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 Gaussian curvature elastic energy of intermediates in membrane fusion

The Gaussian curvature elastic energy contribution to the energy of membrane fusion intermediates has usually been neglected because the Gaussian curvature elastic modulus, κ, was unknown. It is now possible to measure κ for phospholipids that form bicontinuous inverted cubic (Q_II) phases. Here, it is shown that one can estimate κ for lipids that do not form Q_II phases by studying the phase behavior of lipid mixtures. The method is used to estimate κ for several lipid compositions in excess water. The values of κ are used to compute the curvature elastic energies of stalks and catenoidal fusion pores according to recent models. The Gaussian curvature elastic contribution is positive and similar in magnitude to the bending energy contribution: it increases the total curvature energy of all the fusion intermediates by 100 units of k_BT or more. It is important to note that this contribution makes the predicted intermediate energies compatible with observed lipid phase behavior in excess water. An order-of-magnitude fusion rate equation is used to estimate whether the predicted stalk energies are consistent with the observed rates of stalk-mediated processes in pure lipid systems. The current theory predicts a stalk energy that is slightly too large, by ∼30 k_BT, to rationalize the observed rates of stalk-mediated processes in phosphatidylethanolamine or N-monomethylated dioleoylphosphatidylethanolamine systems. Despite this discrepancy, the results show that models of fusion intermediate energy are accurate enough to make semiquantitative predictions about how proteins mediate biomembrane fusion. The same rate model shows that for proteins to drive biomembrane fusion at observed rates, they have to perform mediating functions corresponding to a reduction in the energy of a purely lipidic stalk by several tens of k_BT. By binding particular peptide sequences to the monolayer surface, proteins could lower fusion intermediate energies by altering the elastic constants of the patches of lipid monolayer that form the stalk. Here, it is shown that if peptide binding changes κ or some other combinations of local elastic constants by only tens of percents, the stalk energy and the energy of catenoidal fusion pores would decrease by tens of k_BT relative to the pure lipid value. This is comparable to the required mediating effect. The curvature energies of stalks and catenoidal fusion pores have almost the same dependence on monolayer elastic constants as the curvature energies of the rhombohedral and Q_II phases; respectively. The effects of isolated fusion-relevant peptides on the energies of these intermediates can be determined by studying the effects of the peptides on the stability of rhombohedral and Q_II phases.     

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.     

Possible mechanism of membrane fusion

The stalker mechanism of membrane fusion was considered. Initiation and evolution of monolayer and bilayer bridges-stalks between the membranes were studied. From the expression of elastic energy of the stalk the value of spontaneous curvature of its membrane Ks at which the bridge may appear, was found. It was shown that in terms of the stalker mechanism formation of the stalk of the final radius or complete fusion were possible Ks values for realizing this or that variant were found. The energetic barrier of hydrophobic interaction and the barrier of elastic energy which the membranes had to overcome for stalker formation were found. The experimental data on the fusion of small and large liposomes were analysed.     

Kinetic and thermodynamic studies of the fusion of small unilamellar phospholipid vesicles

Small phospholipid vesicles, prepared so as to minimize impurities, fuse relatively slowly resulting in the time-dependent development of a characteristic endotherm in differential scanning calorimetry and corresponding changes in the Raman spectrum. The stability of small vesicles towards fusion increases with increasing acyl chain length for the series C-14 through 18. Within the protocols of these experiments, the fusion rate remains unchanged whether the vesicles are held at 10°C below T_m or at T_m itself. We have determined enthalpies of transition for small vesicles and fusion product for C-14 through C-18. In each case ΔH for small vesicles is lower than that of the corresponding multilamellar vesicles, while the fusion product ΔH is intermediate between small and multilamellar vesicles. The apparent lack of concensus in the literature as to the nature of the fusion process is ascribed to the variety of protocols used as well as the presence or absence of fusion-inducing impurities.     

The Transmembrane Domain Peptide of Vesicular Stomatitis Virus Promotes Both Intermediate and Pore Formation during PEG-Mediated Vesicle Fusion

We propose mechanisms by which the transmembrane domain of vesicular stomatitis virus (VSV-TMD) promotes both initiation of fusion and formation of a fusion pore. Time courses of polyethyleneglycol (PEG)-mediated fusion of 25 nm small unilamellar vesicles composed of dioleoylphosphatidylcholine, dioleoylphosphatidylethanolamine (DOPE), bovine brain sphingomyelin, and cholesterol (35:30:15:20 molar ratio) were recorded at pH 7.4 at five different temperatures (from 17°C to 37°C) and compared with time courses obtained with the same vesicles containing the fusion-active TMD of the G protein of VSV. Multiple time courses were fitted globally to a one-intermediate ensemble kinetic model to estimate the rate constants for conversion of the aggregated state to an intermediate hemifused state (k₁, stalk, or I₁) that rapidly transits to an unstable intermediate (I₂ state) that converts to a final fusion pore state with a combined rate k₃. The probabilities of lipid mixing, contents mixing, and contents leakage in the three states were also obtained from this analysis. The activation thermodynamics for each step were consistent with previously published models of lipid rearrangements during intermediate and pore formation. The influences of VSV-TMD, hexadecane, and VSV-TMD + hexadecane on the kinetics, activation thermodynamics, and membrane structure support the hypothesis that these two agents do not catalyze fusion by a common mechanism, except possibly at the lowest temperatures examined. VSV-TMD primarily catalyzed initial intermediate formation, although it substantially increased the probability of contents mixing in the intermediate state. Our results support the hypothesis that the catalytic influence of VSV-TMD on the initial-intermediate- and pore-forming steps of PEG-mediated fusion derives from its ability to impose a positive intrinsic curvature and thereby stress small unilamellar vesicle outer leaflets as well as the periphery of intermediate microstructures.     

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.     

Molecular mechanism of Ca-catalyzed fusion of phospholipid micelles

Although membrane fusion plays key roles in intracellular trafficking, neurotransmitter release, and viral infection, its underlying molecular mechanism and its energy landscape are not well understood. In this study, we employed all-atom molecular dynamics simulations to investigate the fusion mechanism, catalyzed by Ca^2 + ions, of two highly hydrated 1-palmitoyl-2-oleoyl-sn-3-phosphoethanolamine (POPE) micelles. This simulation system mimics the small contact zone between two large vesicles at which the fusion is initiated. Our simulations revealed that Ca^2 + ions are capable of catalyzing the fusion of POPE micelles; in contrast, we did not observe close contact of the two micelles in the presence of only Na⁺ or Mg^2 + ions. Determining the free energy landscape of fusion allowed us to characterize the underlying molecular mechanism. The Ca^2 + ions play a key role in catalyzing the micelle fusion in three aspects: creating a more-hydrophobic surface on the micelles, binding two micelles together, and enhancing the formation of the pre-stalk state. In contrast, Na⁺ or Mg^2 + ions have relatively limited effects. Effective fusion proceeds through sequential formation of pre-stalk, stalk, hemifused-like, and fused states. The pre-stalk state is the state featuring lipid tails exposed to the inter-micellar space; its formation is the rate-limiting step. The stalk state is the state where a localized hydrophobic core is formed connecting two micelles; its formation occurs in conjunction with water expulsion from the inter-micellar space. This study provides insight into the molecular mechanism of fusion from the points of view of energetics, structure, and dynamics.     

The Fusion of Membranes and Vesicles: Pathway and Energy Barriers from Dissipative Particle Dynamics

The fusion of lipid bilayers is studied with dissipative particle dynamics simulations. First, to achieve control over membrane properties, the effects of individual simulation parameters are studied and optimized. Then, a large number of fusion events for a vesicle and a planar bilayer are simulated using the optimized parameter set. In the observed fusion pathway, configurations of individual lipids play an important role. Fusion starts with individual lipids assuming a splayed tail configuration with one tail inserted in each membrane. To determine the corresponding energy barrier, we measure the average work for interbilayer flips of a lipid tail, i.e., the average work to displace one lipid tail from one bilayer to the other. This energy barrier is found to depend strongly on a certain dissipative particle dynamics parameter, and, thus, can be adjusted in the simulations. Overall, three subprocesses have been identified in the fusion pathway. Their energy barriers are estimated to lie in the range 8-15 k_BT. The fusion probability is found to possess a maximum at intermediate tension values. As one decreases the tension, the fusion probability seems to vanish before the tensionless membrane state is attained. This would imply that the tension has to exceed a certain threshold value to induce 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.     

Stalk model of membrane fusion: solution of energy crisis.

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

EFFECTS OF THE PHYSICAL ENVIRONMENT ON SOME LIPOPROTEIN LAYER SYSTEMS AND OBSERVATIONS ON THEIR MORPHOGENESIS

Lipoprotein membrane systems such as chloroplasts and the endoplasmic reticulum exhibit a generalized swelling response. The initial effect is an increase in interlamellar spacing, but as swelling proceeds, the membranes are transformed into closed thin-walled spherical vesicles. Available evidence suggests that morphogenesis of the endoplasmic reticulum of Nitella and the lamellar system of the Zea chloroplasts involves fusion of small spherical vesicles to yield closed double membrane structures, which subsequently undergo further differentiation. It is suggested that the vesicles comprise a convenient "micellar" form by which lipides may be transported within the cell from the sites of lipide synthesis to regions of lamellar growth. The characteristic formation of vesicles in swelling and the apparent fusion of vesicles in morphogenesis appear to represent two aspects of a fundamental plasticity of lipoprotein layer systems.     

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.     

Effects of temperature and lipid composition on the serum albumin-induced aggregation and fusion of small unilamellar vesicles

Small unilamellar vesicles of egg phosphatidylcholine (PC) or dimyristoylphosphatidylcholine, mixed with small unilamellar vesicles labelled with 2-(10-(1-pyrene)decanoyl)phosphatidylcholine, exhibit a constant average size and excimer to monomer (E/M) ratio for several hours when incubated at pH 3.6 at a temperature higher than the phase transition temperature (T_c) of the lipids. Addition of bovine serum albumin to this system produces a transient turbidity increase, a fast decrease in the E/M ratio, a partial loss of vesicle-entrapped [¹⁴C]sucrose and a measurable leak-in of externally added sucrose. Sepharose 4B filtration of the system demonstrates that the E/M ratio decrease is strictly paralleled by the formation of liposomes which exhibit a low E/M ratio and a hydrodynamic radius larger than that of small unilamellar vesicles. These data demonstrate that the E/M ratio decrease can be unequivocally ascribed to a vesicle-vesicle fusion process induced by serum albumin. The rate of serum-albumin induced fusion of small unilamellar vesicles is: (a) maximal at a stoichiometric ratio of approx. 2 albumins per vesicle: (b) sensitive to the nature of the lipid and; (c) not altered when human serum albumin replaces bovine serum albumin. The rate of albumin-induced fusion of dimyristoylphosphatidylcholine small unilamellar vesicles is higher below the T_c of the lipid and increases with temperature above the T_c. The formation of protein-bound aggregates with defined stoichiometries and a high local vesicle concentration, as well as changes in the local degree of hydration, are proposed to be the driving forces for the protein-induced vesicle fusion in this system.     

Plasmon Spectroscopy for Subnanometric Copper Particles: Dielectric Function and Core–Shell Sizing

In the last years, there has been a growing interest in the study of transition metal nanoparticles (Nps) due to their potential applications in several fields of science and technology. In particular, their optical properties are governed by the characteristics of the dielectric function of the metal, its size and environment. This work analyses the separated contribution of free and bound electrons on the optical properties of copper Nps. Usually, the contribution of free electrons to the dielectric function is corrected for particle size through the modification of the damping constant, which is changed as usual introducing a term inversely proportional to the particle’s radius to account for the extra collisions with the boundary when the size approaches the electronic mean free path limit (about 10 nm). For bound electron contribution, the interband transitions from the d-band to the conduction band are considered together with the fact that the electronic density of states in the conduction band must be made size-dependent to account for the larger spacing between electronic energy levels as the particle decreases in size below 2 nm. Taking into account these specific modifications of free and bound electron contributions to the dielectric function, it was possible to fit the bulk complex dielectric function, and consequently, determine optical parameters and band energy values such as the coefficient for bound electron contribution Q _bulk?=?2?×?10²⁴, gap energy E _g?=?1.95 eV, Fermi energy E _F?=?2.15 eV, and damping constant for bound electrons γ _b?=?1.15?×?10¹⁴ Hz. With both size-dependent contributions to the dielectric function, extinction spectra of copper Nps in the subnanometer radius range can be calculated using Mie’s theory and its behaviour with size can be analysed. These studies are applied to fit experimental extinction spectra of very small spherical core–shell Cu–Cu₂O Nps generated by ultrafast laser ablation of a solid target in water. Theoretical calculations for subnanometric core radius are in excellent agreement with experimental results obtained from core–shell colloidal Nps. From the fitting, it is possible determining core radius and shell thickness of the Nps, showing that optical extinction spectroscopy is a good complementary technique to standard high-resolution electron microscopy for sizing spherical nanometric-subnanometric Nps.     

The Effect of Membrane Lipid Composition on the Formation of Lipid Ultrananodomains

Some lipid mixtures form membranes containing submicroscopic (nanodomain) ordered lipid domains (rafts). Some of these nanodomains are so small (radius <5 nm) that they cannot be readily detected with Förster resonance energy transfer (FRET)-labeled lipid pairs with large Ro. We define such domains as ultrananodomains. We studied the effect of lipid structure/composition on the formation of ultrananodomains in lipid vesicles using a dual-FRET-pair approach in which only one FRET pair had Ro values that were sufficiently small to detect the ultrananodomains. Using this approach, we measured the temperature dependence of domain and ultrananodomain formation for vesicles composed of various mixtures containing a high-T_m lipid (brain sphingomyelin (SM)) or dipalmitoyl phosphatidylcholine (DPPC)), low-T_m lipid (dioleoylphosphatidylcholine (DOPC) or 1-palmitoyl 2-oleoyl phosphatidylcholine (POPC)), and a lower (28 mol %) or higher (38 mol %) cholesterol concentration. For every lipid combination tested, the thermal stabilities of the ordered domains were similar, in agreement with our prior studies. However, the range of temperatures over which ultrananodomains formed was highly lipid-type dependent. Overall, vesicles that were closest to mammalian plasma membrane in lipid composition (i.e., with brain SM, POPC, and/or higher cholesterol) formed ultrananodomains in preference to larger domains over the widest temperature range. Relative to DPPC, the favorable effect of SM on ultrananodomain formation versus larger domains was especially large. In addition, the favorable effect of a high cholesterol concentration, and of POPC versus DOPC, on the formation of ultrananodomains versus larger domains was greater in vesicles containing SM than in those containing DPPC. We speculate that it is likely that natural mammalian lipids are tuned to maximize the tendency to form ultrananodomains relative to larger domains. The observation that domain size is more sensitive than domain formation to membrane composition has implications for how membrane domain properties may be regulated in vivo.     

Docking, not fusion, as the rate-limiting step in a SNARE-driven vesicle fusion assay

In vitro vesicle fusion assays that monitor lipid mixing between t-SNARE and v-SNARE vesicles in bulk solution exhibit remarkably slow fusion on the nonphysiological timescale of tens of minutes to several hours. Here, single-vesicle, fluorescence resonance energy transfer-based assays cleanly separate docking and fusion steps for individual vesicle pairs containing full-length SNAREs. Docking is extremely inefficient and is the rate-limiting step. Of importance, the docking and fusion kinetics are comparable in the two assays (one with v-SNARE vesicles tethered to a surface and the other with v-SNARE vesicles free in solution). Addition of the V_C peptide synaptobrevin-2 (syb(57–92)) increases the docking efficiency by a factor of ∼30, but docking remains rate-limiting. In the presence of V_C peptide, the fusion step occurs on a timescale of ∼10 s. In previous experiments involving bulk fusion assays in which the addition of synaptotagmin/Ca²⁺, Munc-18, or complexin accelerated the observed lipid-mixing rate, the enhancement may have arisen from the docking step rather than the fusion step.     

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.     

Cholesterol affects divalent cation-induced fusion and isothermal phase transitions of phospholipid membranes

The influence of cholesterol on divalent cation-induced fusion and isothermal phase transitions of large unilamellar vesicles composed of phosphatidylserine (PS) was investigated. Vesicle fusion was monitored by the terbium/dipicolinic acid assay for the intermixing of internal aqueous contents, in the temperature range 10–40°C. The fusogenic activity of the cations decreases in the sequence Ca²⁺ > Ba²⁺ > Sr²⁺ Mg²⁺ for cholesterol concentrations in the range 20–40 mol%, and at all temperatures. Increasing the cholesterol concentration decreases the initial rate of fusion in the presence of Ca²⁺ and Ba²⁺ at 25°C, reaching about 50% of the rate for pure PS at a mole fraction of 0.4. From 10 to 25°C, Mg²⁺ is ineffective in causing fusion at all cholesterol concentrations. However, at 30°C, Mg²⁺-induced fusion is observed with vesicles containing cholesterol. At 40°C, Mg²⁺ induces slow fusion of pure PS vesicles, which is enhanced by the presence of cholesterol. Increasing the temperature also causes a monotonic increase in the rate of fusion induced by Ca²⁺, Ba²⁺ and Sr²⁺. The enhancement of the effect of cholesterol at high temperatures suggests that changes in hydrogen bonding and interbilayer hydration forces may be involved in the modulation of fusion by cholesterol. The phase behavior of PS/cholesterol membranes in the presence of Na⁺ and divalent cations was studied by differential scanning calorimetry. The temperature of the gel-liquid crystalline transition (T_m) in Na⁺ is lowered as the cholesterol content is increased, and the endotherm is broadened. Addition of divalent cations shifts the T_m upward, with a sequence of effectiveness Ba²⁺ > Sr²⁺ > Mg²⁺. The T_m of these complexes decreases as the cholesterol content is increased. Although the transition is not detectable for cholesterol concentrations of 40 and 50 mol% in the presence of Na⁺, Sr²⁺ or Mg²⁺, the addition of Ba²⁺ reveals endotherms with T_m progressively lower than that observed at 30 mol%. Although the presence of cholesterol appears to induce an isothermal gel-liquid crystalline transition by decreasing the T_m, this change in membrane fluidity does not enhance the rate of fusion, but rather decreases it. The effect of cholesterol on the fusion of PS/phosphatidylethanolamine (PE) vesicles was investigated by utilizing a resonance energy transfer assay for lipid mixing. The initial rate of fusion of PS/PE and PS/PE/cholesterol vesicles is saturated at high Mg²⁺ concentrations. With Ca²⁺, saturation is not observed for cholesterol-containing vesicles. The highest rate of fusion for both Ca²⁺- and Mg²⁺-induced fusion is observed with vesicles containing 30 mol% cholesterol.     

Free energy analysis of membrane pore formation process in the presence of multiple melittin peptides

Understanding the molecular mechanism underlying pore formation in lipid membranes by antimicrobial peptides is of great importance in biological sciences as well as in drug design applications. Melittin has been widely studied as a pore forming peptide, though the molecular mechanism for pore formation is still illusive. We examined the free energy barrier for the creation of a pore in lipid membranes with and without multiple melittin peptides. It was found that six melittin peptides significantly stabilized a pore, though a small barrier (a few k_BT) for the formation still existed. With five melittin peptides or fewer, the pore formation barrier was much higher, though the established pore was in a local energy minimum. Although seven melittins effectively reduced the free energy barrier, a single melittin peptide left the pore after a long time MD simulation probably because of the overcrowded environment around the bilayer pore. Thus, it is highly selective for the number of melittin peptides to stabilize the membrane pore, as was also suggested by the line tension evaluations. The free energy cost required to insert a single melittin into the membrane is too high to explain the one-by-one insertion mechanism for pore formation, which also supports the collective melittin mechanism for pore formation.