The Gaussian curvature elastic energy of intermediates in membrane fusion

Membrane structure correlates to function of LLP2 on the cytoplasmic tail of HIV-1 gp41 protein

Mutation studies previously showed that the lentivirus lytic peptide (LLP2) sequence of the cytoplasmic C-terminal tail of the HIV-1 gp41 envelope protein inhibited viral-initiated T-cell death and T-cell syncytium formation, at which time in the HIV life cycle the gp41 protein is embedded in the T-cell membrane. In striking contrast, the mutants did not affect virion infectivity, during which time the gp41 protein is embedded in the HIV envelope membrane. To examine the role of LLP2/membrane interactions, we applied synchrotron x-radiation to determine structure of hydrated membranes. We focused on WT LLP2 peptide (+3 charge) and MX2 mutant (-1 charge) with membrane mimics for the T-cell and the HIV-1 membranes. To investigate the influence of electrostatics, cholesterol content, and peptide palmitoylation, we also studied three other LLP2 variants and HIV-1 mimics without negatively charged lipids or cholesterol as well as extracted HIV-1 lipids. All LLP2 peptides bound strongly to T-cell membrane mimics, as indicated by changes in membrane structure and bending. In contrast, none of the weakly bound LLP2 variants changed the HIV-1 membrane mimic structure or properties. This correlates well with, and provides a biophysical basis for, previously published results that reported lack of a mutant effect in HIV virion infectivity in contrast to an inhibitory effect in T-cell syncytium formation. It shows that interaction of LLP2 with the T-cell membrane modulates biological function.

The grab-and-drop protocol: a novel strategy for membrane protein isolation and reconstitution from single cells

Samples of cell membrane were non-destructively removed from individual, live cells using optically trapped beads, and deposited into a supported lipid bilayer mounted on an S-layer protein-coated substrate.

Bending free energy from simulation: correspondence of planar and inverse hexagonal lipid phases

Simulations of two distinct systems, one a planar bilayer, the other the inverse hexagonal phase, indicate consistent mechanical properties and curvature preferences, with single DOPE leaflets having a spontaneous curvature, R0 = -26 Å (experimentally ~ -29.2 Å) and DOPC leaflets preferring to be approximately flat (R0= -65 Å, experimentally ~ -87.3 Å). Additionally, a well-defined pivotal plane, where a DOPE leaflet bends at constant area, has been determined to be near the glycerol region of the lipid, consistent with the experimentally predicted plane. By examining the curvature frustration of both high and low curvature, the transferability of experimentally determined bending constants is supported. The techniques herein can be applied to predict the effect of biologically active molecules on the mechanical properties of lipid bilayers under well-controlled conditions.

Teardrop shapes minimize bending energy of fusion pores connecting planar bilayers

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

Influenza virus A M2 protein generates negative Gaussian membrane curvature necessary for budding and scission

The M2 protein is a multifunctional protein, which plays several roles in the replication cycle of the influenza A virus. Here we focus on its ability to promote budding of the mature virus from the cell surface. Using high-resolution small-angle X-ray scattering we show that M2 can restructure lipid membranes into bicontinuous cubic phases which are rich in negative Gaussian curvature (NGC). The active generation of negative Gaussian membrane curvature by M2 is essential to influenza virus budding. M2 has been observed to colocalize with the region of high NGC at the neck of a bud. The structural requirements for scission are even more stringent than those for budding, as the neck must be considerably smaller than the virus during 'pinch off'. Consistent with this, the amount of NGC in the induced cubic phases suggests that M2 proteins can generate high curvatures comparable to those on a neck with size 10× smaller than a spherical influenza virus. Similar experiments on variant proteins containing different M2 domains show that the cytoplasmic amphipathic helix is necessary and sufficient for NGC generation. Mutations to the helix which reduce its amphiphilicity and are known to diminish budding attenuated NGC generation. An M2 construct comprising the membrane interactive domains, the transmembrane helix and the cytoplasmic helix, displayed enhanced ability to generate NGC, suggesting that other domains cooperatively promote membrane curvature. These studies establish the importance of M2-induced NGC during budding and suggest that antagonizing this curvature is a viable anti-influenza strategy.

Gaussian curvature elasticity determined from global shape transformations and local stress distributions: a comparative study using the MARTINI model

We calculate the Gaussian curvature modulus kappa of a systematically coarse-grained (CG) one-component lipid membrane by applying the method recently proposed by Hu et al. [Biophys. J., 2012, 102, 1403] to the MARTINI representation of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). We find the value kappa/kappa = -1.04 +/- 0.03 for the elastic ratio between the Gaussian and the mean curvature modulus and deduce kappa(m)/kappa(m) = -0.98 +/- 0.09 for the monolayer elastic ratio, where the latter is based on plausible assumptions for the distance z0 of the monolayer neutral surface from the bilayer midplane and the spontaneous lipid curvature K(0m). By also analyzing the lateral stress profile sigma0(z) of our system, two other lipid types and pertinent data from the literature, we show that determining K(0m) and kappa through the first and second moment of sigma0(z) gives rise to physically implausible values for these observables. This discrepancy, which we previously observed for a much simpler CG model, suggests that the moment conditions derived from simple continuum assumptions miss the effect of physically important correlations in the lipid bilayer.

Coarse-grain simulations reveal movement of the synaptobrevin C-terminus in response to piconewton forces

Fusion of neurosecretory vesicles with the plasma membrane is mediated by SNARE proteins, which transfer a force to the membranes. However, the mechanism by which this force transfer induces fusion pore formation is still unknown. The neuronal vesicular SNARE protein synaptobrevin 2 (syb2) is anchored in the vesicle membrane by a single C-terminal transmembrane (TM) helix. In coarse-grain molecular-dynamics simulations, self-assembly of the membrane occurred with the syb2 TM domain inserted, as expected from experimental data. The free-energy profile for the position of the syb2 membrane anchor in the membrane was determined using umbrella sampling. To predict the free-energy landscapes for a reaction pathway pulling syb2 toward the extravesicular side of the membrane, which is the direction of the force transfer from the SNARE complex, harmonic potentials were applied to the peptide in its unbiased position, pulling it toward new biased equilibrium positions. Application of piconewton forces to the extravesicular end of the TM helix in the simulation detached the synaptobrevin C-terminus from the vesicle's inner-leaflet lipid headgroups and pulled it deeper into the membrane. This C-terminal movement was facilitated and hindered by specific mutations in parallel with experimentally observed facilitation and inhibition of fusion. Direct application of such forces to the intravesicular end of the TM domain resulted in tilting motion of the TM domain through the membrane with an activation energy of ∼70 kJ/mol. The results suggest a mechanism whereby fusion pore formation is induced by movement of the charged syb2 C-terminus within the membrane in response to pulling and tilting forces generated by C-terminal zippering of the SNARE complex.

Introductory lecture: basic quantities in model biomembranes

One of the many aspects of membrane biophysics dealt with in this Faraday Discussion regards the material moduli that describe energies at a supramolecular level. This introductory lecture first critically reviews differences in reported numerical values of the bending modulus K(C), which is a central property for the biologically important flexibility of membranes. It is speculated that there may be a reason that the shape analysis method tends to give larger values of K(C) than the micromechanical manipulation method or the more recent X-ray method that agree very well with each other. Another theme of membrane biophysics is the use of simulations to provide exquisite detail of structures and processes. This lecture critically reviews the application of atomic level simulations to the quantitative structure of simple single component lipid bilayers and diagnostics are introduced to evaluate simulations. Another theme of this Faraday Discussion was lateral heterogeneity in biomembranes with many different lipids. Coarse grained simulations and analytical theories promise to synergistically enhance experimental studies when their interaction parameters are tuned to agree with experimental data, such as the slopes of experimental tie lines in ternary phase diagrams. Finally, attention is called to contributions that add relevant biological molecules to bilayers and to contributions that study the exciting shape changes and different non-bilayer structures with different lipids.

Intracellular release of endocytosed nanoparticles upon a change of ligand-receptor interaction

During passive endocytosis, nanosized particles are initially encapsulated by a membrane separating it from the cytosol. Yet, in many applications the nanoparticles need to be in direct contact with the cytosol in order to be active. We report a simulation study that elucidates the physical mechanisms by which such nanoparticles can shed their bilayer coating. We find that nanoparticle release can be readily achieved by a pH-induced lowering of the attraction between nanoparticle and membrane only if the nanoparticle is either very small or nonspherical. Interestingly, we find that in the case of large spherical nanoparticles, the reduction of attraction needs to be accompanied by exerting an additional tension on the membrane (e.g., via nanoparticle expansion) to achieve release. We expect these findings will contribute to the rational design of drug delivery strategies via nanoparticles.

Acyl-chain correlation in membrane fusion intermediates: x-ray diffraction from the rhombohedral lipid phase

We have studied the acyl-chain conformation in stalk phases of model membranes by x-ray diffraction from oriented samples. As an equilibrium lipid phase induced by dehydration, the stalk or rhombohedral phase exhibits lipidic passages (stalks) between adjacent bilayers, representing a presumed intermediate state in membrane fusion. From the detailed analysis of the acyl-chain correlation peak, we deduce the structural parameters of the acyl-chain fluid above, at, and below the transition from the lamellar to rhombohedral state, at the molecular level.

Membrane-elasticity model of Coatless vesicle budding induced by ESCRT complexes

The formation of vesicles is essential for many biological processes, in particular for the trafficking of membrane proteins within cells. The Endosomal Sorting Complex Required for Transport (ESCRT) directs membrane budding away from the cytosol. Unlike other vesicle formation pathways, the ESCRT-mediated budding occurs without a protein coat. Here, we propose a minimal model of ESCRT-induced vesicle budding. Our model is based on recent experimental observations from direct fluorescence microscopy imaging that show ESCRT proteins colocalized only in the neck region of membrane buds. The model, cast in the framework of membrane elasticity theory, reproduces the experimentally observed vesicle morphologies with physically meaningful parameters. In this parameter range, the minimum energy configurations of the membrane are coatless buds with ESCRTs localized in the bud neck, consistent with experiment. The minimum energy configurations agree with those seen in the fluorescence images, with respect to both bud shapes and ESCRT protein localization. On the basis of our model, we identify distinct mechanistic pathways for the ESCRT-mediated budding process. The bud size is determined by membrane material parameters, explaining the narrow yet different bud size distributions in vitro and in vivo. Our membrane elasticity model thus sheds light on the energetics and possible mechanisms of ESCRT-induced membrane budding.

The role of lateral tension in calcium-induced DPPS vesicle rupture

We assess the role of lateral tension in rupturing anionic dipalmitoylphosphatidyserine (DPPS), neutral dipalmitoylphosphatidylcholine (DPPC), and mixed DPPS-DPPC vesicles. Binding of Ca(2+) is known to have a significant impact on the effective size of DPPS lipids and little effect on the size of DPPC lipids in bilayer structures. In the present work we utilized laser transmission spectroscopy (LTS) to assess the effect of Ca(2+)-induced stress on the stability of the DPPS and DPPC vesicles. The high sensitivity and resolution of LTS has permitted the determination of the size and shape of liposomes in solution. The results indicate a critical size after which DPPS single shell vesicles are no longer stable. Our measurements indicate Ca(2+) promotes bilayer fusion up to a maximum diameter of ca. 320 nm. These observations are consistent with a straightforward free-energy-based model of vesicle rupture involving lateral tension between lipids regulated by the binding of Ca(2+). Our results support a critical role of lateral interactions within lipid bilayers for controlling such processes as the formation of supported bilayer membranes and pore formation in vesicle fusion. Using this free energy model we are able to infer a lower bound for the area dilation modulus for DPPS (252 pN/nm) and demonstrate a substantial free energy increase associated with vesicle rupture.

Line-tension controlled mechanism for influenza fusion

Our molecular simulations reveal that wild-type influenza fusion peptides are able to stabilize a highly fusogenic pre-fusion structure, i.e. a peptide bundle formed by four or more trans-membrane arranged fusion peptides. We rationalize that the lipid rim around such bundle has a non-vanishing rim energy (line-tension), which is essential to (i) stabilize the initial contact point between the fusing bilayers, i.e. the stalk, and (ii) drive its subsequent evolution. Such line-tension controlled fusion event does not proceed along the hypothesized standard stalk-hemifusion pathway. In modeled influenza fusion, single point mutations in the influenza fusion peptide either completely inhibit fusion (mutants G1V and W14A) or, intriguingly, specifically arrest fusion at a hemifusion state (mutant G1S). Our simulations demonstrate that, within a line-tension controlled fusion mechanism, these known point mutations either completely inhibit fusion by impairing the peptide's ability to stabilize the required peptide bundle (G1V and W14A) or stabilize a persistent bundle that leads to a kinetically trapped hemifusion state (G1S). In addition, our results further suggest that the recently discovered leaky fusion mutant G13A, which is known to facilitate a pronounced leakage of the target membrane prior to lipid mixing, reduces the membrane integrity by forming a 'super' bundle. Our simulations offer a new interpretation for a number of experimentally observed features of the fusion reaction mediated by the prototypical fusion protein, influenza hemagglutinin, and might bring new insights into mechanisms of other viral fusion reactions.

Energetics of stalk intermediates in membrane fusion are controlled by lipid composition

We have used X-ray diffraction on the rhombohedral phospholipid phase to reconstruct stalk structures in different pure lipids and lipid mixtures with unprecedented resolution, enabling a quantitative analysis of geometry, as well as curvature and hydration energies. Electron density isosurfaces are used to study shape and curvature properties of the bent lipid monolayers. We observe that the stalk structure is highly universal in different lipid systems. The associated curvatures change in a subtle, but systematic fashion upon changes in lipid composition. In addition, we have studied the hydration interaction prior to the transition from the lamellar to the stalk phase. The results indicate that facilitating dehydration is the key to promote stalk formation, which becomes favorable at an approximately constant interbilayer separation of 9.0 ± 0.5 Å for the investigated lipid compositions.

Determining the Gaussian curvature modulus of lipid membranes in simulations

The Gaussian curvature modulus κ¯ of lipid bilayers likely contributes more than 100 kcal/mol to every cellular fission or fusion event. This huge impact on membrane remodeling energetics might be a factor that codetermines the complex lipid composition of biomembranes through tuning of κ¯. Yet, its value has been measured only for a handful of simple lipids, and no simulation has so far determined it better than a factor of two, rendering a systematic investigation of such enticing speculations impossible. Here we propose a highly accurate method to determine κ¯ in computer simulations. It relies on the interplay between curvature stress and edge tension of partially curved axisymmetric membrane disks and requires determining their closing probability. For a simplified lipid model we obtain κ¯ and its relation to the normal bending modulus κ for membranes differing both in stiffness and spontaneous lipid curvature. The elastic ratio κ¯/κ can be determined with a few percent statistical accuracy. Its value agrees with the scarce experimental data, and its change with spontaneous lipid curvature is compatible with theoretical expectations, thereby granting additional information on monolayer properties. We also show that an alternative determination of these elastic parameters based on moments of the lateral stress profile gives markedly different and unphysical values.

Hemagglutinin fusion peptide mutants in model membranes: structural properties, membrane physical properties, and PEG-mediated fusion

While the importance of viral fusion peptides (e.g., hemagglutinin (HA) and gp41) in virus-cell membrane fusion is established, it is unclear how these peptides enhance membrane fusion, especially at low peptide/lipid ratios for which the peptides are not lytic. We assayed wild-type HA fusion peptide and two mutants, G1E and G13L, for their effects on the bilayer structure of 1,2-dioleoyl-3-sn-phosphatidylcholine/1,2-dioleoyl-3-sn-phosphatidylethanolamine/Sphingomyelin/Cholesterol (35:30:15:20) membranes, their structures in the lipid bilayer, and their effects on membrane fusion. All peptides bound to highly curved vesicles, but fusion was triggered only in the presence of poly(ethylene glycol). At low (1:200) peptide/lipid ratios, wild-type peptide enhanced remarkably the extent of content mixing and leakage along with the rate constants for these processes, and significantly enhanced the bilayer interior packing and filled the membrane free volume. The mutants caused no change in contents mixing or interior packing. Circular dichroism, polarized-attenuated total-internal-reflection Fourier-transform infrared spectroscopy measurements, and membrane perturbation measurements all conform to the inverted-V model for the structure of wild-type HA peptide. Similar measurements suggest that the G13L mutant adopts a less helical conformation in which the N-terminus moves closer to the bilayer interface, thus disrupting the V-structure. The G1E peptide barely perturbs the bilayer and may locate slightly above the interface. Fusion measurements suggest that the wild-type peptide promotes conversion of the stalk to an expanded trans-membrane contact intermediate through its ability to occupy hydrophobic space in a trans-membrane contact structure. While wild-type peptide increases the rate of initial intermediate and final pore formation, our results do not speak to the mechanisms for these effects, but they do leave open the possibility that it stabilizes the transition states for these events.

Fourth-order curvature energy model for the stability of bicontinuous inverted cubic phases in amphiphile-water systems

The bicontinuous inverted cubic (Q(II)) phases of amphiphiles in water have many practical applications. It is necessary to understand the stability of these phases as a function of composition and ambient conditions in order to make the best use of them. Moreover, many biomembrane lipids and some biomembrane lipid extracts form Q(II) phases. The stability of Q(II) phases in a given lipid composition is closely related to the susceptibility of that composition to membrane fusion: changes in composition that stabilize Q(II) phases usually increase the rate of membrane fusion. However, the factors determining Q(II) phase stability are not fully understood. Previously, an expression was derived for the curvature free energy of Q(II) phases with respect to that of the lamellar (L(alpha)) phase using a model for the curvature energy with terms up to fourth order in curvature as formulated by Mitov. Here this model is extended to account for the effects of water content on Q(II) phase stability. It is shown that the observed L(alpha)/Q(II) phase-transition temperature, transition enthalpy, and transition kinetics are all sensitive to water content. The same observables also become sensitive to small noncurvature energy contributions to the total free-energy difference between the Q(II) and L(alpha) phases, especially the unbinding energy in the L(alpha) phase. These predictions rationalize earlier observations of Q(II) phase formation in N-monomethylated dioleoylphosphatidylethanolamine that otherwise appear to be inconsistent. The model also provides a fundamental explanation of the hysteresis typically observed in transitions between the L(alpha) and Q(II) phases. It is an accurate model of Q(II) phase stability when the ratio of the volume fraction of the lipid in the Q(II) phase unit cell is < or = 0.5.

Free energies of stable and metastable pores in lipid membranes under tension

The free energy profile of pore formation in a lipid membrane, covering the entire range from a density fluctuation in an intact bilayer to a large tension-stabilized pore, has been calculated by molecular dynamics simulations with a coarse-grained lipid model. Several fixed elongations are used to obtain the Helmholtz free energy as a function of pore size for thermodynamically stable, metastable, and unstable pores, and the system-size dependence of these elongations is discussed. A link to the Gibbs free energy at constant tension, commonly known as the Litster model, is established by a Legendre transformation. The change of genus upon pore formation is exploited to estimate the saddle-splay modulus or Gaussian curvature modulus of the membrane leaflets. Details are provided of the simulation approach, which combines the potential of mean constraint force method with a reaction coordinate based on the local lipid density.

Minimum membrane bending energies of fusion pores

Membranes fuse by forming highly curved intermediates, culminating in structures described as fusion pores. These hourglass-like figures that join two fusing membranes have high bending energies, which can be estimated using continuum elasticity models. Fusion pore bending energies depend strongly on shape, and the present study developed a method for determining the shape that minimizes bending energy. This was first applied to a fusion pore modeled as a single surface and then extended to a more realistic model treating a bilayer as two monolayers. For the two-monolayer model, fusion pores were found to have metastable states with energy minima at particular values of the pore diameter and bilayer separation. Fusion pore energies were relatively insensitive to membrane thickness but highly sensitive to spontaneous curvature and membrane asymmetry. With symmetrical bilayers and monolayer spontaneous curvatures of -0.1 nm(-1) (a typical value) separated by 6 nm (closest distance determined by repulsive hydration forces), fusion pore formation required 43-65 kT. The pore radius of approximately 2.25 nm fell within the range estimated from conductance measurements. With bilayer separation >6 nm, fusion pore formation required less energy, suggesting that protein scaffolds can promote fusion by bending membranes toward one another. With nonzero spontaneous monolayer curvature, the shape that minimized the energy change during fusion pore formation differed from the shape that minimized its energy after it formed. Thus, a nascent fusion pore will relax spontaneously to a new shape, consistent with the experimentally observed expansion of nascent fusion pores during viral fusion.