Model-based approaches for the determination of lipid bilayer structure from small-angle neutron and X-ray scattering data

Some of our recent work has resulted in the detailed structures of fully hydrated, fluid phase phosphatidylcholine (PC) and phosphatidylglycerol (PG) bilayers. These structures were obtained from the joint refinement of small-angle neutron and X-ray data using the scattering density profile (SDP) models developed by Ku?erka et al. (Biophys J 95:2356–2367, 2008; J Phys Chem B 116:232–239, 2012). In this review, we first discuss models for the standalone analysis of neutron or X-ray scattering data from bilayers, and assess the strengths and weaknesses inherent to these models. In particular, it is recognized that standalone data do not contain enough information to fully resolve the structure of naturally disordered fluid bilayers, and therefore may not provide a robust determination of bilayer structure parameters, including the much-sought-after area per lipid. We then discuss the development of matter density-based models (including the SDP model) that allow for the joint refinement of different contrast neutron and X-ray data, as well as the implementation of local volume conservation within the unit cell (i.e., ideal packing). Such models provide natural definitions of bilayer thicknesses (most importantly the hydrophobic and Luzzati thicknesses) in terms of Gibbs dividing surfaces, and thus allow for the robust determination of lipid areas through equivalent slab relationships between bilayer thickness and lipid volume. In the final section of this review, we discuss some of the significant findings/features pertaining to structures of PC and PG bilayers as determined from SDP model analyses.     

Lipid bilayer ultrastructure: Electron density profiles and chain tilt angles as determined by X-ray diffraction

High resolution (6 Å) electron density profiles have been computed on an absolute electron density scale for bilayers composed of both saturated fatty acids and fatty acids associated with the alkaline earth series of divalent cations. Low-angle X-ray diffraction data have been interpreted by an isomorphous replacement technique. The position on the X-ray film of discrete wide-angle reflections has provided direct information on the hydrocarbon chain packing and chain tilt in these bilayers. These results have been correlated to an electron microscopy study of the same bilayers (Waldbilling, R. C., Robertson J. D. and McIntosh, T.J. (1976) Biochim. Biophys. Acta 448, 1–14) and also to X-ray diffraction studies of fatty acid crystals. A method for forming and structurally analyzing bilayers of well defined chemical asymmetry is also described.     

Lipid bilayer ultrastructure. Electron density profiles and chain tilt angles as determined by X-ray diffraction.

High resolution (6A) electron density profiles have been computed on an absolute electron density scale for bilayers composed of both saturated fatty acids and fatty acids associated with the alkaline earth series of divalent cations. Lowangle X-ray diffraction data have been interpreted by an isomorphous replacement technique. The position on the X-ray film of discrete wide-angle reflections has provided direct information on the hydrocarbon chain packing and chain tilt in these bilayers. These results have been correlated to an electron microscopy study of the same bilayers (Waldbilling, R. C., Robertson, J.D. and McIntosh, T. J. (1976) Biochim. Biophys. Acta 448, 1-14) and also to X-ray diffraction studies of fatty acid crystals. A method for forming and structurally analyzing bilayers of well defined chemical asymmetry is also described.     

Area per molecule and distribution of water in fully hydrated dilauroylphosphatidylethanolamine bilayers

The area per lipid molecule for fully hydrated dilauroylphosphatidylethanolamine (DLPE) has been obtained in both the gel and liquid-crystalline states by combining wide-angle X-ray diffraction, electron density profiles, and previously published dilatometry results [Wilkinson, D. A., & Nagle, J. F. (1981) Biochemistry 20, 187-192]. The molecular area increases from 41.0 +/- 0.2 to 49.1 +/- 1.2 A2 upon melting from the gel to liquid-crystalline phase. The thickness of the bilayer, as measured from the electron density profiles, decreases about 4 A upon melting, from 45.2 +/- 0.3 to 41.0 +/- 0.6 A. A somewhat unexpected result is that the fluid layer between fully hydrated bilayers is the same in both gel and liquid-crystalline phases and is only about 5 A thick. From these data, plus the volume of the anhydrous DLPE molecule, it is possible to determine the number of water molecules per lipid and their approximate distribution relative to the lipid molecule. Our analysis shows that there are about 7 and 9 waters per DLPE molecule in the gel and liquid-crystalline phases, respectively. About half of the water is located in the fluid space between adjacent bilayers, and the remaining waters are intercalated into the bilayer, presumably in the head group region. There are significantly fewer water molecules in the fluid spaces between DLPE bilayers than in the fluid spaces in gel- or liquid-crystalline-phase phosphatidylcholine bilayers. This small fluid space in PE bilayers could arise from interbilayer hydrogen bond formation through the water molecules or electrostatic interactions between the amine and phosphate groups on apposing bilayers.     

Hydration force and bilayer deformation: a reevaluation

The hydration repulsive force between lipid bilayers and the deformability of both gel and liquid-crystalline bilayers have been quantitated by an X-ray diffraction analysis of osmotically stressed liposomes. Both sampling theorem reconstructions and electron density distributions were calculated from diffraction data obtained from multilayers with applied osmotic pressures of 0-50 atm. The bilayer thickness and area per lipid molecule remain nearly constant (to within about 4%) in this pressure range, as adjacent bilayers move from their equilibrium separation in excess water to within 2-4 A of each other. This analysis indicates that the bilayers are relatively incompressible. This results differs from previously published X-ray diffraction studies of bilayer compressibility but agrees with direct mechanical measurements of the bilayer compressibility modulus. It is also found that the hydration repulsive force decays exponentially with separation between bilayers with a decay constant of 1.4 A for gel-state dipalmitoylphosphatidylcholine and 1.7 A for liquid-crystalline egg phosphatidylcholine bilayers. This implies that the exponential decay constant is not necessarily equal to the diameter of a water molecule, as has been previously suggested on experimental and theoretical grounds.     

Revisiting the bilayer structures of fluid phase phosphatidylglycerol lipids: Accounting for exchangeable hydrogens

We recently published two papers detailing the structures of fluid phase phosphatidylglycerol (PG) lipid bilayers (Ku?erka et al., 2012 J. Phys. Chem. B 116: 232–239; Pan et al., 2012 Biochim. Biophys. Acta Biomembr. 1818: 2135–2148), which were determined using the scattering density profile model. This hybrid experimental/computational technique utilizes molecular dynamics simulations to parse a lipid bilayer into components whose volume probabilities follow simple analytical functional forms. Given the appropriate scattering densities, these volume probabilities are then translated into neutron scattering length density (NSLD) and electron density (ED) profiles, which are used to jointly refine experimentally obtained small angle neutron and X-ray scattering data. However, accurate NSLD and ED profiles can only be obtained if the bilayer's chemical composition is known. Specifically, in the case of neutron scattering, the lipid's exchangeable hydrogens with aqueous D₂O must be accounted for, as they can have a measureable effect on the resultant lipid bilayer structures. This was not done in our above-mentioned papers. Here we report on the molecular structures of PG lipid bilayers by appropriately taking into account the exchangeable hydrogens. Analysis indicates that the temperature-averaged PG lipid areas decrease by 1.5 to 3.8 Å², depending on the lipid's acyl chain length and unsaturation, compared to PG areas when hydrogen exchange was not taken into account.     

omega-6 and omega-3 fatty acids: monolayer packing and effects on bilayer permeability and cholesterol exchange.

It has been suggested that the polyunsaturated omega-3 fatty acid, docosahexaenoic acid (DHA), can adopt unique closely packed arrays in lipid bilayers (Glomset and Applegate. (1986) J. Lipid Res. 27, 658-680). These conformations are predicted on the basis of molecular dynamics calculations and are in contrast to the expanded conformations characteristic of omega-6 unsaturated fatty acids. It has also been suggested that close packing of omega-3 acyl chains could have a substantial affect on the physical properties of lipid bilayers (e.g. permeability). We report here some experimental tests of these predictions. Surface pressure-area experiments have been carried out on DHA and its mixtures with stearic and oleic acids. At low surface pressures DHA is more expanded than oleic acid. Extrapolation to the high surface pressures characteristic of lipid bilayers indicates that the area per molecule of DHA is only marginally less than that for oleic acid. Thus there is no compelling evidence to suggest that the average area per molecule of the omega-3 fatty acid is substantially different from the omega-6 fatty acid at high surface pressures. Experiments also show that the permeability of bilayers to glucose and the rates of dissociation of pyrenyl cholesterol from bilayers were similar for bilayers containing DHA compared to bilayers containing oleic acid or linoleic acid.     

Effects of n-alkanes on the morphology of lipid bilayers A freeze-fracture and negative stain analysis

The effect of $\text{n-}\text{alkanes}$ on the ultrastructure of lipid bilayers has been investigated using freeze-fracture and negative stain electron microscopy. It has been found that the morphology of bilayers containing the long alkane tetradecane is quite different from bilayers containing the short alkane hexane. The smooth fracture faces of gel and liquid crystalline state bilayers are unmodified by tetradecane. However, hexane dramatically alters the hydrophobic bilayer interior, producing large (20 to 50 nm) mounds and depressions in the fracture faces. The fracture steps in these multilayer preparations containing hexane are variable in thickness and often considerably wider than the corresponding fracture steps in multilayers which contain tetradecane or are solvent-free. Alkanes also modify the structure of the P_β′ or ‘banded’ phase of phosphatidylcholine bilayers. The incorporation of tetradecane removes the banded structure from both the bilayer's hydrophilic surface, as viewed by negative staining, and the bilayer's hydrophobic interior, as viewed by the freeze-fracture technique. These results are consistent with X-ray diffraction data which imply that long alkanes are primarily located between adjacent lipid hydrocarbon chains in each monolayer of the bilayer, while short alkanes can partition into the geometric center of the bilayer between apposing monolayers.     

Membrane thinning effect of the beta-sheet antimicrobial protegrin

Lipid bilayers containing the antimicrobial peptide protegrin-1 (PG-1) were studied by lamellar X-ray diffraction. Previously, we have shown that the peptide exists in two distinct states when associated with lipid bilayers depending on the peptide concentration [Heller, W. T., Waring, A. J., Lehrer, R. I., and Huang, H. W. (1998) Biochemistry 37, 17331-17338]. For concentrations below a lipid-dependent threshold, PG-1 exhibits a unique oriented circular dichroism spectrum called the S state. X-ray experiments show that in this state PG-1 decreases the thickness of the lipid bilayer in proportion to the peptide concentration, similar to alamethicin's membrane thinning effect. This indicates that the S state is adsorbed in the headgroup region of the lipid bilayer, where the peptide is in an inactive state. For PG-1 above the threshold concentration, X-ray diffraction shows that the interaction between the peptide and the bilayer changes significantly. These results suggest that PG-1 has the same concentration-gated mechanism of action as alamethicin.     

Adhesion and merging of lipid bilayers: a method for measuring the free energy of adhesion and hemifusion

Lipid bilayers can be induced to adhere to each other by molecular mediators, and, depending on the lipid composition, such adhesion can lead to merging of the contacting monolayers in a process known as hemifusion. Such bilayer-bilayer reactions have never been systematically studied. In the course of our studies of membrane-active molecules, we encountered such reactions. We believe that they need to be understood whenever bilayer-bilayer interactions take place, such as during membrane fusion. For illustration, we discuss three examples: spontaneous adhesion between phospholipid bilayers induced by low pH, polymer-induced osmotic depletion attraction between lipid bilayers, and anionic lipid bilayers cross-bridged by multicationic peptides. Our purpose here is to describe a general method for studying such interactions. We used giant unilamellar vesicles, each of which was aspirated in a micropipette so that we could monitor the tension of the membrane and the membrane area changes during the bilayer-bilayer interaction. We devised a general method for measuring the free energy of adhesion or hemifusion. The results show that the energies of adhesion or hemifusion of lipid bilayers could vary over 2 orders of magnitude from −1 to −50 × 10⁻⁵ J/m² in these examples alone. Our method can be used to measure the energy of transition in each step of lipid transformation during membrane fusion. This is relevant for current research on membrane fusion, which focuses on how fusion proteins induce lipid transformations.     

The physical state of quick-frozen membranes and lipids

Lipid bilayers and biomembranes produce nearly identical calorimeter scans regardless of whether they are slowly cooled under near-equilibrium conditions or rapidly frozen at rates used in freeze-fracture electron microscopy. Except for the melting of ice at 273 K, for both cooling regimens no significant thermal events occur from 100 K to the usual gel to liquid crystal transition. The gel to liquid crystal transition itself is somewhat altered by rapid cooling when bilayers contain mixed lipid species. Combined with X-ray diffraction studies, the results indicate that quickly frozen bilayers are crystalline, but that the crystalline domains are quite small or otherwise disordered. In contrast to the behavior of lipids in bilayers, hexagonal-phase calcium cardiolipid easily forms a glass upon cooling.     

The molecular reorganization of lipid bilayers by osmium tetroxide. A spin-label study of orientation and restricted y-axis anisotropic motion in model membrane systems

Phospholipid dispersions spontaneously form oriented lamellar multilayers when dried onto glass slides. These oriented multilayers form useful model systems for studying the molecular dynamics of lipid bilayers. In order to examine the effects of osmium tetroxide on the orientation and motion of hydrocarbon chains in lipid bilayers, lecithin multilayers containing the spin label 3-doxyl-5α-cholestane (the 4′,4′-dimethyloxazolidine-N-oxyl derivative of 5α-cholestan-3-one) were prepared and examined by electron spin resonance spectroscopy. In egg lecithin multilayers at room temperature and 81% relative humidity the osmium tetroxide causes nearly complete loss of orientation and severe reduction of molecular motion. In contrast, the high degree of order in l-α-dipalmitoyl lecithin multilayers is not affected by exposure to osmium tetroxide vapors. Experiments are also reported on macroscopically disordered lecithin preparations, and the data support the conclusions drawn from the ordered lecithin multilayers that rotational mobility of the probe is severely reduced by fixation of the lipid chains.A simple mathematical model has been developed to account for the amplitude of the high-frequency (τ < 10^?8 sec) restricted y-axis anisotropic motion occurring in the bilayer plane. Since the y-axis is roughly parallel to the molecular axis of the rigid steroid spin label, this model enables quantitative comparisons of various degrees of restricted motion about the molecular axis.     

Charge-induced tilt in ordered-phase phosphatidylglycerol bilayers Evidence from x-ray diffraction

X-ray diffraction studies have been performed, as a function of water content, on dipalmitoyl phosphatidyl-glycerol bilayers, both in the charged state at pH 8.0 and in the protonated state at pH 1.5, using buffers of 1.5 M salt concentration. Measurements were made at 20°C, and the high-angle reflections indicated that the bilayers were in the ordered phase at both pH values. Lamellar diffractions were observed under all conditions studied. The lamellar repeat reached a limiting value of 62.4 Å (6.24 nm) at a water/lipid ratio of 0.24 at pH 8.0, and a limiting value of 67.3 Å (6.73 nm) at a water/lipid ratio of 0.22 at pH 1.5. The area per lipid molecule in the plane of the bilayer, deduced from the bilayer thickness and the lipid partial specific volume, is 48 Ų (0.48 nm²) at pH 8.0 and 37 Ų (0.37 nm²) at pH 1.5. The area per molecule in the plane perpendicular to the chain axes, deduced from the X-ray short spacings, is 40.5 Ų (0.405 nm²) at pH 8.0 and 39.2 Ų (0.392 nm²) at pH 1.5. Thus the lipid molecules are tilted by approx. 30° relative to the bilayer normal at pH 8.0, but are not essentially untilted at pH 1.5.     

Effects of hydrostatic pressure on the location of PRODAN in lipid bilayers: a FT-IR study

The effects of hydrostatic pressure on the location of 6-propionyl-2-(dimethylamino)naphthalene (PRODAN), an environmentally sensitive fluorescent probe, in phosphatidylcholine lipid bilayers have been studied by Fourier-transform infrared spectroscopy (FT-IR) over the pressure range of 0.001-25 kbar. The results derived from the PRODAN C = O stretching band, the correlation field splitting of the methylene scissoring mode, and the methylene symmetric stretching mode as well as the absorption of the naphthalene ring show that in the sample of 4% (w/w) PRODAN in dimyristoyl-L-alpha-phosphatidylcholine (DMPC) at pH 6.8, most of the PRODAN molecules are embedded in the bilayers. In contrast, at pH 3.0, PRODAN was found to reside either on the membrane surface or dispersed in water. Compared to DMPC, egg yolk phosphatidylcholine (egg PC), which contains a substantial amount of unsaturated fatty acyl chains, is more susceptible to PRODAN permeation. The present study shows that the pressure dependence of the location of PRODAN in lipid membranes is different from that of tetracaine, a local anesthetic, in lipid bilayers. The model regarding the PRODAN location in lipid bilayers derived from the present infrared data has been compared with that obtained with previous fluorescence studies.     

The application of solid-state NMR spectroscopy to study candesartan cilexetil (TCV-116) membrane interactions. Comparative study with the AT1R antagonist drug olmesartan

ΑΤ1 receptor (AT1R) antagonists exert their antihypertensive effects by preventing the vasoconstrictive hormone AngII to bind to the AT1 receptor. It has been proposed that these biological effects are mediated through a two-step mechanism reaction. In the first step, they are incorporated in the core of the lipid bilayers and in the second step they reach the active site of the receptor through lateral diffusion. In this model, drug/membrane interactions are key elements for the drugs achieving inhibition at the AT1 receptor. In this work, the interactions of the prodrug candesartan cilexetil (TCV-116) with lipid bilayers are studied at molecular detail. Solid-state ¹³C-CP/MAS, 2D ¹H-¹H NOESY NMR spectroscopy and in silico calculations are used. TCV-116 and olmesartan, another drug which acts as an AT1R antagonist are compared for their dynamic effects in lipid bilayers using solid-state ²H-NMR. We find a similar localization of TCV-116 compared to other AT1 antagonists in the intermediate polar region. In addition, we can identify specific local interactions. These interactions may be associated in part with the discrete pharmacological profiles observed for different antagonists.     

The adsorption of adrenocorticotropin-(1-24)-tetracosapeptide to lecithin bilayer membranes formed from liposomes

The interaction of the peptide hormone adrenocorticotropin (ACTH_1-24) with solvent-free planar lipid bilayers has been studied by use of the capacitance minimization method. The membranes were formed from artificial vesicles according to the method described by Schindler. In contrast to analogous studies with hexane-containing membranes, experiments with these vesicle-derived bilayers were completely reproducible and gave no indication that ACTH_1-24 spans such hexane-free bilayers.     

Crystalline anhydrous Ca-phosphatidylserine bilayers

The nature of the Ca-phosphatidylserine complex has been investigated by nuclear magnetic resonance and X-ray diffraction. Ca⁺ binding to the lipid polar group involves the phosphate group and liberates water of hydration from the interbilayer space and from the binding sites of the lipid polar group. Consequently the packing of the lipid polar group becomes tighter and the segmental motion of the phosphate group is reduced. A tightly self-associated, dehydrated (“hydrophobic”) Ca-phosphatidylserine complex is formed with crystalline hydrocarbon chains. The overall bilayer structure is retained. The interaction of phosphatidylserine bilayers with Ca²⁺ is equivalent to an isothermal transition of the bilayer from the liquid crystalline to the crystal state.     

Membrane fusion promoters and inhibitors have contrasting effects on lipid bilayer structure and undulations

It has been established that the fusion of both biological membranes and phospholipid bilayers can be modulated by altering their lipid composition (Chernomordik et al., 1995 .J. Membr. Biol. 146:3). In particular, when added exogenously between apposing membranes, monomyristoylphosphatidylcholine (MMPC) inhibits membrane fusion, whereas glycerol monoleate (GMO), oleic acid (OA), and arachidonic acid (AA) promote fusion. This present study uses x-ray diffraction to investigate the effects of MMPC, GMO, OA, and AA on the bending and stability of lipid bilayers when bilayers are forced together with applied osmotic pressure. The addition of 10 and 30 mol% MMPC to egg phosphatidylcholine (EPC) bilayers maintains the bilayer structure, even when the interbilayer fluid spacing is reduced to approximately 3 A, and increases the repulsive pressure between bilayers so that the fluid spacing in excess water increases by 5 and 15 A, respectively. Thus MMPC increases the undulation pressure, implying that the addition of MMPC promotes out-of-plane bending and decreases the adhesion energy between bilayers. In contrast, the addition of GMO has minor effects on the undulation pressure; 10 and 50 mol% GMO increase the fluid spacing of EPC in excess water by 0 and 2 A, respectively. However, x-ray diffraction indicates that, at small interbilayer separations, GMO, OA, or AA converts the bilayer to a structure containing hexagonally packed scattering units approximately 50 A in diameter. Thus GMO, OA, or AA destabilizes bilayer structure as apposing bilayers are brought into contact, which could contribute to their role in promoting membrane fusion.     

Functional studies of N‐terminally modified CYP2J2 epoxygenase in model lipid bilayers

CYP2J2 epoxygenase is a membrane bound cytochrome P450 that converts omega‐3 and omega‐6 fatty acids into physiologically active epoxides. In this work, we present a comprehensive comparison of the effects of N‐terminal modifications on the properties of CYP2J2 with respect to the activity of the protein in model lipid bilayers using Nanodiscs. We demonstrate that the complete truncation of the N‐terminus changes the association of this protein with the E.coli membrane but does not disrupt incorporation in the lipid bilayers of Nanodiscs. Notably, the introduction of silent mutations at the N‐terminus was used to express full length CYP2J2 in E. coli while maintaining wild‐type functionality. We further show that lipid bilayers are essential for the productive use of NADPH for ebastine hydroxylation by CYP2J2. Taken together, it was determined that the presence of the N‐terminus is not as critical as the presence of a membrane environment for efficient electron transfer from cytochrome P450 reductase to CYP2J2 for ebastine hydroxylation in Nanodiscs. This suggests that adopting the native‐like conformation of CYP2J2 and cytochrome P450 reductase in lipid bilayers is essential for effective use of reducing equivalents from NADPH for ebastine hydroxylation.     

Inactivation of the sodium current in squid giant axons by hydrocarbons.

The voltage dependence of the steady state inactivation parameter (h infinity) of the sodium current in the squid giant axon is known to be shifted in the hyperpolarizing direction by hydrocarbons and it has been suggested that the shifts arise from thickness changes in the axon membrane, analogous to those produced in lipid bilayers (Haydon, D. A., and J. E. Kimura, 1981, J. Physiol. [Lond.], 312:57-70; Haydon, D. A., and B. W. Urban, 1983, J. Physiol. [Lond.], 338:435-450; Haydon, D. A., J. R. Elliott, and B. M. Hendry, 1984, Curr. Top. Membr. Transp., 22:445-482). This hypothesis has been tested systematically by examining the effects of a range of concentrations of cyclopentane on the high-frequency capacitance per unit area both of the axonal membrane and of lipid bilayers formed from monoolein plus squalene. A similar comparison has been made for cyclopropane and n-butane, both at a pressure of 1 atm. The results are consistent with the notion that thickness increases in the axolemma produce the shifts in h infinity. Except at very high concentrations, however, the thickness changes in the lipid bilayer were too small to account for the h infinity shifts. A possible explanation of this finding is discussed.