Bending modulus of lipid bilayers in a liquid-crystalline phase including an anomalous swelling regime estimated by neutron spin echo experiments

Dynamic structure factor of undulating vesicles: finite-size and spherical geometry effects with application to neutron spin echo experiments

We consider the dynamic structure factor (DSF) of quasi-spherical vesicles and present a generalization of an expression that was originally formulated by Zilman and Granek (ZG) for scattering from isotropically oriented quasi-flat membrane plaquettes. The expression is obtained in the form of a multi-dimensional integral over the undulating membrane surface. The new expression reduces to the original stretched exponential form in the limit of sufficiently large vesicles, i.e., in the micron range or larger. For much smaller unilamellar vesicles, deviations from the asymptotic, stretched exponential equation are noticeable even if one assumes that the Seifert-Langer leaflet density mode is completely relaxed and membrane viscosity is neglected. To avoid the need for an exhaustive numerical integration while fitting to neutron spin echo (NSE) data, we provide a useful approximation for polydisperse systems that tests well against the numerical integration of the complete expression. To validate the new expression, we performed NSE experiments on variable-size vesicles made of a POPC/POPS lipid mixture and demonstrate an advantage over the original stretched exponential form or other manipulations of the original ZG expression that have been deployed over the years to fit the NSE data. In particular, values of the membrane bending rigidity extracted from the NSE data using the new approximations were insensitive to the vesicle radii and scattering wavenumber and compared very well with expected values of the effective bending modulus ([Formula: see text]) calculated from results in the literature. Moreover, the generalized scattering theory presented here for an undulating quasi-spherical shell can be easily extended to other models for the membrane undulation dynamics beyond the Helfrich Hamiltonian and thereby provides the foundation for the study of the nanoscale dynamics in more complex and biologically relevant model membrane systems.

The relationship between structure and rheology in a three-dimensional sheared lamellar mesophase

The evolution of a lamellar mesophase from an initially disordered state under shear is examined using simulations of a mesoscale model based on a concentration field ψ that distinguishes the hydrophilic and hydrophobic components. The Landau-Ginzburg free-energy functional is augmented by a term that is minimised for sinusoidal modulations in the concentration field with wavelength λ = (2π/k), and the dynamical equations are the model H equations. The structure and rheology are determined by the relative magnitudes of the diffusion time for coarsening, (λ²/D) and the inverse of the strain rate ^-1, and the Ericksen number, which is the ratio of the shear stress and the layer stiffness. When the diffusion time is small compared with the inverse of the strain rate, there is a local formation of misaligned layers, which are deformed by the imposed flow. There is near-perfect ordering with isolated defects at low values of the Ericksen number, but the defects result in a significant increase in viscosity due to the high layer stiffness. At high values of the Ericksen number, the concentration field is deformed by the mean shear before layers form via diffusion. Cylindrical structures aligned along the flow direction form after about 8-10 strain units, and these evolve into layers with disorder through diffusion perpendicular to the flow. The layers are not perfectly ordered, even after hundreds of strain units, due to the creation and destruction of defects via shear. The excess viscosity is low because the layer stiffness is small compared with the applied shear at a high Ericksen number. This study provides guidance on how the material parameters and imposed flow can be tailored to achieve the desired rheological behaviour.

Neutron scattering studies on dynamics of lipid membranes

Neutron scattering methods are powerful tools for the study of the structure and dynamics of lipid bilayers in length scales from sub Å to tens to hundreds nm and the time scales from sub ps to μs. These techniques also are nondestructive and, perhaps most importantly, require no additives to label samples. Because the neutron scattering intensities are very different for hydrogen- and deuterium-containing molecules, one can replace the hydrogen atoms in a molecule with deuterium to prepare on demand neutron scattering contrast without significantly altering the physical properties of the samples. Moreover, recent advances in neutron scattering techniques, membrane dynamics theories, analysis tools, and sample preparation technologies allow researchers to study various aspects of lipid bilayer dynamics. In this review, we focus on the dynamics of individual lipids and collective membrane dynamics as well as the dynamics of hydration water.

Effect of encapsulated protein on the dynamics of lipid sponge phase: a neutron spin echo and molecular dynamics simulation study

Lipid membranes are highly mobile systems with hierarchical, time and length scale dependent, collective motions including thickness fluctuations, undulations, and topological membrane changes, which play an important role in membrane interactions. In this work we have characterised the effect of encapsulating two industrially important enzymes, β-galactosidase and aspartic protease, in lipid sponge phase nanoparticles on the dynamics of the lipid membrane using neutron spin echo (NSE) spectroscopy and molecular dynamics (MD) simulations. From NSE, reduced membrane dynamics were observed upon enzyme encapsulation, which were dependent on the enzyme concentration and type. By fitting the intermediate scattering functions (ISFs) with a modified Zilman and Granek model including nanoparticle diffusion, an increase in membrane bending rigidity was observed, with a larger effect for β-galactosidase than aspartic protease at the same concentration. MD simulations for the system with and without aspartic protease showed that the lipids relax more slowly in the system with protein due to the replacement of the lipid carbonyl-water hydrogen bonds with lipid-protein hydrogen bonds. This indicates that the most likely cause of the increase in membrane rigidity observed in the NSE measurements was dehydration of the lipid head groups. The dynamics of the protein itself were also studied, which showed a stable secondary structure of protein over the simulation, indicating no unfolding events occurred.

A Mechanical Mechanism for Vitamin E Acetate in E-cigarette/Vaping-Associated Lung Injury

The outbreak of electronic-cigarette/vaping-associated lung injury (EVALI) has made thousands ill. This lung injury has been attributed to a physical interaction between toxicants from the vaping solution and the pulmonary surfactant. In particular, studies have implicated vitamin E acetate as a potential instigator of EVALI. Pulmonary surfactant is vital to proper respiration through the mechanical processes of adsorption and interface stability to achieve and maintain low surface tension at the air-liquid interface. Using neutron spin echo spectroscopy, we investigate the impact of vitamin E acetate on the mechanical properties of two lipid-only pulmonary surfactant mimics: pure 1,2-dipalmitoyl-sn-glycero-3-phosphocholine and a more comprehensive lipid mixture. It was found that increasing vitamin E acetate concentration nonlinearly increased membrane fluidity and area compressibility to a plateau. Softer membranes would promote adsorption to the air-liquid interface during inspiration as well as collapse from the interface during expiration. These findings indicate the potential for the failure of the pulmonary surfactant upon expiration, attributed to monolayer collapse. This collapse could contribute to the observed EVALI signs and symptoms, including shortness of breath and pneumonitis.

On the Origin of the Anomalous Behavior of Lipid Membrane Properties in the Vicinity of the Chain-Melting Phase Transition

Biomembranes are key objects of numerous studies in biology and biophysics of great importance to medicine. A few nanometers thin quasi two-dimensional liquid crystalline membranes with bending rigidity of a few kT exhibit unusual properties and they are the focus of theoretical and experimental physics. The first order chain-melting phase transition of lipid membranes is observed to be accompanied by a pseudocritical behavior of membrane physical-chemical properties. However, the investigation of the nature of the anomalous swelling of a stack of lipid membranes in the vicinity of the transition by different groups led to conflicting conclusions about the level of critical density fluctuations and their impact on the membrane softening. Correspondingly, conclusions about the contribution of Helfrich's undulations to the effect of swelling were different. In our work we present a comprehensive complementary neutron small-angle and spin-echo study directly showing the presence of significant critical fluctuations in the vicinity of the transition which induce membrane softening. However, contrary to the existing paradigm, we demonstrate that the increased undulation forces cannot explain the anomalous swelling. We suggest that the observed effect is instead determined by the dominating increase of short-range entropic repulsion.

Quasi-Elastic Neutron Scattering Studies on Hydration Water in Phospholipid Membranes

The dynamic behavior of hydration water in phospholipid membranes has been investigated to understand the relationship between water and biological molecules using various experimental techniques. Quasi-elastic neutron scattering (QENS) is an effective method for this purpose because the dynamic behaviors of both water and lipid molecules could be identified by using selective deuteration. In addition, the measurable ranges from the 10⁻¹² to 10⁻⁹ s time scale and the 10⁻¹¹ to 10⁻⁸ m length scale are suitable to investigate the slowing down of water molecules due to their interaction with lipid membranes. In this mini-review, QENS experiments on the dynamic behavior of hydration water molecules in neighboring phospholipid membranes are summarized.

Interleaflet coupling of n-alkane incorporated bilayers

The relationship between the membrane bending modulus (κ) and compressibility modulus (K_A) depends on the extent of coupling between the two monolayers (leaflets). Using neutron spin echo (NSE) spectroscopy, we investigate the effects of n-alkanes on the interleaflet coupling of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) bilayers. Structural studies with small-angle X-ray and neutron scattering (SAXS and SANS) showed that the bilayer thickness increased with increasing n-alkane length, while NSE suggested that the bilayers became softer. Additional measurements of the membrane thickness fluctuations with NSE suggested that the changes in elastic moduli were due to a decrease in coupling between the leaflets upon addition of the longer n-alkanes. The decreased coupling with elongating n-alkane length was explained based on the n-alkane distribution within the bilayers characterized by SANS measurement of bilayers composed of protiated DPPC and deuterated n-alkanes. A higher fraction of the incorporated long n-alkanes were concentrated at the central plane of the bilayers and decreased the physical interaction between the leaflets. Using NSE and SANS, we successfully correlated changes in the mesoscopic collective dynamics and microscopic membrane structure upon incorporation of n-alkanes.

Phospholipid Bilayer Softening Due to Hydrophobic Gold Nanoparticle Inclusions

Liposome-nanoparticle assemblies (LNAs) are vital in the context of novel targeted drug-delivery systems, in addition to investigating nanoparticle-lipid bilayer interactions. Quantifying membrane structural properties and dynamics in presence of nanoparticle inclusions provides a simple model to elucidate nanoparticle effects on membrane biophysical properties. We present experimental evidences of bilayer softening due to small hydrophobic gold nanoparticle inclusions. LNA structure has been investigated by a combination of cryo-transmission electron microscopy, dynamic light scattering, and small-angle neutron scattering. Neutron spin echo spectroscopy demonstrated a remarkable ∼15% bending modulus decrease for LNAs relative to pure liposomes. Clear dependence of bending modulus on gold nanoparticle diameter and concentration was observed from our observations. Our findings point toward local bilayer fluidization by nanoparticle inclusions leading to an overall bilayer softening. These findings add valuable information to liposomal drug-delivery vehicle design and membrane biophysics research.

Small Cationic Peptides: Influence of Charge on Their Antimicrobial Activity

The first stage of the action mechanism of small cationic peptides with antimicrobial activity is ruled by electrostatic interactions between the peptide and the pathogen cell membrane. Thus, an increase in its activity could be expected with an increase in the positive charge on the peptide. By contrast, the opposite behavior has been observed when the charge increases to reach a critical value, beyond which the activity falls. This work studies the perturbation effects in a cell membrane model for two small cationic peptides with similar length and morphology but with different cationic charges. The synthesis and antibacterial activity of the two peptides used in this study are described. The thermodynamic study associated with the insertion of these peptides into the membrane and the perturbing effects on the bilayer structure provide valuable insights into the molecular action mechanism associated with the charge of these small cationic peptides.

Analytical calculation of the lipid bilayer bending modulus

Bending and Gaussian moduli of a homogenious single-component lipid bilayer are calculated analytically using microscopic model of the lipid hydrocarbon chains. The approach allows for thermodynamic averaging over different chains conformations. Each chain is modeled as a flexible string with finite bending rigidity and an incompressible cross-section area. The interchain steric repulsion is accounted for self-consistently determined single-chain confining parabolic potential. The model provides a simple analytical expression for the membrane bending modulus, which falls within a range of experimental values. An observed dependence of the modulus on hydrocarbon chain length is also reproduced. Correspondence between our microscopic model and the membrane theory of elasticity is established.

Anomalous partitioning of water in coexisting liquid phases of lipid multilayers near 100% relative humidity

Ternary lipid mixtures incorporating cholesterol are well-known to phase separate into liquid-ordered (L(o)) and liquid-disordered (L(d)) phases. In multilayers of these systems, the laterally phase separated domains register in columnar structures with different bilayer periodicities, resulting in hydrophobic mismatch energies at the domain boundaries. In this paper, we demonstrate via synchrotron-based X-ray diffraction measurements that the system relieves the hydrophobic mismatch at the domain boundaries by absorbing larger amounts of inter-bilayer water into the L(d) phase with lower d-spacing as the relative humidity approaches 100%. The lamellar repeat distance of the L(d) phase swells by an extra 4 Å, well beyond the equilibrium spacing predicted by the inter-bilayer forces. This anomalous swelling is caused by the hydrophobic mismatch energy at the domain boundaries, which produces a surprisingly long-range effect. We also demonstrate that the d-spacings of the lipid multilayers at 100% relative humidity do not change when bulk water begins to condense on the sample.

Characterization of antimicrobial activity against Listeria and cytotoxicity of native melittin and its mutant variants

Antimicrobial peptides (AMPs) are relatively short peptides that have the ability to penetrate the cell membrane, form pores leading to cell death. This study compares both antimicrobial activity and cytotoxicity of native melittin and its two mutants, namely, melittin I17K (GIGAVLKVLTTGLPALKSWIKRKRQQ) with a higher charge and lower hydrophobicity and mutant G1I (IIGAVLKVLTTGLPALISWIKRKRQQ) of higher hydrophobicity. The antimicrobial activity against different strains of Listeria was investigated by bioassay, viability studies, fluorescence and transmission electron microscopy. Cytotoxicity was examined by lactate dehydrogenase (LDH) assay on mammalian Caco-2 cells. The minimum inhibitory concentration of native, mutant I17K, mutant G1I against Listeria monocytogenes F4244 was 0.315±0.008, 0.814±0.006 and 0.494±0.037μg/ml respectively, whereas the minimum bactericidal concentration values were 3.263±0.0034, 7.412±0.017 and 5.366±0.019μg/ml respectively. Lag time for inactivation of L. monocytogenes F4244 was observed at concentrations below 0.20 and 0.78μg/ml for native and mutant melittin I17K respectively. The antimicrobial activity against L. monocytogenes F4244 was in the order native>G1I>I17K. Native melittin was cytotoxic to mammalian Caco-2 cells above concentration of 2μg/ml, whereas the two mutants exhibited negligible cytotoxicity up to a concentration of 8μg/ml. Pore formation in cell wall/membrane was observed by transmission electron microscopy. Molecular dynamics (MD) simulation of native and its mutants indicated that (i) surface native melittin and G1I exhibited higher tendency to penetrate a mimic of bacterial cell membrane and (ii) transmembrane native and I17K formed water channel in mimics of bacterial and mammalian cell membranes.

Effect of shape and bending modulus on the properties of nematic lyotropic liquid crystals

Variation in the structure of the molecular aggregate associated with the increase of the TTAC concentration in the liquid crystal.

Intake of silica nanoparticles by giant lipid vesicles: influence of particle size and thermodynamic membrane state

The uptake of nanoparticles into cells often involves their engulfment by the plasma membrane and a fission of the latter. Understanding the physical mechanisms underlying these uptake processes may be achieved by the investigation of simple model systems that can be compared to theoretical models. Here, we present experiments on a massive uptake of silica nanoparticles by giant unilamellar lipid vesicles (GUVs). We find that this uptake process depends on the size of the particles as well as on the thermodynamic state of the lipid membrane. Our findings are discussed in the light of several theoretical models and indicate that these models have to be extended in order to capture the interaction between nanomaterials and biological membranes correctly.

Effect of millimetre waves on phosphatidylcholine membrane models: a non-thermal mechanism of interaction

The nonthermal biological effects of millimeter waves have been mainly attributed to the interaction with biological membranes. Several data on biomimetic membrane systems seem to support this conclusion. In this paper a mechanistic hypothesis is evaluated to explain such an interaction taking into account experimental NMR data on deuterium-labeled phospholipid vesicles. These data showed that millimeter waves induce a time and a hydration-dependent reduction of the water ordering around the phosphocholine headgroups. This effect is here interpreted as a change in membrane water partitioning, due to the coupling of the radiation with the fast rotational dynamics of bound water molecules, that results in a measurable relocation of water molecules from the inner to the outer binding regions of the membrane interface. When millimeter wave exposure is performed in the vicinity of the transition point, this effect can lead to an upward shift of the membrane phase transition temperature from the fluid to the gel phase. At a macroscopic level, this unique sensitivity may be explained by the universal dynamic behaviour of the membranes in the vicinity of the transition point, where a pretransitional increase of membrane area fluctuations, i.e., of the mean area per phospholipid headgroup, is observed. Exposure to millimeter waves increases the above fluctuations and enhances the second order character of the transition.

Poisson's Ratio and Young's Modulus of Lipid Bilayers in Different Phases

A general computational method is introduced to estimate the Poisson's ratio for membranes with small thickness. In this method, the Poisson's ratio is calculated by utilizing a rescaling of inter-particle distances in one lateral direction under periodic boundary conditions. As an example for the coarse grained lipid model introduced by Lenz and Schmid, we calculate the Poisson's ratio in the gel, fluid, and interdigitated phases. Having the Poisson's ratio, enable us to obtain the Young's modulus for the membranes in different phases. The approach may be applied to other membranes such as graphene and tethered membranes in order to predict the temperature dependence of its Poisson's ratio and Young's modulus.

The dynamic action mechanism of small cationic antimicrobial peptides

Inhomogeneities in the pathogen membrane induced by the presence of small cationic peptides are key to explaining their molecular action.

Bending stiffness of biological membranes: what can be measured by neutron spin echo?

Large vesicles obtained by the extrusion method represent adequate membrane models to probe membrane dynamics with neutron radiation. Particularly, the shape fluctuations around the spherical average topology can be recorded by neutron spin echo (NSE). In this paper we report on the applicable theories describing the scattering contributions from bending-dominated shape fluctuations in diluted vesicle dispersions, with a focus on the relative relevance of the master translational mode with respect to the internal fluctuations. Different vesicle systems, including bilayer and non-bilayer membranes, have been scrutinized. We describe the practical ranges where the exact theory of bending fluctuations is applicable to obtain the values of the bending modulus from experiments, and we discuss about the possible internal modes that could be alternatively contributing to shape fluctuations.

The intermediate scattering function for lipid bilayer membranes: from nanometers to microns

A numerical scheme based upon established hydrodynamic and elastic considerations is introduced and used to predict the intermediate scattering function for lipid bilayer membranes. The predictions span multiple wavelength regimes, including those studied by dynamic light scattering (DLS; microns) and neutron spin-echo (NSE) spectroscopy (10-100 nm). The results validate a recent theory specific to the NSE regime and expose slight inaccuracies associated with the theoretical results available in the DLS regime. The assumptions that underlie both our numerical methods and the related theoretical predictions are reviewed in detail to explain when certain results can be applied to experiment and where caution must be exercised.

Chemical and mechanical impact of silica nanoparticles on the phase transition behavior of phospholipid membranes in theory and experiment

The interaction of nanoparticles (NPs) with lipid membranes is an integral step in the interaction of NPs and living cells. During particle uptake, the membrane has to bend. Due to the nature of their phase diagram, the modulus of compression of these membranes can vary by more than one order of magnitude, and thus both the thermodynamic and mechanical aspects of the membrane have to be considered simultaneously. We demonstrate that silica NPs have at least two independent effects on the phase transition of phospholipid membranes: 1), a chemical effect resulting from the finite instability of the NPs in water; and 2), a mechanical effect that originates from a bending of the lipid membrane around the NPs. Here, we report on recent experiments that allowed us to clearly distinguish both effects, and present a thermodynamic model that includes the elastic energy of the membranes and correctly predicts our findings both quantitatively and qualitatively.

Combination of the CHARMM27 force field with united-atom lipid force fields

Computer simulations offer a valuable way to study membrane systems, from simple lipid bilayers to large transmembrane protein complexes and lipid-nucleic acid complexes for drug delivery. Their accuracy depends on the quality of the force field parameters used to describe the components of a particular system. We have implemented the widely used CHARMM22 and CHARMM27 force fields in the GROMACS simulation package to (i) combine the CHARMM22 protein force field with two sets of united-atom lipids parameters; (ii) allow comparisons of the lipid CHARMM27 force field with other lipid force fields or lipid-protein force field combinations. Our tests do not show any particular issue with the combination of the all-atom CHARMM22 force field with united-atoms lipid parameters, although pertinent experimental data are lacking to assess the quality of the lipid-protein interactions. The conversion utilities allow automatic generation of GROMACS simulation files with CHARMM nucleic acids and protein parameters and topologies, starting from pdb files using the standard GROMACS pdb2gmx method. CMAP is currently not implemented.

Interpreting membrane scattering experiments at the mesoscale: the contribution of dissipation within the bilayer

Neutron spin-echo spectroscopy provides a means to study membrane undulation dynamics over length scales roughly spanning 10-100 nanometers. Modern interpretation of these measurements relies on the theoretical predictions of Zilman and Granek; however, it is necessary to introduce an anomalously large solvent viscosity within this theory to obtain quantitative agreement with experiment. An extended theoretical treatment is presented that includes the effects of internal dissipation within the bilayer. Within the length and time regimes appropriate to neutron spin-echo experiments, the results of Zilman and Granek are largely recovered, except that the bilayer curvature modulus kappa appearing in their theory must be replaced with an effective dynamic curvature modulus kappa =kappa+2d(2)k(m), where d is a distance comparable to the monolayer thickness (the height of the neutral surface from bilayer midplane) and k(m) is the monolayer compressibility modulus. Direct comparison between theory and experiment becomes possible without any rescaling of physical parameters.

Bending elasticity of saturated and monounsaturated phospholipid membranes studied by the neutron spin echo technique

We have used neutron spin echo (NSE) spectroscopy to study the effect of bilayer thickness and monounsaturation (existence of a single double bond on one of the aliphatic chains) on the physical properties of unilamellar vesicles. The bending elasticity of saturated and monounsaturated phospholipid bilayers made of phospholipids with alkyl chain length ranging from 14 to 20 carbons was investigated. The bending elasticity κ(c) of phosphatidylcholines (PCs) in the liquid crystalline (L(α)) phase ranges from 0.38 × 10(-19) J for 1,2-dimyristoyl-sn-glycero-3-phosphocholine to 0.64 × 10(-19) J for 1,2-dieicosenoyl-sn-glycero-3-phosphocholine. It was confirmed that, contrary to the strong effect on the main transition temperature, the monounsaturation has a limited influence on the bending elasticity of lipid bilayers. In addition, when the area modulus K(A) varies little with chain unsaturation or length, the elastic ratios (κ(c)/K(A))(1/2) of saturated and monounsaturated phospholipid bilayers varies linearly with lipid hydrophobic thickness d which agrees well with the theory of ideal fluid membranes.