipid curvature, which is experimentally directly accessible. We discuss different parameters such as H-bonding, electrostatic repulsion, changes in monolayer surface area and lateral pressure that affect induction of membrane curvature, but also vice versa how membrane curvature triggers peptide response. In addition, the impact of membrane lipid composition on the formation of curved membrane structures and its relevance for diverse mode of action of interfacially active peptides and in turn biological activity are described. This article is part of a Special Issue entitled: Interfacially Active Peptides and Proteins. Guest Editors: William C. Wimley and Kalina Hristova.     

MSI-78, an analogue of the magainin antimicrobial peptides,disrupts lipid bilayer structure via positive curvature strain

In this work, we present the first characterization of the cell lysing mechanism of MSI-78, an antimicrobial peptide. MSI-78 is an amphipathic alpha-helical peptide designed by Genaera Corporation as a synthetic analog to peptides from the magainin family. (31)P-NMR of mechanically aligned samples and differential scanning calorimetry (DSC) were used to study peptide-containing lipid bilayers. DSC showed that MSI-78 increased the fluid lamellar to inverted hexagonal phase transition temperature of 1,2-dipalmitoleoyl-phosphatidylethanolamine indicating the peptide induces positive curvature strain in lipid bilayers. (31)P-NMR of lipid bilayers composed of MSI-78 and 1-palmitoyl-2-oleoyl-phosphatidylethanolamine demonstrated that the peptide inhibited the fluid lamellar to inverted hexagonal phase transition of 1-palmitoyl-2-oleoyl-phosphatidylethanolamine, supporting the DSC results, and the peptide did not induce the formation of nonlamellar phases, even at very high peptide concentrations (15 mol %). (31)P-NMR of samples containing 1-palmitoyl-2-oleoyl-phosphatidylcholine and MSI-78 revealed that MSI-78 induces significant changes in the bilayer structure, particularly at high peptide concentrations. At lower concentrations (1-5%), the peptide altered the morphology of the bilayer in a way consistent with the formation of a toroidal pore. Higher concentrations of peptide (10-15%) led to the formation of a mixture of normal hexagonal phase and lamellar phase lipids. This work shows that MSI-78 induces significant changes in lipid bilayers via positive curvature strain and presents a model consistent with both the observed spectral changes and previously published work.     

Correlation between the free energy of a channel-forming voltage-gated peptide and the spontaneous curvature of bilayer lipids

The aqueous-membrane partitioning of alamethicin, a voltage-gated channel-forming peptide, was measured as a function of the membrane spontaneous curvature. EPR spectroscopy was used to measure the partitioning of the peptide in lipid compositions formed from dioleoylphosphatidylcholine (DOPC) and varied percentages of dioleoylphosphatidylethanolamine (DOPE), dioleoylphosphatidylethanolamine-N-methyl (DOPE-Me), or dioleoylphosphatidylethanolamine-N,N-dimethyl (DOPE-Me2). When the mole fraction of DOPE in mixtures of DOPC/DOPE is increased the binding of alamethicin decreases, and the increase in binding free energy is found to be linearly dependent upon the mole fraction of DOPE in the mixture. Addition of DOPE-Me or DOPE-Me2 also increases the binding free energy, except that the effect is reduced relative to that of DOPE. The free-energy increase per mole fraction of DOPE was found to be 1400 cal/mol, whereas for DOPE-Me and DOPE-Me2 the free-energy changes were 980 and 630 cal/mol, respectively. When the free-energy changes for alamethicin binding are compared with the previously determined spontaneous curvatures for mixtures of DOPC/DOPE and DOPC/DOPE-Me, the free energy of binding is found to be linearly dependent upon the spontaneous curvature of the bilayer lipids. The effects of membrane lipid unsaturation on the partitioning of alamethicin were also measured and are qualitatively consistent with this conclusion. The sensitivity to spontaneous curvature and the cooperativity that is seen in the binding curves for alamethicin are postulated to be a result of a localized thinning of the bilayer promoted by this peptide.     

Cholesterol favors phase separation of sphingomyelin

The phase behavior of mixed lipid dispersions representing the inner leaflet of the cell membrane has been characterized by X-ray diffraction. Aqueous dispersions of phosphatidylethanolamine:phosphatidylserine (4:1 mole/mole) have a heterogeneous structure comprising an inverted hexagonal phase H(II) and a lamellar phase. Both phases coexist in the temperature range 20-45 degrees C. The fluid-to-gel mid-transition temperature of the lamellar phase assigned to phosphatidylserine is decreased from 27 to 24 degrees C in the presence of calcium. Addition of sphingomyelin to phosphatidylethanolamine/phosphatidylserine prevents phase separation of the hexagonal H(II) phase of phosphatidylethanolamine but the ternary mixture phase separates into two lamellar phases of periodcity 6.2 and 5.6 nm, respectively. The 6.2-nm periodicity is assigned to the gel phase enriched in sphingomyelin of molecular species comprising predominantly long saturated hydrocarbon chains because it undergoes a gel-to-fluid phase transition above 40 degrees C. The coexisting fluid phase we assign to phosphatidylethanolamine and phosphatidylserine and low melting point molecular species of sphingomyelin which suppresses the tendency of phosphatidylethanolamine to phase-separate into hexagonal H(II) structure. There is evidence for considerable hysteresis in the separation of lamellar fluid and gel phases during cooling. The addition of cholesterol prevents phase separation of the gel phase of high melting point sphingomyelin in mixtures with phosphatidylserine and phosphatidylethanolamine. In the quaternary mixture the lamellar fluid phase, however, is phase separated into two lamellar phases of periodicities of 6.3 and 5.6 nm (20 degrees C), respectively. The lamellar phase of periodicity 5.6 nm is assigned to a phase enriched in aminoglycerophospholipids and the periodicity 6.3 nm to a liquid-ordered phase formed from cholesterol and high melting point molecular species of sphingomyelin characterized previously by ESR. Substituting 7-dehydrocholesterol for cholesterol did not result in evidence for lamellar phase separation in the mixture within the temperature range 20-40 degrees C. The specificity of cholesterol in creation of liquid-ordered lamellar phase is inferred.     

X-ray diffraction study of feline leukemia virus fusion peptide and lipid polymorphism

The structural effects of the fusion peptide of feline leukemia virus (FeLV) on the lipid polymorphism of N-methylated dioleoylphosphatidylethanolamine were studied using a temperature ramp with sequential X-ray diffraction. This peptide, the hydrophobic amino-terminus of p15E, has been proven to be fusogenic and to promote the formation of highly curved, intermediate structures on the lamellar liquid-crystal to inverse hexagonal phase transition pathway. The FeLV peptide produces marked effects on the thermotropic mesomorphic behaviour of MeDOPE, a phospholipid with an intermediate spontaneous radius of curvature. The peptide is shown to reduce the lamellar repeat distance of the membrane prior to the onset of an inverted cubic phase. This suggests that membrane thinning may play a role in peptide-induced membrane fusion and strengthens the link between the fusion pathway and inverted cubic phase formation. The results of this study are interpreted in relation to models of the membrane fusion mechanism.     

Effect of bile salts on monolayer curvature of a phosphatidylethanolamine/water model membrane system.

A partial phase diagram of the ternary system dioleoylphosphatidylethanolamine (DOPE)/sodium cholate/water has been determined using 31P Nuclear Magnetic Resonance (NMR) spectroscopy. In the absence of cholate, it is well known that the DOPE/water system forms a reversed hexagonal (HII) phase. We have found that addition of even small amounts of cholate to the DOPE/water system leads to a transition to a lamellar (L alpha) phase. At higher cholate concentrations, a cubic (I) phase (low water content) or a micellar solution (L1) phase (high water content) is present. Thus, cholate molecules have a strong tendency to alter the lipid monolayer curvature. Increasing the concentration of cholate changes the curvature of DOPE from negative (HII phase), through zero (L alpha phase), and finally to a phase of positive curvature (micellar solution). This observation can be rationalized in terms of the molecular structure of cholate, which is amphipathic and has one hydrophobic and one hydrophilic side of the steroid ring system. The cholate molecules have a tendency to lie flat on the lipid aggregate surface, thereby increasing the effective interfacial area of the polar head groups, and altering the curvature free energy of the system.     

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.     

The Ca2+- and phospholipid-binding protein Annexin A2 is able to increase and decrease plasma membrane order

Annexin A2 (AnxA2) is a calcium- and phospholipid-binding protein that plays roles in cellular processes involving membrane and cytoskeleton dynamics and is able to associate to several partner proteins. However, the principal molecular partners of AnxA2 are negatively charged phospholipids such as phosphatidylserine and phosphatidyl-inositol-(4,5)-phosphate. Herein we have studied different aspects of membrane lipid rearrangements induced by AnxA2 membrane binding. X-ray diffraction data revealed that AnxA2 has the property to stabilize lamellar structures and to block the formation of highly curved lipid phases (inverted hexagonal phase, H_II). By using pyrene-labelled cholesterol and the environmental probe di-4-ANEPPDHQ, we observed that in model membranes, AnxA2 is able to modify both, cholesterol distribution and lipid compaction. In epithelial cells, we observed that AnxA2 localizes to membranes of different lipid order. The protein binding to membranes resulted in both, increases and/or decreases in membrane order depending on the cellular membrane regions. Overall, AnxA2 showed the capacity to modulate plasma membrane properties by inducing lipid redistribution that may lead to an increase in order or disorder of the membranes.     

Intrinsic curvature in normal and inverted lipid structures and in membranes.

The intrinsic or spontaneous radius of curvature, R(o), of lipid monolayer assemblies is expressed in terms of a lipid molecular packing parameter, V/AI, for various geometries. It is shown that the equivalent lipid length, 1, in inverted hexagonal (HII) phases, defined by a cylindrical shell of equal total lipid volume, yields an expression for R o identical to that for inverted cylindrical micelles (or, equivalently, HII phases in the presence of excess hydrocarbon). This identity is used to obtain values of the effective packing parameter for various phosphatidylethanolamines. The temperature dependence of the intrinsic radius of curvature is predicted to be negative and to be considerably greater than that for the lipid length in nearly all cases. The thermal expansion coefficient is not constant but is found to vary, depending on the value of the lipid packing parameter. A possible addition rule is constructed for the intrinsic radius of curvature of lipid mixtures, based on the linear additivity of the effective molecular volumes, V, and molecular areas, A. This relation is found to hold for mixtures of dioleoyl phosphatidylcholine (DOPC) with dioleoyl phosphatidylethanolamine, and a value of R(o) of > or = 9 A (V/AI = 1.08) is obtained for DOPC. The energetics of the intrinsic curvature and lamellar-nonlamellar transitions are also discussed within the framework of the model.     

X-ray diffraction measurement of the monolayer spontaneous curvature of dioleoylphosphatidylglycerol

Phosphatidylglycerol (PG) is an anionic lipid commonly found in large proportions in the cell membranes of bacteria and plants and, to a lesser extent, in animal cells. PG plays an important role in the regulation and determination of the elastic properties of the membrane. Using small angle X-ray scattering experiments, we obtain that the monolayer spontaneous curvature of dioleoylphosphatidylglycerol (DOPG) is -1/150+/-0.021 nm(-1) when measured in 150 mM NaCl. When the experiments are carried out in 150 mM NaCl and 20mM MgCl(2), the value obtained for the monolayer spontaneous curvature is -1/8.7+/-0.037 nm(-1). These values are of importance in modelling the effects of curvature elastic stress in membrane lipid homeostasis in the bacterium Acholeplasma laidlawii [Alley, S.H., Barahona, M., Ces, O., Templer, R.H., in press. Biophysical regulation of lipid biosynthesis in the plasma membrane. Biophys. J.] and indicate that divalent cations can play a significant role in altering curvature elastic stress.     

The effects of gramicidin on the structure of phospholipid assemblies

Gramicidin is an antibiotic peptide that can be incorporated into the monolayers of cell membranes. Dimerization through hydrogen bonding between gramicidin monomers in opposing leaflets of the membrane results in the formation of an iontophoretic channel. Surrounding phospholipids influence the gating properties of this channel. Conversely, gramicidin incorporation has been shown to affect the structure of spontaneously formed lipid assemblies. Using small-angle x-ray diffraction and model systems composed of phospholipids and gramicidin, the effects produced by gramicidin on lipid layers were measured. These measurements explore how peptides are able to modulate the spontaneous curvature properties of phospholipid assemblies. The reverse hexagonal, H(II), phase formed by dioleoylphosphatidylethanolamine (DOPE) monolayers decreased in lattice dimension with increasing incorporation of gramicidin. This indicated that gramicidin itself was adding negative curvature to the lipid layers. In this system, gramicidin was measured to have an apparent intrinsic radius of curvature, R0pgram, of -7.1 A. The addition of up to 4 mol% gramicidin in DOPE did not result in the monolayers becoming stiffer, as measured by the monolayer bending moduli. Dioleoylphosphatidylcholine (DOPC) alone forms the lamellar (L(alpha)) phase when hydrated, but undergoes a transition into the reverse hexagonal (H(II)) phase when mixed with gramicidin. The lattice dimension decreases systematically with increased gramicidin content. Again, this indicated that gramicidin was adding negative curvature to the lipid monolayers but the mixture behaved structurally much less consistently than DOPE/gramicidin. Only at 12 mol% gramicidin in dioleoylphosphatidylcholine could an apparent radius of intrinsic curvature of gramicidin (R0pgram) be estimated as -7.4 A. This mixture formed monolayers that were very resistant to bending, with a measured bending modulus of 115 kT.     

Spontaneous curvature of ganglioside GM1--effect of cross-linking

The membrane-curvature dependent lateral distribution of outer leaflet ganglioside GM1 (GM1) and the influence of GM1 cross-linking induced by fluorophore-tagged cholera toxin subunit B (CTB) plus anti-CTB was analysed in cell membranes by fluorescence microscopy. Data are presented indicating that cross-linked GM1-ligand patches accumulated at the tips of human erythrocyte echinocytic spiculae induced by Ca(2+)/ionophore A23187. However, when lipid fixative osmium tetroxide was added prior to the ligand no accumulation in spiculae occurred. GM1-staining remained here distributed over the spheroid cell body and in spiculae. Similarly, osmium tetroxide completely prohibited CTB plus anti-CTB-induced GM1 patching in representatives for flat membrane, i.e. discoid erythrocytes and K562 cells. Our results demonstrate that GM1 per se shows low membrane curvature dependent distribution and therefore holds flexible spontaneous curvature. In contrast, the cross-linked GM1-ligand complex has a strong preference for highly outward curved membrane and possesses overall positive spontaneous curvature. Osmium tetroxide efficiently immobilises GM1.