Small-Angle Neutron Scattering Study of a Phosphatidylcholine–Phosphatidylethanolamine Mixture

The properties of single-component phospholipid lipid bilayers have been extensively characterized. Natural cell membranes are not so simple, consisting of a diverse mixture of lipids and proteins. While having detailed structural information on complex membranes would be useful for understanding their structure and function, experimentally characterizing such membranes at a level of detail applied to model phospholipid bilayers is challenging. Here, small-angle neutron scattering with selective deuteration was used to characterize a binary lipid mixture composed of 1,2-dimyristoyl-3-sn-glycero-phosphatidylcholine and 1,2-dimyristoyl-3-sn-glycero-phosphatidylethanolamine. The data analysis provided the area per lipid in each leaflet as well as the asymmetry of the composition of the inner and outer leaflets of the bilayer. The results provide new insight into the structure of the lipid bilayer when this lipid mixture is used to prepare vesicles.


INTRODUCTION
The function of biological membranes arises from the diversity of proteins with specific functions and the many different lipids of which they are composed.For example, phosphatidylcholine and phosphatidylethanolamine lipids make up a large fraction of eukaryotic membranes, which also contain other phospholipids, cholesterol, sphingomyelin, and spingolipids. 1Phosphatidylglycerol lipids tend to be more prevalent in bacterial membranes than phosphatidylcholines. 2,3 These compositionally complex membranes form well-structured bilayers as a result of the amphipathic nature of lipids.Hydrophobic effects are not the only governing factor driving the structure.Cells actively maintain different compositions for the inner and outer leaflets of the bilayer. 4,5Similarly, biological membranes are structured in a lateral sense. 6As a result, it is important to understand the structure of compositionally complex membranes.
Performing a detailed experimental study of lipid bilayers composed of more than one lipid species necessitates differentiating among the various lipids in the intact structure.Neutron scattering methods can do so through the use of selective deuterium labeling and contrast variation methods. 7ydrogen (H) and its isotope deuterium (D) have very different neutron scattering lengths, 8 even though they are indistinguishable when using X-rays.When combined with a neutron scattering technique that can probe length scales relevant to a lipid bilayer (sub-Å to μm), such as diffraction, small-angle neutron scattering (SANS), or neutron reflectometry (NR), it is possible to differentiate between lipids when more than one kind is present in the structure.
A study of the structure of lipid bilayer vesicles composed of a 7:3 molar mixture of deuterium-labeled 1,2-dimyristoyl-3-snglycero-phosphatidylcholine (DMPC) and unlabeled 1,2dimyristoyl-3-sn-glycero-phosphatidylethanolamine (DMPE) is presented here.−19 In the present work, SANS was used to experimentally characterize the structure of unilamellar vesicles as a function of temperature.Deuterium labeling made it possible to determine if DMPE preferentially locates in the inner or outer leaflet of the bilayer of the vesicle, and it does so without introducing a spectroscopic label to the headgroup of either lipid used, which may alter the behavior of the lipid.The results shine improved light on the structure of unilamellar vesicles of this lipid mixture containing very different intrinsic curvatures by revealing a strong asymmetry in the composition of the inner and outer leaflets of the vesicle.
The four layers of the model are the inner headgroup (HG), the inner hydrocarbon core (HC), the outer HC, and the outer HG.A schematic of the structure is shown in Figure 1.The model is parametrized in terms of the areas per lipid of the inner and outer leaflets, A L,in and A L,out , and Δ, the deviation of the DMPE content of the outer leaflet from the molar fraction of DMPE in the sample, which is denoted f.Negative values of Δ mean that the inner leaflet has more DMPE.Δ can adopt values from − f to f.
The thicknesses of the layers of the hydrocarbon core of the bilayer, T HC,in and T HC,out , are calculated according to eqs 1 and 2, respectively.
V chains is the volume of the dimyristoyl chains and is 780 Å 3 . 36or the thicknesses of the two headgroup regions of the bilayer, T HG,in and T HG,out , a fixed value of 10 Å 37 was employed to minimize the number of degrees of freedom used in the data analysis.The total bilayer thickness is given by T tot = T HG,in + T HC,in + T HC,out + T HG,out .The headgroup regions of the bilayer may contain water, the number of which can be determined using eqs 3 and 4.
The headgroup volumes are taken from previously published studies, specifically V HG,PC = 320 Å 336 and V HG,PE = 252 Å 3 . 38he volume of a water molecule, V Hd 2 O , is 30 Å 3 .The scattering length densities, ρ, of the four layers in the model are calculated from the compositions of the layers and the structural parameters of the model.The scattering length densities of the inner and outer hydrocarbon regions, ρ HC,in and ρ HC,out , are shown in eqs 5 and 6, respectively.The values of b chain,D and b chain,H are calculated from the scattering lengths of the isotopes 8 and the chemical formulas.
The scattering length densities of the inner and outer headgroup regions of the bilayer, ρ HG,in and ρ HG,out , are calculated using eqs 7 and 8, respectively.
Here, b water = 0.9b Dd 2 O + 0.1b Hd 2 O .The chemical formulas of the lipid headgroups were used to calculate their total scattering lengths, b PC,HG and b PE,HG .Data analysis also employed two additional models in order to test whether the bilayer was indeed asymmetric.The model remains the same as above, but constraints were applied to test different symmetric structures.The first symmetric structure tested fixed the value of Δ to be 0.0, meaning that the two leaflets of the bilayer had the same composition, i.e., each leaflet had 70 mol % d54-DMPC and 30 mol % DMPE.The A L of the inner and outer leaflets were allowed to be different.In the second symmetric model tested, not only was Δ fixed to be 0.0, but the A L of the two leaflets of the bilayer were also constrained to have the same value.
The model described above was implemented in the Python programming language.The process of fitting the model to the SANS data was accomplished using the sas-temper software, 39 which leverages the sasmodels package of Sasview. 40Model intensity profiles were convoluted with the instrument resolution function of the EQ-SANS, 28 which is a function of the sizes of the beam-defining apertures, the detector pixel sizes, and the wavelength distribution and uncertainty, before comparison against the data.This convolution smears out features in the calculated profiles, making them accurately represent what the instrument would measure.After an initial run of the fitting that produced 25 independent models was performed at each temperature, three additional refinement runs of the fitting were performed that employed narrowed constraints on the parameters.Each of these runs also produced 25 independent models.The averages and standard deviations of the free parameters used in the modeling found in the final run performed are presented here as the results.Most parameters began with physically reasonable but relaxed constraints during the first fitting.For example, A L,in and A L,out began by being constrained to be between 30 and 70 Å 2 .Tests of the fitting without a constraint on Δ, when it was allowed to vary, suggested that it had a preference for negative values, and so it was constrained to be so.This constraint was deemed to be reasonable because the intrinsic curvature of DMPE is considerably more negative than that of DMPC, 17−19 in spite of a previous study of DMPC−DMPE mixtures. 27

RESULTS
The SANS data and example fits to the data are shown in Figure 2A.The position of the minima that is near 0.1 Å −1 moves to higher q as the temperature increases.It shifts from q ∼ 0.099 Å −1 to q ∼ 0.111 Å −1 .The change indicates that the bilayer thins with increasing temperature.−27 The asymmetric model fit curve for the 55 °C data set is shown in Figure 2B, with example fit curves found using the two different symmetric models described in the Section 2 to support the choice of the asymmetric model for fitting the data.Figure 2B focuses on the region of the data containing the minimum The small, sharp feature in the two symmetric model curves near 0.20 Å −1 visible on the broad peak due to the bilayer structure is an artifact of the underlying mathematical functions of Python used in the model calculation that has been convoluted with the EQ-SANS q-resolution 28 (see Section 2.4).Similar features at different locations in q can be seen in panel (A).and oscillation, similar to the approach recently used by Frewein and co-workers when discussing the suitability of the model used for their data analysis. 41The fit curves for the two symmetric models employed are nearly indistinguishable but are quite different from the asymmetric model curve.While all three curves reproduce the position of the minimum (q ∼ 0.111 Å −1 ), the position of the subsequent local maximum (q ∼ 0.172 Å −1 ) in the SANS data is not fit well by the symmetric model curves, which have their local maximum at a lower q-value (q ∼ 0.164 Å −1 ) than the SANS data or the asymmetric model fit curve do.The width of this feature in the symmetric model curves is also too narrow to fit the feature in the SANS data.The symmetric models found by fitting the SANS data collected at the other measured temperatures (not shown) also fit the SANS data less well than the asymmetric model.Therefore, it is reasonable to conclude that using the asymmetric model described in the Section 2 is justified.
The model SANS profiles reproduce the features in the SANS data well (Figure 2).The fitting results are presented in Table 1, which include both free parameters used for the fitting and relevant derived parameters.The A L values determined from the data analysis are presented in Figure 3A.As can be seen in Figure 3A and Table 1, A L,in is always larger than A L,out .There is a relatively large difference in A L,in and A L,out , being ∼15 Å 2 at the highest temperatures studied.A L,in also increases more rapidly with temperature than A L,out , even though it levels off at the highest temperatures studied.The trend in the latter is monotonic, while the trend in the former is not, which may be evidence that the "liquid + solid" phase is present in that particular leaflet at the lowest temperature.Both bulk 26 and unilamellar vesicle 27 phase diagrams show that a 7:3 mixture of DMPC and DMPE are in the "liquid + solid" portion of the phase diagram at the lowest temperature studied here, while the rest of the temperatures studied are in the L α phase.
The T HC,in and T HC,out values that were derived from the A L obtained from the SANS fitting are presented in Table 1, as is T tot .The trends follow those in A L for both leaflets because these parameters are derived from the A L .The two leaflets differ in thickness by 3−4 Å across the entire temperature range studied.The smallest difference is observed when the lipids are in the "liquid + solid" region of the phase diagram at 30 °C.The total thickness of the bilayer is 3.6 Å thinner at 55 °C than it is at 30 °C.The total number of water molecules found to be associated with the lipid headgroups, per the self-consistent slab model, 32−35 described in Section 2.4, is also presented in the table.
The relatively strong asymmetry in the content of the inner and outer leaflets of the bilayer can be seen in the plot of Δ as a function of the temperature in Figure 3B.A L,in is the larger of the two lipid areas, even though Δ indicates that the inner leaflet has considerably more DMPE than the outer leaflet.Δ is considerably less negative at the two highest temperatures studied than it is at the lower temperatures.A single sample was used for the entire experiment, and the temperature series was measured from high to low temperature; therefore, the result implies that some lipids moved between leaflets of the bilayer as the temperature decreased.A simplified representation of the vesicle and the bilayer at 55 °C found by the SANS data analysis A "*" denotes a parameter derived from the fitting results for the free parameters.The standard deviation in the value found by sas-temper 39 is shown in parentheses and is for the last digit or digits.that illustrates the asymmetry in the structure is shown in Figure 4.The vesicle radius, bilayer thickness, and A L are presented to scale.The zoomed-in view illustrates that the curvature of the bilayer is non-negligible, even on a relatively local scale.The intrinsic curvatures, c 0 , of the inner and outer leaflets of the vesicle can be estimated from the values of the intrinsic curvatures of each lipid by using eq 2 of the review by Dymond 19 and the mole fractions of each lipid.For DMPC at 35 °C, c 0 = 0.007 ± 0.002 Å −1 , 43 while for DMPE, c 0 = −0.0314± 0.0006 Å −144 at 80 °C.Table 2 presents the values determined from Δ as a function of temperature using eq 2 of the review by Dymond. 19It is important to note that c 0 generally decreases with increasing temperature above the phase transition. 19owever, the rates of change of c 0 with temperature of DMPC and DMPE were not presented in the recent review by Dymond. 19Applying the logic of the general trend would result in the c 0 for DMPE being less negative than the value used for the calculations presented here and the value of DMPC being more negative at most of the temperatures studied here, although it is not ideal to extrapolate such behavior for a mixture of lipids.It is reasonable to conclude that the c 0 values for the inner and outer leaflets would be closer if it were possible to correct for the temperature.As a result, the values shown in Table 2 should be considered estimates.

DISCUSSION
The present results provide new information about the structure of the lipid bilayer vesicles made of a 7:3 molar mixture of DMPC and DMPE and how it depends on the temperature.The use of deuterium-labeled DMPC made it possible to observe differences in the structures of the two leaflets of the bialyer. 7,35he A L of the lipids in the inner leaflet of the bilayer displays a stronger temperature dependence than that of the outer one.The SANS results also revealed considerable asymmetry in the composition of the inner and outer leaflets of the bilayer, which Figure 4 highlights clearly.The amount of asymmetry found here also depends on temperature.Δ becomes ∼4 mol % more positive with increasing temperature.
While the SANS data revealed that the compositions of the inner and outer leaflets of the bilayer were not identical, there was no indication that the samples were not laterally homogeneous at the length scales sampled by the SANS measurements, which ranged from distances comparable to the radius of the vesicle to those less than the thickness of the bilayer.−49 Such lateral structures can take the form of lipid rafts, being large-scale patches (≥50 Å in size) enriched in specific lipids, 45,48,49 which must have existed as a persistent population over the course of the SANS measurement time to be observable in the data.These structures create a SANS signal that takes the form of a peaklike feature at low-q, which is not found in any of the SANS data presented herein.Evidence of lateral structuring can also be present in data at shorter length scales and may not result from raft-like domains.In vesicles made of DMPC and cholesterol, the presence of two different thicknesses in the vesicles was inferred from the SANS data. 46,47n both studies, the first oscillation in the SANS data (the equivalent of the feature highlighted in Figure 2B) was noticeably flattened and could not be modeled using a bilayer with a single thickness, suggesting lateral segregation.Again, this kind of structure must exist as a persistent population over time scales comparable to the measurement time to be observable.The SANS data of these earlier studies of DMPC and cholesterol did not possess any features at lower q that were indicative of larger-scale structures. 46,47The SANS data presented herein do not display a clear distortion of this feature that suggests that the vesicle is not uniform in a lateral sense.Based on these possibilities and the q-range sampled in the SANS measurements and fit during data analysis, the vesicles are laterally homogeneous from ∼20 Å to over ∼250 Å.
The average A L for the 7:3 DMPC/DMPE mixture studied here by SANS ranges from 52.9 to 60.3 Å 2 with increasing temperature, which is below the A L for pure L α phase DMPC.The A L of gel-phase DMPC is 47.2 Å 2 , 10 while fluid (L α ) phase DMPC has an A L of 59.9 Å 2 at 30 °C, 63.3 Å 2 at 50 °C, and 65.7 Å 2 at 60 °C. 12Gel-phase DMPE has an experimentally determined A L that ranges from ∼40.5 16,50 to ∼56.1 Å 2 , 51 while the A L of fluid-phase DMPE was determined experimentally to be 63−70 Å 2 . 15The large ranges of the DMPE A L is somewhat surprising, but in light of the well-characterized A L of DMPC, the A L of DMPE is more likely to be near the lower ends of the reported ranges instead of near the upper ends.−55 In light of the known phase behavior of DMPC/ DMPE mixtures, 26 including for small unilamellar vesicles, 27 the DMPC is colored white and gray, while DMPE is colored shades of blue.The left image shows the vesicle at a scale with a 90°wedge removed to reveal the content of the inner and outer leaflets.The right image shows a zoomed-in view of the top of the vesicle that better presents the differences in A L and leaflet thicknesses of the inner and outer leaflets.The image was rendered using Persistence of Vision Raytracer software 42 from an input file produced by software written for the generation of this kind of vesicle schematic that has been used previously. 31,35The software was modified to show the differences in the structures of the inner and outer leaflets.sample at 30 °C was in the "liquid + solid" coexistence region of the phase diagram.The higher temperatures studied were well within the liquid crystalline L α phase. 26,27The average A L in Table 1 supports this conclusion, but the A L of each leaflet suggests that the outer leaflet is considerably more ordered than a typical liquid crystalline phase at all temperatures studied, while the inner leaflet is less ordered.
The differences in A L for the two vesicle leaflets found by SANS make reasonable sense physically if one considers the vesicle radius and leaflet thicknesses.Consider the structure found at 55 °C (Table 1).The area of the spheres at the inner surface, at the position of the terminal methyl groups of the lipid acyl chains, and at the outer surface are 2.88 × 10 6 , 3.14 × 10 6 , and 3.46 × 10 6 Å 2 , respectively.The inner and outer surface areas are 8.4% smaller and 10.2% larger than the area of the sphere at the center of the bilayer, respectively.The differences in A L are physically reasonable when the differences in available surface area in the structure are taken into account.The inner leaflet's lipid acyl chains must expand to make up for the difference between the area available at the inner surface and at the methyl groups, making it thinner.Similarly, those of the lipids in the outer leaflet must pack more tightly to ensure that water is excluded from the hydrocarbon core.As a result, the outer leaflet of the bilayer becomes thicker.
Previous experiments revealed asymmetry in DMPC/DMPE mixtures. 27While asymmetric bilayers were observed, the outer leaflet of the bilayer was found to be considerably enriched in DMPE (see Figure 3 of ref 27), unlike the present study.The extent of enrichment of the outer leaflet was comparable to that of the inner leaflet seen in the present study.The experiments performed previously differed considerably from those in this study considerably.The vesicles were prepared by sonication followed by ultracentrifugation, which produced smaller vesicles than were studied here. 27The assay used to determine the PE content of the outer layer involves adding 0.2 mL of a 0.8 M NaHCO 3 (pH 8.5) solution to the sample, followed by an additional 0.4 mL of a 1.2% Triton X-100 solution.Thus, the procedure used in the previous work is very different than that employed in the present study.Further, the PE headgroup adopts a slight negative charge at basic pH, 56 and charge repulsion was one of the reasons suggested by the authors of the previous study for the asymmetry observed. 27The present study used D 2 O as is, with no additional salt or buffering (pH ∼ 6.7, i.e., pD ∼ 7.1), so the DMPE should be neutral in the present study.Interestingly, an earlier study of mixtures of PC and PE lipids derived from egg yolks, which contain more unsaturated acyl chains, found enrichment of PE in the inner leaflet of the bilayer 57 using a very similar experimental procedure to the study of DMPC/DMPE mixtures. 27The different results were attributed to the egg yolk PE having a stronger negative radius of curvature than DMPE. 27

CONCLUSIONS
The characterization of the multicomponent lipid bilayer vesicles presented here provides new insight into the structure of lipid bilayer vesicles that are binary mixtures of lipids having very different curvatures.Differences in leaflet composition were resolved.Importantly, differences in the inner and outer A L could be resolved.The results make it very clear that SANS and contrast variation methods 7,35 are powerful tools for performing detailed structural studies of mixed-composition lipid bilayer vesicles in order to capture differences in the composition of the bilayer leaflets and any asymmetry that may exist.

Figure 1 .
Figure 1.Schematic of the four-layer self-consistent slab model used for the SANS data analysis.

Figure 2 .
Figure 2. (A) SANS data collected for the 7:3 DMPC/DMPE vesicles as a function of temperature.The curves are 30 °C (black square), 40 °C (red circle), 45 °C (blue triangle), 50 °C (green down-pointing triangle), and 55 °C (magenta diamond).The SANS data set collected at 55 °C was presented previously in Figure 3A of reference 35 and is reused with permission Copyright 2022, by the author under the CC-BY 4.0 license (https:// creativecommons.org/licenses/by/4.0/).The solid black lines in panel (A) are example model intensity profiles found during SANS data analysis.The data were offset from the 30 °C data for clarity.The vertical dashed lines are provided as guides for the eye.(B) Zoomed-in view of the SANS data collected at 55 °C (deg) and example best fit model curves for the three models described in Section 2.4.Three model curves are presented: the asymmetric model (solid black line), the symmetric composition model that can have different A L values in the leaflets (solid red line), and the fully symmetric model (blue dotted line).The small, sharp feature in the two symmetric model curves near 0.20 Å −1 visible on the broad peak due to the bilayer structure is an artifact of the underlying mathematical functions of Python used in the model calculation that has been convoluted with the EQ-SANS q-resolution 28 (see Section 2.4).Similar features at different locations in q can be seen in panel (A).

Figure 3 .
Figure 3. (A) A L determined by fitting the SANS data and (B) Δ parameter as a function of temperature from the SANS data analysis.In panel (A), A L,in and A L,out from the SANS data fitting are in red and blue, respectively.The average A L,ave is black.

Figure 4 .
Figure 4. Simplified representation of the vesicle structure at 55 °C.DMPC is colored white and gray, while DMPE is colored shades of blue.The left image shows the vesicle at a scale with a 90°wedge removed to reveal the content of the inner and outer leaflets.The right image shows a zoomed-in view of the top of the vesicle that better presents the differences in A L and leaflet thicknesses of the inner and outer leaflets.The image was rendered using Persistence of Vision Raytracer software 42 from an input file produced by software written for the generation of this kind of vesicle schematic that has been used previously.31,35The software was modified to show the differences in the structures of the inner and outer leaflets.

Table 1 .
Table of Parameters from SANS Fitting a a