MEDUSA: A cloud-based tool for the analysis of X-ray diffuse scattering to obtain the bending modulus from oriented membrane stacks.

An important mechanical property of cells is their membrane bending modulus, κ. Here, we introduce MEDUSA (MEmbrane DiffUse Scattering Analysis), a cloud-based analysis tool to determine the bending modulus, κ, from the analysis of X-ray diffuse scattering. MEDUSA uses GPU (graphics processing unit) accelerated hardware and a parallelized algorithm to run the calculations efficiently in a few seconds. MEDUSA's graphical user interface allows the user to upload 2-dimensional data collected from different sources, perform background subtraction and distortion corrections, select regions of interest, run the fitting procedure and output the fitted parameters, the membranes' bending modulus κ, and compressional modulus B.

Closer look at the calorimetric lower transition in lipid bilayers.

The thermal behavior of unilamellar vesicles has been revisited with differential scanning calorimetry to address the issue of whether it is essential to include interactions between neighboring bilayers in theories and simulations of the ripple phase. The issue focuses on the lower, aka pretransition, and the ripple phase that clearly exists between the lower and main transitions in multilamellar vesicles (MLV). We find anomalous thermal behavior in unilamellar vesicles (ULV) beginning at the same temperature as the lower transition in MLVs, but this feature is considerably broadened and somewhat weaker compared to the lower transition in MLVs. We ascribe this to the difficulty of packing a regular ripple pattern on small spheres. In agreement with a few reports of a ripple phase in direct images of single bilayers, we conclude that interactions between neighboring bilayers are not essential for the ripple phase in lipid bilayers.

Understanding the phase behavior of a protobiomembrane.

The rich thermotropic behavior of lipid bilayers is addressed using phenomenological theory informed by many experiments. The most recent experiment not yet addressed by theory has shown that the tilt modulus in DMPC lipid bilayers decreases dramatically as the temperature is lowered toward the main transition temperature T_{M}. It is shown that this behavior can be understood by introducing a simple free energy functional for tilt that couples to the area per molecule. This is combined with a chain melting free energy functional in which the area is the primary order parameter that is the driver of the main transition. Satisfactory agreement with experiment is achieved with values of the model parameters determined by experiments, but the transition is directly into the gel phase. The theory is then extended to include the enigmatic ripple phase by making contact with the most recent experimentally determined ripple structure.

Location of dopamine in lipid bilayers and its relevance to neuromodulator function.

Dopamine (DA) is a neurotransmitter that also acts as a neuromodulator, with both functions being essential to brain function. Here, we present the first experimental measurement of DA location in lipid bilayers using x-ray diffuse scattering, solid-state deuterium NMR, and electron paramagnetic resonance. We find that the association of DA with lipid headgroups as seen in electron density profiles leads to an increase of intermembrane repulsion most likely due to electrostatic charging. DA location in the lipid headgroup region also leads to an increase of the cross-sectional area per lipid without affecting the bending rigidity significantly. The order parameters measured by solid-state deuterium NMR decrease in the presence of DA for the acyl chains of PC and PS lipids, consistent with an increase in the area per lipid due to DA. Most importantly, these results support the hypothesis that three-dimensional diffusion of DA to target membranes could be followed by relatively more efficient two-dimensional diffusion to receptors within those membranes.

Structure of the gel phase of diC22:1PC lipid bilayers determined by x-ray diffraction.

High-resolution x-ray data are reported for the ordered phases of long-chain di-monounsaturated C22:1 phosphocholine lipid bilayers. Similar to PC lipids that have saturated chains, diC22:1PC has a subgel phase and a gel phase, but dissimilarly, we find no ripple phase. Our quantitative focus is on the structure of the gel phase. We have recorded 17 lamellar orders, indicating a very well-ordered structure. Fitting to a model provides the phases of the orders. The Fourier construction of the electron density profile has two well-defined headgroup peaks and a very sharp and deep methyl trough. The wide-angle scattering exhibits two Bragg rods that provide the area per molecule. They have an intensity pattern quite different than that of lipids with saturated chains. Models of chain packing indicate that ground state chain configurations are tilted primarily toward next nearest neighbors with an angle that is also consistent with the modeling of the electron density profile. Wide-angle modeling also indicates broken mirror symmetry between the monolayers. Our wide-angle results and our electron density profile together leads to the hypothesis that the sn-1 and sn-2 chains have equivalent penetration depths in contrast to the gel phase structure of lipids with saturated hydrocarbon chains.

The bending rigidity of the red blood cell cytoplasmic membrane.

An important mechanical property of cells is the membrane bending modulus, κ. In the case of red blood cells (RBCs) there is a composite membrane consisting of a cytoplasmic membrane and an underlying spectrin network. Literature values of κ are puzzling, as they are reported over a wide range, from 5 kBT to 230 kBT. To disentangle the contribution of the cytoplasmic membrane from the spectrin network, we investigated the bending of red blood cell cytoplasmic membranes (RBCcm) in the absence of spectrin and adenosine triphosphate (ATP). We used a combination of X-ray diffuse scattering (XDS), neutron spin-echo (NSE) spectrometry and Molecular Dynamics (MD) simulations. Our results indicate values of κ of order 4 kBT to 6 kBT, relatively small compared to literature values for most single component lipid bilayers. We suggest two ways this relative softness might confer biological advantage.

Measuring the bending modulus of lipid bilayers with cholesterol.

The effect of cholesterol on the bending modulus of DOPC lipid bilayers has become a controversial topic that has implications for methods of measuring the bending modulus. Recent results using neutron spin echo and nuclear magnetic resonance relaxation methods that involve linear transport properties have conflicted with earlier results from purely equilibrium experiments that do not involve linear transport properties. A general discussion indicates how one can be misled by data obtained by methods that involve linear transport properties. It is then shown specifically how the recent neutron spin echo results can be interpreted to agree with the earlier purely equilibrium experimental results, thereby resolving that conflict. Regarding the nuclear magnetic resonance relaxation method, it is noted that current interpretation of the data is unclear regarding the identity of the modulus that is involved, and an alternative interpretation is explored that does not disagree with the results of the equilibrium experiments.

Mechanical properties of lipid bilayers: a note on the Poisson ratio.

We investigate the Poisson ratio ν of fluid lipid bilayers, i.e., the question how area strains compare to the changes in membrane thickness (or, equivalently, volume) that accompany them. We first examine existing experimental results on the area- and volume compressibility of lipid membranes. Analyzing them within the framework of linear elasticity theory for homogeneous thin fluid sheets leads us to conclude that lipid membrane deformations are to a very good approximation volume-preserving, with a Poisson ratio that is likely about 3% smaller than the common soft matter limit . These results are fully consistent with atomistic simulations of a DOPC membrane at varying amount of applied lateral stress, for which we instead deduce ν by directly comparing area- and volume strains. To assess the problematic assumption of transverse homogeneity, we also define a depth-resolved Poisson ratio ν(z) and determine it through a refined analysis of the same set of simulations. We find that throughout the membrane's thickness, ν(z) is close to the value derived assuming homogeneity, with only minor variations of borderline statistical significance.

Area Compressibility Moduli of the Monolayer Leaflets of Asymmetric Bilayers from Simulations.

Extraction from simulations of the area compressibility moduli of the monolayers in a bilayer is considered theoretically. A statistical mechanical derivation shows that the bilayer modulus is the sum of the two monolayer moduli, as is often supposed but contrary to a recent study. Seemingly plausible assumptions regarding fluctuations are tested rigorously. Prospects for future research are discussed.

Revisiting Volumes of Lipid Components in Bilayers.

In addition to obtaining the highly precise volumes of lipids in lipid bilayers, it has been desirable to obtain the volumes of parts of each lipid, such as the methylenes and terminal methyls on the hydrocarbon chains and the head group. Obtaining such component volumes from experiment and from simulations is re-examined, first by distinguishing methods based on apparent versus partial molar volumes. Although somewhat different, both these methods give results that are counterintuitive and that differ from results obtained by a more local method that can only be applied to simulations. These comparisons reveal differences in the average methylene component volume that result in larger differences in the head group component volumes. Literature experimental volume data for unsaturated phosphocholines and for alkanes have been used and new data have been acquired for saturated phosphocholines. Data and simulations cover extended ranges of temperature to assess both the temperature and chain length dependence of the component volumes. A new method to refine the determination of component volumes is proposed that uses experimental data for different chain lengths at temperatures guided by the temperature dependence determined in simulations. These refinements enable more precise comparisons of the component volumes of different lipids and alkanes in different phases. Finally, the notion of free volume is extended to components using the Lennard-Jones radii to estimate the excluded volume of each component. This analysis reveals that head group free volumes are relatively independent of thermodynamic phase, whereas both the methylene and methyl free volumes increase dramatically when bilayers transition from gel to fluid.

Structure of gel phase DPPC determined by X-ray diffraction.

High resolution low angle x-ray data are reported for the gel phase of DPPC lipid bilayers, extending the previous q range of 1.0 Å-1 to 1.3 Å-1, and employing a new technique to obtain more accurate intensities and form factors |F(q)| for the highest orders of diffraction. Combined with previous wide angle x-ray and volumetric data, a space filling model is employed to obtain gel phase structure at a mesoscopic level. This analysis provides direct evidence that the hydrocarbon chains from opposing monolayers are mini-interdigitated, consistent with the previously well-established result that the opposing monolayers are strongly coupled with respect to their chain tilt directions. Even more detailed structural features are described that have not been obtained from experiment but that could, in principle, be obtained from simulations that would first be validated by agreement with the wide angle and the new low angle |F(q)| x-ray data.

Phase behavior of palmitoyl and egg sphingomyelin.

Despite the biological significance of sphingomyelins (SMs), there is far less structural information available for SMs compared to glycerophospholipids. Considerable confusion exists in the literature regarding even the phase behavior of SM bilayers. This work studies both palmitoyl (PSM) and egg sphingomyelin (ESM) in the temperature regime from 3 °C to 55 °C using X-ray diffraction and X-ray diffuse scattering on hydrated, oriented thick bilayer stacks. We observe clear evidence for a ripple phase for ESM in a large temperature range from 3 °C to the main phase transition temperature (TM) of ∼38 °C. This unusual stability of the ripple phase was not observed for PSM, which was in a gel phase at 3 °C, with a gel-to-ripple transition at ∼24 °C and a ripple-to-fluid transition at ∼41 °C. We also report structural results for all phases. In the gel phase at 3 °C, PSM has chains tilted by ∼30° with an area/lipid ∼45 Å2 as determined by wide angle X-ray scattering. The ripple phases for both PSM and ESM have temperature dependent ripple wavelengths that are ∼145 Šnear 30 °C. In the fluid phase, our electron density profiles combined with volume measurements allow calculation of area/lipid to be ∼64 Å2 for both PSM and ESM, which is larger than that from most of the previous molecular dynamics simulations and experimental studies. Our study demonstrates that oriented lipid films are particularly well-suited to characterize ripple phases since the scattering pattern is much better resolved than in unoriented samples.

Experimentally determined tilt and bending moduli of single-component lipid bilayers.

Values of the bending modulus KC and the tilt modulus Kθ are reported for single component lipid bilayers. The lipids studied have the common names DOPC, DMPC, diC22:1PC, SOPC, POPC, diPhyPC, DLPC, DPPC, DHPC and DEPC, listed in the order of number of samples examined. The experimental method, thus far the only one that measures the tilt modulus of lipid bilayers, first obtains diffuse X-ray scattering data from oriented stacks of bilayers. The values of the moduli emerge from fitting the data to the accepted tilt-dependent continuum model for the free energy of a single bilayer, further enhanced by interactions between bilayers in the stack. The results indicate the broad trend that the tilt modulus for these PC lipids is smaller the closer the temperature is to the main transition temperature. Another trend is that inclusion of tilt raises the value of the bending modulus more for lipids with smaller values of the tilt modulus. Values of both moduli are compared to recent literature values obtained from simulations and values of the bending modulus are compared to the literature values obtained by other experimental methods.

X-ray scattering reveals molecular tilt is an order parameter for the main phase transition in a model biomembrane.

Synchrotron diffuse x-ray scattering data reveal a dramatic softening of the molecular tilt modulus K_{θ} of the model biomembrane composed of DMPC lipids as the temperature is lowered towards the main phase transition temperature at T_{M}=24^{∘}C. Spontaneous tilt occurs below T_{M}, suggesting that tilt is a symmetry breaking order parameter. Consistent with this hypothesis, it is also found that a different lipid POPS has no spontaneous tilt below its T_{M} at 14^{∘}C and correspondingly its tilt modulus did not soften as T_{M} was approached from above. As previously known, the bending modulus K_{C} of DMPC also softens close to T_{M}, but unlike the tilt modulus, K_{C} has a maximum 3^{∘} above T_{M}, which also marks the limit of the well-known anomalous swelling regime. Tilt adds a different perspective to our previous understanding of the main phase transition in lipid bilayers.

HIV-1 matrix-31 membrane binding peptide interacts differently with membranes containing PS vs. PI(4,5)P2.

Efficient assembly of HIV-1 at the plasma membrane (PM) of the T-cell specifically requires PI(4,5)P2. It was previously shown that a highly basic region (HBR) of the matrix protein (MA) on the Gag precursor polyprotein Pr55Gag is required for membrane association. MA is N-terminally myristoylated, which enhances its affinity to membranes. In this work we used X-ray scattering and neutron reflectivity to determine how the physical properties and structure of lipid bilayers respond to the addition of binding domain peptides, either in the myristoylated form (MA31myr) or without the myristoyl group (MA31). Neutron reflectivity measurements showed the peptides predominantly located in the hydrocarbon interior. Diffuse X-ray scattering showed differences in membrane properties upon addition of peptides and the direction of the changes depended on lipid composition. The PI(4,5)P2-containing bilayers softened, thinned and became less ordered as peptide concentration increased. In contrast, POPS-containing bilayers with equivalent net charge first stiffened, thickened and became more ordered with increasing peptide concentration. As softening the host cell's PM upon contact with the protein lowers the free energy for membrane restructuring, thereby potentially facilitating budding of viral particles, our results suggest that the role of PI(4,5)P2 in viral assembly goes beyond specific stereochemical membrane binding. These studies reinforce the importance of lipids in virology.

Sugar does not affect the bending and tilt moduli of simple lipid bilayers.

The diffuse X-ray scattering method has been applied to samples composed of SOPC, DOPC, DMPC, and POPC with added sugar, either sucrose, glucose, fructose, maltose, or trehalose. Several sugar concentrations in the range 200-500 mM were investigated for each of the lipid/sugar samples. We observed no systematic change in the bending modulus KC or in the tilt modulus Kθ with increasing sugar concentration. The average values of both these moduli were the same as those of the respective pure lipid controls within statistical uncertainty of 2%. These results are inconsistent with previous reports of sugar concentration dependent values of KC.

Determination of mosaicity in oriented stacks of lipid bilayers.

Two methods of measuring the misorientation of domains in oriented multilamellar stacks of lipid bilayers superficially appeared to give different values for the mosaic spread. It is first shown that the traditional rocking method and a newer ring method give the same value of the mosaic spread when the two types of data are similarly analyzed. Both indicate a long-tailed, nearly Lorentzian, mosaic distribution function. Our primary innovation is the analysis of ring data as a function of the rocking angle. For our best oriented DOPC sample, this analysis is consistent with a single Lorentzian mosaic distribution function with width 0.05°. In contrast, samples of DMPC indicate a more complex mosaic distribution and larger widths.

Correlation between length and tilt of lipid tails.

It is becoming recognized from simulations, and to a lesser extent from experiment, that the classical Helfrich-Canham membrane continuum mechanics model can be fruitfully enriched by the inclusion of molecular tilt, even in the fluid, chain disordered, biologically relevant phase of lipid bilayers. Enriched continuum theories then add a tilt modulus κθ to accompany the well recognized bending modulus κ. Different enrichment theories largely agree for many properties, but it has been noticed that there is considerable disagreement in one prediction; one theory postulates that the average length of the hydrocarbon chain tails increases strongly with increasing tilt and another predicts no increase. Our analysis of an all-atom simulation favors the latter theory, but it also shows that the overall tail length decreases slightly with increasing tilt. We show that this deviation from continuum theory can be reconciled by consideration of the average shape of the tails, which is a descriptor not obviously includable in continuum theory.

Bending Rigidities and Interdomain Forces in Membranes with Coexisting Lipid Domains.

To precisely quantify the fundamental interactions between heterogeneous lipid membranes with coexisting liquid-ordered (Lo) and liquid-disordered (Ld) domains, we performed detailed osmotic stress small-angle x-ray scattering experiments by exploiting the domain alignment in raft-mimicking lipid multibilayers. Performing a Monte Carlo-based analysis allowed us to determine with high reliability the magnitude and functional dependence of interdomain forces concurrently with the bending elasticity moduli. In contrast to previous methodologies, this approach enabled us to consider the entropic undulation repulsions on a fundamental level, without having to take recourse to crudely justified mean-field-like additivity assumptions. Our detailed Hamaker-coefficient calculations indicated only small differences in the van der Waals attractions of coexisting Lo and Ld phases. In contrast, the repulsive hydration and undulation interactions differed significantly, with the latter dominating the overall repulsions in the Ld phase. Thus, alignment of like domains in multibilayers appears to originate from both, hydration and undulation repulsions.