Short-range order and collective dynamics of DMPC bilayers: a comparison between molecular dynamics simulations, X-ray, and neutron scattering experiments

We present an extensive comparison of short-range order and short wavelength dynamics of a hydrated phospholipid bilayer derived by molecular dynamics simulations, elastic x-ray, and inelastic neutron scattering experiments. The quantities that are compared between simulation and experiment include static and dynamic structure factors, reciprocal space mappings, and electron density profiles. We show that the simultaneous use of molecular dynamics and diffraction data can help to extract real space properties like the area per lipid and the lipid chain ordering from experimental data. In addition, we assert that the interchain distance can be computed to high accuracy from the interchain correlation peak of the structure factor. Moreover, it is found that the position of the interchain correlation peak is not affected by the area per lipid, while its correlation length decreases linearly with the area per lipid. This finding allows us to relate a property of the structure factor quantitatively to the area per lipid. Finally, the short wavelength dynamics obtained from the simulations and from inelastic neutron scattering are analyzed and compared. The conventional interpretation in terms of the three-effective-eigenmode model is found to be only partly suitable to describe the complex fluid dynamics of lipid chains.     

Bridging microscopic and mesoscopic simulations of lipid bilayers

A lipid bilayer is modeled using a mesoscopic model designed to bridge atomistic bilayer simulations with macro-scale continuum-level simulation. Key material properties obtained from detailed atomistic-level simulations are used to parameterize the meso-scale model. The fundamental length and time scale of the meso-scale simulation are at least an order of magnitude beyond that used at the atomistic level. Dissipative particle dynamics cast in a new membrane formulation provides the simulation methodology. A meso-scale representation of a dimyristoylphosphatidylcholine membrane is examined in the high and low surface tension regimes. At high surface tensions, the calculated modulus is found to be slightly less than the atomistically determined value. This result agrees with the theoretical prediction that high-strain thermal undulations still persist, which have the effect of reducing the value of the atomistically determined modulus. Zero surface tension simulations indicate the presence of strong thermal undulatory modes, whereas the undulation spectrum and the calculated bending modulus are in excellent agreement with theoretical predictions and experiment.     

Molecular dynamics simulations and 2H NMR study of the GalCer/DPPG lipid bilayer

Molecular dynamics simulations were performed on a two-component lipid bilayer system in the liquid crystalline phase at constant pressure and constant temperature. The lipid bilayers were composed of a mixture of neutral galactosylceramide (GalCer) and charged dipalmitoylphosphatidylglycerol (DPPG) lipid molecules. Two lipid bilayer systems were prepared with GalCer:DPPG ratio 9:1 (10%-DPPG system) and 3:1 (25%-DPPG system). The 10%-DPPG system represents a collapsed state lipid bilayer, with a narrow water space between the bilayers, and the 25%-DPPG system represents an expanded state with a fluid space of approximately 10 nm. The number of lipid molecules used in each simulation was 1024, and the length of the production run simulation was 10 ns. The simulations were validated by comparing the results with experimental data for several important aspects of the bilayer structure and dynamics. Deuterium order parameters obtained from (2)H NMR experiments for DPPG chains are in a very good agreement with those obtained from molecular dynamics simulations. The surface area per GalCer lipid molecule was estimated to be 0.608 +/- 0.011 nm(2). From the simulated electron density profiles, the bilayer thickness defined as the distance between the phosphorus peaks across the bilayer was calculated to be 4.21 nm. Both simulation systems revealed a tendency for cooperative bilayer undulations, as expected in the liquid crystalline phase. The interaction of water with the GalCer and DPPG oxygen atoms results in a strong water ordering in a spherical hydration shell and the formation of hydrogen bonds (H-bonds). Each GalCer lipid molecule makes 8.6 +/- 0.1 H-bonds with the surrounding water, whereas each DPPG lipid molecule makes 8.3 +/- 0.1 H-bonds. The number of water molecules per GalCer or DPPG in the hydration shell was estimated to be 10-11 from an analysis of the radial distribution functions. The formation of the intermolecular hydrogen bonds was observed between hydroxyl groups from the opposing GalCer sugar headgroups, giving an energy of adhesion in the range between -1.0 and -3.4 erg/cm(2). We suggest that this value is the contribution of the hydrogen-bond component to the net adhesion energy between GalCer bilayers in the liquid crystalline phase.     

Undulation Contributions to the Area Compressibility in Lipid Bilayer Simulations

It is here shown that there is a considerable system size-dependence in the area compressibility calculated from area fluctuations in lipid bilayers. This is caused by the contributions to the area fluctuations from undulations. This is also the case in experiments. At present, such a contribution, in most cases, is subtracted from the experimental values to obtain a true area compressibility. This should also be done with the simulation values. Here, this is done by extrapolating area compressibility versus system size, down to very small (zero) system size, where undulations no longer exist. The area compressibility moduli obtained from such simulations do not agree with experimental true area compressibility moduli as well as the uncorrected ones from contemporary or earlier simulations, but tend, instead, to be ∼50% too large. As a byproduct, the bending modulus can be calculated from the slope of the compressibility modulus versus system-size. The values obtained in this way for the bending modulus are then in good agreement with experiment.     

Computational Hydrodynamics and Statistical Modeling on Biologically Inspired Undulating Robotic Fins: A Two-Dimensional Study

Undulation fishes, whose propulsion is mainly achieved by undulating ribbon fins, are good at maneuvering or stabilizing at low speeds. This paper suggests and proposes a two-dimensional approximate computational model, which is used to conduct an initial analysis on undulation propulsion scheme. It is believed that this undulating mode has a better potential for exploitation in artificial underwater systems. Hydrodynamics of two-dimensional undulating fins under a series of kinematical parameter sets is explored via numerical simulation. The periodicity of undulation forces and moments is studied. The effects of inlet velocity, wavelength, undulation frequency, and undulation amplitude are investigated. Furthermore, a dimensionless two-parameter model for undulation surge force is established with a given wavelength (in terms of, a single wavelength or a dual wavelength) using statistical method. The work in this paper is able to provide studies on bionic undulation mode. It has also formed a meaningful basis for three-dimensional (3D) hydrodynamics and corresponding control methods in bionic un-dulation robots.     

Biomembrane simulations of 12 lipid types using the general amber force field in a tensionless ensemble

The AMBER family of force fields is one of the most commonly used alternatives to describe proteins and drug-like molecules in molecular dynamics simulations. However, the absence of a specific set of parameters for lipids has been limiting the widespread application of this force field in biomembrane simulations, including membrane protein simulations and drug-membrane simulations. Here, we report the systematic parameterization of 12 common lipid types consistent with the General Amber Force Field (GAFF), with charge-parameters determined with RESP at the HF/6–31G(d) level of theory, to be consistent with AMBER. The accuracy of the scheme was evaluated by comparing predicted and experimental values for structural lipid properties in MD simulations in an NPT ensemble with explicit solvent in 100:100 bilayer systems. Globally, a consistent agreement with experimental reference data on membrane structures was achieved for some lipid types when using the typical MD conditions normally employed when handling membrane proteins and drug-membrane simulations (a tensionless NPT ensemble, 310?K), without the application of any of the constraints often used in other biomembrane simulations (such as the surface tension and the total simulation box area). The present set of parameters and the universal approach used in the parameterization of all the lipid types described here, as well as the consistency with the AMBER force field family, together with the tensionless NPT ensemble used, opens the door to systematic studies combining lipid components with small drug-like molecules or membrane proteins and show the potential of GAFF in dealing with biomembranes.     

Simulations of zwitterionic and anionic phospholipid monolayers

Results of atomistic molecular dynamics simulations of dipalmitoylphosphatidylcholine and dipalmitoylphosphatidylglycerol monolayers at the air/water interface are presented. Dipalmitoylphosphatidylcholine is zwitterionic and dipalmitoylphosphatidylglycerol is anionic at physiological pH. NaCl and CaCl2 water subphases are simulated. The simulations are carried out at different surface densities, and a simulation cell geometry is chosen that greatly facilitates the investigation of phospholipid monolayer properties. Ensemble average monolayer properties calculated from simulation are in agreement with experimental measurements. The dependence of the properties of the monolayers on the surface density, the type of the headgroup, and the ionic environment are explained in terms of atomistically detailed pair distribution functions and electron density profiles, demonstrating the strength of simulations in investigating complex, multicomponent systems of biological importance.     

A Molecular Dynamics Study of DMPC Lipid Bilayers Interacting with Dimethylsulfoxide–Water Mixtures

The diffusion process of dimethylsulfoxide (DMSO) through zwitterionic dimyristoylphosphatidylcholine (DMPC) lipid bilayer was studied by means of molecular dynamics (MD) simulations. To account for the cryoprotectant concentration difference between the inside and the outside of the cell, dual DMPC lipid bilayers which separate two aqueous reservoirs with and without DMSO were modeled. The initial configuration of the simulation model had DMSO molecules present in one of the aqueous phases (outside the cell) at two different concentrations of ~3 and ~6?mol%. MD simulations were performed on the systems for 50?ns at 323?K and 1?bar. Although the simulation time considered in the study was insufficient for the DMSO molecules to reach the other aqueous phase and equilibrium, early stages of the diffusion process indicated that DMSO molecules had a tendency to diffuse towards the other aqueous phase. The effects of DMSO on bilayer structural characteristics during the diffusion process were investigated. Simulations were analyzed to correlate the following properties of lipid bilayers in the presence of two different aqueous phases: area per lipid, lipid thickness, mass density profiles, lipid tail order parameter and water dipole orientation. Area per lipid calculated for the leaflet facing the aqueous DMSO?Cwater mixture did not show any significant difference compared to area per lipid for the DMSO-free pure DMPC bilayer. Mass density profiles revealed that DMSO molecules had a strong tendency to diffuse toward the aqueous phase with pure water. The lipid tail order parameter calculated for the sn-1 tail of the leaflet facing the aqueous DMSO?Cwater mixture showed that the ordering of lipid tails decreased compared to the leaflet exposed to pure water. However, the ordering of lipid tails in a system where a single bilayer is hydrated by an aqueous DMSO?Cwater mixture is far lower.     

Structural investigation of the covalent and electrostatic binding of yeast cytochrome c to the surface of various ultrathin lipid multilayers using x-ray diffraction.

X-Ray diffraction was used to characterize the profile structures of ultrathin lipid multilayers having a bound surface layer of cytochrome c. The lipid multilayers were formed on an alkylated glass surface, using the Langmuir-Blodgett method. The ultrathin lipid multilayers of this study were: five monolayers of arachidic acid, four monolayers of arachidic acid with a surface monolayer of dimyristoyl phosphatidylserine, and four monolayers of arachidic acid acid with a surface monolayer of thioethyl stearate. Both the phosphatidylserine and the thioethyl stearate surfaces were found previously to covalently bind yeast cytochrome c, while the arachidic acid surface electrostatically binds yeast cytochrome c. Meridional x-ray diffraction data were collected from these lipid multilayer films with and without a bound yeast cytochrome c surface layer. A box refinement technique, previously shown to be effective in deriving the profile structures of ultrathin multilayer lipid films with and without electrostatically bound cytochrome c, was used to determine the multilayer electron density profiles. The surface monolayer of bound cytochrome c was readily apparent upon comparison of the multilayer electron density profiles for the various pairs of ultrathin multilayer films plus/minus cytochrome c for all cases. In addition, cytochrome c binding to the multilayer surface significantly perturbs the underlying lipid monolayers.     

Lipid tempering simulation of model biological membranes on parallel platforms

In this report we have tested a parallel implementation for the simulation of lipid bilayers at the atomistic level, based on a generalized ensemble protocol where only the torsional degrees of freedom of the alkyl chains of the lipids are heated. The results in terms of configurational sampling enhancement have been compared with a conventional simulation produced with a widespread molecular dynamics code. Results show that the proposed thermodynamic-based multiple trajectories parallel protocol for membrane simulations allows for an efficient use of CPU resources with respect to the conventional single trajectory, providing accurate results for area and volume per lipid, membrane thickness, undulation spectra and boosting significantly diffusion and mixing in lipid bilayers due to the sampling enhancement of gauche/trans ratios of the alkyl chain dihedral angles.     

Experimental validation of molecular dynamics simulations of lipid bilayers: a new approach

A novel protocol has been developed for comparing the structural properties of lipid bilayers determined by simulation with those determined by diffraction experiments, which makes it possible to test critically the ability of molecular dynamics simulations to reproduce experimental data. This model-independent method consists of analyzing data from molecular dynamics bilayer simulations in the same way as experimental data by determining the structure factors of the system and, via Fourier reconstruction, the overall transbilayer scattering-density profiles. Multi-nanosecond molecular dynamics simulations of a dioleoylphosphatidylcholine bilayer at 66% RH (5.4 waters/lipid) were performed in the constant pressure and temperature ensemble using the united-atom GROMACS and the all-atom CHARMM22/27 force fields with the GROMACS and NAMD software packages, respectively. The quality of the simulated bilayer structures was evaluated by comparing simulation with experimental results for bilayer thickness, area/lipid, individual molecular-component distributions, continuous and discrete structure factors, and overall scattering-density profiles. Neither the GROMACS nor the CHARMM22/27 simulations reproduced experimental data within experimental error. The widths of the simulated terminal methyl distributions showed a particularly strong disagreement with the experimentally observed distributions. A comparison of the older CHARMM22 with the newer CHARMM27 force fields shows that significant progress is being made in the development of atomic force fields for describing lipid bilayer systems empirically.     

Interpretation of small angle X-ray measurements guided by molecular dynamics simulations of lipid bilayers

Reconstruction and interpretation of lipid bilayer structure from X-ray scattering often rely on assumptions regarding the molecular distributions across the bilayer. It is usually assumed that changes in head-head spacings across the bilayer, as measured from electron density profiles, equal the variations in hydrocarbon thicknesses. One can then determine the structure of a bilayer by comparison to the known structure of a lipid with the same headgroup. Here we examine this procedure using simulated electron density profiles for the benchmark lipids DMPC and DPPC. We compare simulation and experiment in both real and Fourier space to address two main aspects: (i) the measurement of head-head spacings from relative electron density profiles, and (ii) the determination of the absolute scale for these profiles. We find supporting evidence for the experimental procedure, thus explaining the robustness and consistency of experimental structural results derived from electron density profiles. However, we also expose potential pitfalls in the Fourier reconstruction that are due to the limited number of scattering peaks. Volumetric analysis of simulated bilayers allows us to propose an improved, yet simple method for scale determination. In this way we are able to remove some of the restrictions imposed by limited scattering data in constructing reliable electron density profiles.     

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

The fully hydrated liquid crystalline phase of the dimyristoylphosphatidycholine lipid bilayer at 30 degrees C was simulated using molecular dynamics with the CHARMM potential for five surface areas per lipid (A) in the range 55-65 A(2) that brackets the previously determined experimental area 60.6 A(2). The results of these simulations are used to develop a new hybrid zero-baseline structural model, denoted H2, for the electron density profile, rho(z), for the purpose of interpreting x-ray diffraction data. H2 and also the older hybrid baseline model were tested by fitting to partial information from the simulation and various constraints, both of which correspond to those available experimentally. The A, rho(z), and F(q) obtained from the models agree with those calculated directly from simulation at each of the five areas, thereby validating this use of the models. The new H2 was then applied to experimental dimyristoylphosphatidycholine data; it yields A = 60.6 +/- 0.5 A(2), in agreement with the earlier estimate obtained using the hybrid baseline model. The electron density profiles also compare well, despite considerable differences in the functional forms of the two models. Overall, the simulated rho(z) at A = 60.7 A(2) agrees well with experiment, demonstrating the accuracy of the CHARMM lipid force field; small discrepancies indicate targets for improvements. Lastly, a simulation-based model-free approach for obtaining A is proposed. It is based on interpolating the area that minimizes the difference between the experimental F(q) and simulated F(q) evaluated for a range of surface areas. This approach is independent of structural models and could be used to determine structural properties of bilayers with different lipids, cholesterol, and peptides.     

Physical Properties of Bacterial Outer Membrane Models: Neutron Reflectometry & Molecular Simulation

The outer membrane (OM) of Gram-negative bacteria is an asymmetric bilayer having phospholipids in the inner leaflet and lipopolysaccharides in the outer leaflet. This unique asymmetry and the complex carbohydrates in lipopolysaccharides make it a daunting task to study the asymmetrical OM structure and dynamics, its interactions with OM proteins, and its roles in translocation of substrates, including antibiotics. In this study, we combine neutron reflectometry and molecular simulation to explore the physical properties of OM mimetics. There is excellent agreement between experiment and simulation, allowing experimental testing of the conclusions from simulations studies and also atomistic interpretation of the behavior of experimental model systems, such as the degree of lipid asymmetry, the lipid component (tail, head, and sugar) profiles along the bilayer normal, and lateral packing (i.e., average surface area per lipid). Therefore, the combination of both approaches provides a powerful new means to explore the biological and biophysical behavior of the bacterial OM.     

Reparameterization of all-atom dipalmitoylphosphatidylcholine lipid parameters enables simulation of fluid bilayers at zero tension

Molecular dynamics simulations of dipalmitoylphosphatidylcholine (DPPC) lipid bilayers using the CHARMM27 force field in the tensionless isothermal-isobaric (NPT) ensemble give highly ordered, gel-like bilayers with an area per lipid of approximately 48 A(2). To obtain fluid (L(alpha)) phase properties of DPPC bilayers represented by the CHARMM energy function in this ensemble, we reparameterized the atomic partial charges in the lipid headgroup and upper parts of the acyl chains. The new charges were determined from the electron structure using both the Mulliken method and the restricted electrostatic potential fitting method. We tested the derived charges in molecular dynamics simulations of a fully hydrated DPPC bilayer. Only the simulation with the new restricted electrostatic potential charges shows significant improvements compared with simulations using the original CHARMM27 force field resulting in an area per lipid of 60.4 +/- 0.1 A(2). Compared to the 48 A(2), the new value of 60.4 A(2) is in fair agreement with the experimental value of 64 A(2). In addition, the simulated order parameter profile and electron density profile are in satisfactory agreement with experimental data. Thus, the biologically more interesting fluid phase of DPPC bilayers can now be simulated in all-atom simulations in the NPT ensemble by employing our modified CHARMM27 force field.     

Sphingomyelin-cholesterol domains in phospholipid membranes: atomistic simulation

We have carried out an atomic-level molecular dynamics simulation of a system of nanoscopic size containing a domain of 18:0 sphingomyelin and cholesterol embedded in a fully hydrated dioleylposphatidylcholine (DOPC) bilayer. To analyze the interaction between the domain and the surrounding phospholipid, we calculate order parameters and area per molecule as a function of molecule type and proximity to the domain. We propose an algorithm based on Voronoi tessellation for the calculation of the area per molecule of various constituents in this ternary mixture. The calculated areas per sphingomyelin and cholesterol are in agreement with previous simulations. The simulation reveals that the presence of the liquid-ordered domain changes the packing properties of DOPC bilayer at a distance as large as approximately 8 nm. We calculate electron density profiles and also calculate the difference in the thickness between the domain and the surrounding DOPC bilayer. The calculated difference in thickness is consistent with data obtained in atomic force microscopy experiments.     

A consistent model for thermal fluctuations and protein-induced deformations in lipid bilayers

We present an elastic Hamiltonian for membrane energetics that captures bilayer undulation and peristaltic deformations over all wavelengths, including the short wavelength protrusion regime. The model implies continuous functional forms for thermal undulation and peristaltic amplitudes as a function of wavelength and predicts previously overlooked relationships between these curves. Undulation and peristaltic spectra display excellent agreement with data from both atomistic and coarse-grained models over all simulated length scales. Additionally, the model accurately predicts the bilayer's response to a cylindrical protein inclusion as observed in coarse-grained simulation. This elastic response provides an explanation for gramicidin ion channel lifetime versus membrane thickness data that requires no fit constants. The physical parameters inherent to this picture may be expressed in terms of familiar material properties associated with lipid monolayers. Inclusion of a finite monolayer spontaneous curvature is essential to obtain fully consistent agreement between theory and the full range of available simulation/experimental data.     

Structure of lipid bilayers

The quantitative experimental uncertainty in the structure of fully hydrated, biologically relevant, fluid (L(alpha)) phase lipid bilayers has been too large to provide a firm base for applications or for comparison with simulations. Many structural methods are reviewed including modern liquid crystallography of lipid bilayers that deals with the fully developed undulation fluctuations that occur in the L(alpha) phase. These fluctuations degrade the higher order diffraction data in a way that, if unrecognized, leads to erroneous conclusions regarding bilayer structure. Diffraction measurements at high instrumental resolution provide a measure of these fluctuations. In addition to providing better structural determination, this opens a new window on interactions between bilayers, so the experimental determination of interbilayer interaction parameters is reviewed briefly. We introduce a new structural correction based on fluctuations that has not been included in any previous studies. Updated measurements, such as for the area compressibility modulus, are used to provide adjustments to many of the literature values of structural quantities. Since the gel (L(beta)') phase is valuable as a stepping stone for obtaining fluid phase results, a brief review is given of the lower temperature phases. The uncertainty in structural results for lipid bilayers is being reduced and best current values are provided for bilayers of five lipids.     

Molecular dynamics simulation of a phospholipid membrane

We present the results of molecular dynamics (MD) simulations of a phospholipid membrane in water, including full atomic detail. The goal of the simulations was twofold: first we wanted to set up a simulation system which is able to reproduce experimental results and can serve as a model membrane in future simulations. This goal being reached it is then further possible to gain insight in to those properties that are experimentally more difficult to access. The system studied is dipalmitoylphosphatidylcholine/water, consisting of 5408 atoms. Using original force field parameters the membrane turned out to approach a gel-like state. With slight changes of the parameters, the system adopted a liquid-crystalline state. Separate 80 ps runs were performed on both the gel and liquid-crystalline systems. Comparison of MD results with reliable experimental data (bilayer repeat distance, surface area per lipid, tail order parameters, atom distributions) showed that our simulations, especially the one in the liquid-crystalline phase, can serve as a realistic model for a phospholipid membrane. Further analysis of the trajectories revealed valuable information on various properties. In the liquid-crystalline phase, the interface turns out to be quite diffuse, with water molecules penetrating into the bilayer to the position of the carbonyl groups. The 10–90% width of the interface turns out to be 1.3 nm and the width of the hydrocarbon interior 3.0 nm. The headgroup dipoles are oriented at a small angle with respect to the bilayer plane. The resulting charge distribution is almost completely cancelled by the water molecules. The electron density distribution shows a large dip in the middle of the membrane. In this part the tails are more flexible. The mean life time between dihedral transitions is 20 ps. The average number of gauche angles per tail is 3.5. The occurrence of kinks is not a significant feature.Abbreviations MD molecular dynamics - DPPC dipalmitoylphosphatidylcholine - SPC simple point charges - DPPE dipalmitoylphosphatidylethanolamine Correspondence to: H. J. C. Berendsen