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.     

Alamethicin in lipid bilayers: Combined use of X-ray scattering and MD simulations

We study fully hydrated bilayers of two di-monounsaturated phospholipids diC18:1PC (DOPC) and diC22:1PC with varying amounts of alamethicin (Alm). We combine the use of X-ray diffuse scattering and molecular dynamics simulations to determine the orientation of alamethicin in model lipids. Comparison of the experimental and simulated form factors shows that Alm helices are inserted transmembrane at high humidity and high concentrations, in agreement with earlier results. The X-ray scattering data and the MD simulations agree that membrane thickness changes very little up to 1/10 Alm/DOPC. In contrast, the X-ray data indicate that the thicker diC22:1PC membrane thins with added Alm, a total decrease in thickness of 4 Å at 1/10 Alm/diC22:1PC. The different effect of Alm on the thickness changes of the two bilayers is consistent with Alm having a hydrophobic thickness close to the hydrophobic thickness of 27 Å for DOPC; Alm is then mismatched with the 7 Å thicker diC22:1PC bilayer. The X-ray data indicate that Alm decreases the bending modulus (K_C) by a factor of ∼ 2 in DOPC and a factor of ∼ 10 in diC22:1PC membranes (P/L ∼ 1/10). The van der Waals and fluctuational interactions between bilayers are also evaluated through determination of the anisotropic B compressibility modulus.     

Constant surface tension molecular dynamics simulations of lipid bilayers with trehalose

Surface areas and fluctuations evaluated from 50 ns molecular dynamics simulations of fully hydrated dipalmitoylphosphatidylcholine (DPPC) bilayers in a 1:2 trehalose:lipid ratio carried out at surface tensions 10, 17 and 25 dyn/cm/leaflet are compared with those of pure bilayers under the same conditions. Trehalose increases the surface area, as consistent with the surface tension lowering observed in simulations at constant area. The system bulk elastic modulus K _b  = 1.5 ± 0.3 × 10¹⁰ dyn/cm². It is independent of bilayer surface area and trehalose content within statistical error. In contrast, the area elastic modulus K _a shows a strong area dependence. At 64 Å²/lipid (the experimental surface area), K _a  = 138 ± 26 dyn/cm for a pure DPPC bilayer and 82 ± 10 dyn/cm for one with trehalose; i.e. trehalose increases fluidity of the bilayer surface at this area per lipid.     

Naratriptan aggregation in lipid bilayers: perspectives from molecular dynamics simulations

In order to understand the interaction between naratriptan and a fully hydrated bilayer of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidyl-choline (POPC), we carried out molecular dynamics simulations. The simulations were performed considering neutral and protonated ionization states, starting from different initial conditions. At physiological pH, the protonated state of naratriptan is predominant. It is expected that neutral compounds could have larger membrane partition than charged compounds. However, for the specific case of triptans, it is difficult to study neutral species in membranes experimentally, making computer simulations an interesting tool. When the naratriptan molecules were originally placed in water, they partitioned between the bilayer/water interface and water phase, as has been described for similar compounds. From this condition, the drugs displayed low access to the hydrophobic environment, with no significant effects on bilayer organization. The molecules anchored in the interface, due mainly to the barrier function of the polar and oriented lipid heads. On the other hand, when placed inside the bilayer, both neutral and protonated naratriptan showed self-aggregation in the lipid tail environment. In particular, the protonated species exhibited a pore-like structure, dragging water through this environment.

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Graphical Abstract Different behaviour of Naratriptan and Sumatriptan, when the drugs were originally placed in the lipid core

     

Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations

Molecular dynamics simulations of fully hydrated Dipalmitoylphosphatidylcholine bilayers, extending temporal and spatial scales by almost one order of magnitude, are presented. The present work reaches system sizes of 1024 lipids and times 10-60 ns. The simulations uncover significant dynamics and fluctuations on scales of several nanoseconds, and enable direct observation and spectral decomposition of both undulatory and thickness fluctuation modes. Although the former modes are strongly damped, the latter exhibit signs of oscillatory behavior. From this, it has been possible to calculate mesoscopic continuum properties in good agreement with experimental values. A bending modulus of 4 x 10(-20) J, bilayer area compressibility of 250-300 mN/m, and mode relaxation times in the nanosecond range are obtained. The theory of undulatory motions is revised and further extended to cover thickness fluctuations. Finally, it is proposed that thickness fluctuations is the explanation to the observed system-size dependence of equilibrium-projected area per lipid.     

Insertion of Dengue E into lipid bilayers studied by neutron reflectivity and molecular dynamics simulations

The envelope (E) protein of Dengue virus rearranges to a trimeric hairpin to mediate fusion of the viral and target membranes, which is essential for infectivity. Insertion of E into the target membrane serves to anchor E and possibly also to disrupt local order within the membrane. Both aspects are likely to be affected by the depth of insertion, orientation of the trimer with respect to the membrane normal, and the interactions that form between trimer and membrane. In the present work, we resolved the depth of insertion, the tilt angle, and the fundamental interactions for the soluble portion of Dengue E trimers (sE) associated with planar lipid bilayer membranes of various combinations of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-rac-glycerol (POPG), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE), and cholesterol (CHOL) by neutron reflectivity (NR) and by molecular dynamics (MD) simulations. The results show that the tip of E containing the fusion loop (FL) is located at the interface of the headgroups and acyl chains of the outer leaflet of the lipid bilayers, in good agreement with prior predictions. The results also indicate that E tilts with respect to the membrane normal upon insertion, promoted by either the anionic lipid POPG or CHOL. The simulations show that tilting of the protein correlates with hydrogen bond formation between lysines and arginines located on the sides of the trimer close to the tip (K246, K247, and R73) and nearby lipid headgroups. These hydrogen bonds provide a major contribution to the membrane anchoring and may help to destabilize the target membrane.     

Molecular dynamics simulations of phospholipid bilayers with cholesterol

To investigate the microscopic interactions between cholesterol and lipids in biological membranes, we have performed a series of molecular dynamics simulations of large membranes with different levels of cholesterol content. The simulations extend to 10 ns, and were performed with hydrated dipalmitoylphosphatidylcholine (DPPC) bilayers. The bilayers contain 1024 lipids of which 0-40% were cholesterol and the rest DPPC. The effects of cholesterol on the structure and mesoscopic dynamics of the bilayer were monitored as a function of cholesterol concentration. The main effects observed are a significant ordering of the DPPC chains (as monitored by NMR type order parameters), a reduced fraction of gauche bonds, a reduced surface area per lipid, less undulations--corresponding to an increased bending modulus for the membrane, smaller area fluctuations, and a reduced lateral diffusion of DPPC-lipids as well as cholesterols.     

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.     

The condensing effect of cholesterol in lipid bilayers

The condensing effect of cholesterol on phospholipid bilayers was systematically investigated for saturated and unsaturated chains, as a function of cholesterol concentration. X-ray lamellar diffraction was used to measure the phosphate-to-phosphate distances, PtP, across the bilayers. The measured PtP increases nonlinearly with the cholesterol concentration until it reaches a maximum. With further increase of cholesterol concentration, the PtP remains at the maximum level until the cholesterol content reaches the solubility limit. The data in all cases can be quantitatively explained with a simple model that cholesterol forms complexes with phospholipids in the bilayers. The phospholipid molecules complexed with cholesterol are lengthened and this lengthening effect extends into the uncomplexed phospholipids surrounding the cholesterol complexes. This long-range thickening effect is similar to the effect of gramicidin on the thickness of lipid bilayers due to hydrophobic matching.     

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.     

Investigation of phase transitions of saturated phosphocholine lipid bilayers via molecular dynamics simulations

Lipid bilayers play an important role in biological systems as they protect cells against unwanted chemicals and provide a barrier for material inside a cell from leaking out. In this paper, nearly 30 μs of molecular dynamics (MD) simulations were performed to investigate phase transitions of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 1,2-dipalmitoyl-sn-glycero-phosphocholine (DPPC) lipid bilayers from the liquid crystalline (L_α) to the ripple (P_β) and to the gel phase (L_β). Our MD simulations accurately predict the main transition temperature for the single-component bilayers. A key focus of this work is to quantify the structure of the P_β phase for DMPC and compare with measures from x-ray experiments. The P_β major arm has similar structure to that of the L_β, while the thinner minor arm has interdigitated chains and the transition region between these two regions has large chain splay and disorder. At lower temperatures, our MD simulations predict the formation of the L_β phase with tilted fatty acid chains. The P_β and L_β phases are studied for mixtures of DMPC and DPPC and compare favorably with experiment. Overall, our MD simulations provide evidence for the relevancy of the CHARMM36 lipid force field for structures and add to our understanding of the less-defined P_β phase.     

Molecular dynamics simulations of proteins in lipid bilayers

With recent advances in X-ray crystallography of membrane proteins promising many new high-resolution structures, molecular dynamics simulations will become increasingly valuable for understanding membrane protein function, as they can reveal the dynamic behavior concealed in the static structures. Dramatic increases in computational power, in synergy with more efficient computational methodologies, now allow us to carry out molecular dynamics simulations of any structurally known membrane protein in its native environment, covering timescales of up to 0.1 micros. At the frontiers of membrane protein simulations are ion channels, aquaporins, passive and active transporters, and bioenergetic proteins.     

Structural change in lipid bilayers and water penetration induced by shock waves: molecular dynamics simulations

The structural change of a phospholipid bilayer in water under the action of a shock wave is numerically studied with unsteady nonequilibrium molecular dynamics simulations. The action of shock waves is modeled by the momentum change of water molecules, and thereby we demonstrate that the resulting collapse and rebound of the bilayer are followed by the penetration of water molecules into the hydrophobic region of the bilayer. The high-speed phenomenon that occurs during the collapse and rebound of the bilayer is analyzed in detail, particularly focusing on the change of bilayer thickness, the acyl chain bend angles, the lateral fluidity of lipid molecules, and the penetration rate of water molecules. The result shows that the high-speed phenomenon can be divided into two stages: in the first stage the thickness of bilayer and the order parameter are rapidly reduced, and then in the second stage they are recovered relatively slowly. It is in the second stage that water molecules are steadily introduced into the hydrophobic region. The penetration of water molecules is enhanced by the shock wave impulse and this qualitatively agrees with a recent experimental result.     

Molecular structures of fluid phase phosphatidylglycerol bilayers as determined by small angle neutron and X-ray scattering

We have determined the molecular structures of commonly used phosphatidylglycerols (PGs) in the commonly accepted biologically relevant fluid phase. This was done by simultaneously analyzing small angle neutron and X-ray scattering data, with the constraint of measured lipid volumes. We report the temperature dependence of bilayer parameters obtained using the one-dimensional scattering density profile model - which was derived from molecular dynamics simulations - including the area per lipid, the overall bilayer thickness, as well as other intrabilayer parameters (e.g., hydrocarbon thickness). Lipid areas are found to be larger than their phosphatidylcholine (PC) counterparts, a result likely due to repulsive electrostatic interactions taking place between the charged PG headgroups even in the presence of sodium counterions. In general, PG and PC bilayers show a similar response to changes in temperature and chain length, but differ in their response to chain unsaturation. For example, compared to PC bilayers, the inclusion of a first double bond in PG lipids results in a smaller incremental change to the area per lipid and bilayer thickness. However, the extrapolated lipid area of saturated PG lipids to infinite chain length is found to be similar to that of PCs, an indication of the glycerol-carbonyl backbone's pivotal role in influencing the lipid-water interface.     

Molecular dynamics simulations of SOPS and sphingomyelin bilayers containing cholesterol

We performed a molecular dynamics simulation of an asymmetric bilayer that contained different lipid mixtures in its outer and inner leaflets. The outer leaflet contained a mixture of sphingomyelin (SM) with cholesterol and the inner leaflet a mixture of stearoyl-oleoyl-phosphatidylserine (SOPS) with cholesterol. For comparison purposes, we also performed two simulations on symmetric bilayers: the first simulation was performed on a bilayer containing a binary mixture of SOPS with cholesterol; the second contained a mixture of SM with cholesterol. We studied the hydrogen-bonding network of the bilayers in our simulations and the difference in the network properties in the monolayers either with SM or SOPS. We observed that in the asymmetric bilayer the properties of monolayers were the same as in the corresponding monolayers in the symmetric bilayers.     

Collective chain dynamics in lipid bilayers by inelastic x-ray scattering

We investigated the application of inelastic x-ray scattering (IXS) to lipid bilayers. This technique directly measures the dynamic structure factor S(q,omega) which is the space-time Fourier transform of the electron density correlation function of the measured system. For a multiatomic system, the analysis of S(q,omega) is usually complicated. But for multiple bilayers of lipid, S(q,omega) is dominated by chain-chain correlations within individual bilayers. Thus IXS provides a unique probe for the collective dynamics of lipid chains in a bilayer that cannot be obtained by any other method. IXS of dimyristoyl phosphatidylcholine and dimyristoyl phosphatidylcholine + cholesterol at two different concentrations were measured. S(q,omega) was analyzed by three-mode hydrodynamic equations, including a thermal diffusive mode and two propagating acoustic modes. We obtained the dispersion curves for the phonons that represent the collective in-plane excitations of lipid chains. The effect of cholesterol on chain dynamics was detected. Our analysis shows the importance of having a high instrument resolution as well as the requirement of sufficient signal-to-noise ratio to obtain meaningful results from such an IXS experiment. The requirement on signal-to-noise also applies to molecular dynamics simulations.     

Comparative molecular dynamics simulations of the antimicrobial peptide CM15 in model lipid bilayers

We report altogether 3-μs molecular dynamics (MD) simulations of the antimicrobial peptide CM15 to systematically investigate its interaction with two model lipid bilayers, pure POPC and mixed POPG:POPC (1:2). Starting with either an α-helical or a random-coil conformation, CM15 is found to insert into both bilayers. Peptide-lipid interaction is stronger with the anionic POPG:POPC than the zwitterionic POPC, which is largely attributed to the electrostatic attraction between CM15 and the negatively charged POPG. Simulations initiated with CM15 as a random coil allowed us to study peptide folding at the lipid-water interface. Interestingly, CM15 folding appears to be faster in POPC than POPG:POPC, which may be explained by a lower activation energy barrier of structural rearrangement in the former system. Our data also suggest that compared with the random-coil conformation, CM15 in a pre-folded α-helix has significantly reduced interactions with the lipids, indicating that peptide initial structures may bias the simulation results considerably on the 100-ns timescale. The implications of this result should be considered when preparing and interpreting future AMP simulations.     

Molecular dynamics simulations of hydrophilic pores in lipid bilayers

Hydrophilic pores are formed in peptide free lipid bilayers under mechanical stress. It has been proposed that the transport of ionic species across such membranes is largely determined by the existence of such meta-stable hydrophilic pores. To study the properties of these structures and understand the mechanism by which pore expansion leads to membrane rupture, a series of molecular dynamics simulations of a dipalmitoylphosphatidylcholine (DPPC) bilayer have been conducted. The system was simulated in two different states; first, as a bilayer containing a meta-stable pore and second, as an equilibrated bilayer without a pore. Surface tension in both cases was applied to study the formation and stability of hydrophilic pores inside the bilayers. It is observed that below a critical threshold tension of approximately 38 mN/m the pores are stabilized. The minimum radius at which a pore can be stabilized is 0.7 nm. Based on the critical threshold tension the line tension of the bilayer was estimated to be approximately 3 x 10(-11) N, in good agreement with experimental measurements. The flux of water molecules through these stabilized pores was analyzed, and the structure and size of the pores characterized. When the lateral pressure exceeds the threshold tension, the pores become unstable and start to expand causing the rupture of the membrane. In the simulations the mechanical threshold tension necessary to cause rupture of the membrane on a nanosecond timescale is much higher in the case of the equilibrated bilayers, as compared with membranes containing preexisting pores.     

Behavior of cholesterol and its effect on head group and chain conformations in lipid bilayers: a molecular dynamics study.

Cholesterol molecules were put into a computer-modeled hydrated bilayer of dimyristoyl phosphatidyl choline molecules, and molecular dynamics simulations were run to characterize the effect of this important molecule on membrane structure and dynamics. The effect was judged by observing differences in order parameters, tilt angles, and the fraction of gauche bonds along the hydrocarbon chains between lipids adjacent to cholesterol molecules and comparing them with those further away. It was observed that cholesterol causes an increase in the fraction of trans dihedrals and motional ordering of chains close to the rigid steroid ring system with a decrease in the kink population. The hydrogen-bonding interactions between cholesterol and lipid molecules were determined from radial distribution calculations and showed the cholesterol hydroxyl groups either solvated by water, or forming hydrogen bond contacts with the oxygens of lipid carbonyl and phosphate groups. The dynamics and conformation of the cholesterol molecules were investigated and it was seen that they had a smaller tilt with respect to the bilayer normal than the lipid chains and furthermore that the hydrocarbon tail of the cholesterol was conformationally flexible.