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.

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.

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.

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.

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.

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.

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.

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.

HIV-1 Tat membrane interactions probed using X-ray and neutron scattering, CD spectroscopy and MD simulations.

We report the effect on lipid bilayers of the Tat peptide Y47GRKKRRQRRR57 from the HIV-1 virus transactivator of translation (Tat) protein. Synergistic use of low-angle X-ray scattering (LAXS) and atomistic molecular dynamic simulations (MD) indicate Tat peptide binding to neutral dioleoylphosphocholine (DOPC) lipid headgroups. This binding induced the local lipid phosphate groups to move 3Å closer to the center of the bilayer. Many of the positively charged guanidinium components of the arginines were as close to the center of the bilayer as the locally thinned lipid phosphate groups. LAXS data for DOPC, DOPC/dioleoylphosphoethanolamine (DOPE), DOPC/dioleoylphosphoserine (DOPS), and a mimic of the nuclear membrane gave similar results. Generally, the Tat peptide decreased the bilayer bending modulus KC and increased the area/lipid. Further indications that Tat softens a membrane, thereby facilitating translocation, were provided by wide-angle X-ray scattering (WAXS) and neutron scattering. CD spectroscopy was also applied to further characterize Tat/membrane interactions. Although a mechanism for translation remains obscure, this study suggests that the peptide/lipid interaction makes the Tat peptide poised to translocate from the headgroup region.

Structure of the DMPC lipid bilayer ripple phase.

High resolution structure is presented for the ripple (Pß') phase of the phospholipid dimyristoylphosphatidylcholine. Low angle X-ray scattering from oriented samples yielded 57 orders, more than twice as many as recorded previously. The determined electron density map has a sawtooth profile similar to the result from lower resolution data, but the features are sharper allowing better estimates for the modulated bilayer profile and the distribution of headgroups along the aqueous interface. Analysis of high resolution wide angle X-ray data shows that the hydrocarbon chains in the longer, major side of the asymmetric sawtooth are packed similarly to the LßF gel phase, with chains in both monolayers coupled and tilted by 18° in the same direction. The absence of Bragg rods that could be associated with the minor side is consistent with disordered chains, as often suggested in the literature. However, the new high resolution bilayer profile strongly suggests that the chains in the two monolayers in the minor side and the curved region are not in registry. This staggered monolayer modulated melting suggests a direction for improving theories of the ripple phase.

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.

Testing procedures for extracting fluctuation spectra from lipid bilayer simulations.

To address concerns about how to obtain the height-height spectrum from simulations of biomembranes, we emulated the fluctuations in real space using exact input spectra. Two different methods that have given different results in the literature were then used to extract spectra from the emulated fluctuations that were then compared to the exact input spectra. A real space method shows systematic, but small deviations attributed to splines introducing an artifactual filter. A direct Fourier method obtains accurate results when the in-plane placement of the emulated particles is uncorrelated with the out-of-plane undulations, but systematic underestimates occur when the particle placement is more realistically correlated with the undulations. Although quantitative corrections cannot be estimated from our one-dimensional model, the results are qualitatively consistent with the direct Fourier method underestimating the 1/q(2) spectral dependence that is characteristic of a tilt degree of freedom in simulations.

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.

Membrane structure correlates to function of LLP2 on the cytoplasmic tail of HIV-1 gp41 protein.

Mutation studies previously showed that the lentivirus lytic peptide (LLP2) sequence of the cytoplasmic C-terminal tail of the HIV-1 gp41 envelope protein inhibited viral-initiated T-cell death and T-cell syncytium formation, at which time in the HIV life cycle the gp41 protein is embedded in the T-cell membrane. In striking contrast, the mutants did not affect virion infectivity, during which time the gp41 protein is embedded in the HIV envelope membrane. To examine the role of LLP2/membrane interactions, we applied synchrotron x-radiation to determine structure of hydrated membranes. We focused on WT LLP2 peptide (+3 charge) and MX2 mutant (-1 charge) with membrane mimics for the T-cell and the HIV-1 membranes. To investigate the influence of electrostatics, cholesterol content, and peptide palmitoylation, we also studied three other LLP2 variants and HIV-1 mimics without negatively charged lipids or cholesterol as well as extracted HIV-1 lipids. All LLP2 peptides bound strongly to T-cell membrane mimics, as indicated by changes in membrane structure and bending. In contrast, none of the weakly bound LLP2 variants changed the HIV-1 membrane mimic structure or properties. This correlates well with, and provides a biophysical basis for, previously published results that reported lack of a mutant effect in HIV virion infectivity in contrast to an inhibitory effect in T-cell syncytium formation. It shows that interaction of LLP2 with the T-cell membrane modulates biological function.

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.

Volumetric stability of lipid bilayers.

In agreement with recent reports, a commercial densimeter has yielded a gradual decrease in lipid molecular volume of DPPC multilamellar vesicle dispersions in the gel phase upon repeated thermal cycling between 10 °C and 50 °C. The considerable size of this decrease would have significant implications for the physical chemistry of biomembranes. In contrast, neutral buoyancy measurements performed with similar thermal cycling indicate no gradual change in lipid volume in the gel phase at 20 °C. Remixing the lipid in the densimeter shows that the apparent volume decrease is an artifact. We conclude that gel phase DPPC bilayers exist in a volumetrically stable phase.

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.

Interpretation of fluctuation spectra in lipid bilayer simulations.

Atomic resolution and coarse-grained simulations of dimyristoylphosphatidylcholine lipid bilayers were analyzed for fluctuations perpendicular to the bilayer using a completely Fourier-based method. We find that the fluctuation spectrum of motions perpendicular to the bilayer can be decomposed into just two parts: 1), a pure undulation spectrum proportional to q(-4) that dominates in the small-q regime; and 2), a molecular density structure factor contribution that dominates in the large-q regime. There is no need for a term proportional to q(-2) that has been postulated for protrusion fluctuations and that appeared to have been necessary to fit the spectrum for intermediate q. We suggest that earlier reports of such a term were due to the artifact of binning and smoothing in real space before obtaining the Fourier spectrum. The observability of an intermediate protrusion regime from the fluctuation spectrum is discussed based on measured and calculated material constants.

Determination of electron density profiles and area from simulations of undulating membranes.

The traditional method for extracting electron density and other transmembrane profiles from molecular dynamics simulations of lipid bilayers fails for large bilayer systems, because it assumes a flat reference surface that does not take into account long wavelength undulations. We have developed what we believe to be a novel set of methods to characterize these undulations and extract the underlying profiles in the large systems. Our approach first obtains an undulation reference surface for each frame in the simulation and subsequently isolates the long-wavelength undulations by filtering out the intrinsic short wavelength modes. We then describe two methods to obtain the appropriate profiles from the undulating reference surface. Most combinations of methods give similar results for the electron density profiles of our simulations of 1024 DMPC lipids. From simulations of smaller systems, we also characterize the finite size effect related to the boundary conditions of the simulation box. In addition, we have developed a set of methods that use the undulation reference surface to determine the true area per lipid which, due to undulations, is larger than the projected area commonly reported from simulations.