Simulation-based methods for interpreting x-ray data from lipid bilayers

Evaluating Polarizable Biomembrane Simulations against Experiments

Owing to the increase of available computational capabilities and the potential for providing a more accurate description, polarizable molecular dynamics force fields are gaining popularity in modeling biomolecular systems. It is, however, crucial to evaluate how much precision is truly gained with increasing cost and complexity of the simulation. Here, we leverage the NMRlipids open collaboration and Databank to assess the performance of available polarizable lipid models─the CHARMM-Drude and the AMOEBA-based parameters─against high-fidelity experimental data and compare them to the top-performing nonpolarizable models. While some improvement in the description of ion binding to membranes is observed in the most recent CHARMM-Drude parameters, and the conformational dynamics of AMOEBA-based parameters are excellent, the best nonpolarizable models tend to outperform their polarizable counterparts for each property we explored. The identified shortcomings range from inaccuracies in describing the conformational space of lipids to excessively slow conformational dynamics. Our results provide valuable insights for the further refinement of polarizable lipid force fields and for selecting the best simulation parameters for specific applications.

Membrane Condensation and Curvature Induced by SARS-CoV-2 Envelope Protein

The envelope (E) protein of SARS-CoV-2 participates in virion encapsulation and budding at the membrane of the endoplasmic reticulum Golgi intermediate compartment (ERGIC). The positively curved membrane topology required to fit an 80 nm viral particle is energetically unfavorable; therefore, viral proteins must facilitate ERGIC membrane curvature alteration. To study the possible role of the E protein in this mechanism, we examined the structural modification of the host lipid membrane by the SARS-CoV-2 E protein using synchrotron-based X-ray methods. Our reflectometry results on solid-supported planar bilayers show that E protein markedly condenses the surrounding lipid bilayer. For vesicles, this condensation effect differs between the two leaflets such that the membrane becomes asymmetric and increases its curvature. The formation of such a curved and condensed membrane is consistent with the requirements to stably encapsulate a viral core and supports a role for E protein in budding during SARS-CoV-2 virion assembly.

Small-angle scattering from flat bilayers containing correlated scattering length density inhomogeneities

Model lipid bilayers have been widely employed as a minimal system to investigate the structural properties of biological membranes by small-angle X-ray (SAXS) and neutron scattering (SANS) techniques. These have nanometre resolution and can give information regarding membrane thickness and scattering length densities (SLDs) of polar and apolar regions. However, biological membranes are complex systems containing different lipids and protein species, in which lipid domains can be dynamically assembled and disassembled. Therefore, SLD variations can occur within the biomembrane. In this work, a novel method has been developed to simulate SAXS and SANS profiles obtained from large unilamellar vesicles containing SLD inhomogeneities that are spatially correlated over the membrane surface. Such inhomogeneities are represented by cylindrical entities with equivalent SLDs. Stacking of bilayers is also included in the model, with no correlation between horizontal and vertical order. The model is applied to a lipid bilayer containing SLD inhomogeneities representing pores, lipid domains, and transmembrane, partially immersed and anchored proteins. It is demonstrated that all the structural information from the host lipid bilayer and from the SLD inhomogeneity can be consistently retrieved by a combined analysis of experimental SAXS and SANS data through the methodology proposed here.

Quantitative Comparison against Experiments Reveals Imperfections in Force Fields' Descriptions of POPC-Cholesterol Interactions

Cholesterol is a central building block in biomembranes, where it induces orientational order, slows diffusion, renders the membrane stiffer, and drives domain formation. Molecular dynamics (MD) simulations have played a crucial role in resolving these effects at the molecular level; yet, it has recently become evident that different MD force fields predict quantitatively different behavior. Although easily neglected, identifying such limitations is increasingly important as the field rapidly progresses toward simulations of complex membranes mimicking the in vivo conditions: pertinent multicomponent simulations must capture accurately the interactions between their fundamental building blocks, such as phospholipids and cholesterol. Here, we define quantitative quality measures for simulations of binary lipid mixtures in membranes against the C-H bond order parameters and lateral diffusion coefficients from NMR spectroscopy as well as the form factors from X-ray scattering. Based on these measures, we perform a systematic evaluation of the ability of commonly used force fields to describe the structure and dynamics of binary mixtures of palmitoyloleoylphosphatidylcholine (POPC) and cholesterol. None of the tested force fields clearly outperforms the others across the tested properties and conditions. Still, the Slipids parameters provide the best overall performance in our tests, especially when dynamic properties are included in the evaluation. The quality evaluation metrics introduced in this work will, particularly, foster future force field development and refinement for multicomponent membranes using automated approaches.

Structural insights on ionizable Dlin-MC3-DMA lipids in DOPC layers by combining accurate atomistic force fields, molecular dynamics simulations and neutron reflectivity

Ionizable lipids such as the promising Dlin-MC3-DMA (MC3) are essential for the successful design of lipid nanoparticles (LNPs) as drug delivery agents. Combining molecular dynamics simulations with experimental data, such as neutron reflectivity experiments and other scattering techniques, is essential to provide insights into the internal structure of LNPs, which is not fully understood to date. However, the accuracy of the simulations relies on the choice of force field parameters and high-quality experimental data is indispensable to verify the parametrization. For MC3, different parameterizations in combination with the CHARMM and the Slipids force fields have recently emerged. Here, we complement the existing efforts by providing parameters for cationic and neutral MC3 compatible with the AMBER Lipid17 force field. Subsequently, we carefully assess the accuracy of the different force fields by providing a direct comparison to neutron reflectivity experiments of mixed lipid bilayers consisting of MC3 and DOPC at different pHs. At low pH (cationic MC3) and at high pH (neutral MC3) the newly developed MC3 parameters in combination with AMBER Lipid17 for DOPC give good agreement with the experiments. Overall, the agreement is similar compared to the Park-Im parameters for MC3 in combination with the CHARMM36 force field for DOPC. The Ermilova-Swenson MC3 parameters in combination with the Slipids force field underestimate the bilayer thickness. While the distribution of cationic MC3 is very similar, the different force fields for neutral MC3 reveal distinct differences ranging from strong accumulation in the membrane center (current MC3/AMBER Lipid17 DOPC), over mild accumulation (Park-Im MC3/CHARMM36 DOPC) to surface accumulation (Ermilova-Swenson MC3/Slipids DOPC). These pronounced differences highlight the importance of accurate force field parameters and their experimental validation.

Small-Angle Neutron Scattering Reveals the Nanostructure of Liposomes with Embedded OprF Porins of Pseudomonas aeruginosa

The use of liposomes as drug delivery systems emerged in the last decades in view of their capacity and versatility to deliver a variety of therapeutic agents. By means of small-angle neutron scattering (SANS), we performed a detailed characterization of liposomes containing outer membrane protein F (OprF), the main porin of the Pseudomonas aeruginosa bacterium outer membrane. These OprF-liposomes are the basis of a novel vaccine against this antibiotic-resistant bacterium, which is one of the main hospital-acquired pathogens and causes each year a significant number of deaths. SANS data were analyzed by a specific model we created to quantify the crucial information about the structure of the liposome containing OprF, including the lipid bilayer structure, the amount of protein in the lipid bilayer, the average protein localization, and the effect of the protein incorporation on the lipid bilayer. Quantification of such structural information is important to enhance the design of liposomal delivery systems for therapeutic applications.

Small-Angle Neutron Scattering for Studying Lipid Bilayer Membranes

Small-angle neutron scattering (SANS) is a powerful tool for studying biological membranes and model lipid bilayer membranes. The length scales probed by SANS, being from 1 nm to over 100 nm, are well-matched to the relevant length scales of the bilayer, particularly when it is in the form of a vesicle. However, it is the ability of SANS to differentiate between isotopes of hydrogen as well as the availability of deuterium labeled lipids that truly enable SANS to reveal details of membranes that are not accessible with the use of other techniques, such as small-angle X-ray scattering. In this work, an overview of the use of SANS for studying unilamellar lipid bilayer vesicles is presented. The technique is briefly presented, and the power of selective deuteration and contrast variation methods is discussed. Approaches to modeling SANS data from unilamellar lipid bilayer vesicles are presented. Finally, recent examples are discussed. While the emphasis is on studies of unilamellar vesicles, examples of the use of SANS to study intact cells are also presented.

Tilted State Population of Antimicrobial Peptide PGLa Is Coupled to the Transmembrane Potential

Cationic antimicrobial peptide PGLa gets into close contact with the anionic bacterial cell membrane, facilitating cross-membrane transport phenomena and membrane disruption depending on the concentration. The mechanisms of action are closely associated with the tilted insertion geometry of PGLa. Therefore, we aimed to understand the interaction between the transmembrane potential (TMP) and the orientation of the membrane-bound PGLa helix. Molecular dynamics simulations were performed with TMP, and we found that the PGLa tilt angle relative to the membrane is coupled with the TMP. Elevated TMP increases the population of the tilted state. We observed positive feedback between the tilt angle and the TMP, which occurs due to the electrostatic interaction between the peptidic helix and the Na⁺ cations at the membrane-water interface. These TMP coupled phenomena can contribute to understanding the direct antimicrobial and adjuvant effects of PGLa in combination with regular antibiotics.

Antimicrobial Peptide Mechanism Studied by Scattering-Guided Molecular Dynamics Simulation

In an effort to combat rising antimicrobial resistance, our labs have rationally designed cationic, helical, amphipathic antimicrobial peptides (AMPs) as alternatives to traditional antibiotics since AMPs incur bacterial resistance in weeks, rather than days. One highly positively charged AMP, WLBU2 (+13e), (RRWV RRVR RWVR RVVR VVRR WVRR), has been shown to be effective in killing both Gram-negative (G(-)) and Gram-positive (G(+)) bacteria by directly perturbing the bacterial membrane nonspecifically. Previously, we used two equilibrium experimental methods: synchrotron X-ray diffuse scattering (XDS) providing lipid membrane thickness and neutron reflectometry (NR) providing WLBU2 depth of penetration into three lipid model membranes (LMMs). The purpose of the present study is to use the results from the scattering experiments to guide molecular dynamics (MD) simulations to investigate the detailed biophysics of the interactions of WLBU2 with LMMs of Gram-negative outer and inner membranes, and Gram-positive cell membranes, to elucidate the mechanisms of bacterial killing. Instead of coarse-graining, backmapping, or simulating without bias for several microseconds, all-atom (AA) simulations were guided by the experimental results and then equilibrated for ∼0.5 μs. Multiple replicas of the inserted peptide were run to probe stability and reach a combined time of at least 1.2 μs for G(-) and also 2.0 μs for G(+). The simulations with experimental comparisons help rule out certain structures and orientations and propose the most likely set of structures, orientations, and effects on the membrane. The simulations revealed that water, phosphates, and ions enter the hydrocarbon core when WLBU2 is positioned there. For an inserted peptide, the three types of amino acids, arginine, tryptophan, and valine (R, W, V), are arranged with the 13 Rs extending from the hydrocarbon core to the phosphate group, Ws are located at the interface, and Vs are more centrally located. For a surface state, R, W, and V are positioned relative to the bilayer interface as expected from their hydrophobicities, with Rs closest to the phosphate group, Ws close to the interface, and Vs in between. G(-) and G(+) LMMs are thinned ∼1 Å by the addition of WLBU2. Our results suggest a dual anchoring mechanism for WLBU2 both in the headgroup and in the hydrocarbon region that promotes a defect region where water and ions can flow across the slightly thinned bacterial cell membrane.

Harnessing Deep Learning for Optimization of Lennard-Jones Parameters for the Polarizable Classical Drude Oscillator Force Field

The outcomes of computational chemistry and biology research, including drug design, are significantly influenced by the underlying force field (FF) used in molecular simulations. While improved FF accuracy may be achieved via inclusion of explicit treatment of electronic polarization, such an extension must be accompanied by optimization of van der Waals (vdW) interactions, in the context of the Lennard-Jones (LJ) formalism in the present study. This is particularly challenging due to the extensive nature of chemical space combined with the correlated nature of LJ parameters. To address this challenge, a deep learning (DL)-based parametrization framework is developed, allowing for sampling of wide ranges of LJ parameters targeting experimental condensed phase thermodynamic properties. The present work utilizes this framework to develop the LJ parameters for atoms associated with four distinct groups covering 10 different atom types. Final parameter selection was facilitated by quantum mechanical data on rare-gas interactions with the training set molecules. The chosen parameters were then validated through experimental hydration free energies and condensed phase thermodynamic properties of validation set molecules to confirm transferability. The ultimate outcome of utilizing this framework is a set of LJ parameters in the context of the polarizable Drude FF, which demonstrated improvement in the reproduction of both experimental pure solvent and crystal properties and hydration free energies of the molecules compared to the additive CHARMM General FF (CGenFF) including the ability of the Drude FF to accurately reproduce both experimental pure solvent properties and hydration free energies. The study also shows how correlations between difference in the reproduction of condensed phase data between model compounds may be used to direct the selection of new atom types and training set molecules during FF development.

Lipid21: Complex Lipid Membrane Simulations with AMBER

We extend the modular AMBER lipid force field to include anionic lipids, polyunsaturated fatty acid (PUFA) lipids, and sphingomyelin, allowing the simulation of realistic cell membrane lipid compositions, including raft-like domains. Head group torsion parameters are revised, resulting in improved agreement with NMR order parameters, and hydrocarbon chain parameters are updated, providing a better match with phase transition temperature. Extensive validation runs (0.9 μs per lipid type) show good agreement with experimental measurements. Furthermore, the simulation of raft-like bilayers demonstrates the perturbing effect of increasing PUFA concentrations on cholesterol molecules. The force field derivation is consistent with the AMBER philosophy, meaning it can be easily mixed with protein, small molecule, nucleic acid, and carbohydrate force fields.

Vesicle Viewer: Online visualization and analysis of small-angle scattering from lipid vesicles

Small-angle X-ray and neutron scattering are among the most powerful experimental techniques for investigating the structure of biological membranes. Much of the critical information contained in small-angle scattering (SAS) data is not easily accessible to researchers who have limited time to analyze results by hand or to nonexperts who may lack the necessary scientific background to process such data. Easy-to-use data visualization software can allow them to take full advantage of their SAS data and maximize the use of limited resources. To this end, we developed an internet-based application called Vesicle Viewer to visualize and analyze SAS data from unilamellar lipid bilayer vesicles. Vesicle Viewer utilizes a modified scattering density profile (SDP) analysis called EZ-SDP in which key bilayer structural parameters, such as area per lipid and bilayer thickness, are easily and robustly determined. Notably, we introduce a bilayer model that is able to describe an asymmetric bilayer, whether it be chemically or isotopically asymmetric. The application primarily uses Django, a Python package specialized for the development of robust web applications. In addition, several other libraries are used to support the more technical aspects of the project; notable examples are Matplotlib (for graphs) and NumPy (for calculations). By eliminating the barrier of downloading and installing software, this web-based application will allow scientists to analyze their own vesicle scattering data using their preferred operating system. The web-based application can be found at https://vesicleviewer.dmarquardt.ca/.

Structure of benzothiadiazine at zwitterionic phospholipid cell membranes

The use of drugs derived from benzothiadiazine, which is a bicyclic heterocyclic benzene derivative, has become a widespread treatment for diseases such as hypertension (treated with diuretics such as bendroflumethiazide or chlorothiazide), low blood sugar (treated with non-diuretic diazoxide), or the human immunodeficiency virus, among others. In this work, we have investigated the interactions of benzothiadiazine with the basic components of cell membranes and solvents, such as phospholipids, cholesterol, ions, and water. The analysis of the mutual microscopic interactions is of central importance to elucidate the local structure of benzothiadiazine as well as the mechanisms responsible for the access of benzothiadiazine to the interior of the cell. We have performed molecular dynamics simulations of benzothiadiazine embedded in three different model zwitterionic bilayer membranes made by dimyristoylphosphatidylcholine, dioleoylphosphatidylcholine, 1,2-dioleoyl-sn-glycero-3-phosphoserine, and cholesterol inside aqueous sodium-chloride solution in order to systematically examine microscopic interactions of benzothiadiazine with the cell membrane at liquid-crystalline phase conditions. From data obtained through radial distribution functions, hydrogen-bonding lengths, and potentials of mean force based on reversible work calculations, we have observed that benzothiadiazine has a strong affinity to stay at the cell membrane interface although it can be fully solvated by water in short periods of time. Furthermore, benzothiadiazine is able to bind lipids and cholesterol chains by means of single and double hydrogen-bonds of different characteristic lengths.

Dissimilar action of tamoxifen and 4-hydroxytamoxifen on phosphatidylcholine model membranes

The anticancer drug tamoxifen and its primary metabolite 4-hydroxytamoxifen tend to accumulate in membranes due to its strong hydrophobic character. Thus, in this work we have carried out a systematic study to investigate their effects on model phosphatidylcholine membranes. Tamoxifen and 4-hydroxytamoxifen affect the phase behaviour of phosphatidylcholine model membranes, giving rise to formation of drug/dipalmitoylphosphatidylcholine domains, which is more evident in the case of 4-hydroxytamoxifen. These drugs have differential effects on the polar and apolar regions of the phospholipid supporting a different location of both compounds within the bilayer. Both compounds induce contents leakage in fluid phosphatidylcholine unilamellar liposomes, the effect of 4-hydroxytamoxifen being negligible as compared to that of tamoxifen. Molecular dynamics confirmed the tendency of both drugs to form clusters, tamoxifen locating all along the bilayer, whereas 4-hydroxytamoxifen mostly locates near the lipid/water interface, which can explain the different effects of both drugs in fluid phosphatidylcholine membranes.

Reflectometry and molecular dynamics study of the impact of cholesterol and melatonin on model lipid membranes

The effect of melatonin and/or cholesterol on the structural properties of a model lipid bilayer prepared from 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) has been investigated both experimentally and via molecular dynamics (MD) simulations. Neutron reflectometry experiments performed with single supported membranes revealed changes in lipid bilayer thickness upon the introduction of additional components. While the presence of cholesterol led to an increase in membrane thickness, the opposite effect was observed in the case of melatonin. The results obtained are in a good agreement with MD simulations which provided further information on the organization of components within the systems examined, indicating a mechanism underlying the membranes' thickness changes due to cholesterol and melatonin that had been observed experimentally. Cholesterol and melatonin preferentially accumulate in different membrane regions, presumably affecting the conformation of lipid hydrophobic moieties differently, and in turn having distinct impacts on the structure of the entire membrane. Our findings may be relevant for understanding the effects of age-related changes in cholesterol and melatonin concentrations, including those in the brains of individuals with Alzheimer's disease.

Intrinsic lipid curvatures of mammalian plasma membrane outer leaflet lipids and ceramides

We developed a global X-ray data analysis method to determine the intrinsic curvatures of lipids hosted in inverted hexagonal phases. In particular, we combined compositional modelling with molecular shape-based arguments to account for non-linear mixing effects of guest-in-host lipids on intrinsic curvature. The technique was verified by all-atom molecular dynamics simulations and applied to sphingomyelin and a series of phosphatidylcholines and ceramides with differing composition of the hydrocarbon chains. We report positive lipid curvatures for sphingomyelin and all phosphatidylcholines with disaturated and monounsaturated hydrocarbons. Phosphatidylcholines with diunsaturated hydrocarbons in turn yielded intrinsic lipid curvatures with negative values. All ceramides, with chain lengths varying between C2:0 and C24:0, displayed significant negative lipid curvature values. Moreover, we report non-additive mixing for C2:0 ceramide and sphingomyelin. This suggests for sphingolipids that in addition to lipid headgroup and hydrocarbon chain volumes also lipid-specific interactions are important contributors to membrane curvature stress.

DOPC versus DOPE as a helper lipid for gene-therapies: molecular dynamics simulations with DLin-MC3-DMA

Ionizable lipids are important compounds of modern therapeutic lipid nano-particles (LNPs). One of the most promising ionizable lipids (or amine lipids) is DLin-MC3-DMA. Depending on their pharmaceutical application these LNPs can also contain various helper lipids, such as phospho- and pegylated lipids, cholesterol and nucleic acids as a cargo. Due to their complex compositions the structures of these therapeutics have not been refined properly. Therefore, the role of each lipid in the pharmacological properties of LNPs has not been determined. In this work an atomistic model for the neutral form of DLin-MC3-DMA was derived and all-atom molecular dynamics (MD) simulations were carried out in order to investigate the effect of the phospholipid headgroup on the possible properties of the shell-membranes of LNPs. Bilayers containing either DOPC or DOPE lipids at two different ratios of DLin-MC3-DMA (5 mol% and 15 mol%) were constructed and simulated at neutral pH 7.4. The results from the analysis of MD trajectories revealed that DOPE lipid headgroups associated strongly with lipid tails and carbonyl oxygens of DLin-MC3-DMA, while for DOPC lipid headgroups no significant associations were observed. Furthermore, the strong associations between DOPE and DLin-MC3-DMA result in the positioning of DLin-MC3-DMA at the surface of the membrane. Such an interplay between the lipids slows down the lateral diffusion of all simulated bilayers, where a more dramatic decrease of the diffusion rate is observed in membranes with DOPE. This can explain the low water penetration of lipid bilayers with phosphatidylethanolamines and, probably, can relate to the bad transfection properties of LNPs with DOPE and DLin-MC3-DMA.

Understanding the Structure and Dynamics of Complex Biomembrane Interactions by Neutron Scattering Techniques

The membrane is one of the key structural materials of biology at the cellular level. Composed predominantly of a bilayer of lipids with embedded and bound proteins, it defines the boundaries of the cell and many organelles essential to life and therefore is involved in almost all biological processes. Membrane-specific interactions, such as drug binding to a membrane receptor or the interactions of an antimicrobial compound with the lipid matrix of a pathogen membrane, are of interest across the scientific disciplines. Herein we present a review, aimed at nonexperts, of the major neutron scattering techniques used in membrane studies: small-angle neutron scattering, neutron membrane diffraction, neutron reflectometry, quasielastic neutron scattering, and neutron spin echo. Neutron scattering techniques are well suited to studying biological membranes. The nondestructive nature of cold neutrons means that samples can be measured for long periods without fear of beam damage from ultraviolet, electron, or X-ray radiation, and neutron beams are highly penetrating, thus offering flexibility in samples and sample environments. Most important is the strong difference in neutron scattering lengths between the two most abundant forms of hydrogen, protium and deuterium. Changing the relative amounts of protium/deuterium in a sample allows the production of a series of neutron scattering data sets, enabling the observation of differing components within complex membrane architectures. This approach can be as simple as using the naturally occurring neutron contrast between different biomolecules to study components in a complex by changing the solution H₂O/D₂O ratio or as complex as selectively labeling individual components with hydrogen isotopes. This review presents an overview of each experimental technique with the neutron instrument configuration, related sample preparation and sample environment, and data analysis, highlighted by a special emphasis on using prominent neutron contrast to understand structure and dynamics. This review gives researchers a practical introduction to the often enigmatic suite of neutron beamlines, thereby lowering the barrier to taking advantage of these large-facility techniques to achieve new understandings of membranes and their interactions with other molecules.

Molecular Structure of Sphingomyelin in Fluid Phase Bilayers Determined by the Joint Analysis of Small-Angle Neutron and X-ray Scattering Data

We have determined the fluid bilayer structure of palmitoyl sphingomyelin (PSM) and stearoyl sphingomyelin (SSM) by simultaneously analyzing small-angle neutron and X-ray scattering data. Using a newly developed scattering density profile (SDP) model for sphingomyelin lipids, we report structural parameters including the area per lipid, total bilayer thickness, and hydrocarbon thickness, in addition to lipid volumes determined by densitometry. Unconstrained all-atom simulations of PSM bilayers at 55 °C using the C36 CHARMM force field produced a lipid area of 56 Ų, a value that is 10% lower than the one determined experimentally by SDP analysis (61.9 Ų). Furthermore, scattering form factors calculated from the unconstrained simulations were in poor agreement with experimental form factors, even though segmental order parameter (S_CD) profiles calculated from the simulations were in relatively good agreement with S_CD profiles obtained from NMR experiments. Conversely, constrained area simulations at 61.9 Ų resulted in good agreement between the simulation and experimental scattering form factors, but not with S_CD profiles from NMR. We discuss possible reasons for the discrepancies between these two types of data that are frequently used as validation metrics for molecular dynamics force fields.

Examining Tail and Headgroup Effects on Binary and Ternary Gel-Phase Lipid Bilayer Structure

The structural properties of two- and three-component gel-phase bilayers were studied using molecular dynamics simulations. The bilayers contain distearoylphosphatidylcholine (DSPC) phospholipids mixed with alcohols and/or fatty acids of varying tail lengths, with carbon chain lengths of 12, 16, and 24 studied. Changes in both headgroup chemistry and tail length are found to affect the balance between steric repulsion and van der Waals attraction within the bilayers, manifesting in different bilayer structural properties. Lipid components are found to be located at different depths within the bilayer depending on both chain length and headgroup chemistry. The highest bilayer ordering and lowest area per tail are found in systems with medium-length tails. While longer tails can enhance van der Waals attractions, the increased tail-length asymmetry is found to induce disorder and reduce tail packing. Bulkier headgroups further increase steric repulsion, as reflected in increased component offsets and reduced tail packing. These findings help explain how bilayer composition affects the structure of gel-phase bilayers.

Computer simulations of protein-membrane systems

The interactions between proteins and membranes play critical roles in signal transduction, cell motility, and transport, and they are involved in many types of diseases. Molecular dynamics (MD) simulations have greatly contributed to our understanding of protein-membrane interactions, promoted by a dramatic development of MD-related software, increasingly accurate force fields, and available computer power. In this chapter, we present available methods for studying protein-membrane systems with MD simulations, including an overview about the various all-atom and coarse-grained force fields for lipids, and useful software for membrane simulation setup and analysis. A large set of case studies is discussed.

BILMIX: a new approach to restore the size polydispersity and electron density profiles of lipid bilayers from liposomes using small-angle X-ray scattering data

Small-angle X-ray scattering (SAXS) is one of the major tools for the study of model membranes, but interpretation of the scattering data remains non-trivial. Current approaches allow the extraction of some structural parameters and the electron density profile of lipid bilayers. Here it is demonstrated that parametric modelling can be employed to determine the polydispersity of spherical or ellipsoidal vesicles and describe the electron density profile across the lipid bilayer. This approach is implemented in the computer program BILMIX. BILMIX delivers a description of the electron density of a lipid bilayer from SAXS data and simultaneously generates the corresponding size distribution of the unilamellar lipid vesicles.

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.

Application of small-angle neutron diffraction to the localization of general anesthetics in model membranes

We set out to explore the applicability of small-angle neutron diffraction (SAND) to the localization of biomembrane components by studying the general anesthetic n-decane in a model lipid bilayer system composed of dioleoyl-phosphocholine (DOPC). Samples in the form of planar membrane multilayers were hydrated by varied mixtures of deuterated and protonated water, and examined by the means of SAND. Neutron scattering length density (NSLD) profiles of the system were then reconstructed from the experimental data. We exploited the significantly different neutron scattering properties of hydrogen and deuterium atoms via labeling in addition to water contrast variation. Enhancing the signals from particular components of bilayer system led to a set of characteristic membrane profiles and from their comparison we localized n-decane molecules unequivocally in the bilayer's hydrocarbon chain region.

Molecular Dynamics Simulations of Membrane Permeability

This Review illustrates the evaluation of permeability of lipid membranes from molecular dynamics (MD) simulation primarily using water and oxygen as examples. Membrane entrance, translocation, and exit of these simple permeants (one hydrophilic and one hydrophobic) can be simulated by conventional MD, and permeabilities can be evaluated directly by Fick's First Law, transition rates, and a global Bayesian analysis of the inhomogeneous solubility-diffusion model. The assorted results, many of which are applicable to simulations of nonbiological membranes, highlight the limitations of the homogeneous solubility diffusion model; support the utility of inhomogeneous solubility diffusion and compartmental models; underscore the need for comparison with experiment for both simple solvent systems (such as water/hexadecane) and well-characterized membranes; and demonstrate the need for microsecond simulations for even simple permeants like water and oxygen. Undulations, subdiffusion, fractional viscosity dependence, periodic boundary conditions, and recent developments in the field are also discussed. Last, while enhanced sampling methods and increasingly sophisticated treatments of diffusion add substantially to the repertoire of simulation-based approaches, they do not address directly the critical need for force fields with polarizability and multipoles, and constant pH methods.

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.

Membrane charge and lipid packing determine polymyxin-induced membrane damage

With the advent of polymyxin B (PmB) resistance in bacteria, the mechanisms for mcr-1 resistance are of crucial importance in the design of novel therapeutics. The mcr-1 phenotype is known to decrease membrane charge and increase membrane packing by modification of the bacterial outer membrane. We used X-ray diffraction, Molecular Dynamics simulations, electrochemistry, and leakage assays to determine the location of PmB in different membranes and assess membrane damage. By varying membrane charge and lipid tail packing independently, we show that increasing membrane surface charge promotes penetration of PmB and membrane damage, whereas increasing lipid packing decreases penetration and damage. The penetration of the PmB molecules is well described by a phenomenological model that relates an attractive electrostatic and a repulsive force opposing insertion due to increased membrane packing. The model applies well to several gram-negative bacterial strains and may be used to predict resistance strength.

Simulation Best Practices for Lipid Membranes [Article v1.0]

We establish a reliable and robust standardization of settings for practical molecular dynamics (MD) simulations of pure and mixed (single- and multi-component) lipid bilayer membranes. In lipid membranes research, particle-based molecular simulations are a powerful tool alongside continuum theory, lipidomics, and model, in vitro, and in vivo experiments. Molecular simulations can provide precise and reproducible spatiotemporal (atomic- and femtosecond-level) information about membrane structure, mechanics, thermodynamics, kinetics, and dynamics. Yet the simulation of lipid membranes can be a daunting task, given the uniqueness of lipid membranes relative to conventional liquid-liquid and solid-liquid interfaces, the immense and complex thermodynamic and statistical mechanical theory, the diversity of multiscale lipid models, limitations of modern computing power, the difficulty and ambiguity of simulation controls, finite size effects, competitive continuum simulation alternatives, and the desired application, including vesicle experiments and biological membranes. These issues can complicate an essential understanding of the field of lipid membranes, and create major bottlenecks to simulation advancement. In this article, we clarify these issues and present a consistent, thorough, and user-friendly framework for the design of state-of-the-art lipid membrane MD simulations. We hope to allow early-career researchers to quickly overcome common obstacles in the field of lipid membranes and reach maximal impact in their simulations.

Cholesterol Effects on the Physical Properties of Lipid Membranes Viewed by Solid-state NMR Spectroscopy

In this chapter, we review the physical properties of lipid/cholesterol mixtures involving studies of model membranes using solid-state NMR spectroscopy. The approach allows one to quantify the average membrane structure, fluctuations, and elastic deformation upon cholesterol interaction. Emphasis is placed on understanding the membrane structural deformation and emergent fluctuations at an atomistic level. Lineshape measurements using solid-state NMR spectroscopy give equilibrium structural properties, while relaxation time measurements study the molecular dynamics over a wide timescale range. The equilibrium properties of glycerophospholipids, sphingolipids, and their binary and tertiary mixtures with cholesterol are accessible. Nonideal mixing of cholesterol with other lipids explains the occurrence of liquid-ordered domains. The entropic loss upon addition of cholesterol to sphingolipids is less than for glycerophospholipids, and may drive formation of lipid rafts. The functional dependence of ²H NMR spin-lattice relaxation (R _1Z) rates on segmental order parameters (S _CD) for lipid membranes is indicative of emergent viscoelastic properties. Addition of cholesterol shows stiffening of the bilayer relative to the pure lipids and this effect is diminished for lanosterol. Opposite influences of cholesterol and detergents on collective dynamics and elasticity at an atomistic scale can potentially affect lipid raft formation in cellular membranes.

Resolving the structural interactions between antimicrobial peptides and lipid membranes using small-angle scattering methods: the case of indolicidin

Using small angle X-ray and neutron scattering (SAXS/SANS) and detailed theoretical modelling we have elucidated the structure of the antimicrobial peptide, indolicidin, and the interaction with model lipid membranes of different anionic lipid compositions mimicking typical charge densities found in the cytoplasmic membrane of bacteria. First, we show that indolicidin displays a predominantly disordered, random chain conformation in solution with a small fraction (≈1%) of fiber-like nanostructures that are not dissolved at higher temperatures. The peptide is shown to strongly interact with the membranes at all charge densities without significantly perturbing the lipid bilayer structure. Instead, the results show that indolicidin inserts into the outer leaflet of the lipid vesicles causing a reduced local order of the lipid packing. This result is supported by an observed change in the melting point of the lipids upon addition of the peptide, as seen by differential scanning calorimetry experiments. The peptide does not to our observation affect the thickness of the membrane or form distinct structural pores in the membrane at physiologically relevant concentrations as has been previously suggested as an important mode of action. Finally, using sophisticated contrast variation SANS, we show that the peptide does not affect the random lateral distribution of anionic lipids in the membrane. Together, these results demonstrate that the structural aspects of the mode of action of antimicrobial peptides can be elucidated in detail using SAS techniques with liposomes as model systems.

Physics of HIV

This review summarizes over a decade of investigations into how membrane-binding proteins from the HIV-1 virus interact with lipid membrane mimics various HIV and host T-cell membranes. The goal of the work was to characterize at the molecular level both the elastic and structural changes that occur due to HIV protein/membrane interactions, which could lead to new drugs to thwart the HIV virus. The main technique used to study these interactions is diffuse X-ray scattering, which yields the bending modulus, K_C, as well as structural parameters such as membrane thickness, area/lipid and position of HIV peptides (parts of HIV proteins) in the membrane. Our methods also yield information about lipid chain order or disorder caused by the peptides. This review focuses on three stages of the HIV-1 life cycle: 1) infection, 2) Tat membrane transport, and 3) budding. In the infection stage, our lab studied three different parts of HIV-1 gp41 (glycoprotein 41 fusion protein): 1) FP23, the N-terminal 23 amino acids that interact non-specifically with the T-cell host membrane to cause fusion of two membranes, and its trimer version, 2) CRAC (cholesterol recognition amino acid consensus sequence), on the MPER (membrane proximal external region) near the membrane-spanning domain, and 3) LLP2 (lentiviral lytic peptide 2) on the CTT (cytoplasmic C-terminal tail). For Tat transport, we used membrane mimics of the T-cell nuclear membrane as well as simpler models that varied charge and negative curvature. For membrane budding, we varied the myristoylation of the MA₃₁ peptide as well as the negatively charged lipid. These studies show that HIV peptides with different roles in the HIV life cycle affect differently the relevant membrane mimics. In addition, the membrane lipid composition plays an important role in the peptides' effects.

Lipid Configurations from Molecular Dynamics Simulations

The extent to which current force fields faithfully reproduce conformational properties of lipids in bilayer membranes, and whether these reflect the structural principles established for phospholipids in bilayer crystals, are central to biomembrane simulations. We determine the distribution of dihedral angles in palmitoyl-oleoyl phosphatidylcholine from molecular dynamics simulations of hydrated fluid bilayer membranes. We compare results from the widely used lipid force field of Berger et al. with those from the most recent C36 release of the CHARMM force field for lipids. Only the CHARMM force field produces the chain inequivalence with sn-1 as leading chain that is characteristic of glycerolipid packing in fluid bilayers. The exposure and high partial charge of the backbone carbonyls in Berger lipids leads to artifactual binding of Na+ ions reported in the literature. Both force fields predict coupled, near-symmetrical distributions of headgroup dihedral angles, which is compatible with models of interconverting mirror-image conformations used originally to interpret NMR order parameters. The Berger force field produces rotamer populations that correspond to the headgroup conformation found in a phosphatidylcholine lipid bilayer crystal, whereas CHARMM36 rotamer populations are closer to the more relaxed crystal conformations of phosphatidylethanolamine and glycerophosphocholine. CHARMM36 alone predicts the correct relative signs of the time-average headgroup order parameters, and reasonably reproduces the full range of NMR data from the phosphate diester to the choline methyls. There is strong motivation to seek further experimental criteria for verifying predicted conformational distributions in the choline headgroup, including the 31P chemical shift anisotropy and 14N and CD3 NMR quadrupole splittings.

Homology Modeling and Molecular Dynamics Simulation Combined with X-ray Solution Scattering Defining Protein Structures of Thromboxane and Prostacyclin Synthases

A combination of molecular dynamics (MD) simulations and X-ray scattering (SAXS) has emerged as the approach of choice for studying protein structures and dynamics in solution. This approach has potential applications for membrane proteins that neither are soluble nor form crystals easily. We explore the water-coupled dynamic structures of thromboxane synthase (TXAS) and prostacyclin synthase (PGIS) from scanning HPLC-SAXS measurements combined with MD ensemble analyses. Both proteins are heme-containing enzymes in the cytochrome P450 family, known as prostaglandin H₂ (PGH₂) isomerase, with counter-functions in regulation of platelet aggregation. Currently, the X-ray crystallographic structures of PGIS are available, but those for TXAS are not. The use of homology modeling of the TXAS structure with ns-μs explicit water solvation MD simulations allows much more accurate estimation of the configuration space with loop motion and origin of the protein behaviors in solution. In contrast to the stability of the conserved PGIS structure in solution, the pronounced TXAS flexibility has been revealed to have unstructured loop regions in connection with the characteristic P450 structural elements. The MD-derived and experimental-solution SAXS results are in excellent agreement. The significant protein internal motions, whole-molecule structures, and potential problems with protein folding, crystallization, and functionality are examined.

Alcohol Interactions with Lipid Bilayers

We investigate the structural changes to lipid membrane that ensue from the addition of aliphatic alcohols with various alkyl tail lengths. Small angle neutron diffraction from flat lipid bilayers that are hydrated through water vapor has been employed to eliminate possible artefacts of the membrane curvature and the alcohol's membrane-water partitioning. We have observed clear changes to membrane structure in both transversal and lateral directions. Most importantly, our results suggest the alteration of the membrane-water interface. The water encroachment has shifted in the way that alcohol loaded bilayers absorbed more water molecules when compared to the neat lipid bilayers. The experimental results have been corroborated by molecular dynamics simulations to reveal further details. Namely, the order parameter profiles have been fruitful in correlating the mechanical model of structural changes to the effect of anesthesia.

Curcumin Protects Membranes through a Carpet or Insertion Model Depending on Hydration

Curcumin is the main ingredient in turmeric, a common Indian spice. Curcumin shows a broad spectrum of effects, including anti-Alzheimer's and antioxidant properties. An interaction between curcumin and lipid membranes has been speculated as the root cause of this activity, and the molecule is often proposed to protect the bilayer. However, the detailed molecular mechanism of this protection is disputed. There is evidence that curcumin either (a) lies flat on the bilayer and provides a "carpet" for protection by forming a steric barrier, or (b) inserts into the membrane and stiffens tails, thereby protecting against peptide insertion. We studied the interaction between curcumin and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) bilayers at different concentrations using high-resolution X-ray diffraction and molecular dynamics (MD) computer simulations. We observed curcumin molecules forming a carpet in dehydrated bilayers, whereas in hydrated membranes the curcumin molecules were found to insert into the bilayers. From calculations of the potential of mean force (PMF), we find two minima, a metastable state in the headgroup region, at |z| ≈ 22 Å, and a global minimum in the hydrophobic membrane core, at |z| ≈ 9 Å. The population of the two states depends on membrane hydration. Experiments may thus observe curcumin in a carpet or inserted position, depending on the osmotic pressure conditions created, for instance, by salts, buffer solutions, substrates, or macromolecular solutes. In the carpet model, curcumin dehydrates lipid bilayers and decreases fluidity. When inserted, curcumin leads to a further fluidification of the membranes and an increase in tail fluctuations, contrary to cholesterol's condensing effect.

Drude Polarizable Force Field for Molecular Dynamics Simulations of Saturated and Unsaturated Zwitterionic Lipids

Additive force fields are designed to account for induced electronic polarization in a mean-field average way, using effective empirical fixed charges. The limitation of this approximation is cause for serious concerns, particularly in the case of lipid membranes, where the molecular environment undergoes dramatic variations over microscopic length scales. A polarizable force field based on the classical Drude oscillator offers a practical and computationally efficient framework for an improved representation of electrostatic interactions in molecular simulations. Building on the first-generation Drude polarizable force field for the dipalmitoylphosphatidylcholine 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) molecule, the present effort was undertaken to improve this initial model and expand the force field to a wider range of phospholipid molecules. New lipids parametrized include dimyristoylphosphatidylcholine (DMPC), dilauroylphosphatidylcholine (DLPC), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), dipalmitoylphosphatidylethanolamine (DPPE), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE), and 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE). The iterative optimization protocol employed in this effort led to lipid models that achieve a good balance between reproducing quantum mechanical data on model compound representative of phospholipids and reproducing a range of experimental condensed phase properties of bilayers. A parametrization strategy based on a restrained ensemble-maximum entropy methodology was used to help accurately match the experimental NMR order parameters in the polar headgroup region. All the parameters were developed to be compatible with the remainder of the Drude polarizable force field, which includes water, ions, proteins, DNA, and selected carbohydrates.

Complex biomembrane mimetics on the sub-nanometer scale

Biomimetic lipid vesicles are indispensable tools for gaining insight into the biophysics of cell physiology on the molecular level. The level of complexity of these model systems has steadily increased, and now spans from domain-forming lipid mixtures to asymmetric lipid bilayers. Here, we review recent progress in the development and application of elastic neutron and X-ray scattering techniques for studying these systems in situ and under physiologically relevant conditions on the nanometer to sub-nanometer length scales. In particular, we focus on: (1) structural details of coexisting liquid-ordered and liquid-disordered domains, including their thickness and lipid packing mismatch as a function of a size transition from nanoscopic to macroscopic domains; (2) membrane-mediated protein partitioning into lipid domains; (3) the role of the aqueous medium in tuning interactions between membranes and domains; and (4) leaflet-specific structure in asymmetric bilayers and passive lipid flip-flop.

High-resolution structure of coexisting nanoscopic and microscopic lipid domains

We studied coexisting micro- and nanoscopic liquid-ordered/liquid-disordered domains in fully hydrated multilamellar vesicles using small-angle X-ray scattering. Large domains exhibited long-range out-of-plane positional correlations of like domains, consistent with previous reports. In contrast, such correlations were absent in nanoscopic domains. Advancing a global analysis of the in situ data allowed us to gain a deep insight into the structural and elastic properties of the coexisting domains, including the partitioning of cholesterol in each domain. In agreement with a previous report, we found that the thickness mismatch between ordered and disordered domains decreased for nanoscopic domains. At the same time, we found also the lipid packing mismatch to be decreased for nano-domains, mainly due to the liquid-disordered domains becoming more densely packed when decreasing their size.