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

Abstract

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.

Introduction

The cell envelope surrounding the cytoplasm of Gram-negative bacteria is composed of the inner membrane, the periplasm, and the outer membrane (OM). The latter is a unique asymmetrical bilayer with an inner leaflet of phospholipids and an outer leaflet of lipopolysaccharides (LPS) (1). An LPS molecule is composed of three components: lipid A, a core oligosaccharide that is usually further subdivided into an inner and outer region, and an O-antigen polysaccharide (Fig. 1 A). Lipid A contains two β-(1 → 6)-linked glucosamine residues that are phosphorylated and have acylated tails anchoring the LPS into the OM. The inner core is proximal to lipid A and contains a high proportion of negatively charged bacteria-specific sugars, such as 2-keto-3-deoxyoctulosonate (Kdo) and phosphorylated l-glycero-d-manno-heptose (Hep). The outer core consists of common sugars, such as hexoses and hexosamines. Negatively charged inner core and lipid A form a dense, divalent cation-stabilized layer (Fig. 1 B). These strong electrostatic (cross-linking) interactions are essential for OM integrity and function. Attached onto the outer core is a polymer of repeating saccharide subunits called O-antigen, which usually consists of 3–6 sugar residues and whose primary structure is not conserved and varies according to serological group.

Figure 1.

(A) Chemical structure of lipid A and sequence of the E. coli K12 core sugars. The lipid A molecule in this study consists of two GlcN (d-glucosamine) residues joined by a β-(1 → 6)-linkage, two monophosphoester groups at O1 and O4′, and six amide/ester-linked fatty acids. The K12 inner core consists of two Kdo (2-keto-3-deoxyoctulosonate) residues and three Hep (l-glycero-d-manno-heptose) residues, among which two residues are phosphorylated at the O4 positions, and the outer core is made up of three Glc (d-glucose) residues, one Hep residue, and one Gal (d-galactose) residue. (B) Representative snapshot of the MD simulation of a fully asymmetric LPS-DPPC model system at 310 K. Lipid A is represented as green spheres, core sugars as gray sticks, DPPC as blue spheres, and Ca²⁺ ions as small yellow spheres that are strongly interacting with phosphate groups (red and orange spheres) of lipid A and Hep sugars. (C) Schematic of the experimental system is shown. A silicon substrate is coated with a layer of permalloy and then gold coated with a self-assembled monolayer of 1-oleoyl-2-(16-thiopalmitoyl)-sn-glycero-3-phosphocholine (gray/pink) upon which a bilayer composed of DPPC (yellow/blue) and Ra-chemoform LPS (brown/green) has been sequentially deposited. To see this figure in color, go online.

The OM separates the periplasm from the external environment and functions as a selective barrier that prevents the entry of toxic molecules, such as antibiotics and bile salts into the bacteria, which is crucial for the survival of bacteria in diverse/hostile environments. Clearly, such a complex nature of the LPS makes it challenging to study the asymmetrical OM structure and dynamics, its interactions with OM proteins, and its roles in translocation of substrates, including antibiotics. Given these difficulties in gaining nanoscale biological structural information in vivo, model biological systems become a useful tool in examining phenomena under conditions that permit molecular-scale investigation and also allow a level of control to render these systems suitable for biophysical or structural investigation.

OM model membranes were constructed using an inner leaflet of phospholipids and an outer leaflet of LPS without O-antigen. These were made and deposited directly onto silicon or onto lipid-coated gold surfaces (2, 3, 4, 5). The former produces membranes that are essentially in contact with the substrate, whereas the latter produces asymmetric membranes that float ∼15 Å above the solid support, reducing the frictional influence of the support on the membrane and making these biomimetics suitable for biophysical and structural studies using neutron reflectometry (NR). A “cartoon” structure of the experimental model system is shown in Fig. 1 C. In parallel, there has recently been significant progress in the development of atomic-scale molecular dynamics (MD) simulations of the bacterial OM, including various O-antigens. Although the MD simulation results were comparable with solution NMR conformational dynamics measured with isolated O-antigen polysaccharides (6, 7, 8, 9), direct comparison and verification of these simulations with experimental data in similar bacterial asymmetric OM environments remains a challenging problem.

In this study, we combine the NR and MD approaches and show that there is excellent agreement between the experiment and the simulation for complex asymmetrical LPS-containing membrane systems in terms of the overall bilayer density profiles along the bilayer normal. We also show that this joint experimental/simulation approach enables us to extract biophysical information from these complex environments, particularly 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). We further show that we are able to estimate the bending modulus of the membrane from the dynamical behavior of the experimental system and that this is consistent with the modulus expected from the lipid packing in the bilayer.

Materials and Methods

Experimental

Ra mutant rough strain LPS (RaLPS chemotype) from EH100 Escherichia coli was obtained from Sigma-Aldrich (Dorset, UK). ω-thiolipid (1-oleoyl-2-(16-thiopalmitoyl)-sn-glycero-3-phosphocholine) and tail-deuterated DPPC ((d-DPPC) 1,2-dipalmitoyl (d62)-sn-glycero-3-phosphocholine) were obtained from Avanti Polar Lipids (Alabaster, AL). All phospholipid and LPS samples were used without further purification. All other chemicals were sourced from Sigma-Aldrich.

Permalloy/gold coating of silicon crystals

Ozone-cleaned silicon crystals (50 × 80 × 15 mm) with a polished 80 × 50 mm face (111 orientation; Pi-KEM, Tamworth, UK) were sequentially sputter coated with permalloy (Ni: Fe 4: 1) and gold at the National Institute of Standards and Technology center for Nanoscience and Technology (Gaithersburg, MD) in a Denton Discovery 550 sputtering chamber.

Fabrication of the ω-thiolipid self-assembled monolayer

ω-thiolipid (1 mg/mL in chloroform/methanol (4:1)) was dried in a glass tube to produce lipid films and then resuspended in 1% β-octylglucopyranoside and 50 mM Tris (pH 8.0). Immediately before use, Tris (2-carboxyethyl)phosphine HCl) was added to a concentration of 1 mM. The gold surfaces were cleaned sequentially with 1% Hellmanex solution (Hellma, Müllheim, Germany) and 1% sodium dodecyl sulfate (SDS) solution followed by a final ultraviolet/ozone cleaned. The cleaned surfaces were immersed in the ω-thiolipid/β-octylglucopyranoside solution for 2 h at ∼50°C. The surfaces were removed and cleaned again in SDS and rinsed with ultrapure water before reimmersion in the lipid solution for a further 2 h. The surfaces were then removed from the coating solution, washed with SDS, rinsed with ultrapure water, and dried under nitrogen.

Gram-negative bacterial OM model deposition

Deposition of the OM models on the ω-thiolipid self-assembled monolayer (SAM)-coated gold surfaces used a custom-built Langmuir-Blodgett trough (Nima Technologies, Coventry, UK). The trough was cleaned and filled with 1 mM CaCl₂ solution. The air-liquid interface was aspirated until clean, and a ω-thiolipid SAM-coated silicon block was submerged and placed in the trough dipping well.

The OM models were deposited onto the ω-thiolipid-coated substrates in two steps; first, the inner phospholipid leaflet of the bilayer was deposited by Langmuir-Blodgett deposition of a DPPC monolayer followed by deposition of the LPS outer leaflet by Langmuir-Schaefer transfer of a RaLPS monolayer. For the Langmuir-Blodgett deposition of the inner bilayer leaflet, d-DPPC was deposited from a 5 mg/mL solution in chloroform onto the clean air-liquid interface. Three to four compression and relaxation cycles of the interfacial monolayer (with a maximal pressure of 38 mN/m) were conducted before the monolayer was compressed to 35 mN/m, and the submerged ω-thiolipid SAM/gold/permalloy-coated silicon crystal was lifted through the monolayer at a speed of 3 mm/min while the monolayer surface pressure was held constant.

The Langmuir-Blodgett trough was again cleaned and refilled with 2 mM CaCl₂, which was cooled to ∼10°C. RaLPS was then deposited onto the air-liquid interface from a 2 mg/mL suspension in chloroform/methanol/water solution (60:39:1 v/v) and pressure cycled three times before being held at a pressure of 35 mN/m. The d-DPPC/ω-thiolipid-coated substrate was then placed in a holder above the air-liquid interface. The polished face of the silicon crystal was adjusted using a purpose-built leveling device to make the crystal face parallel to the water surface. The substrate was then dipped through the interface at a constant speed of 3 mm/min and lowered into a purpose-built sample cell in the well of the trough. This process is described in greater detail in the recent publication (2).

NR measurements on floating OM models

NR measurements of the Gram-negative bacteria OM models were undertaken on the POLREF white-beam reflectometers at the Rutherford Appleton Laboratory (Oxfordshire, UK), which operates in a polarized mode. NR measures the neutron reflection as a function of the angle and/or wavelength (λ) of the beam relative to the sample. The reflected intensity was measured as a function of the momentum transfer, Q_z (Q_z = (4π sin θ)/λ, where λ is wavelength and θ is the incident angle). The white-beam instruments are able to probe a wide area of Q_z space at a single angle of reflection because of the use of a broad neutron spectrum. Therefore, to obtain reflectivity data across a Q_z, a range of ∼0.01–0.25, glancing angles of 0.25, 0.5, 1.0, and 2.3° were used for POLREF, employing a wavelength spectrum of 2–12 Å at each angle.

Sample cells were mounted on a variable-angle sample stage in the SNR instrument. The samples were subsequently placed in a magnetic field. The two spin orientations result in two distinct neutron scattering length density (nSLD) for the permalloy layer but unchanged nSLD for the rest of the sample. The inlet to the liquid cell was connected to a liquid chromatography pump (L7100 high performance liquid chromatography pump; Merck, Kenilworth, NJ; Hitachi, Yokohama, Japan), which was programmed to remotely change the solution Hydrogen/Deuterium mix. The bilayer structure was analyzed in three solution isotopic contrasts: 1) 100% D₂O, 2) 75% D₂O (which has the same nSLD as gold and is thus called Au-matched water [GMW]), and 3) 100% H₂O. GMW are used to simplify the layer structure by effectively making the biological layer stand out from a completely matched substrate and solution on either side.

For measurements above ambient temperature, the sample cells were heated to 37°C using a water bath circulating temperature-controlled water through channels in the cell lid, as described previously.

Reflectivity data analysis

The aim of the analysis is a comparison between simulated asymmetric Gram-negative membranes and their experimental equivalent. Both the sample and the simulations are of a simplified Gram-negative OM with synthetic DPPC in the inner leaflet and rough mutant (Ra chemotype) LPS in the outer leaflet. The key questions are as follows: 1) can the measured data be replicated by the simulated structures, and 2) is the membrane asymmetry preserved in the experimental sample? We approach these questions with a Bayesian analysis of the model fit. The comparison between simulation and experiment is done using a recently published procedure to include simulations into the analysis of reflectivity data (10).

The SLD is a function of the number and type of atoms per unit volume. So, the first stage in converting a simulation trajectory into an SLD is a calculation of component volumes according to the method described by Petrache et al. (11). The simulation system is grouped into components (Fig. S1 A) that could behave as a single unit (e.g., a DPPC lipid might be divided into groups representing the head (Dphead), -CH2 chain (Dpch2), and terminal methyl (Dpch3) regions, for example), and number density distributions are calculated for each component. To do this, the simulation box of the membrane is divided into slices of thickness D_z (where the z axis is defined as normal to the bilayer plane), and the number of occurrences of each particular group within each slice, N(z), is counted and histogrammed. The number density is then

$$n\left(z\right)=\frac{N\left(z\right)}{V_s}=\frac{N\left(z\right)}{A_c\times \Delta z},$$ (1)

where V_s is the volume of the slice, which is given by the slice thickness times the projected area of the unit cell into the bilayer plane (A_c). The volume of each component can be calculated by imposing a condition of space filling so that

$$V_1{n}_1\left(z\right)+V_2{n}_2\left(z\right)+\cdots V_n{n}_n\left(z\right)=1,$$ (2)

over all z, where V_ξ are the component volumes and $V_{\xi }{n}_{\xi }\left(z\right)\equiv p_{\xi }\left(z\right)$ are the probability distributions (equivalently volume fractions) shown in Fig. S1 C (the example shown is for the LPS-DPPC^100% system). In practice, the component volumes are obtained by iteratively minimizing ${\sum }_z{\left({\sum }_{\xi }{p}_{\xi }\left(z\right)-1\right)}^2$, with V_ξ as the fitting parameters (11). It should be noted that the volumes for the 293 and 310 K simulations (see below) were calculated separately to allow for any membrane thermal expansion, and these are given in Table S2.

The reflectivity is eventually calculated from the SLD, which is obtained from the probability distributions multiplied by the relevant scattering length of each group, s, so that

$$s_{\xi }=\sum _i{n}_i{b}_i,$$ (3)

where b_i is the bound coherent scattering length for the ith type of atom for the neutrons case. For each distribution, the SLD is then given by

$$\rho \left(z\right)=\frac{p_{\xi }\left(z\right)\times s_{\xi }}{V_{\xi }}.$$ (4)

The SLD profile calculated from the distributions in Fig. S1 C are shown in Fig. S1 B. The SLD profile of the membrane alone is insufficient to model the reflectivity from the whole interface, and it is necessary to “splice” the calculated membrane SLD to the SLD profile of the lower layers. In the model, the substrate and metal-coating layers are represented by step functions, indicating full volume occupancy in these regions (10), whereas the SAM is modeled in a similar way to the membrane, except that the group distributions are approximated by Gaussians, with literature volumes taken for the phosphatidylcholine headgroup (12).

To join the substrate and membrane models together, the two parts of the model (i.e., membrane and lower layers) are combined in terms of occupied volume. Then, any remaining free volume across the interface is “filled” with water as shown previously (10). The volume occupied by the simulated membrane (in terms of volume fraction) is shown in Fig. S1 B, and the complete volume occupancy across the interface is shown in Fig. S1 D. The unoccupied volume remaining in the system (i.e., not occupied by bilayer or substrate) is shown by the blue-shaded areas in Fig. S1 D, and these are then the water distributions of the model. The whole set of distributions shown in Fig. S1 C is then converted to an SLD profile, which is then used to calculate the reflectivity.

One of the goals of the analysis is to determine the degree of asymmetry of the membrane in the experimental sample. We approach this by producing simulations of extreme cases of mixing (i.e., LPS-DPPC^90% and LPS-DPPC^50%; as discussed below, LPS-DPPC^100% shows an atypical structure compared to the other mixed films, and hence the 90% simulation is used). Then, we produce composite profiles of any asymmetry using a scaled sum of the individual profiles of these extreme cases, such that

$${\rho }_{mix}=M{\rho }_{90}+\left(1-M\right){\rho }_{50},$$ (5)

where ρ₉₀ and ρ₅₀ are the SLD profiles of the relevant simulations, $\text{M}$ is the mixing parameter, and ρ_mix is the SLD of the mixed simulation. M is a dimensionless value between 0 and 1, and so M = 1 is a 90% asymmetric membrane, and M = 0 is completely mixed. It is also necessary to apply the same procedure to the volume fractions as shown in Fig. S2. Both the membrane SLD and volume are then convoluted with a Gaussian to account for out-of-plane membrane fluctuations (roughness) and scaled to account for lower than optimal coverage as shown previously (10).

To fit the experimental data, the membrane roughness, coverage, and the mean membrane position relative to the substrate are fitting parameters, along with the substrate parameters defining thickness and roughness of substrate layers and those defining the SAM model. In addition, instrument parameters for background, resolution, and scale factors are also required, and these are treated as fitting parameters as previously described. Additionally, the SLDs of the water bulk phases can show some variation from the expected value dies to incomplete solvent exchange, and so these are also fitted. Of these, the SLDs of the D₂O and GMW contrasts can be determined from the positions of the critical edges of the relevant data sets, and so these were held constant. However, the H₂O SLDs were treated as fitting parameters because there is no critical edge. Separate values for bulk SLDs were used for the 293 and 310 K data (to allow for possible inconsistency in solvent exchange). Background parameters were shared between the temperatures, with each equivalent spin state and bulk SLD sharing the same background parameter, requiring six in total. As described below, each temperature requires its own set of M, the membrane center position (D_B), and coverage. The complete list of parameters is shown in Table S3, showing either the fitted value or constant value as indicated and the priors where relevant. The model was fitted to the data using a Bayesian Markov-chain Monte Carlo algorithm (13). The posterior parameter distributions associated with the values in Table S3 are shown in Fig. S3.

MD simulation

Each replica of all LPS-DPPC systems (details of MD system setup available in Supporting Materials and Methods) was equilibrated for 450 ps using CHARMM (14), in which a Langevin temperature control was used for NVT (constant particle number, volume, and temperature) dynamics. Equilibration run was followed by 500-ns NPT (constant particle number, pressure, and temperature) production dynamics at 310 K for each replica using NAMD (15). This resulted in a total simulation time of 2.5 μs for each LPS-DPPC system. We also extended simulations for a 100-ns production run for each replica at 293 K, in which starting coordinates for each replica were obtained from a corresponding snapshot at 300 ns from 310 K simulations. Langevin dynamics was used to maintain constant temperature with a Langevin coupling coefficient of 1 ps⁻¹, and a Nosé-Hoover Langevin piston (16, 17) was used to maintain constant pressure (1 bar) with a piston period of 50 fs and a piston decay time of 25 fs while keeping barostating anisotropic for all LPS-DPPC systems during production runs. The NAMD input scripts had been generated by CHARMM-GUI (18, 19). During LPS-DPPC system equilibration, various planar and dihedral restraints were applied to the LPS molecules and water molecules; these restraint forces were gradually reduced to zero for the production simulations. Additional dihedral angle restraints were applied to restrain all sugar rings to the pertinent chair conformation, which were maintained during the production simulations. A 2-fs time step was used for integration together with the SHAKE algorithm (20). The van der Waals interactions were smoothly switched off at 10–12 Å by a force-switching function (21), whereas the long-range electrostatic interactions were calculated using the particle-mesh Ewald method (22). All the systems were simulated with the CHARMM36 force field for lipids (23), carbohydrates (24, 25), and LPS (26) using the TIP3P water model (27). Most results are presented by the averages of five independent runs and the standard errors. For LPS-DPPC systems at 310 K, the last 200-ns trajectories were analyzed, and for the systems at 293 K, the last 50-ns trajectories were used.

Results and Discussion

Reflectivity analysis of OM membrane mimics

The experimental system is the “floating” model membrane that we have described previously (2). The asymmetric membrane consists of E. coli Ra LPS (i.e., without O-antigen) in the outer leaflet and deuterated 1,2-dipalmitoyl-sn-phosphatidylcholine (DPPC) in the inner leaflet, with a certain level of LPS-DPPC mixing depending on experimental conditions. The membrane is deposited on a phosphatidylcholine-terminated SAM. This process is well known to result in “floating” membranes, which are robustly associated with the substrate but separated from frictional effects by substantial water cushions (28, 29, 30). The experimental “floating” model system is shown schematically in Fig. 1 C.

Polarized NR (PNR) was used to experimentally probe our OM model. A single PNR measurement produces nonunique results because multiple structural solutions can exist for a given data set, analogous to the diffraction phase problem. Therefore, it is customary to measure the same sample multiple times with a differing isotopic substitution. This “isotopic contrast” approach can identify a unique solution to the interfacial structure and allow for the contribution of individual components of a complex sample to be highlighted using selective deuteration (31). In this work, we measured the system against bulk water of varying deuteration, together with perdeuterated lipids in the inner leaflet.

Experimentally, the asymmetric membrane is formed with each leaflet deposited separately from pure monolayers of each component (DPPC on the inside and LPS on the outside). However, as we have previously observed (2, 3), maintaining this asymmetry is dependent on conditions (particularly the presence of divalent cations), and translocation between leaflets is possible even for LPS. Therefore, any data analysis procedure must be able to assess the level of mixing.

In the analysis of reflectivity data from such systems, traditionally rather crude models have been employed to approximate the sample structure in terms of simple groups of layers. However, recently, Hughes et al. (10) demonstrated how to incorporate MD simulations into the analysis of NR data from supported phospholipid-only membrane samples, leading to a more detailed interpretation of NR experiments using molecular-level information.

To extend this approach to the more complicated asymmetric system described here, it is necessary to allow for the unknown degree of mixing in the sample, with the level of mixing incorporated into the model as a fitting parameter. As described in Materials and Methods, we do this by constructing a composite model from the extremes of the mixed and demixed states, which allows for a continuous variation in asymmetry. However, to investigate the change in structure at different mixing ratios at a molecular level, we also constructed and simulated a range of systems at intermediate mixing levels between the two extremes. In total, six asymmetric and one symmetric LPS-DPPC bilayer systems were constructed with varying ratios of LPS and DPPC in the outer and inner leaflets (Table S1); system LPS-DPPC^100% denotes the fully demixed system with the outer leaflet of pure LPS (Fig. 1 B) and the inner leaflet of pure DPPC, whereas system LPS-DPPC^50% represents the fully mixed system with equal numbers of LPS and DPPC (i.e., symmetric bilayers; Fig. 2 A).

Figure 2.

Representative snapshots from the MD simulation of (A) system LPS-DPPC^50% and (B) system LPS-DPPC^90% at 310 K. Lipid A is represented as green spheres, core sugars are represented as gray sticks, and DPPC is represented as blue spheres. To see this figure in color, go online.

To analyze the measured data using the simulated membranes, it is necessary to produce a model that describes the experimental scattering of the whole interface, including the contributions not just from the asymmetric membrane but also those from the substrate and the lower SAM layers shown in Fig. 1 C. This is done in terms of the occupied volume across the entire interface, as described previously (10) and in Materials and Methods (Fig. S1; Table S2).

We approach the problem of unknown mixing level by analyzing the data in terms of a composite structure, building the membrane nSLD and volume distributions by a linear combination of two separate simulations at extremes of the mixing ratios (i.e., LPS-DPPC^50% and LPS-DPPC^90%; as we discuss in the next section, the fully demixed LPS-DPPC^100% shows an atypical structure compared to the mixed ones, hence the choice of LPS-DPPC^90% to represent the “separated” case). A mixed membrane of any level of asymmetry can then be modeled according to Eq. 5, with a mixing ratio (M) as a fitting parameter. The underlying assumption behind this procedure is that the film structure varies linearly with the composition (32), which is the case between LPS-DPPC^50% and LPS-DPPC^90%, based on the simulation results below. (In Supporting Materials and Methods, we provide a justification for this approach by comparison with the alternative of fitting the data with the series of six simulation runs at different levels of mixing. A Bayesian analysis shows that both approaches give equivalent results for the level of leaflet mixing.)

In the combined analysis, the membrane structure is defined by the simulation, but including this into the construction of the entire interfacial nSLD profile requires additional parameters. In addition to including the structure of the SAM and lower layers, it is necessary to define the position of the membrane relative to the substrate, which we do by a simple translation of the membrane nSLD along the z axis, defining the membrane center position (D_B) to be the distance between the SAM headgroup and the bilayer center (10). We also include a roughness parameter to describe out-of-plane fluctuations of the experimental membrane that are not inherent to the simulation (effectively, the fluctuations manifest in the data as a time-averaged variation of membrane SLD around the mean D_B, which we model with a Fourier convolution of the membrane structure with a Gaussian) (33). The magnitude of the thermal membrane fluctuations (and hence, the mean, D_B) is expected to be temperature dependent. Therefore, the PNR data of the asymmetric membrane sample was measured at 293 and 310 K to assess any temperature effect. Both temperatures were measured sequentially on the same sample, so the parameters describing the substrate and supporting layers should not vary between the two measurements. To ensure this commonality, we analyzed both data sets simultaneously. However, to allow for any temperature changes to the membrane structure, D_B, roughness, and M are defined separately for each temperature.

At each temperature, the sample was measured at two spin states of the polarized neutron beam and also against three bulk water contrasts—D₂O, H₂O, and gold-matched water (GMW) (a mixture of 75% D₂O and 25% H₂O); GMW was chosen to match the resulting nSLD with that of the gold substrate enhancing certain features in the scattering data. This yielded six isotopic and magnetic contrasts at each temperature (for each water contrast, the permalloy layer has a different SLD depending on whether the permalloy magnetization is parallel or antiparallel to the neutron spin) (33), producing a combined fit of 12 contrasts in total. The combined analysis is then carried out for the full parameter set shown in Table S3.

The simultaneous best fits across all 12 contrasts are shown in Fig. 3 A, and there is excellent agreement between the model and data, with only a few data points lying outside the model prediction bounds across all data sets. The accompanying nSLD profiles for the fits are shown in Fig. 3 B. The parameter posterior distributions from the Bayesian analysis for the membrane parameters (i.e., bilayer position, roughness, and asymmetry) are shown in Fig. 4, and the best-fit values and 95% prediction intervals are given in Table 1 (the full set of parameter values and posterior intervals for the whole parameter set, including the substrate parameters, are given in Fig. S3; Table S3). The solid lines in the fits and nSLD profiles in Fig. 3 are obtained from the best-fit values in Table S4. Fig. 4 A shows a closer view of the nSLD profiles in the membrane region, and the clear difference between them is that the membrane profile is less well defined and broadened in the 310 K case.

Figure 3.

(A) Simultaneous fits of all 12 experimental contrasts with the model described in Materials and Methods. The upper six curves are from the 310 K measurements, and the lower six are measured at 293 K. Each pair of curves are the “spin up” and “spin down” magnetic contrasts associated with each of the three water contrasts. All substrate parameters are shared but with separate membrane parameters for each temperature, as shown in Table 1. (B) nSLD profiles are associated with the best fit in (A). The 310 K profiles are shown in red, and the 293 K profiles are shown in blue. To see this figure in color, go online.

Figure 4.

(A) Closer look of the nSLD profiles in the membrane region of Fig. 3B (red for 310 K and blue for 293 K). The largest difference between the profiles is that the membrane signal is more diffusive at 310 K, indicating more pronounced out-of-plane fluctuations. (B) A comparison of posterior distributions of membrane parameter values between the two temperatures (red for 310 K and blue for 293 K) is shown. The degree of asymmetry and membrane coverage did not change between temperatures. However, there is a large increase in the convolution applied to the membrane as the temperature increases, accompanied by a small movement of the membrane away from the substrate. To see this figure in color, go online.

Table 1.

Membrane Parameters for Each Temperature

Parameter	Fitted Value (95% Interval)	Prior
Bilayer coverage	0.999 (0.995, 1)	uniform (min = 0, max = 1)
M (310 K)	0.976 (0.93, 0.999)	uniform (min = 0, max = 1)
DB (310 K)	74.8 (74.2, 75.4)	uniform (min = 40, max = 100)
Bilayer rough (310 K)	22.4 (21.6, 23.2)	uniform (min = 3, max = 50)
M (293 K)	0.924 (0.87, 0.97)	uniform (min = 0, max = 1)
DB (293 K)	73.68 (73.23, 74.17)	uniform (min = 40, max = 100)
Bilayer rough (293 K)	14.78 (14.07, 15.54)	uniform (min = 3, max = 50)

max, maximum; min, minimum.

In Fig. 4 B, we compare the posterior distributions of the 293 and 310 K membrane parameters (i.e., those from Table 1). There is a very small difference in the membrane asymmetry between the two temperatures (M₂₉₃ = 0.924 and M₃₁₀ = 0.95), but the large overlap of the posterior distributions (and hence, confidence intervals) means that this is not statistically significant, suggesting that there is no significant temperature-induced translocation of lipids between leaflets on heating. Because the mixing is between the 90 and 50% simulations, a value of M = 0.95 corresponds to an actual mixing ratio of 0.95(90 − 50) + 50 = 88%.

The largest difference between the two temperatures is a noticeable increase in out-of-plane fluctuations, with a Gaussian width of 14.7 Å required for the nSLD convolution at 293 K to 22 Å at 310 K. The fluctuations are thermally driven and would be expected to increase with temperature. For any given membrane, the fluctuation amplitude is a function of the intrinsic bending rigidity of the bilayer. The fluctuation spectrum is given by:

$$\left|u^q\right|=\frac{k_{B}T}{\widetilde{U^{\text{'}\text{'}}}+\gamma q^2+\kappa q^4},$$ (6)

where $\widetilde{{\text{U}}^{\text{''}}}$ is the second derivative of the effective potential, γ is the membrane tension, and κ is the bending modulus (30). The bending modulus can be obtained experimentally but requires a measurement of the full fluctuation spectrum by investigating a different region of q space using diffusive x-ray scattering (34). Nevertheless, we can extract some broad conclusions regarding the membrane rigidity just from these specular results by comparison with other similar systems. By integration, the fluctuation spectrum can be related to the overall fluctuation amplitude (σ²) (30, 34):

$${\mathit{\sigma }}^2={\left|u\right|}^2=\int \overrightarrow{q}\left|u_q\right|d^2.$$ (7)

Taking typical values from a DPPC floating bilayer for $\widetilde{{\text{U}}^{\text{''}}}$ ≈ 10¹²–10¹³ Jm⁻⁴, γ ≈ 10⁻⁴–10⁻⁵ Nm⁻¹, and κ ≈ 10–50 k_BT leads to an expected value of σ² < 10 Å. This tallies with our previous results for DPPC, measured under the same conditions as here and analyzed with the same model, in which the Gaussian convolution of the simulated DPPC SLD required to fit the data was 2.06 (0.20, 4.58) Å (10). At the main transition, the bending modulus of DPPC drops significantly to around ∼k_BT, and the resulting fluctuation amplitude increases to 20–30 Å (34), which, at the lower end, is similar to the convolution required here. So it is reasonable to conclude that the bending modulus of the asymmetric membrane is also of this order. This is of course quite approximate, and more detailed investigations will be required, but clearly, the model asymmetric Gram-negative bilayer is inherently a very soft, flexible membrane.

Molecular-level structures of OM mimics

The use of MD simulations to analyze the scattering data then allows us to proceed further by investigating what the atomistic arrangement of each component might be contributing to the overall flexibility of the system. Detailed arrangement of different molecular components of lipids with varying asymmetry can be analyzed using the nSLD profiles (Fig. 5 A) and number density profiles (Fig. 5 B) along the bilayer normal. Fig. 5 B shows the average locations of the different molecular components in the LPS-DPPC^100% membrane, such as the terminal methyl groups (at the bilayer center), methylene chains (medium density region around ±10 Å), headgroups of DPPC and lipid-A-containing phosphates (high density peaks around ±20 Å), and LPS oligosaccharides located beyond ±20 Å with two peaks corresponding to the inner (peaks around ±30 Å) and outer (peaks around ±40 Å) core sugars. As the degree of asymmetry reduces (i.e., in going from LPS-DPPC^100% to LPS-DPPC^50%), the LPS oligosaccharides progressively appear on the opposite side of the membrane (Fig. S4). The lipid packing of these asymmetric bilayers was analyzed in terms of area per lipid (A_L) of each lipid type and the bilayer hydrophobic thickness (d_H) (Fig. 5 C; Table S5). The NMR acyl-chain-order parameter |S_CD| were also calculated and are shown in Figs. S5 and S6.

Figure 5.

(A) nSLD profiles for all the simulated mixtures described in the text. The mixtures range from the fully separated LPS-DPPC^100% to the fully mixed LPS-DPPC^50%. Each simulation was used individually to fit the data for the Bayesian model selection comparison. (B) Number density profiles are shown of system LPS-DPPC^100% at 310 K (solid lines) and 293 K (dotted lines) along the membrane normal for each membrane component (terminal methyl group, methylene chains of lipid A and DPPC, phosphate-containing DPPC and lipid A headgroups, LPS oligosaccharides having inner and outer core sugars, and water). (C) Hydrophobic thickness and area per lipid for each of the simulated mixtures is shown. To see this figure in color, go online.

It is immediately apparent from Fig. 5 C that LPS-DPPC^100% has a structure that is anomalous to the other mixtures, which is particularly visible in A_L of the LPS. The A_L and bilayer thickness of both lipid A and DPPC increase monotonically from LPS-DPPC^50% to LPS-DPPC^90% at both temperatures, but the fully separated LPS-DPPC^100% does not conform to the linear trend. For the mixtures, a closer look at the structures reveals domains of different lipid packing (Fig. S7) at 293 K with regions in which the local A_L of DPPC corresponds to a quite closely packed lipid, interspersed with regions in which the packing is far more diffuse. The relative proportions of each increase linearly with increased mixing, which is reflected in the linear trend in the average bulk membrane properties of the mixtures, as shown in Fig. 5 C. (It should be emphasized that reflectivity measures a structure that is spatially and temporally averaged over the beam footprint, which covers several square centimeters, and the measured nSLD of inhomogeneous films is a linear average of lipid packing regions).

In terms of lipid area, even for LPS-DPPC^100%, the average DPPC A_L of 64.03 ± 0.13 Å² at 293 K is significantly higher than the experimental A_L of the pure gel phase of DPPC (47.9 Å²) and closer to that of the fluid phase. The chain order parameters of DPPC are also more closely matched to the fluid phase. As shown in Fig. S7, there appears to be domains of gel-like areas mixed with higher A_L. The distribution of A_L and fits to three Gaussian peaks are shown in Figs. S8 and S9. At 293 K, there is a significant fraction of lipids that are gel-like A_L (48.3 Å², see μL in Table S6 at 293 K). This occurs even for the symmetric LPS-DPPC^50% membrane but at a much lower fraction in comparison with LPS-DPPC^100% at 293 K. For LPS-DPPC^50%, this indicates that LPS is significantly affecting the packing of the DPPC, reducing the preference of DPPC to a close-packed state at temperatures below the main phase transition of the pure lipid. For the fully asymmetric LPS-DPPC^100%, these A_L results suggest that more DPPC prefers to be packed in the inner leaflet, but this cannot occur because of our initial constraint on the amount of DPPC and the reduced packing (compared to DPPC) of the opposing leaflet with its bulky LPS headgroups. Thus, LPS-DPPC^100% was not included in our mixing model to interpret the level of leaflet asymmetry.

As is evident from Fig. 2 B, there is extensive interdigitation at the interface between the leaflets. So, the inner leaflet DPPC is under strain and forced to occupy a larger area than the tensionless A_L of the pure DPPC case. Similarly, lipid A is under compression and forced to occupy a smaller area than the ∼192 Å² calculated in an asymmetric E. coli K12 OM system at 310 K (35). The link between atomic structure and bulk membrane properties has been considered by Illya et al. (36), and they showed that lipids under tension caused by mismatch in packing parameters (in their case, asymmetric tails and differently sized headgroups) results in an increase in area stretch modulus and a corresponding decrease in membrane stiffness (37). Similarly, Karamdad et al. (38) studied asymmetric vesicles and found that asymmetry increased the membrane flexibility, which they interpreted to be caused by an increased curvature elastic stress caused by mismatched lipid intrinsic areas. Park et al. (39) showed the same results from the theoretical studies based on bilayer simulations with systematic area mismatch. So, even qualitatively, the molecular packing revealed by these membrane simulations suggests that the Gram-negative OM is a bilayer that would be expected to have a high degree of flexibility as seen in the experimental and simulation results.

Conclusions

The Gram-negative OM acts as a defense barrier and shields the bacterium from hostile environments and agents. Therefore, developing a controllable, unconstrained experimental model of this system opens ways to detailed systematic investigation of its properties and interactions. Similarly, developing methods for atomistic simulation of the membrane offers high-resolution investigations of membrane organization and behavior. However, up to now, both advances have been limited by the lack of independent, testable corroboration of the fidelity of the different approaches. Models for interpreting NR data are usually rather crude and offer only limited low-resolution interpretation of the membrane structure. Similarly, simulations require cross validation with experiments. The fact that our results show such close corroboration between simulations and the experiment both in terms of structure and dynamics in effect validates both, allowing experimental testing of the conclusions of simulations studies and also atomistic interpretation of the behavior of experimental model systems. The combination of both opens a powerful new approach to understanding the biological and biophysical behavior of the bacterial OM. Future experimental studies will employ the combination of experimental strategies used here to examine diverse phenomena, such as antimicrobial agent disruption of the OM, the interaction of integral membrane proteins with the surrounding lipid matrix, and the interaction of bacteriophage viruses with the OM to name a few.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Editor: Tommy Nylander.