Bilayer thickness modulates the conductance of the BK channel in model membranes

The conductance of the BK channel was evaluated in reconstituted bilayers made of POPE/POPS (3.3:1), or POPE/POPS with an added 20% of either SPM (3.3:1:1), CER (3.3:1:1), or CHL (3.3:1:1). The presence of SPM, which is known to increase bilayer thickness, significantly reduced the conductance of the BK channel. To directly test the role of membrane thickness, the conductance of the BK channel was measured in bilayers formed from PCs with acyl chains of increasing length (C14:1-C24:1), all in the absence of SPM. Slope conductance was maximal at a chain length of (C18:1) and much reduced for both thinner (C14:1) and thicker (C24:1) bilayers, indicating that membrane thickness alone can modify slope conductance. Further, in a simplified binary mixture of DOPE/SPM that forms a confined, phase-separated bilayer, the measured conductance of BK channels shows a clear bimodal distribution. In contrast, the addition of CER, which has an acyl chain structure similar to SPM but without its bulky polar head group to POPE/POPS, was without effect, as was the addition of CHL. The surface structure of membranes made from these same lipid mixtures was examined with AFM. Incorporation of both SPM and CER resulted in the formation of microdomains in POPE/POPS monolayers, but only SPM promoted a substantial increase in the amount of the high phase observed for the corresponding bilayers. The addition of CHL to POPE/POPS eliminated the phase separation observed in the POPE/POPS bilayer. The decrease in channel conductance observed with the incorporation of SPM into POPE/POPS membranes was, therefore, attributed to larger SPM-rich domains that appear thicker than the neighboring bilayer.     

Evidence of cholesterol accumulated in high curvature regions: implication to the curvature elastic energy for lipid mixtures

Recent experiments suggested that cholesterol and other lipid components of high negative spontaneous curvature facilitate membrane fusion. This is taken as evidence supporting the stalk-pore model of membrane fusion in which the lipid bilayers go through intermediate structures of high curvature. How do the high-curvature lipid components lower the free energy of the curved structure? Do the high-curvature lipid components modify the average spontaneous curvature of the relevant monolayer, thereby facilitate its bending, or do the lipid components redistribute in the curved structure so as to lower the free energy? This question is fundamental to the curvature elastic energy for lipid mixtures. Here we investigate the lipid distribution in a monolayer of a binary lipid mixture before and after bending, or more precisely in the lamellar, hexagonal, and distorted hexagonal phases. The lipid mixture is composed of 2:1 ratio of brominated di18:0PC and cholesterol. Using a newly developed procedure for the multiwavelength anomalous diffraction method, we are able to isolate the bromine distribution and reconstruct the electron density distribution of the lipid mixture in the three phases. We found that the lipid distribution is homogenous and uniform in the lamellar and hexagonal phases. But in the distorted hexagonal phase, the lipid monolayer has nonuniform curvature, and cholesterol almost entirely concentrates in the high curvature region. This finding demonstrates that the association energies between lipid molecules vary with the curvature of membrane. Thus, lipid components in a mixture may redistribute under conditions of nonuniform curvature, such as in the stalk structure. In such cases, the spontaneous curvature depends on the local lipid composition and the free energy minimum is determined by lipid distribution as well as curvature.     

Elastic constants of polymer-grafted lipid membranes

The surface expansion that is induced by the lateral pressure in the brush region of lipid membranes containing grafted polymers is deduced from the scaling and mean-field theories for the polymer brush, together with the equation of state for a lipid monolayer at the equivalence pressure with fluid lipid bilayers. Depending on the length and mole fraction of the polymer lipid, the membrane expansion can be appreciable. Direct experimental evidence for this lateral expansion comes from recent spin-label measurements with lipid membranes containing poly(ethylene glycol)-grafted lipids. The expansion in lipid area modifies the elastic constants of the polymer-grafted membranes in a way that opposes the direct elastic response of the polymer itself. Calculations as a function of polymer lipid content indicate that the net change in isothermal area expansion modulus of the membrane is negative but small, in contrast to previous predictions. A similar situation applies to the curvature elastic moduli of membranes containing short polymer lipids. For longer polymer lipids, however, the direct contribution of the polymer brush to the bending elastic constants dominates, and the increase in bending moduli with increasing polymer lipid content rapidly exceeds the basal values of the bare lipid membrane. The spontaneous (or intrinsic) curvature of the component monolayer of polymer lipid-containing membranes is calculated for the first time. The polymer brush contribution to spontaneous curvature scales quadratically with the polymer length, and at least quadratically with the mole fraction of polymer lipid.     

Nonequilibrium behavior in supported lipid membranes containing cholesterol

We investigate lateral organization of lipid domains in vesicles versus supported membranes and monolayers. The lipid mixtures used are predominantly DOPC/DPPC/Chol and DOPC/BSM/Chol, which have been previously shown to produce coexisting liquid phases in vesicles and monolayers. In a monolayer at an air-water interface, these lipids have miscibility transition pressures of approximately 12-15 mN/m, which can rise to 32 mN/m if the monolayer is exposed to air. Lipid monolayers can be transferred by Langmuir-Sch?fer deposition onto either silanized glass or existing Langmuir-Blodgett supported monolayers. Micron-scale domains are present in the transferred lipids only if they were present in the original monolayer before deposition. This result is valid for transfers at 32 mN/m and also at lower pressures. Domains transferred to glass supports differ from liquid domains in vesicles because they are static, do not align in registration across leaflets, and do not reappear after temperature is cycled. Similar static domains are found for vesicles ruptured onto glass surfaces. Although supported membranes on glass capture some aspects of vesicles in equilibrium (e.g., gel-liquid transition temperatures and diffusion rates of individual lipids), the collective behavior of lipids in large liquid domains is poorly reproduced.     

Melittin-induced bilayer leakage depends on lipid material properties: evidence for toroidal pores

The membrane-lytic peptide melittin has previously been shown to form pores in lipid bilayers that have been described in terms of two different structural models. In the "barrel stave" model the bilayer remains more or less flat, with the peptides penetrating across the bilayer hydrocarbon region and aggregating to form a pore, whereas in the "toroidal pore" melittin induces defects in the bilayer such that the bilayer bends sharply inward to form a pore lined by both peptides and lipid headgroups. Here we test these models by measuring both the free energy of melittin transfer (DeltaG degrees ) and melittin-induced leakage as a function of bilayer elastic (material) properties that determine the energetics of bilayer bending, including the area compressibility modulus (K(a)), bilayer bending modulus (k(c)), and monolayer spontaneous curvature (R(o)). The addition of cholesterol to phosphatidylcholine (PC) bilayers, which increases K(a) and k(c), decreases both DeltaG degrees and the melittin-induced vesicle leakage. In contrast, the addition to PC bilayers of molecules with either positive R(o), such as lysoPC, or negative R(o), such as dioleoylglycerol, has little effect on DeltaG degrees , but produces large changes in melittin-induced leakage, from 86% for 8:2 PC/lysoPC to 18% for 8:2 PC/dioleoylglycerol. We observe linear relationships between melittin-induced leakage and both K(a) and 1/R(o)(2). However, in contrast to what would be expected for a barrel stave model, there is no correlation between observed leakage and bilayer hydrocarbon thickness. All of these results demonstrate the importance of bilayer material properties on melittin-induced leakage and indicate that the melittin-induced pores are defects in the bilayer lined in part by lipid molecules.     

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.     

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 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.     

Regulation of sodium channel function by bilayer elasticity: the importance of hydrophobic coupling. Effects of Micelle-forming amphiphiles and cholesterol

Membrane proteins are regulated by the lipid bilayer composition. Specific lipid-protein interactions rarely are involved, which suggests that the regulation is due to changes in some general bilayer property (or properties). The hydrophobic coupling between a membrane-spanning protein and the surrounding bilayer means that protein conformational changes may be associated with a reversible, local bilayer deformation. Lipid bilayers are elastic bodies, and the energetic cost of the bilayer deformation contributes to the total energetic cost of the protein conformational change. The energetics and kinetics of the protein conformational changes therefore will be regulated by the bilayer elasticity, which is determined by the lipid composition. This hydrophobic coupling mechanism has been studied extensively in gramicidin channels, where the channel-bilayer hydrophobic interactions link a "conformational" change (the monomer<-->dimer transition) to an elastic bilayer deformation. Gramicidin channels thus are regulated by the lipid bilayer elastic properties (thickness, monolayer equilibrium curvature, and compression and bending moduli). To investigate whether this hydrophobic coupling mechanism could be a general mechanism regulating membrane protein function, we examined whether voltage-dependent skeletal-muscle sodium channels, expressed in HEK293 cells, are regulated by bilayer elasticity, as monitored using gramicidin A (gA) channels. Nonphysiological amphiphiles (beta-octyl-glucoside, Genapol X-100, Triton X-100, and reduced Triton X-100) that make lipid bilayers less "stiff", as measured using gA channels, shift the voltage dependence of sodium channel inactivation toward more hyperpolarized potentials. At low amphiphile concentration, the magnitude of the shift is linearly correlated to the change in gA channel lifetime. Cholesterol-depletion, which also reduces bilayer stiffness, causes a similar shift in sodium channel inactivation. These results provide strong support for the notion that bilayer-protein hydrophobic coupling allows the bilayer elastic properties to regulate membrane protein function.     

Direct measurement of the mechanical properties of lipid phases in supported bilayers

Biological membranes define not only the cell boundaries but any compartment within the cell. To some extent, the functionality of membranes is related to the elastic properties of the lipid bilayer and the mechanical and hydrophobic matching with functional membrane proteins. Supported lipid bilayers (SLBs) are valid biomimetic systems for the study of membrane biophysical properties. Here, we acquired high-resolution topographic and quantitative mechanics data of phase-separated SLBs using a recent atomic force microscopy (AFM) imaging mode based on force measurements. This technique allows us to quantitatively map at high resolution the mechanical differences of lipid phases at different loading forces. We have applied this approach to evaluate the contribution of the underlying hard support in the determination of the elastic properties of SLBs and to determine the adequate indentation range for obtaining reliable elastic moduli values. At ~200 pN, elastic forces dominated the force-indentation response and the sample deformation was <20% of the bilayer thickness, at which the contribution of the support was found to be negligible. The obtained Young's modulus (E) of 19.3 MPa and 28.1 MPa allowed us to estimate the area stretch modulus (k(A)) as 106 pN/nm and 199 pN/nm and the bending stiffness (k(c)) as 18 k(B)T and 57 k(B)T for the liquid and gel phases, respectively.     

Effect of chain length and unsaturation on elasticity of lipid bilayers

Micropipette pressurization of giant bilayer vesicles was used to measure both elastic bending k(c) and area stretch K(A) moduli of fluid-phase phosphatidylcholine (PC) membranes. Twelve diacyl PCs were chosen: eight with two 18 carbon chains and degrees of unsaturation from one double bond (C18:1/0, C18:0/1) to six double bonds per lipid (diC18:3), two with short saturated carbon chains (diC13:0, diC14:0), and two with long unsaturated carbon chains (diC20:4, diC22:1). Bending moduli were derived from measurements of apparent expansion in vesicle surface area under very low tensions (0.001-0.5 mN/m), which is dominated by smoothing of thermal bending undulations. Area stretch moduli were obtained from measurements of vesicle surface expansion under high tensions (>0.5 mN/m), which involve an increase in area per molecule and a small-but important-contribution from smoothing of residual thermal undulations. The direct stretch moduli varied little (< +/-10%) with either chain unsaturation or length about a mean of 243 mN/m. On the other hand, the bending moduli of saturated/monounsaturated chain PCs increased progressively with chain length from 0.56 x 10(-19) J for diC13:0 to 1.2 x 10(-19) J for diC22:1. However, quite unexpectedly for longer chains, the bending moduli dropped precipitously to approximately 0.4 x 10(-19) J when two or more cis double bonds were present in a chain (C18:0/2, diC18:2, diC18:3, diC20:4). Given nearly constant area stretch moduli, the variations in bending rigidity with chain length and polyunsaturation implied significant variations in thickness. To test this hypothesis, peak-to-peak headgroup thicknesses h(pp) of bilayers were obtained from x-ray diffraction of multibilayer arrays at controlled relative humidities. For saturated/monounsaturated chain bilayers, the distances h(pp) increased smoothly from diC13:0 to diC22:1 as expected. Moreover, the distances and elastic properties correlated well with a polymer brush model of the bilayer that specifies that the elastic ratio (k(c)/K(A))(1/2) = (h(pp) - h(o))/24, where h(o) approximately 1 nm accounts for separation of the headgroup peaks from the deformable hydrocarbon region. However, the elastic ratios and thicknesses for diC18:2, diC18:3, and diC20:4 fell into a distinct group below the correlation, which showed that poly-cis unsaturated chain bilayers are thinner and more flexible than saturated/monounsaturated chain bilayers.     

Measured effects of diacylglycerol on structural and elastic properties of phospholipid membranes.

Diacylglycerol, a biological membrane second messenger, is a strong perturber of phospholipid planar bilayers. It converts multibilayers to the reverse hexagonal phase (HII), composed of highly curved monolayers. We have used x-ray diffraction and osmotic stress of the HII phase to measure structural dimensions, spontaneous curvature, and bending moduli of dioleoylphosphatidylethanolamine (DOPE) monolayers doped with increasing amounts of dioleoylglycerol (DOG). The diameter of the HII phase cylinders equilibrated in excess water decreases significantly with increasing DOG content. Remarkably, however, all structural dimensions at any specific water/lipid ratio that is less than full hydration are insensitive to DOG. By plotting structural parameters of the HII phase with changing water content in a newly defined coordinate system, we show that the elastic deformation of the lipid monolayers can be described as bending around a pivotal plane of constant area. This dividing surface includes 30% of the lipid volume independent of the DOG content (polar heads and a small fraction of hydrocarbon chains). As the mole fraction of DOG increases to 0.3, the radius of spontaneous curvature defined for the pivotal surface decreases from 29 A to 19 A, and the bending modulus increases from approximately 11 to 14 (+/-0.5) kT. We derive the conversion factors and estimate the spontaneous curvatures and bending moduli for the neutral surface which, unlike the pivotal plane parameters, are intrinsic properties that apply to other deformations and geometries. The spontaneous curvature of the neutral surface differs from that of the pivotal plane by less than 10%, but the difference in the bending moduli is up to 40%. Our estimate shows that the neutral surface bending modulus is approximately 9kT and practically does not depend on the DOG content.     

Charged lipid vesicles: effects of salts on bending rigidity, stability, and size

The swelling behavior of charged phospholipids in pure water is completely different from that of neutral or isoelectric phospholipids. It was therefore suggested in the past that, instead of multilamellar phases, vesicles represent the stable structures of charged lipids in excess water. In this article, we show that this might indeed be the case for dioleoylphosphatidylglycerol and even for dioleoylphosphatidylcholine in certain salts. The size of the vesicles formed by these lipids depends on the phospholipid concentration in a way that has been predicted in the literature for vesicles of which the curvature energy is compensated for by translational entropy and a renormalization of the bending moduli (entropic stabilization). Self-consistent field calculations on charged bilayers show that the mean bending modulus kc and the Gaussian bending modulus k have opposite sign and /k/>kc, especially at low ionic strength. This has the implication that the energy needed to curve the bilayer into a closed vesicle Eves=4pi(2kc+k) is much less than one would expect based on the value of kc alone. As a result, Eves can relatively easily be entropically compensated. The radii of vesicles that are stabilized by entropy are expected to depend on the membrane persistence length and thus on kc. Experiments in which the vesicle size is studied as a function of the salt and the salt concentration correlate well with self-consistent field predictions of kc as a function of ionic strength.     

Bending elasticities of model membranes: influences of temperature and sterol content

Giant liposomes obtained by electroformation and observed by phase-contrast video microscopy show spontaneous deformations originating from Brownian motion that are characterized, in the case of quasispherical vesicles, by two parameters only, the membrane tension sigma and the bending elasticity k(c). For liposomes containing dimyristoyl phosphatidylcholine (DMPC) or a 10 mol% cholesterol/DMPC mixture, the mechanical property of the membrane, k(c), is shown to be temperature dependent on approaching the main (thermotropic) phase transition temperature T(m). In the case of DMPC/cholesterol bilayers, we also obtained evidence for a relation between the bending elasticity and the corresponding temperature/cholesterol molecular ratio phase diagram. Comparison of DMPC/cholesterol with DMPC/cholesterol sulfate bilayers at 30 degrees C containing 30% sterol ratio shows that k(c) is independent of the surface charge density of the bilayer. Finally, bending elasticities of red blood cell (RBC) total lipid extracts lead to a very low k(c) at 37 degrees C if we refer to DMPC/cholesterol bilayers. At 25 degrees C, the very low bending elasticity of a cholesterol-free RBC lipid extract seems to be related to a phase coexistence, as it can be observed by solid-state (31)P-NMR. At the same temperature, the cholesterol-containing RBC lipid extract membrane shows an increase in the bending constant comparable to the one observed for a high cholesterol ratio in DMPC membranes.     

Effects of lipid composition on the membrane activity and lipid phase behaviour of Vibrio sp. DSM14379 cells grown at various NaCl concentrations

The membrane lipid composition of living cells generally adjusts to the prevailing environmental and physiological conditions. In this study, membrane activity and lipid composition of the Gram-negative bacterium Vibrio sp. DSM14379, grown aerobically in a peptone-yeast extract medium supplemented with 0.5, 1.76, 3, 5 or 10% (w/v) NaCl, was determined. The ability of the membrane to reduce a spin label was studied by EPR spectroscopy under different salt concentrations in cell suspensions labeled with TEMPON. For lipid composition studies, cells were harvested in a late exponential phase and lipids were extracted with chloroform-methanol-water, 1:2:0.8 (v/v). The lipid polar head group and acyl chain compositions were determined by thin-layer and gas-liquid chromatographies. ³¹P-NMR spectroscopy was used to study the phase behaviour of the cell lipid extracts with 20 wt.% water contents in a temperature range from −10 to 50 °C. The results indicate that the ability of the membrane to reduce the spin label was highest at optimal salt concentrations. The composition of both polar head groups and acyl chains changed markedly with increasing salinity. The fractions of 16:0, 16:1 and 18:0 acyl chains increased while the fraction of 18:1 acyl chains decreased with increasing salinity. The phosphatidylethanolamine fraction correlated inversely with the lysophosphatidylethanolamine fraction, with phosphatidylethanolamine exhibiting a minimum, and lysophosphatidylethanolamine a maximum, at the optimum growth rate. The fraction of lysophosphatidylethanolamine was surprisingly high in the lipid extracts. This lipid can form normal micellar and hexagonal phases and it was found that all lipid extracts form a mixture of lamellar and normal isotropic liquid crystalline phases. This is an anomalous behaviour since the nonlamellar phases formed by total lipid extracts are generally of the reversed type.     

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.     

Lipid lateral diffusion and membrane heterogeneity

The pulsed field gradient (pfg)-NMR method for measurements of translational diffusion of molecules in macroscopically aligned lipid bilayers is described. This technique is proposed to have an appreciable potential for investigations in the field of lipid and membrane biology. Transport of molecules in the plane of the bilayer can be successfully studied, as well as lateral phase separation of lipids and their dynamics within the bilayer organizations. Lateral diffusion coefficients depend on lipid packing and acyl chain ordering and investigations of order parameters of perdeuterated acyl chains, using ²H NMR quadrupole splittings, are useful complements. In this review we summarize some of our recent achievements obtained on lipid membranes. In particular, bilayers exhibiting two-phase coexistence of liquid disordered (l_d) and liquid ordered (l_o) phases are considered in detail. Methods for obtaining good oriented lipid bilayers, necessary for the pfg-NMR method to be efficiently used, are also briefly described. Among our major results, besides determinations of l_d and l_o phases, belongs the finding that the lateral diffusion is the same for all components, independent of the molecular structure (including cholesterol (CHOL)), if they reside in the same domain or phase in the membrane. Furthermore, quite unexpectedly CHOL seems to partition into the l_dand l_o phases to roughly the same extent, indicating that CHOL has no strong preference for any of these phases, i.e. CHOL seems to have similar interactions with all of the lipids. We propose that the lateral phase separation in bilayers containing one high-T_m and one low-T_m lipid together with CHOL is driven by the increasing difficulty of incorporating an unsaturated or prenyl lipid into the highly ordered bilayer formed by a saturated lipid and CHOL, i.e. the phase transition is entropy driven to keep the disorder of the hydrocarbon chains of the unsaturated lipid.     

Kinematics,material symmetry,and energy densities for lipid bilayers with spontaneous curvature

Continuum mechanical tools are used to describe the deformation, energy density, and material symmetry of a lipid bilayer with spontaneous curvature. In contrast to conventional approaches in which lipid bilayers are modeled by material surfaces, here we rely on a three-dimensional approach in which a lipid bilayer is modeling by a shell-like body with finite thickness. In this setting, the interface between the leaflets of a lipid bilayer is assumed to coincide with the mid-surface of the corresponding shell-like body. The three-dimensional deformation gradient is found to involve the curvature tensors of the mid-surface in the spontaneous and the deformed states, the deformation gradient of the mid-surface, and the transverse deformation. Attention is also given to the coherency of the leaflets and to the area compatibility of the closed lipid bilayers (i.e., vesicles). A hyperelastic constitutive theory for lipid bilayers in the liquid phase is developed. In combination, the requirements of frame indifference and material symmetry yield a representation for the energy density of a lipid bilayer. This representation shows that three scalar invariants suffice to describe the constitutive response of a lipid bilayer exhibiting in-plane fluidity and transverse isotropy. In addition to exploring the geometrical and physical properties of these invariants, fundamental constitutively associated kinematical quantities are emphasized. On this basis, the effect on the energy density of assuming that the lipid bilayer is incompressible is considered. Lastly, a dimension reduction argument is used to extract an areal energy density per unit area from the three-dimensional energy density. This step explains the origin of spontaneous curvature in the areal energy density. Importantly, along with a standard contribution associated with the natural curvature of the lipid bilayer, our analysis indicates that constitutive asymmetry between the leaflets of the lipid bilayer gives rise to a secondary contribution to the spontaneous curvature.     

Mechanism of pH-triggered collapse of phosphatidylethanolamine liposomes stabilized by an ortho ester polyethyleneglycol lipid

The mechanism of pH-triggered destabilization of liposomes composed of a polyethyleneglycol-orthoester-distearoylglycerol lipid (POD) and phosphatidyl ethanolamine (PE) has been studied using an ANTS/DPX leakage and a lipid-mixing assay. We developed a kinetic model that relates POD hydrolysis to liposome collapse. This minimum-surface-shielding model describes the kinetics of the pH-triggered release of POD/PE liposomes. In the model, when acid-catalyzed hydrolysis lowers the mole percentage of POD on the liposome surface to a critical level, intervesicular lipid mixing is initiated, resulting in a burst of contents release. Two phases of content leakage are observed: a lag phase and a burst phase. During the lag phase, less than 20% of liposomal contents are released and the leakage begins to accelerate when approaching to the transition point. During the burst phase, the leakage rate is dependent on interbilayer contact. The burst phase occurs when the surface density of the PEG lipid is 2.3 +/- 0.6 mol%, regardless of the pH. Vesicles containing 4 mol% of a pH-insensitive PEG-lipid conjugate and 10% POD did not leak contents or collapse at any pH. These data are consistent with the stalk theory to describe the lamellar-to-inverted hexagonal phase transition and set a lower bound of approximately 16 PE lipids on the external monolayer as the contact site required for lipid mixing between two bilayers.