Dissipative curvature fluctuations in bilayer vesicles: Coexistence of pure-bending and hybrid curvature-compression modes

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.

Impact of transmembrane peptides on individual lipid motions and collective dynamics of lipid bilayers

The fluid nature of lipid bilayers is indispensable for the dynamic regulation of protein function and membrane morphology in biological membranes. Membrane-spanning domains of proteins interact with surrounding lipids and alter the physical properties of lipid bilayers. However, there is no comprehensive view of the effects of transmembrane proteins on the membrane's physical properties. Here, we investigated the effects of transmembrane peptides with different flip-flop-promoting abilities on the dynamics of a lipid bilayer employing complemental fluorescence and neutron scattering techniques. The quasi-elastic neutron scattering and fluorescence experiments revealed that lateral diffusion of the lipid molecules and the acyl chain motions were inhibited by the inclusion of transmembrane peptides. The neutron spin-echo spectroscopy measurements indicated that the lipid bilayer became more rigid but more compressible and the membrane viscosity increased when the transmembrane peptides were incorporated into the membrane. These results suggest that the inclusion of rigid transmembrane structures hinders individual and collective lipid motions by slowing down lipid diffusion and increasing interleaflet coupling. The present study provides a clue for understanding how the local interactions between lipids and proteins change the collective dynamics of the lipid bilayers, and therefore, the function of biological membranes.

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.

Nanoscale Bending Dynamics in Mixed-Chain Lipid Membranes

Lipids that have two tails of different lengths are found throughout biomembranes in nature, yet the effects of this asymmetry on the membrane properties are not well understood, especially when it comes to the membrane dynamics. Here we study the nanoscale bending fluctuations in model mixed-chain 14:0–18:0 PC (MSPC) and 18:0–14:0 PC (SMPC) lipid bilayers using neutron spin echo (NSE) spectroscopy. We find that despite the partial interdigitation that is known to persist in the fluid phase of these membranes, the collective fluctuations are enhanced on timescales of tens of nanoseconds, and the chain-asymmetric lipid bilayers are softer than an analogous chain-symmetric lipid bilayer with the same average number of carbons in the acyl tails, di-16:0 PC (DPPC). Quantitative comparison of the NSE results suggests that the enhanced bending fluctuations at the nanosecond timescales are consistent with experimental and computational studies that showed the compressibility moduli of chain-asymmetric lipid membranes are 20% to 40% lower than chain-symmetric lipid membranes. These studies add to growing evidence that the partial interdigitation in mixed-chain lipid membranes is highly dynamic in the fluid phase and impacts membrane dynamic processes from the molecular to mesoscopic length scales without significantly changing the bilayer thickness or area per lipid.

Biophysics of Membrane Stiffening by Cholesterol and Phosphatidylinositol 4,5-bisphosphate (PIP2)

Cell membranes regulate a wide range of phenomena that are implicated in key cellular functions. Cholesterol, a critical component of eukaryotic cell membranes, is responsible for cellular organization, membrane elasticity, and other critical physicochemical parameters. Besides cholesterol, other lipid components such as phosphatidylinositol 4,5-bisphosphate (PIP2) are found in minor concentrations in cell membranes yet can also play a major regulatory role in various cell functions. In this chapter, we describe how solid-state deuterium nuclear magnetic resonance (²H NMR) spectroscopy together with neutron spin-echo (NSE) spectroscopy can inform synergetic changes to lipid molecular packing due to cholesterol and PIP2 that modulate the bending rigidity of lipid membranes. Fundamental structure-property relations of molecular self-assembly are illuminated and point toward a length and time-scale dependence of cell membrane mechanics, with significant implications for biological activity and membrane lipid-protein interactions.

Cholesterol Stiffening of Lipid Membranes

Biomembrane order, dynamics, and other essential physicochemical parameters are controlled by cholesterol, a major component of mammalian cell membranes. Although cholesterol is well known to exhibit a condensing effect on fluid lipid membranes, the extent of stiffening that occurs with different degrees of lipid acyl chain unsaturation remains an enigma. In this review, we show that cholesterol locally increases the bending rigidity of both unsaturated and saturated lipid membranes, suggesting there may be a length-scale dependence of the bending modulus. We review our published data that address the origin of the mechanical effects of cholesterol on unsaturated and polyunsaturated lipid membranes and their role in biomembrane functions. Through a combination of solid-state deuterium NMR spectroscopy and neutron spin-echo spectroscopy, we show that changes in molecular packing cause the universal effects of cholesterol on the membrane bending rigidity. Our findings have broad implications for the role of cholesterol in lipid–protein interactions as well as raft-like mixtures, drug delivery applications, and the effects of antimicrobial peptides on lipid membranes.

Hydrodynamic shear dissipation and transmission in lipid bilayers

Vital biological processes, such as trafficking, sensing, and motility, are facilitated by cellular lipid membranes, which interact mechanically with surrounding fluids. Such lipid membranes are only a few nanometers thick and composed of a liquid crystalline structure known as the lipid bilayer. Here, we introduce an active, noncontact, two-point microrheology technique combining multiple optical tweezers probes with planar freestanding lipid bilayers accessible on both sides. We use the method to quantify both fluid slip close to the bilayer surface and transmission of fluid flow across the structure, and we use numerical simulations to determine the monolayer viscosity and the intermonolayer friction. We find that these physical properties are highly dependent on the molecular structure of the lipids in the bilayer. We compare ordered-phase with liquid disordered-phase lipid bilayers, and we find the ordered-phase bilayers to be 10 to 100 times more viscous but with 100 times less intermonolayer friction. When a local shear is applied by the optical tweezers, the ultralow intermonolayer friction results in full slip of the two leaflets relative to each other and as a consequence, no shear transmission across the membrane. Our study sheds light on the physical principles governing the transfer of shear forces by and through lipid membranes, which underpin cell behavior and homeostasis.

How cholesterol stiffens unsaturated lipid membranes

Cholesterol is an integral component of eukaryotic cell membranes and a key molecule in controlling membrane fluidity, organization, and other physicochemical parameters. It also plays a regulatory function in antibiotic drug resistance and the immune response of cells against viruses, by stabilizing the membrane against structural damage. While it is well understood that, structurally, cholesterol exhibits a densification effect on fluid lipid membranes, its effects on membrane bending rigidity are assumed to be nonuniversal; i.e., cholesterol stiffens saturated lipid membranes, but has no stiffening effect on membranes populated by unsaturated lipids, such as 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). This observation presents a clear challenge to structure-property relationships and to our understanding of cholesterol-mediated biological functions. Here, using a comprehensive approach-combining neutron spin-echo (NSE) spectroscopy, solid-state deuterium NMR (²H NMR) spectroscopy, and molecular dynamics (MD) simulations-we report that cholesterol locally increases the bending rigidity of DOPC membranes, similar to saturated membranes, by increasing the bilayer's packing density. All three techniques, inherently sensitive to mesoscale bending fluctuations, show up to a threefold increase in effective bending rigidity with increasing cholesterol content approaching a mole fraction of 50%. Our observations are in good agreement with the known effects of cholesterol on the area-compressibility modulus and membrane structure, reaffirming membrane structure-property relationships. The current findings point to a scale-dependent manifestation of membrane properties, highlighting the need to reassess cholesterol's role in controlling membrane bending rigidity over mesoscopic length and time scales of important biological functions, such as viral budding and lipid-protein interactions.

Transverse lipid organization dictates bending fluctuations in model plasma membranes

Membrane undulations play a vital role in many biological processes, including the regulation of membrane protein activity. The asymmetric lipid composition of most biological membranes complicates theoretical description of these bending fluctuations, yet experimental data that would inform any such a theory is scarce. Here, we used neutron spin-echo (NSE) spectroscopy to measure the bending fluctuations of large unilamellar vesicles (LUV) having an asymmetric transbilayer distribution of high- and low-melting lipids. The asymmetric vesicles were prepared using cyclodextrin-mediated lipid exchange, and were composed of an outer leaflet enriched in egg sphingomyelin (ESM) and an inner leaflet enriched in 1-palmitoyl-2-oleoyl-phosphoethanolamine (POPE), which have main transition temperatures of 37 °C and 25 °C, respectively. The overall membrane bending rigidity was measured at three temperatures: 15 °C, where both lipids are in a gel state; 45 °C, where both lipids are in a fluid state; and 30 °C, where there is gel-fluid co-existence. Remarkably, the dynamics for the fluid asymmetric LUVs (aLUVs) at 30 °C and 45 °C do not follow trends predicted by their symmetric counterparts. At 30 °C, compositional asymmetry suppressed the bending fluctuations, with the asymmetric bilayer exhibiting a larger bending modulus than that of symmetric bilayers corresponding to either the outer or inner leaflet. We conclude that the compositional asymmetry and leaflet coupling influence the internal dissipation within the bilayer and result in membrane properties that cannot be directly predicted from corresponding symmetric bilayers.

DMPC vesicle structure and dynamics in the presence of low amounts of the saponin aescin

Vesicle shape and bilayer parameters are studied by small-angle X-ray (SAXS) and small-angle neutron (SANS) scattering in the presence of the saponin aescin. Bilayer dynamics is studied by neutron spin-echo (NSE) spectroscopy.

Dissipative dynamics of fluid lipid membranes enriched in cholesterol

Cholesterol is an intriguing component of fluid lipid membranes: It makes them stiffer but also more fluid. Despite the enormous biological significance of this complex dynamical behavior, which blends aspects of membrane elasticity with viscous friction, their mechanical bases remain however poorly understood. Here, we show that the incorporation of physiologically relevant contents of cholesterol in model fluid membranes produces a fourfold increase in the membrane bending modulus. However, the increase in the compression rigidity that we measure is only twofold; this indicates that cholesterol increases coupling between the two membrane leaflets. In addition, we show that although cholesterol makes each membrane leaflet more fluid, it increases the friction between the membrane leaflets. This dissipative dynamics causes opposite but advantageous effects over different membrane motions: It allows the membrane to rearrange quickly in the lateral dimension, and to simultaneously dissipate out-of-plane stresses through friction between the two membrane leaflets. Moreover, our results provide a clear correlation between coupling and friction of membrane leaflets. Furthermore, we show that these rigid membranes are optimal to resist slow deformations with minimum energy dissipation; their optimized stability might be exploited to design soft technological microsystems with an encoded mechanics, vesicles or capsules for instance, useful beyond classical applications as model biophysical systems.

On scattered waves and lipid domains: detecting membrane rafts with X-rays and neutrons

In order to understand the biological role of lipids in cell membranes, it is necessary to determine the mesoscopic structure of well-defined model membrane systems. Neutron and X-ray scattering are non-invasive, probe-free techniques that have been used extensively in such systems to probe length scales ranging from angstroms to microns, and dynamics occurring over picosecond to millisecond time scales. Recent developments in the area of phase separated lipid systems mimicking membrane rafts will be presented, and the underlying concepts of the different scattering techniques used to study them will be discussed in detail.

Fluctuation dynamics of bilayer vesicles with intermonolayer sliding: experiment and theory

The presence of coupled modes of membrane motion in closed shells is extensively predicted by theory. The bilayer structure inherent to lipid vesicles is suitable to support hybrid modes of curvature motion coupling membrane bending with the local reorganization of the bilayer material through relaxation of the dilatational stresses. Previous experiments evidenced the existence of such hybrid modes facilitating membrane bending at high curvatures in lipid vesicles [Rodríguez-García, R., Arriaga, L.R., Mell, M., Moleiro, L.H., López-Montero, I., Monroy, F., 2009. Phys. Rev. Lett. 102, 128201.]. For lipid bilayers that are able to undergo intermonolayer sliding, the experimental fluctuation spectra are found compatible with a bimodal schema. The usual tension/bending fluctuations couple with the hybrid modes in a mechanical interplay, which becomes progressively efficient with increasing vesicle radius, to saturate at infinity radius into the behavior expected for a flat membrane. Grounded on the theory of closed shells, we propose an approximated expression of the bimodal spectrum, which predicts the observed dependencies on the vesicle radius. The dynamical features obtained from the autocorrelation functions of the vesicle fluctuations are found in quantitative agreement with the proposed theory.

Softening of phospholipid membranes by the adhesion of silica nanoparticles--as seen by neutron spin-echo (NSE)

The interactions between nanoparticles and vesicles are of significant interest both from a fundamental as well as from a practical point of view, as vesicles can serve as a model system for cell membranes. Accordingly the effect of nanoparticles that bind to the vesicle bilayer is very important with respect to understanding their biological impact and also may shed some light on the mechanisms behind the effect of nanotoxicity. In this study we have investigated the influence of small adsorbed silica nanoparticles (SiNPs) on the structure of zwitterionic DOPC vesicles. By a combination of SANS, cryo-TEM, and DLS, we observed that the SiNPs are bound to the outer vesicle surface without significantly affecting the vesicle structure. Most interestingly, by means of neutron spin-echo (NSE) local bilayer fluctuations were studied and one finds a small but marked decrease of the membrane rigidity upon binding of the nanoparticles. This surprising finding may be a relevant aspect for the further understanding of the effects that nanoparticles have on phospholipid bilayers.

Bilayer undulation dynamics in unilamellar phospholipid vesicles: effect of temperature, cholesterol and trehalose

We report a combined dynamic light scattering (DLS) and neutron spin-echo (NSE) study on the local bilayer undulation dynamics of phospholipid vesicles composed of 1,2-dimyristoyl-glycero-3-phosphatidylcholine (DMPC) under the influence of temperature and the additives cholesterol and trehalose. The additives affect vesicle size and self-diffusion. Mechanical properties of the membrane and corresponding bilayer undulations are tuned by changing lipid headgroup or acyl chain properties through temperature or composition. On the local length scale, changes at the lipid headgroup influence the bilayer bending rigidity κ less than changes at the lipid acyl chain: We observe a bilayer softening around the main phase transition temperature Tm of the single lipid system, and stiffening when more cholesterol is added, in concordance with literature. Surprisingly, no effect on the mechanical properties of the vesicles is observed upon the addition of trehalose.

Perfluorooctanoic acid rigidifies a model lipid membrane

We report a combined dynamic light scattering and neutron spin-echo (NSE) study on vesicles composed of the phospholipid 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine under the influence of varying amounts of perfluorooctanoic acid. We study local lipid bilayer undulations using NSE on time scales up to 200 ns. Similar to the effect evoked by cholesterol, we attribute the observed lipid bilayer stiffening to a condensing effect of the perfluorinated compound on the membrane.

Influence of charge density on bilayer bending rigidity in lipid vesicles: a combined dynamic light scattering and neutron spin-echo study

We report a combined dynamic light scattering and neutron spin-echo study on vesicles composed of the uncharged stabilizing lipid 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine (DMPC) and the cationic lipid 1,2-dioleoyl-3-trimethylammonium-propane (DOTAP). Mechanical properties of a model membrane and thus the corresponding bilayer undulation dynamics can be specifically tuned by changing its composition through lipid headgroup or acyl chain properties. We compare the undulation dynamics in lipid vesicles composed of DMPC/DOTAP to vesicles composed of a mixture of the uncharged helper lipid DMPC with the also uncharged reference lipid 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). We have performed dynamic light scattering on the lipid mixtures to investigate changes in lipid vesicle size and the corresponding center-of-mass diffusion. We study lipid translational diffusion in the membrane plane and local bilayer undulations using neutron spin-echo spectroscopy, on two distinct time scales, namely around 25 ns and around 150 ns. Finally, we calculate the respective bilayer bending rigidities κ for both types of lipid vesicles. We find that on the local length scale inserting lipid headgroup charge into the membrane influences the bilayer undulation dynamics and bilayer bending rigidity κ less than inserting lipid acyl chain unsaturation: We observe a bilayer softening with increasing inhomogenity of the lipid mixture, which could be caused by a hydrophobic mismatch between the acyl chains of the respective lipid components, causing a lateral phase segregation (domain formation) in the membrane plane.

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.

Lipid bilayers and membrane dynamics: insight into thickness fluctuations

Thickness fluctuations have long been predicted in biological membranes but never directly observed experimentally. Here, we utilize neutron spin echo spectroscopy to experimentally reveal such fluctuations in a pure, fully saturated, phosphocholine lipid bilayer system. These fluctuations appear as an excess in the dynamics of undulation fluctuations. Like the bending rigidity, the thickness fluctuations change dramatically as the lipid transition temperature is crossed, appearing to be completely suppressed below the transition. Above the transition, the relaxation rate is on the order of 100 ns and is independent of temperature. The amplitude of the thickness fluctuations is 3.7 Å ± 0.7 Å, which agrees well with theoretical calculations and molecular dynamics simulations. The dependence of the fluctuations on lipid tail lengths is also investigated and determined to be minimal in the range of 14 to 18 carbon tails.

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.

Advantages of statistical analysis of giant vesicle flickering for bending elasticity measurements

We show how to greatly improve precision when determining bending elasticity of giant unilamellar vesicles. Taking advantage of the well-known quasi-spherical model of liposome flickering, we analyze the full probability distributions of the configurational fluctuations instead of limiting the analysis to the second moment measurements only as usually done in previously published works. This leads to objective criteria to reject vesicles that do not behave according to the model. As a result, the confidence in the bending elasticity determination of individual vesicles that fit the model is improved and, consequently, the reproducibility of this measurement for a given membrane system. This approach uncovers new possibilities for bending elasticity studies like detection of minute influences by solutes in the buffer or into the membrane. In the same way, we are now able to detect the inhomogeneous behavior of giant vesicle systems such as the hazardous production of peroxide in bilayers containing fluorescent dyes.

Biological reactivity of nanoparticles: mosaics from optical microscopy videos of giant lipid vesicles

Emerging fields such as nanomedicine and nanotoxicology, demand new information on the effects of nanoparticles on biological membranes and lipid vesicles are suitable as an experimental model for bio-nano interaction studies. This paper describes image processing algorithms which stitch video sequences into mosaics and recording the shapes of thousands of lipid vesicles, which were used to assess the effect of CoFe(2)O(4) nanoparticles on the population of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine lipid vesicles. The applicability of this methodology for assessing the potential of engineered nanoparticles to affect morphological properties of lipid membranes is discussed.

Shape fluctuations of nearly spherical lipid vesicles and emulsion droplets

It is known that the relaxation of the shape fluctuations of nearly spherical lipid vesicles is accompanied by a lateral displacement of the monolayers, comprising their bilayers. In this work a dissipation mechanism of the mechanical energy stored in the fluctuation is revealed that concerns the viscous friction of the flow in the liquid around the vesicle caused by this displacement. The time correlation functions of each of the vesicle's fluctuation modes are calculated as a function of the mechanical and rheological properties of the system which are the tension of the vesicle bilayer, its bending elasticities at free and blocked flip-flop, the viscosities of the liquids bathing the bilayer, the friction coefficient between the two monolayers, as well as the vesicle's dimensions: its bilayer thickness and radius. The correlations of the shape fluctuations of nearly spherical emulsion droplets are also calculated for different viscosities of the liquid inside and outside the droplet.