On the Electroporation Thresholds of Lipid Bilayers: Molecular Dynamics Simulation Investigations

Electroporation relates to the cascade of events that follows the application of high electric fields and that leads to cell membrane permeabilization. Despite a wide range of applications, little is known about the electroporation threshold, which varies with membrane lipid composition. Here, using molecular dynamics simulations, we studied the response of dipalmitoyl-phosphatidylcholine, diphytanoyl-phosphocholine-ester and diphytanoyl-phosphocholine-ether lipid bilayers to an applied electric field. Comparing between lipids with acyl chains and methyl branched chains and between lipids with ether and ester linkages, which change drastically the membrane dipole potential, we found that in both cases the electroporation threshold differed substantially. We show, for the first time, that the electroporation threshold of a lipid bilayer depends not only on the “electrical” properties of the membrane, i.e., its dipole potential, but also on the properties of its component hydrophobic tails.     

Annular Anionic Lipids Stabilize the Integrin αIIbβ3 Transmembrane Complex

Cationic membrane-proximal amino acids determine the topology of membrane proteins by interacting with anionic lipids that are restricted to the intracellular membrane leaflet. This mechanism implies that anionic lipids interfere with electrostatic interactions of membrane proteins. The integrin αIIbβ3 transmembrane (TM) complex is stabilized by a membrane-proximal αIIb(Arg⁹⁹⁵)-β3(Asp⁷²³) interaction; here, we examine the influence of anionic lipids on this complex. Anionic lipids compete for αIIb(Arg⁹⁹⁵) contacts with β3(Asp⁷²³) but paradoxically do not diminish the contribution of αIIb(Arg⁹⁹⁵)-β3(Asp⁷²³) to TM complex stability. Overall, anionic lipids in annular positions stabilize the αIIbβ3 TM complex by up to 0.50 ± 0.02 kcal/mol relative to zwitterionic lipids in a headgroup structure-dependent manner. Comparatively, integrin receptor activation requires TM complex destabilization of 1.5 ± 0.2 kcal/mol, revealing a sizeable influence of lipid composition on TM complex stability. We implicate changes in lipid headgroup accessibility to small molecules (physical membrane characteristics) and specific but dynamic protein-lipid contacts in this TM helix-helix stabilization. Thus, anionic lipids in ubiquitous annular positions can benefit the stability of membrane proteins while leaving membrane-proximal electrostatic interactions intact.     

Asymmetric structural features in single supported lipid bilayers containing cholesterol and GM1 resolved with synchrotron X-Ray reflectivity

The cell membrane comprises numerous protein and lipid molecules capable of asymmetric organization between leaflets and liquid-liquid phase separation. We use single supported lipid bilayers (SLBs) to model cell membranes, and study how cholesterol and asymmetrically oriented ganglioside receptor G_M1 affect membrane structure using synchrotron x-ray reflectivity. Using mixtures of cholesterol, sphingomyelin, and 1,2-dioleoyl-sn-glycero-3-phosphocholine, we characterize the structure of liquid-ordered and liquid-disordered SLBs in terms of acyl-chain density, headgroup size, and leaflet thickness. SLBs modeling the liquid-ordered phase are 10 Å thicker and have a higher acyl-chain electron density (〈ρ_chain〉 = 0.33 e⁻/ų) compared to SLBs modeling the liquid-disordered phase, or pure phosphatidylcholine SLBs (〈ρ_chain〉 = 0.28 e⁻/ų). Incorporating G_M1 into the distal bilayer leaflet results in membrane asymmetry and thickening of the leaflet of 4-9 Å. The structural effect of G_M1 is more complex in SLBs of cholesterol/sphingomyelin/1,2-dioleoyl-sn-glycero-3-phosphocholine, where the distal chains show a high electron density (〈ρ_chain〉 = 0.33 e⁻/ų) and the lipid diffusion constant is reduced by ∼50%, as measured by fluorescence microscopy. These results give quantitative information about the leaflet asymmetry and electron density changes induced by receptor molecules that penetrate a single lipid bilayer.     

Molecular dynamics simulations of palmitoyloleoylphosphatidylglycerol bilayers

Phosphatidylglycerol (PG) is one of the important components of biological membranes, but there is a paucity of experimental data to test the accuracy of molecular dynamics (MD) simulations. This work consists of testing the accuracy of the CHARMM36 (C36) lipid force field on 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol (POPG) lipid bilayers. MD simulations of POPG lipid bilayers are compared to recently available X-ray and neutron scattering and deuterium NMR measurements. Overall, the C36 lipid force field accurately represents the X-ray and neutron form factors, bilayer and hydrocarbon thicknesses and chain deuterium order parameters. The surface area per lipid from MD simulations with C36 (67.7 ± 0.2 Å²) is in excellent agreement with the experimentally determined value of 66.0 ± 1.3 Å². C36 outperforms the lipid force field developed by Berger et al. [15] and suggests that past studies with this force field may result in lateral areas that are too small. Moreover, our studies give some insight into the structural model used in experiments and suggest that the functional form for the head group may not be Gaussian-like. Based on our simulations, the POPG lipid in the C36 lipid force field is well parameterised and can be used for other PG lipids and membrane models with mixed lipids.     

Synergistic effect of electric field and lipid oxidation on the permeability of cell membranes

BackgroundStrong electric fields are known to affect cell membrane permeability, which can be applied for therapeutic purposes, e.g., in cancer therapy. A synergistic enhancement of this effect may be accomplished by the presence of reactive oxygen species (ROS), as generated in cold atmospheric plasmas. Little is known about the synergy between lipid oxidation by ROS and the electric field, nor on how this affects the cell membrane permeability.MethodWe here conduct molecular dynamics simulations to elucidate the dynamics of the permeation process under the influence of combined lipid oxidation and electroporation. A phospholipid bilayer (PLB), consisting of di-oleoyl-phosphatidylcholine molecules covered with water layers, is used as a model system for the plasma membrane.Results and conclusionsWe show how oxidation of the lipids in the PLB leads to an increase of the permeability of the bilayer to ROS, although the permeation free energy barriers still remain relatively high. More importantly, oxidation of the lipids results in a drop of the electric field threshold needed for pore formation (i.e., electroporation) in the PLB. The created pores in the membrane facilitate the penetration of reactive plasma species deep into the cell interior, eventually causing oxidative damage.General significanceThis study is of particular interest for plasma medicine, as plasma generates both ROS and electric fields, but it is also of more general interest for applications where strong electric fields and ROS both come into play.     

Membrane-Mediated Protein-Protein Interactions and Connection to Elastic Models: A Coarse-Grained Simulation Analysis of Gramicidin A Association

To further foster the connection between particle based and continuum mechanics models for membrane mediated biological processes, we carried out coarse-grained (CG) simulations of gramicidin A (gA) dimer association and analyzed the results based on the combination of potential of mean force (PMF) and stress field calculations. Similar to previous studies, we observe that the association of gA dimers depends critically on the degree of hydrophobic mismatch, with the estimated binding free energy of >10 kcal/mol in a distearoylphosphatidylcholine bilayer. Qualitative trends in the computed PMF can be understood based on the stress field distributions near a single gA dimer and between a pair of gA dimers. For example, the small PMF barrier, which is ∼1 kcal/mol independent of lipid type, can be captured nearly quantitatively by considering membrane deformation energy associated with the region confined by two gA dimers. However, the PMF well depth is reproduced poorly by a simple continuum model that only considers membrane deformation energy beyond the annular lipids. Analysis of lipid orientation, configuration entropy, and stress distribution suggests that the annular lipids make a significant contribution to the association of two gA dimers. These results highlight the importance of explicitly considering contributions from annular lipids when constructing approximate models to study processes that involve a significant reorganization of lipids near proteins, such as protein-protein association and protein insertion into biomembranes. Finally, large-scale CG simulations indicate that multiple gA dimers also form clusters, although the preferred topology depends on the protein concentration. Even at high protein concentrations, every gA dimer requires contact to lipid hydrocarbons to some degree, and at most three to four proteins are in contact with each gA dimer; this observation highlights another aspect of the importance of interactions between proteins and annular lipids.     

CHARMM-GUI HMMM Builder for Membrane Simulations with the Highly Mobile Membrane-Mimetic Model

Slow diffusion of the lipids in conventional all-atom simulations of membrane systems makes it difficult to sample large rearrangements of lipids and protein-lipid interactions. Recently, Tajkhorshid and co-workers developed the highly mobile membrane-mimetic (HMMM) model with accelerated lipid motion by replacing the lipid tails with small organic molecules. The HMMM model provides accelerated lipid diffusion by one to two orders of magnitude, and is particularly useful in studying membrane-protein associations. However, building an HMMM simulation system is not easy, as it requires sophisticated treatment of the lipid tails. In this study, we have developed CHARMM-GUI HMMM Builder (http://www.charmm-gui.org/input/hmmm) to provide users with ready-to-go input files for simulating HMMM membrane systems with/without proteins. Various lipid-only and protein-lipid systems are simulated to validate the qualities of the systems generated by HMMM Builder with focus on the basic properties and advantages of the HMMM model. HMMM Builder supports all lipid types available in CHARMM-GUI and also provides a module to convert back and forth between an HMMM membrane and a full-length membrane. We expect HMMM Builder to be a useful tool in studying membrane systems with enhanced lipid diffusion.     

Thermal unfolding of the archaeal DNA and RNA binding protein Ssh10

The reversible thermal unfolding of the archaeal histone-like protein Ssh10b from the extremophile Sulfolobus shibatae was studied using differential scanning calorimetry and circular dichroism spectroscopy. Analytical ultracentrifugation and gel filtration showed that Ssh10b is a stable dimer in the pH range 2.5–7.0. Thermal denaturation data fit into a two-state unfolding model, suggesting that the Ssh10 dimer unfolds as a single cooperative unit with a maximal melting temperature of 99.9 °C and an enthalpy change of 134 kcal/mol at pH 7.0. The heat capacity change upon unfolding determined from linear fits of the temperature dependence of ΔH^cal is 2.55 kcal/(mol K). The low specific heat capacity change of 13 cal/(mol K residue) leads to a considerable flattening of the protein stability curve (ΔG (T)) and results in a maximal ΔG of only 9.5 kcal/mol at 320 K and a ΔG of only 6.0 kcal/mol at the optimal growth temperature of Sulfolobus.     

Subcellular localization of binding sites for cytochalasin D: Evidence from activation energies

The activation energies for binding of tritiated cytochalasin D to HEp-2 cells and isolated plasma membrane were determined by Arrhenius plots. The higher value for intact cells (24 kcal/mol) compared to the plasma membrane fraction (4 kcal/mol at > 11.5 °C, 18 kcal/mol at < 11.5 °C) was taken as evidence that [³H]cytochalasin D must penetrate the plasma membrane in order to reach its binding sites. The data support the conclusion that binding sites for [³H]cytochalasin D are intracellular, on the cytoplasmic face of the plasma membrane (rather than within the lipid bilayer), and on microsomes (endomembranes).     

The effect of calcium on the properties of charged phospholipid bilayers

We have performed molecular dynamics simulations to investigate the structure and dynamics of charged bilayers as well as the distribution of counterions at the bilayer interface. For this, we have considered the negatively charged di-myristoyl-phosphatidyl-glycerol (DMPG) and di-myristoyl-phosphatidyl-serine (DMPS) bilayers as well as a protonated di-myristoyl-phosphatidyl-serine (DMPSH) bilayer. We were particularly interested in calcium ions due to their important role in biological systems. Simulations performed in the presence of calcium ions (DMPG, DMPS) or sodium ions (DMPS) were run for 45-60 ns. Simulation results for DMPG are compared with fluorescence measurements. The average areas per molecule were 47.4 ± 0.5 Å² (DMPG with calcium), 47.3 ± 0.5 Å² (DMPS with calcium), 51.3 ± 1.0 Å² (DMPS with sodium) and 45.3 ± 0.5 Å² (DMPSH). The structure of the negatively charged lipids is significantly affected by the counterions, where calcium ions have a more pronounced effect than sodium ions. Calcium ions were found to be tightly bound to the anionic groups of the lipid molecules and as such appear to constitute an integral part of the membrane interface on nanoseconds time scales. In contrast to sodium ions, calcium ions are localised in a narrow (∼ 10 Å) band around the phosphate group. The interaction of calcium with the lipid molecules enhances the molecular packing of the PG and PS lipids. This observation is in good agreement with emission spectra of the membrane partitioning probe Laurdan in DMPG multilamellar vesicles that indicate an increase in the ordering of the DMPG bilayer due to the presence of calcium. Our results indicate that calcium ions, which often function as a second messengers in living cells have a pronounced effect on membrane structures, which may have implications during signal transduction events.     

Molecular studies of the gel to liquid-crystalline phase transition for fully hydrated DPPC and DPPE bilayers

Molecular dynamics simulations were used for a comprehensive study of the structural properties of saturated lipid bilayers, DPPC and DPPE, near the main phase transition. Though the chemical structure of DPPC and DPPE are largely similar (they only differ in the choline and ethanolamine groups), their transformation process from a gel to a liquid-crystalline state is contrasting. For DPPC, three distinct structures can be identified relative to the melting temperature (T_m): below T_m with “mixed” domains consisting of lipids that are tilted with partial overlap of the lipid tails between leaflet; near T_m with a slight increase in the average area per lipid, resulting in a rearrangement of the lipid tails and an increase in the bilayer thickness; and above T_m with unhindered lipid tails in random motion resulting in an increase in %gauche formed and increase in the level of interdigitation between lipid leaflets. For DPPE, the structures identified were below T_m with “ordered” domains consisting of slightly tilted lipid tails and non-overlapping lipid tails between leaflets, near T_m with minimal rearrangement of the lipids as the bilayer thickness reduces slightly with increasing temperature, and above T_m with unhindered lipid tails as that for DPPC. For DPPE, most of the lipid tails do not overlap as observed to DPPC, which is due to the tight packing of the DPPE molecules. The non-overlapping behavior of DPPE above T_m is confirmed from the density profile of the terminal carbon atoms in each leaflet, which shows a narrow distribution near the center of the bilayer core. This study also demonstrates that atomistic simulations are capable of capturing the phase transition behavior of lipid bilayers, providing a rich set of molecular and structural information at and near the transition state.     

Molecular Dynamics Simulations of the Rotary Motor F0 under External Electric Fields across the Membrane

The membrane-bound component F₀, which is a major component of the F₀F₁-ATP synthase, works as a rotary motor and plays a central role in driving the F₁ component to transform chemiosmotic energy into ATP synthesis. We conducted molecular dynamics simulations of b₂-free F₀ in a 1-palmitoyl-2-oleoyl-phosphatidylcholine lipid bilayer for tens of nanoseconds with two different protonation states of the cAsp-61 residue at the interface of the a-c complex in the absence of electric fields and under electric fields of ±0.03 V/nm across the membrane. To our surprise, we observed that the upper half of the N-terminal helix of the c₁ subunit rotated about its axis clockwise by 30°. An energetic analysis revealed that the electrostatic repulsion between this N-terminal helix and subunit c₁₂ was a major contributor to the observed rotation. A correlation map analysis indicated that the correlated motions of residues in the interface of the a-c complex were significantly reduced by external electric fields. The deuterium order parameter (S_CD) profile calculated by averaging all the lipids in the F₀-bound bilayer was not very different from that of the pure bilayer system, in agreement with recent ²H solid-state NMR experiments. However, by delineating the lipid properties according to their vicinity to F₀, we found that the S_CD profiles of different lipid shells were prominently different. Lipids close to F₀ formed a more ordered structure. Similarly, the lateral diffusion of lipids on the membrane surface also followed a shell-dependent behavior. The lipids in the proximity of F₀ exhibited very significantly reduced diffusional motion. The numerical value of S_CD was anticorrelated with that of the diffusion coefficient, i.e., the more ordered lipid structures led to slower lipid diffusion. Our findings will help elucidate the dynamics of F₀ depending on the protonation state and electric field, and may also shed some light on the interactions between the motor F₀ and its surrounding lipids under physiological conditions, which could help to rationalize its extraordinary energy conversion efficiency.     

Electroporative deformation of salt filled lipid vesicles

Membrane electroporation, vesicle shape deformation and aggregation of small, NaCl-filled lipid vesicles (of radius a = 50 nm) in DC electric fields was characterized using conductometric and turbidimetrical data. At pulse durations t_E≤ 55 ± 5 ms the increase in the conductivity of the vesicle suspension is due to the field-induced efflux of electrolyte through membrane electropores. Membrane electroporation and Maxwell stress on the vesicle membrane lead to vesicle elongation concomitant with small volume reduction (up to 0.6% in an electric field of E = 1 MV m^–1). At t_E > 55 ± 5 ms, further increases in the conductivity and the optical density suggest electroaggregation and electrofusion of vesicles. The conductivity changes after the electric pulse termination reflect salt ion efflux through slowly resealing electropores. The analysis of the volume reduction kinetics yields the bending rigidity κ = (4.1 ± 0.3) ⋅ 10^–20 J of the vesicle membrane. If the flow of Na⁺ and Cl^– ions from the vesicle interior is treated in terms of Hagen-Poiseuille's equation, the number of permeable electropores is N = 39 per vesicle with mean pore radius r_p = 0.85 ± 0.05 nm at E = 1 MVm^–1 and t_E≤ 55 ± 5 ms. The turbidimetric and conductometric data suggest that small lipid vesicles (a ≤ 50 nm) are not associated with extensive membrane thermal undulations or superstructures. In particular with respect to membrane curvature, the vesicle results are suggestive for the design and optimization of electroporative delivery of drugs and genes to cell tissue at small field strengths (≤1 MVm^–1) and large pulse durations (≤100 ms). Received: 8 July 1997 / Accepted: 15 September 1997     

A model mosaic membrane: Association of phospholipids and cytochrome oxidase

The structure and physical properties of model membranes formed from lipids and cytochromec oxidase have been examined. The lipid-depleted protein is in the form of 90 Å rods or globules. When phospholipid is added the rods swell and then. form sheets and concentric membrane vesicles. The protein is saturated with lipid at 65 g/atoms of phosphorus per mole of hemea. Electron microscope examination by negative staining, sectioning, and freeze etching indicates a 50 Å thick unit membrane with 50–60 Å protein globules in the lipid bilayer. Infrared, circular dichroism and fluorescence binding studies are consistent with globular protein units surrounded with lipid. Diolein will substitute for phospholipid but the membrane formed remains as sheets rather than vesicles. Saturated phospholipids will not interact with the oxidase to form membrane. The capacity to form membrane is specific to protein associated with the hemea, and other insoluble protein in the original oxidase preparation cannot form membrane.     

Numerical study of lipid translocation driven by nanoporation due to multiple high-intensity,ultrashort electrical pulses

The dynamical translocation of lipids from one leaflet to another due to membrane permeabilization driven by nanosecond, high-intensity (> 100 kV/cm) electrical pulses has been probed. Our simulations show that lipid molecules can translocate by diffusion through water-filled nanopores which form following high voltage application. Our focus is on multiple pulsing, and such simulations are relevant to gauge the time duration over which nanopores might remain open, and facilitate continued lipid translocations and membrane transport. Our results are indicative of a N^½ scaling with pulse number for the pore radius. These results bode well for the use of pulse trains in biomedical applications, not only due to cumulative behaviors and in reducing electric intensities and pulsing hardware, but also due to the possibility of long-lived thermo-electric physics near the membrane, and the possibility for pore coalescence.     

Effect of lipid peroxidation on the properties of lipid bilayers: a molecular dynamics study

Lipid peroxidation plays an important role in cell membrane damage. We investigated the effect of lipid peroxidation on the properties of 1-palmitoyl-2-linoleoyl-sn-glycero-3-phosphatidylcholine (PLPC) lipid bilayers using molecular dynamics simulations. We focused on four main oxidation products of linoleic acid with either a hydroperoxide or an aldehyde group: 9-trans, cis-hydroperoxide linoleic acid, 13-trans, cis-hydroperoxide linoleic acid, 9-oxo-nonanoic acid, and 12-oxo-9-dodecenoic acid. These oxidized chains replaced the sn-2 linoleate chain. The properties of PLPC lipid bilayers were characterized as a function of the concentration of oxidized lipids, with concentrations from 2.8% to 50% for each oxidation product. The introduction of oxidized functional groups in the lipid tail leads to an important conformational change in the lipids: the oxidized tails bend toward the water phase and the oxygen atoms form hydrogen bonds with water and the polar lipid headgroup. This conformational change leads to an increase in the average area per lipid and, correspondingly, to a decrease of the bilayer thickness and the deuterium order parameters for the lipid tails, especially evident at high concentrations of oxidized lipid. Water defects are observed in the bilayers more frequently as the concentration of the oxidized lipids is increased. The changes in the structural properties of the bilayer and the water permeability are associated with the tendency of the oxidized lipid tails to bend toward the water interface. Our results suggest that one mechanism of cell membrane damage is the increase in membrane permeability due to the presence of oxidized lipids.     

The preparation of lipid-depleted bacteriorhodopsin

Bacteriorhodopsin, the protein of the purple membrane of Halobacterium halobium, was freed to the extent of 90–95% from the natural membrane lipids without loss of function. The residual lipid corresponded to less than 1 mol/mol of bacteriorhodopsin. Delipidation was achieved by treatment of the purple membrane with a mixture of the detergent dimethyldodecylamine oxide and sodium chloride. The detergent was removed by dialysis or by sucrose density gradient centrifugation. Analysis of the lipids removed and those still bound to bacteriorhodopsin was facilitated by the use of purple membrane preparations labelled with ³⁵S, ³²P, or ¹⁴C. The composition of the residual lipids associated with bacteriorhodopsin was similar to that of the total lipid in the purple membrane.     

Molecular dynamics simulation of cation–phospholipid clustering in phospholipid bilayers: Possible role in stalk formation during membrane fusion

In this study, we performed all-atom long-timescale molecular dynamics simulations of phospholipid bilayers incorporating three different proportions of negatively charged lipids in the presence of K⁺, Mg^2 +, and Ca^2 + ions to systemically determine how membrane properties are affected by cations and lipid compositions. Our simulations revealed that the binding affinity of Ca^2 + ions with lipids is significantly stronger than that of K⁺ and Mg^2 + ions, regardless of the composition of the lipid bilayer. The binding of Ca^2 + ions to the lipids resulted in bilayers having smaller lateral areas, greater thicknesses, greater order, and slower rotation of their lipid head groups, relative to those of corresponding K⁺- and Mg^2 +-containing systems. The Ca^2 + ions bind preferentially to the phosphate groups of the lipids. The complexes formed between the cations and the lipids further assembled to form various multiple-cation-centered clusters in the presence of anionic lipids and at higher ionic strength—most notably for Ca^2 +. The formation of cation–lipid complexes and clusters dehydrated and neutralized the anionic lipids, creating a more-hydrophobic environment suitable for membrane aggregation. We propose that the formation of Ca^2 +–phospholipid clusters across apposed lipid bilayers can work as a “cation glue” to adhere apposed membranes together, providing an adequate configuration for stalk formation during membrane fusion.     

Membrane-Mediated Regulation of the Intrinsically Disordered CD3? Cytoplasmic Tail of the TCR

The regulation of T-cell-mediated immune responses depends on the phosphorylation of immunoreceptor tyrosine-based activation motifs (ITAMs) on T-cell receptors. Although many details of the signaling cascades are well understood, the initial mechanism and regulation of ITAM phosphorylation remains unknown. We used molecular dynamics simulations to study the influence of different compositions of lipid bilayers on the membrane association of the CD3ϵ cytoplasmic tails of the T-cell receptors. Our results show that binding of CD3ϵ to membranes is modulated by both the presence of negatively charged lipids and the lipid order of the membrane. Free-energy calculations reveal that the protein-membrane interaction is favored by the presence of nearby basic residues and the ITAM tyrosines. Phosphorylation minimizes membrane association, rendering the ITAM motif more accessible to binding partners. In systems mimicking biological membranes, the CD3ϵ chain localization is modulated by different facilitator lipids (e.g., gangliosides or phosphoinositols), revealing a plausible regulatory effect on activation through the regulation of lipid composition in cell membranes.     

Molecular basis of endosomal-membrane association for the dengue virus envelope protein

Dengue virus is coated by an icosahedral shell of 90 envelope protein dimers that convert to trimers at low pH and promote fusion of its membrane with the membrane of the host endosome. We provide the first estimates for the free energy barrier and minimum for two key steps in this process: host membrane bending and protein–membrane binding. Both are studied using complementary membrane elastic, continuum electrostatics and all-atom molecular dynamics simulations. The predicted host membrane bending required to form an initial fusion stalk presents a 22–30 kcal/mol free energy barrier according to a constrained membrane elastic model. Combined continuum and molecular dynamics results predict a 15 kcal/mol free energy decrease on binding of each trimer of dengue envelope protein to a membrane with 30% anionic phosphatidylglycerol lipid. The bending cost depends on the preferred curvature of the lipids composing the host membrane leaflets, while the free energy gained for protein binding depends on the surface charge density of the host membrane. The fusion loop of the envelope protein inserts exactly at the level of the interface between the membrane's hydrophobic and head-group regions. The methods used in this work provide a means for further characterization of the structures and free energies of protein-assisted membrane fusion.