Danielle Laurencin

Yang Li

Melinda J Duer

Dinu Iuga

Christel Gervais

Christian Bonhomme

A 43 Ca NMR perspective on octacalcium phosphate and its hybrid derivatives

Keywords: . 43 Ca solid state NMR, quadrupolar nuclei, octa-calcium phosphate Ca8(HPO4)2

PO 4 ) 8 •10H 2 O OCP Cit A Ca 16 (HPO 4 ) 3 (PO 4 ) 8 (HCIT)•10H 2 O OCP Cit A+ H 2 O Ca 16 (HPO 4 ) 3 (PO 4 ) 8 (HCIT)•11H 2 O citrate

INTRODUCTION: RECENT TRENDS IN 43 Ca SOLID STATE NMR

The elements in the second column of the periodic table (alkaline earth) are of particular importance in materials science as well as in the more specific field of biomaterials. Curiously, all the stable magnetically active isotopes of these elements are quadrupolar in nature (I > 1/2) (see Table 1). The NMR characteristics of each nucleus vary greatly from one element to the other both in terms of natural abundance (from 0.14% for [START_REF] Burgess | [END_REF] Ca to 100% for 9 Be) and associated quadrupolar moments.

Nucleus I Natural

Abundance (%) As a result, the NMR spectroscopist must adapt the solid-state NMR methodology to optimize the sensitivity of the NMR experiment by using the latest advances in instrumentation and sequence development. Considering for example 87 Sr, 2 which is an important element in the context of materials against osteoporosis (including bioglasses): 3 as shown in Table 1, it is a nucleus of moderate natural abundance, with a very low gyromagnetic ratio and a high quadrupole moment. This generally results in strongly broadened central transitions (due to second order quadrupolar interaction), making standard sample rotation techniques such as fast MAS (Magic Angle Spinning) or MQ-MAS (Multiple-Quantum Magic Angle Spinning) totally ineffective. Static mode experiments combining: (i) the use of the highest B0 magnetic fields and large volume rotors, (ii) the WURST-QCPMG (Wideband Uniform Rate Smooth Truncation -Quadrupolar Carr-Purcell Meiboom-Gill) approach, 4 (iii) the DFS (Double-Frequency Sweep) 5 or multi-DFS (m-DFS) 6 signal-enhancement scheme, are to be preferred. The case of [START_REF] Burgess | [END_REF] Ca is radically different. Since the pioneering work of Dupree et al., 7 it has been widely demonstrated that rotation of the sample at a moderate rotation frequency (4 to 5 kHz) at a high magnetic field (≥ 14 T) is largely sufficient in the vast majority of cases to recover isotropic signals, weakly broadened by the quadrupole second order interaction. Very recently, it has been shown that at ultra-high magnetic field (35.2 T, which corresponds to a Larmor frequency of 100.96 MHz for [START_REF] Burgess | [END_REF] Ca), 8 the ultimate high resolution in [START_REF] Burgess | [END_REF] Ca can even be reached in some cases. The main problem of [START_REF] Burgess | [END_REF] Ca solid phase NMR remains the very low sensitivity due to both the very low natural abundance (0.14%) and the low gyromagnetic ratio. Nevertheless, over the last fifteen years, [START_REF] Burgess | [END_REF] Ca NMR has experienced very strong developments including for natural abundance [START_REF] Burgess | [END_REF] Ca. 9,10 In this case, it is necessary to use large MAS rotors (from 7.0 to 9.5mm) and the highest accessible magnetic fields in order to maximize sensitivity. It should be kept in mind that for a magnetic field of 20.0 T (850 MHz for 11 The advantages in terms of NMR spectroscopy are then numerous: (i) the implementation of high-resolution methods dedicated to quadrupolar nuclei in 1D (DOR, DOuble Rotation) 12 or 2D (MQ-MAS), 13 (ii) the possible implementation of heteronuclear correlation methods in 1D and 2D, [START_REF] Burgess | [END_REF] Ca-X (X with I = 1/2 generally) to evaluate spatial proximities and internuclear distances, 9 (iii) the study of very small masses of sample with adapted instrumental systems such as micro-coils under MAS. 14 Of course, two major disadvantages of this approach must be mentioned, namely the very high price of enrichment (62% [START_REF] Burgess | [END_REF] Ca labeled *CaCO3 costs ≈ 1500 € per 10mg) and obviously, the near-impossibility of studying natural samples.

Among very recent applications of [START_REF] Burgess | [END_REF] Ca NMR for synthetic samples one can highlight:

(1) The precise determination of the calcium environment in atorvastatin calcium which corresponds to the active pharmaceutical ingredient of Lipitor (against high blood plasma low density lipoprotein cholesterol and triglycerides and hypertension). 15 This study makes extensive use of the NMR crystallography approach which was initiated by Bryce and Gervais et al. in 2008. 16,17 All [START_REF] Burgess | [END_REF] Ca NMR parameters (iso, CSA, quadrupolar interaction, Euler angles between CSA and EFG, Electric Field Gradient -tensors) were used as constraints for local structural determination (here in absence of XRD data). The approach was then extended to a solvate (ethylene glycol) of atorvastatin calcium. It is worth mentioning here for NMR crystallography, utilizing [START_REF] Burgess | [END_REF] Ca parameters, that a recent study also compared different theoretical methods to calculate NMR parameters such as Hartree-Fock theory and more than 15 DFT approaches 18 to calculate NMR parameters with special attention to the calculation of calcium-containing MOFs. 19 It was shown that [START_REF] Burgess | [END_REF] Ca NMR could demonstrate the presence of guest molecules in the local environment of calcium atoms. Once again, in the absence of XRD data, NMR acts as a powerful technique to demonstrate host-guest interactions. In the particular case of MIL-121 and loading with Ca 2+ , detailed characterization was performed by [START_REF] Burgess | [END_REF] Ca NMR. 20 (3) The study by natural abundance [START_REF] Burgess | [END_REF] Ca NMR in natural abundance of bioceramic materials based on silico-carnotite, Ca5(PO4)2SiO4, synthesized mechano-chemically.

Calculated iso( 43 Ca) were used to analyze carefully the experimentally-determined results. 21 43 Ca NMR is also very informative in the study of natural compounds (in natural abundance).

Examples include kidney stones, bones and teeth. The mineral part of human kidney stones is essentially composed of calcium oxalate monohydrate (CaC2O4.H2O) and more rarely of calcium oxalate dihydrate (CaC2O4.2H2O). The third hydrate, CaC2O4.3H2O, is almost absent.

Apatitic components (see below) can be observed as well. While synthetic calcium oxalates and kidney stones have been studied mainly by 1 H and 13 C solid state NMR, Wong et al. 22 , Bowers et al. 23 and Colas et al. 24 have shown that [START_REF] Burgess | [END_REF] Ca MAS NMR spectra of synthetic and natural compounds can also be obtained in natural abundance.

Another Ca-containing mineral of considerable interest is hydroxyapatite (HAp), Ca10(PO4)6(OH)2, which is related to the major inorganic component in mammalian bones and teeth. In mineralized tissues, apatitic mineral is usually partially substituted, especially by carbonates. Numerous 1 H, 31 P and 13 C NMR studies related to natural and biomimetic calcium phosphate phases have been published. These include 13 C-31 P REDOR, Rotational Echo Double

Resonance 25,[START_REF] Davies | Proc. Natl. Acad. Sci[END_REF][START_REF] Li | [END_REF]28,29 to study the interfaces between the mineral part of bone (crystalline hydroxyapatite-related and non-apatitic, amorphous components) and the organic part (collagen and other organic molecules). Within the topic of the organic-inorganic interface in bone, OCP, Ca8(HPO4)2(PO4)4.5H2O, occupies a very special position. Its role as a potential precursor phase of biological HAp has been evoked in the literature. 30 The OCP atomic structure contains apatitic layers, sandwiched by hydrated layers (Figure 1). It has been demonstrated that citrate anions may bridge the mineral platelets in bones. [START_REF] Davies | Proc. Natl. Acad. Sci[END_REF]31 Moreover, it is also well established that other metabolic acids can be present in bone. The OCP atomic structure is capable of intercalating all of these metabolic acid species, making OCP an interesting calcium phosphate phase in which to study the incorporation of metabolic anions in bone mineral. Some of the biologically-relevant anions are presented in Figure 1. The incorporation of these metabolic acids in bone mineral are modelled as interaction in the hydrated layer of an OCP component. H: light pink, Ca: green, O: red, PO4 3-: blue tetrahedral.

The weight percentages of the different metabolic acids in bone vary according to animal age: fetal bone, which is much softer than adult bone, contains very large quantities of lactate, 32 OCP unit cell

Hydrated layer

Apatitic-like layer

Apatitic-like layer whereas in adult bone, the quantity of citrate is directly related to bone mineral quality. 33 Currently, the role and characterization of metabolic acids in bone is very poorly understood as well as their underlying role in biomineralization.

In this contribution, we explore the potential of using [START_REF] Burgess | [END_REF] Ca NMR to study the structure of synthetic OCP and related hybrid phases, both at natural abundance and on enriched samples.

For OCP, we show how the study of a [START_REF] Burgess | [END_REF] Ca labeled sample enabled advanced experiments, such as DOR and heteronuclear [START_REF] Burgess | [END_REF] Ca{X} REDOR and X{ [START_REF] Burgess | [END_REF] Ca} REAPDOR correlations (X = 1 H and 31 P, respectively). We calculated [START_REF] Burgess | [END_REF] Ca NMR parameters for OCP by first principles calculations (GIPAW method, Gauge-Including Projector Augmented Wave), to compare with the experimental parameters. These calculations follow those proposed in 2012 by Duer et al. for 31 P. 31 In a second step, we studied several intercalated hybrid OCPs containing metabolic acids relevant to bone mineral (citrate, succinate, formate, adipate and mixed citrate/formate ions).

We demonstrate that [START_REF] Burgess | [END_REF] Ca MAS NMR allowed two families of hybrid compounds with different intrinsic structures to be distinguished in a very simple way. In a third and last step, the OCP-citrate hybrid compound was investigated in more detail using NMR crystallography and considering five computational models of this phase.

SAMPLE PREPARATION AND 43 Ca NMR METHODS

Syntheses of OCP and OCP hybrid materials.

The general procedure is already reported in a previous contribution by Duer et al. [START_REF] Li | [END_REF] Briefly, OCP was synthesized by reaction of CaCO3 (1.604 g, 16 mmol) with H3PO4 (0.6 ml, 10 mmol) in 200 mL of water at 60 °C without any control of the pH (reagents were purchased from Sigma-Aldrich and used as received). In the case of OCP-metabolic acid derivatives (involving citrate, succinate, formate, adipate and mixed citrate/formate ions), the relevant organic acid was dissolved in water (200 mL) at pH = 5.5 by addition of NaOH (dropwise). After heating at 60 °C (under stirring), CaCO3 and H3PO4 (quantities as mentioned above) were added to the aqueous solutions. White powders were collected after 6 hours by filtration and dried in air.

All samples were analyzed by elemental analyses and powder XRD. [START_REF] Li | [END_REF] 2.2. [START_REF] Burgess | [END_REF] Ca NMR spectroscopy.

OCP and intercalated hybrid OCP phases were studied using natural abundance [START_REF] Burgess | [END_REF] Ca NMR experiments, which were acquired at 20.0 T on a Bruker Avance III-850 (850 MHz 1 H frequency) spectrometer operating at [START_REF] Burgess | [END_REF] Ca Larmor frequency of 57.22 MHz, using a low- 7 mm Bruker MAS probe spinning at 5 kHz. For the OCP phase, a RAPT (Rotor Assisted Population Transfer) enhancement scheme 34 was used (offset of 150 kHz, RF ~ 9 kHz), followed by a 90° selective solid pulse of 1.7 μs. A total of 137864 transients were acquired, with a recycle delay of 0.5 s. For all intercalated hybrid OCP samples, a multi-DFS (double frequency sweep) 5,13 enhancement scheme followed by a 90° selective pulse of 1.5 μs, was used which was first optimized on a [START_REF] Burgess | [END_REF] Ca-labeled *CaHPO4 (monetite) sample leading to 3 blocks of DFS with a DFS pulse length of 2 ms (RF ~ 8 kHz) and a convergence sweep from 400 kHz to 50 kHz), followed by a 90° selective pulse of 12.5 μs (RF ~ 5 kHz). It was clearly demonstrated that m-DFS is highly efficient when compared to RAPT and single-DFS approaches. However, the number of DFS blocks has to be limited to avoid distortions of the lineshapes. A total of 65500 transients were acquired for the intercalated OCP phases (studied at the natural abundance of [START_REF] Burgess | [END_REF] Ca), with a recycle delay of 0.5 s. All [START_REF] Burgess | [END_REF] Ca chemical shifts were referenced at 0.0 ppm to a 1.0 mol.L -1 aqueous solution of CaCl2. 17 Details of the recycle delays, number of transients acquired, and total experimental times needed for each sample can be found in Table S1 (in Supplementary Information). The [START_REF] Burgess | [END_REF] Ca-enriched OCP sample was first characterized by MAS, using a 4 mm HX probe, spinning at 12.5 kHz. A multi-DFS enhancement (3 loops) was used, followed by a 12.0 μs selective pulse. A total of 10000 transients was acquired, with a shortened recycle delay of 0.1 s in order to saturate the signal of the *CaCO3 impurity signal (*CaCO3 was used as [START_REF] Burgess | [END_REF] Ca labeled starting material -see below).

The [START_REF] Burgess | [END_REF] Ca-enriched OCP was then characterized by DOR with the external rotor spinning at ~ 1.53 kHz, and the internal rotor at  7.69 kHz. A RAPT enhancement scheme was applied (10 RAPT 20 s pulses with an offset of +/-150 kHz were followed by a 5 s selective 90° pulse of about 12.5 kHz). No 1 H decoupling was applied due to the poor 1 H RF performance of the DOR probe. A total of 155000 transients were acquired, with a recycle delay of 0.1 s. REDOR and REAPDOR experiments were performed using a 4 mm HXY probe tuned to 1 H, 31 P and [START_REF] Burgess | [END_REF] Ca. Samples were carefully centered in the middle of the MAS rotors. The 43 Ca{ 1 H} REDOR pulse sequence (with [START_REF] Burgess | [END_REF] Ca detection) is presented in Figure S1. For *OCP (studied at 14 kHz MAS), a 90° pulse of 3.0 μs ( 43 Ca) was applied and 180° pulses of 7.0 μs were applied on the 1 H channel. The recycle delay was set to 0.1 s. The number of scans were 40000, 48000 and 60000 for 8, 12 and 24 recoupling loops, respectively. For *HAp (studied at 14 kHz MAS), a 90° pulse of 3.0 μs ( 43 Ca) was applied and 180° pulses of 7.0 μs were applied on the 1 H channel.

The recycle delay was set to 0.4 s. The number of scans was 10000 for 24 recoupling loops.

The 31 P{ [START_REF] Burgess | [END_REF] Ca} CP (cross polarization) REAPDOR pulse sequence (with 31 2.3. [START_REF] Burgess | [END_REF] Computational modeling and GIPAW-DFT calculations. [START_REF] Burgess | [END_REF] Ca NMR parameters were calculated within Kohn-Sham DFT using the QUANTUM-ESPRESSO code 35 based on the GIPAW method 36 . Calculations were performed on previously published [START_REF] Davies | Proc. Natl. Acad. Sci[END_REF] geometry-optimized structural models of OCP and OCP-citrate, in which a singly protonated (models A and B) or a non-protonated (model C) citrate anion replaces a hydrogen phosphate site, without performing any further geometry relaxation. The PBE generalised gradient approximation 37 was used and the valence electrons were described by norm conserving pseudopotentials 38 (Q = -40.8 × 10 -30 m 2 , see Table 1) was used to calculate CQ. Absolute shielding tensors are obtained. To fix the [START_REF] Burgess | [END_REF] Ca scale, calculated δiso for a series of reference compounds were compared to experimental values 17,40 so that the average sum of experimental and calculated shifts coincide.

RESULTS and DISCUSSION

3.1 [START_REF] Burgess | [END_REF] Ca NMR of OCP

We begin with a detailed study of the OCP phase. In Figure 2a, the [START_REF] Burgess | [END_REF] Ca MAS spectrum of OCP at very high magnetic field (20.0 T) is presented. In natural abundance, it is possible to obtain a spectrum of reasonable quality (revealing discontinuities in the overall lineshape) using a 7mm rotor in  20 hours. According to the OCP crystal structure, the spectrum obtained should correspond to the superposition of eight [START_REF] Burgess | [END_REF] Ca central transitions potentially broadened by quadrupolar second-order effects (not completely averaged by MAS even at 20.0 T). Isotopic enrichment in [START_REF] Burgess | [END_REF] Ca brings a considerable gain in terms of signal-to-noise ratio: in 10 minutes a spectrum with minimal noise is obtained. In the case of *OCP, an impurity corresponding to [START_REF] Burgess | [END_REF] Ca labeled calcium carbonate is detected as a very sharp feature ("•" in Figure 2). The very high signal to noise ratio of this spectrum makes it possible to envisage DOR and multinuclear correlation experiments. DOR is an efficient 1D technique capable of fully averaging the second-order quadrupolar effect, by involving two macroscopic reorientation angles of the sample. [START_REF] Burgess | [END_REF] Ca DOR data were rarely reported in the literature. This is mainly due to the inherent complexity of DOR probes making them still specialist equipment. 41 To the best of our knowledge, three contributions were published in the last years including the spectroscopic characterization of monoclinic hydroxyapatite and -TCP (tetra-calcium phosphate) phases, [START_REF] Mcdonald | Multinuclear Solid State NMR Studies of -Tricalcium Phosphate and Silicon Substituted -Tricalcium Phosphate[END_REF] the vaterite polymorph of CaCO3 [START_REF] Burgess | [END_REF] and Ca(OAc)2.0.5H2O. 13 In the last case, the three calcium resonances were clearly evidenced. Although the rotation frequencies of the two rotors are limited (see section 2.2), it should be possible to efficiently distinguish the isotropic resonances, shifted by a quadrupolar isotropic shift (which depends explicitly on CQ and Q, mostly on CQ) (Figure 2b). although the obtained resolution in the DOR spectrum is still not sufficient to fully resolve all eight isotropic [START_REF] Burgess | [END_REF] Ca contributions.

As mentioned above, the high isotope enrichment allows the implementation of heteronuclear correlation experiments on OCP. The 43 Ca{ 1 H} REDOR experiment allows relative Ca…H distances to be estimated. As only weak [START_REF] Burgess | [END_REF] Ca{ 1 H} REDOR dephasing is expected (the heteronuclear [START_REF] Burgess | [END_REF] Ca-1 H dipolar couplings are intrinsically small due to small ( 43 Ca)), the experiment was first tested using *HAp enriched in [START_REF] Burgess | [END_REF] Ca (Figure S2). The observed dephasing is in full agreement with data already published in the literature. 44 The same experiment was then performed on *OCP (Figure 3). The dephasing in Figure 3 observed for 24tR recoupling cycles is reproducible despite the weakness of the [START_REF] Burgess | [END_REF] Ca-1 H dipolar coupling. Interestingly, the dephasing occurs essentially around the center of the overall lineshape and not at the most shielded and deshielded shoulders of the lineshape. follows that Ca5, Ca7, Ca9, Ca13 contributions should dephase more efficiently using the [START_REF] Burgess | [END_REF] Ca{ 1 H} REDOR experiment, in the absence of any water molecular motion. It is worth mentioning here that the shortest Ca…H distance in HAp is ~ 2.7 Å, which is close to the shortest Ca…H distances in OCP. However, when comparing the [START_REF] Burgess | [END_REF] Ca{ 1 H} REDOR data of both phases (Figures 3 andS2), the observed dephasing is much more pronounced for HAp than for OCP. This clearly indicates a drastic reduction of the heteronuclear [START_REF] Burgess | [END_REF] Ca-1 H dipolar couplings for the closest Ca…H sites in OCP, which is likely to be due to local dynamics of water molecules at room temperature. 31 This point has not been further investigated here.

It is obvious that MAS alone does not allow observation of resolved isotropic [START_REF] Burgess | [END_REF] Ca signals for OCP individually, and that they cannot be identified using the DOR sequence alone. Unfortunately, it was not possible to combine REDOR and DOR for technical reasons (essentially the power on the 1 H channel of the double channels DOR probe was far too low). Given that differences in Ca…P distances are also expected for the different sites in OCP (Table S2), we looked into trying to implement NMR experiments allowing to probe [START_REF] Burgess | [END_REF] Ca-31 P spin pair (which had not yet been analyzed by NMR). Here, as a first attempt for such heteronuclear correlations, we implemented the 31 P{ [START_REF] Burgess | [END_REF] Ca} CP REAPDOR sequence with 31 P detection (Figure S1). Again, *HAp was used as a model compound to check the progressive dephasing of the 31 P signal with increasing dipolar recoupling time. For 60tR recoupling cycles, the dephasing of the 31 P signal is almost complete (Figure S3). These tests demonstrated that the 31 P{ [START_REF] Burgess | [END_REF] Ca} CP REAPDOR sequence can in principle be used to estimate relative [START_REF] Burgess | [END_REF] Ca-31 P heteronuclear dipolar couplings in calcium phosphate phases. In the case of *OCP, the dephasing of the most shielded 31 P resonances (centered at ~ 0.0 ppm) is slightly less pronounced than for the other resonances (Figure S4). Following the assignments made by Li et al., the 31 P signals around 0.0 ppm corresponds to P3, P5 and P6 resonances. [START_REF] Li | [END_REF] In Table S3, it is shown that the minimum P…Ca distance is roughly 3.1 Å for all six phosphorus sites, but that the number of the closest calcium neighbors (< 4 Å) is much reduced for P5 and P6. This explains the reduced dephasing in the 31 P{ [START_REF] Burgess | [END_REF] Ca} CP REAPDOR experiment, and demonstrate the efficiency of this sequence for distinguishing 31 P sites on the basis of their relative [START_REF] Burgess | [END_REF] Ca proximities. Future developments will involve the "reverse" study, by using [START_REF] Burgess | [END_REF] Ca detection instead, to try to help differentiate the Ca sites depending on their closest P neighbors.

At this stage, although the 43 Ca{ 1 H} REDOR experiments provide some clues as to which [START_REF] Burgess | [END_REF] Ca resonances correspond to Ca sites closer to H, in order to go further in the assignment of the individual resonances of OCP, it is necessary to use first principles GIPAW calculations to estimate the NMR parameters of each calcium site (iso., CQ and Q). The calculated parameters are presented in Table 2 and are used for the simulation of the OCP MAS spectrum in Figure 2b, top. Actually, 16 sets of data corresponding to 8 duplicates are presented for OCP as a doubled cell was used in the more general case of OCP-citrate structures (see section 2.3).

The agreement between the experimental and calculated data is fairly good. Indeed, the main features (spectral maxima, i.e. red arrows, and shoulders, i.e. orange dashed arrows) of the overall lineshape are correctly reproduced by the calculations (Figure 2b, comparison of top and medium spectra). We then used the first principles calculated data to estimate second-order quadrupolar isotropic shifts. These are represented below the DOR spectrum in Figure 2b. One observes a global underestimation of the computed shifts (see below).

Interestingly, we note a large variation of iso.( 43 Ca) in OCP (over about 50 ppm which corresponds to  20% of the total [START_REF] Burgess | [END_REF] Ca chemical shift range. 17 In a number of previous studies, iso.( 43 Ca) can be related to a certain extent to the average of the Ca-O distances in the first coordination sphere of calcium. 17 In Figure S5 (red dots), the average Ca-O distances for each of the eight calcium sites of pure OCP have been plotted as a function of the calculated iso.( 43 Ca) for two different cut-offs (corresponding to maximum Ca-O distances of 2.7 and 2.9 Å. In both cases, the data are scattered and no clear trend can be established, possibly because of the large diversity in Ca local environment (the oxygen atoms linked to Ca 2+ coming from water, phosphate and/or hydrogen-phosphate ligands). However, one notes that three groups of [START_REF] Burgess | [END_REF] Ca isotropic chemical shifts can be highlighted (above 20 ppm, between 0 and 10 ppm, and below 0 ppm) and that the most deshielded value (27.7 ppm) corresponds indeed to the shortest average Ca-O distance (when considering a cut-off of 2.7 Å).

The three groups of [START_REF] Burgess | [END_REF] Ca isotropic chemical shifts are clear, corresponding to: Ca11, (Ca3, Ca9, Ca13) and (Ca1, Ca5, Ca7, Ca15), in decreasing order of iso.( 43 Ca). These groups are compatible with the overall lineshape of the [START_REF] Burgess | [END_REF] Ca MAS spectrum (Figure 2b), the most extreme chemical shifts (Ca11, Ca15) contributing to shoulders (dashed orange arrows). However, the calculated [START_REF] Burgess | [END_REF] Ca isotropic chemical shift values are globally underestimated when compared to the experimental ones. This is also observed when looking at the calculated isotropic values in the DOR spectrum (Figure 2b, blue solid lines). Most importantly, Ca5, Ca7, Ca9 and Ca13 contributions are centered in the middle of the lineshape, in agreement with the dephasing observed in the [START_REF] Burgess | [END_REF] Ca{ 1 H} REDOR experiments (Figure 3). A contrario, the most extreme contributions are not dephased in REDOR, as expected from the long Ca…H distances involving Ca11 and Ca15 (Table S2).

Thus our initial summary is that [START_REF] Burgess | [END_REF] Ca MAS NMR is a suitable tool of investigation for the structural analysis of complex hydrated calcium phosphate such as OCP. Unfortunately, the DOR resolution was not sufficient to completely resolve signals from the eight calcium sites and to allow definite assignments by combining experimental and GIPAW computed data.

Nevertheless, we can conclude that there are three groups of [START_REF] Burgess | [END_REF] Ca chemical shifts in OCP and that Ca11 and Ca15 correspond to the most deshielded and shielded sites, respectively. More generally, this study demonstrates that [START_REF] Burgess | [END_REF] Ca NMR is a very sensitive spectroscopy to study local environment in OCP, which prompted us to apply the technique to hybrid derivatives, as detailed below.

43 Ca NMR of intercalated OCP hybrids

We then studied the interaction of selected metabolic acids in OCP leading to intercalated OCP hybrids. Figure 4 demonstrates that natural abundance [START_REF] Burgess | [END_REF] Ca MAS NMR spectroscopy is suitable for the direct comparison of various intercalated OCP phases involving citrate, formate, adipate, and succinate molecules, as well as a mixed citrate/formate phase. The [START_REF] Burgess | [END_REF] Ca spectra for the citrate, formate and citrate/formate are quite comparable. On the other hand, quite different [START_REF] Burgess | [END_REF] Ca spectra are obtained for the succinate and adipate hybrids, for which the [START_REF] Burgess | [END_REF] Ca lineshape is somewhat sharper. It is interesting to note that these two bis-carboxylates (succinate and adipate) lead to similar [START_REF] Burgess | [END_REF] Ca signatures, suggesting a similar mode of intercalation of the molecules in the hydrated layer. We tentatively ascribe these structural differences to the length and symmetry of the organic chains in the various metabolic acids (Figure 4). Succinate and adipate are capable of being incorporated into the OCP structure in a manner that retains the unit cell center of symmetry, whereas the symmetry of formate and citrate makes this impossible for these anions. Thus the succinate and adipate hybrids can in 20 principle retain much of the original OCP crystalline structure whereas the formate and citrate hybrids cannot. [START_REF] Li | [END_REF] In order to try to further interpret the [START_REF] Burgess | [END_REF] Ca MAS NMR spectra of these hybrids, and to account for the difference observed in comparison to pure OCP, a more extensive modeling study (at the DFT level) was performed for OCP-citrate. [START_REF] Davies | Proc. Natl. Acad. Sci[END_REF] Figure 4. [START_REF] Burgess | [END_REF] Ca natural abundance MAS NMR spectra of hydrid OCP phases involving metabolic acids (from top to bottom: mixed OCP-citrate/formate, adipate, formate, succinate, and citrate). The [START_REF] Burgess | [END_REF] Ca MAS NMR spectrum of OCP is also presented for comparison (natural abundance as well).

3.3 [START_REF] Burgess | [END_REF] NMR modeling study was performed on five DFT relaxed models resulting from the partial exchange of HPO4 2-groups by citrates in the hydrated layer OCP (Figure 1), each of these models having been previously described in the literature. [START_REF] Davies | Proc. Natl. Acad. Sci[END_REF] Three different incorporation modes were tested for citrates. Models A and B correspond to protonated citrate molecules (HCIT) whereas model C corresponds to non-protonated citrate molecules (CIT). Adding 1 water molecule to models A and B leads to models A+H2O and B+H2O (Figure 5). All OCP-citrate models were used as starting points for GIPAW calculations. The calculated [START_REF] Burgess | [END_REF] Ca NMR parameters are presented in Table 2. The corresponding calculated MAS spectra are presented in Figure 6a.

OCP-citrate

OCP

Experimental spectra Calculated spectra

resonances, with the corresponding sum (red lines). Each blue line corresponds to a set of data (iso( 43 Ca), CQ, Q) given in Table 2, using the DMFit software 45 with unit intensity for the associated area. The GIPAW calculated [START_REF] Burgess | [END_REF] Ca MAS spectrum for OCP is shown for comparison (in black). (b) Experimental MAS spectra of OCP (black) and OCP-citrate (orange). The vertical green dashed line is a guide for the eye to highlight the difference in lineshape for OCP and OCP-citrate.

Looking carefully at Table 2, the vast majority of computed δiso( 43 Ca) is restricted in the 25 ppm/-25 ppm range of chemical shift. However, the corresponding distribution is not identical from one model to the other one. As an example, in the case of OCP Cit B model, two distinct resonances are observed in the sum spectrum -red line, in obvious contradiction with the experimental data (Figure 6b). In the case of the OCP Cit C model, the line width of the central part of the corresponding sum spectrum is underestimated when compared to the experimental data. This demonstrates that a single model is not adequate to describe the OCP derived structure. Given that the "real" mode of intercalation of citrate more likely corresponds to a combination of the five individual models, an average calculated spectrum is presented in Figure 6a (named Average OCP Cit) as well (top orange spectrum). This calculated spectrum shows a particular lineshape which is clearly different from the one calculated for "pure" OCP. Indeed, the spectrum of OCP-citrate is "smoother" around 0.0 ppm with a slightly deshielded shoulder. The differences observed on the experimental spectra for OCP and OCP-citrate are overall similar as those observed for the calculated data. This is highlighted by the green dashed line in Figure 6b. The left shoulder is clearly associated to a few calcium sites present in all five models, exhibiting deshielded [START_REF] Burgess | [END_REF] Ca isotropic chemical shifts (Table 2). In Figure S6, we have tried to establish a structural correlation between the most extreme iso.( 43 Ca) and local environment around the calcium atoms. For a given calcium site, the shortest Ca-O distances were extracted with particular emphasis on the chemical nature of the neighboring groups: phosphates/hydrogen-phosphates, citrates, water molecules. Interestingly, all deshielded calcium atoms are 6-fold coordinated exhibiting several short Ca-O ( 2.2-2.3 Å) distances and a large variety of coordinated molecules (citrate, phosphate groups, water). In contrast, the most shielded chemical shifts correspond more to 7-fold coordinated calcium atoms. As mentioned above, the diversity in the coordinated molecules and the variation of the coordination number could explain the lack of correlation between computed iso.( 43 Ca) and average Ca-O distances (Figure S5).

We conclude that [START_REF] Burgess | [END_REF] Ca MAS NMR in combination with NMR crystallography remains pertinent for the description and interpretation of subtle structural details observed in the NMR spectra of hybrid intercalated OCP derived. As shown in Figure 4, OCP-adipate and OCP-succinate derivatives were clearly distinguished by their [START_REF] Burgess | [END_REF] Ca MAS NMR spectra suggesting symmetric positions/orientations of the metabolic acids in the hydrated layer of OCP. New DFT models involving adipate and succinate molecules should help us to interpret these spectra in a near future.

CONCLUSIONS

In this contribution, we have demonstrated that despite unfavorable NMR characteristics of calcium-43 (low  and very low natural abundance), [START_REF] Burgess | [END_REF] Ca NMR spectroscopy is a valuable tool of investigation for complex calcium phosphate phases like OCP derivatives. In particular, we have focused on the detailed interpretation of single and double resonance experiments on OCP in combination with [START_REF] Burgess | [END_REF] Ca NMR crystallography. The experiments presented here included the first 31 P{ [START_REF] Burgess | [END_REF] Ca} CP REAPDOR studies on calcium-phosphate, which could be of interest for future analyses of disordered or amorphous biomaterials. We have also demonstrated that natural abundance [START_REF] Burgess | [END_REF] Ca NMR spectroscopy remains pertinent for intercalated OCP hybrids (notably for discussing the validity of DFT optimized models), and that is thus a valuable tool to include in the study of complex biomaterials and biominerals.

Figure 1 .

 1 Figure 1. OCP structure and a selection of metabolic acids potentially incorporated in bone.

  in the Kleinman-Bylander 39 form. The wave functions are expanded on a plane wave basis set with a kinetic energy cut-off of 80 Ry. The integral over the first Brillouin zone is performed using a Monkhorst-Pack 122 k-point grid. The principal components Vxx, Vyy, and Vzz of the EFG tensor defined with |Vzz|  |Vxx|  |Vyy| are obtained by diagonalization of the tensor. The quadrupolar interaction can then be characterized by the quadrupolar coupling constant CQ and the asymmetry parameter ηQ, which are defined as CQ = eQVzz/h and ηQ = (Vyy -Vxx)/Vzz. The experimental value of the quadrupole moment of 43 Ca

Figure 2 .*

 2 Figure 2. (a) OCP 43 Ca MAS and DOR spectra for natural abundance and enriched samples (*)

Figure 3 .

 3 Figure 3. 43 Ca{ 1 H} REDOR experiment results for *OCP (20.0 T, 14 kHz MAS). Blue spectrum

Figure 5 .

 5 Figure 5. DFT relaxed OCP and OCP-citrate models. 26 C: black, H: light pink, Ca: green, O: red,

Figure 6 .

 6 Figure 6. (a) GIPAW calculated[START_REF] Burgess | [END_REF] Ca MAS NMR spectra for all five OCP-citrate models. Average

Table 1 :

 1 Stable magnetically active isotopes for alkaline earths (comparison with 1 H). The data are extracted partly from 1 .

	Quadrupole	Larmor frequency	Gyromagnetic ratio
	moment (fm 2 )	(MHz)	(10 7 rad.s -1 .T -1 )

  For decoupling, 7.8 μs 1 H pulses were used (spinal-64 high power decoupling). The number of scans was 16 for 10, 20, 40, and 60 recoupling loops. For *OCP (studied at 14 kHz MAS), a 180° pulse of 34.0 μs ( 43 Ca) was applied, and 180° pulses of 17.2 μs were applied on the 31 P channel. The recycle delay was set to 4.0 s and the cross polarization contact time to 2 ms. For decouling, 7.8 μs 1 H pulses were used (spinal-64 high power decoupling). The number of scans was 16 for 20 recoupling loops.

	P detection) is
	presented in Figure S1 as well. For *HAp (studied at 14 kHz MAS), a 180° pulse of 34.0 μs ( 43 Ca)

was applied, and 180° pulses of 17.2 μs were applied on the 31 P channel. The recycle delay was set to 4.0 s, the 1 H 90° (before cross polarization) to 4.0 s and the cross polarization contact time to 2 ms.

  Ca NMR crystallography of OCP-citrate

	OCP-citrate/formate
	OCP-adipate
	OCP-formate
	OCP-succinate
	OCP-citrate
	OCP
	150	100	50	0	-50	-100	-150
			δ( 43 Ca) /ppm

Table 2 .

 2 GIPAW computed[START_REF] Burgess | [END_REF] Ca NMR parameters for OCP and for five structural models of OCP-citrate in which a singly protonated (A and B) or a non-protonated (C) citrate anion (CIT) replaces a hydrogen phosphate site. Models for OCP-citrate are presented in Figure5. In the case of OCP, 16 sets of 8 duplicate values are presented due to the use of a doubled cell.

	2 O

ACKNOWLEDGMENTS

NMR spectroscopic calculations were performed using HPC resources from GENCI-IDRIS (Grant 097535). YL was funded by a UK EPSRC doctoral training award. The UK 850 MHz solid-state NMR Facility used in this research was funded by EPSRC and BBSRC (contract reference PR140003), as well as the University of Warwick including via part funding through Birmingham Science City Advanced Materials Projects 1 and 2 supported by Advantage West Midlands (AWM) and the European Regional Development Fund (ERDF).


Dr Deborah L Gater
email: deborah.gater@kustar.ac.ae

Dr Valérie Réat

Georges Czaplicki

Dr Olivier Saurel

Franck Jolibois
email: franck.jolibois@univ-tlse3.fr

Vadim Cherezov
email: vcherezo@scripps.edu

Professor Alain Milon
email: alain.milon@ipbs.fr.

Prof Georges Czaplicki

Prof Vadim Cherezov

Prof Alain Milon

] Franck

Hydrogen Bonding of Cholesterol in the Lipidic Cubic Phase

Keywords: ab initio calculations, monoolein, NMR spectroscopy, sterol-membrane interactions, HRMAS

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Monoolein (MO) forms a range of lyotropic liquid crystal phases, depending on temperature and hydration. [START_REF] Larsson | Two cubic phases in monoolein-water system[END_REF][START_REF] Qiu | The phase diagram of the monoolein/water system: metastability and equilibrium aspects[END_REF] The lipidic cubic phase (LCP) of MO has been used to facilitate the crystallization of various integral membrane proteins for X-ray structural studies. [START_REF] Caffrey | Crystallizing membrane proteins using lipidic mesophases[END_REF] The success of this approach to membrane protein crystallization, often termed the in meso method, has been particularly notable for its use in obtaining the structures of several G protein-coupled receptors (GPCRs). The inclusion of cholesterol in the LCP was necessary to stabilize the receptors and to obtain high-resolution crystal structures for several GPCRs, including: the β 2 adrenergic, the adenosine A 2A , the dopamine D3, the chemokine CXCR4, the histamine H 1 , the muscarinic acetylcholine M2 and M3, the nociceptin, the μ-, κand δopioid, and the neurotensin 1 receptors. In certain cases with the β 2 adrenergic and A 2A adenosine receptors, apparent cholesterol binding sites were observed in the crystal structures, adding to rapidly growing data about the role of cholesterol in modulating the function and stability of several GPCRs (see a recent review for references and recent advances in the field). [START_REF] Stevens | The GPCR Network: a large-scale collaboration to determine human GPCR structure and function[END_REF] The success of using LCP for membrane protein crystallization can be rationalized by the ability of this phase to provide a stabilizing membrane-like environment for membrane proteins and to support type I crystal packing. Additionally, the MO-based LCP has a relatively high stability, and is tolerant of the inclusion of the detergents used to solubilize the membrane protein prior to incorporation in the LCP, [START_REF] Ai | Membrane protein crystallization in lipidic mesophases: Detergent effects[END_REF][START_REF] Misquitta | Detergents destabilize the cubic phase of monoolein: Implications for membrane protein crystallization[END_REF][START_REF] Persson | The 1-monooleoyl-rac-glycerol/noctyl-beta-D-glucoside/water system. Phase diagram and phase structures determined by NMR and X-ray diffraction[END_REF] and of other amphiphilic additives including cholesterol and certain phospholipids. [START_REF] Cherezov | Membrane protein crystallization in meso: Lipid type-tailoring of the cubic phase[END_REF] The maximum solubility of cholesterol in LCPs is ~28 mol% in excess water at 20°C. [START_REF] Cherezov | Membrane protein crystallization in meso: Lipid type-tailoring of the cubic phase[END_REF] However ~10 mol% cholesterol is more commonly used in crystallization studies. The LCP lattice parameter increases with increasing amounts of cholesterol, [START_REF] Cherezov | Membrane protein crystallization in meso: Lipid type-tailoring of the cubic phase[END_REF] and the addition of cholesterol to LCP also results in a reduction in the self-diffusion coefficient of MO. [START_REF] Eriksson | Lipid and Water Diffusion in Bicontinuous Cubic Phases Measured by Nmr[END_REF] Beyond these data describing the effect of cholesterol on the bulk structure, lipid diffusion and phase transitions of LCPs, relatively little is known regarding the properties of cholesterol-containing LCP at the molecular or atomic level. However, as interest in LCP, and its use in protein crystallization, continues to increase, there is a need for an improved knowledge of the effects of additives, such as cholesterol, on the structure and dynamics of this phase. Equally, it is important to understand how cholesterol interactions with membrane proteins in LCP are affected by solvation in monoolein, as compared with cholesterol protein interactions in natural lipid bilayers made predominately of phospholipids.

In contrast to the relatively limited knowledge of the physical-chemical properties of cholesterol containing LCP, there is a wealth of data describing the effect of cholesterol on the properties of lipidic lamellar phases, at least in part as a result of the 'lipid raft' hypothesis. [START_REF] Mouritsen | The liquid-ordered state comes of age[END_REF][START_REF] Simons | Revitalizing membrane rafts: new tools and insights[END_REF][START_REF] Coskun | Membrane rafting: from apical sorting to phase segregation[END_REF] Consequently, a wide variety of biophysical techniques have been developed and used to study the properties of cholesterol-containing lamellar phases in both synthetic and biological systems (see references [START_REF] Simons | Revitalizing membrane rafts: new tools and insights[END_REF][START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] for recent reviews). Many of these methods can also be adapted to characterize LCP samples. For example, fluorescence-based techniques have been used to measure diffusion and clustering of membrane components within bilayers, [START_REF] He | Detecting nanodomains in living cell membrane by fluorescence correlation spectroscopy[END_REF][START_REF] Kenworthy | Fluorescence recovery after photobleaching studies of lipid rafts[END_REF][START_REF] Loura | Fluorescence resonance energy transfer to characterize cholesterol-induced domains[END_REF] and methods such as fluorescence recovery after photobleaching (FRAP) have been applied to LCPs. [START_REF] Cherezov | LCP-FRAP Assay for Pre-Screening Membrane Proteins for In Meso Crystallization[END_REF][START_REF] Xu | Development of an Automated High Throughput LCP-FRAP Assay to Guide Membrane Protein Crystallization in Lipid Mesophases[END_REF] Small-and wide-angle X-ray scattering has been used to measure bilayer thickness and inter-chain packing distances, [START_REF] Quinn | An X-ray diffraction study of model membrane raft structures[END_REF] and again, these methods have been applied to the study of LCPs. [START_REF] Cherezov | Membrane protein crystallization in meso: Lipid type-tailoring of the cubic phase[END_REF][START_REF] Conn | Incorporation of the dopamine D2L receptor and bacteriorhodopsin within bicontinuous cubic lipid phases. 1. Relevance to in meso crystallization of integral membrane proteins in monoolein systems[END_REF] Finally, a range of NMR spectroscopic tools have been used to analyze structural and dynamic properties of lipid bilayers. These methods include the use of 2 H NMR of lipids with deuterated chains to measure acyl chain order [START_REF] Bartels | Raftlike mixtures of sphingomyelin and cholesterol investigated by solid-state 2H NMR spectroscopy[END_REF] and bilayer fluctuations, [START_REF] Petrache | X-ray scattering and solid-state deuterium nuclear magnetic resonance probes of structural fluctuations in lipid membranes[END_REF] the use of [START_REF] Shaka | Evaluation of a New Broadband Decoupling Sequence: WALTZ-16[END_REF] P NMR to investigate the head-groups of phospholipids, [START_REF] Seelig | 31P nuclear magnetic resonance and the head group structure of phospholipids in membranes[END_REF][START_REF] Holland | Distinguishing individual lipid headgroup mobility and phase transitions in raft-forming lipid mixtures with 31P MAS NMR[END_REF] and the use of the [START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] C chemical shifts to investigate the hydrogenbonding partners of cholesterol. [START_REF] Soubias | Understanding sterol-membrane interactions, Part II: Complete H-1 and C-13 assignments by solid-state NMR spectroscopy and determination of the hydrogen-bonding partners of cholesterol in a lipid bilayer[END_REF][START_REF] Jolibois | Understanding sterol-membrane interactions Part I: Hartree-Fock versus C-13 and H-1 NMR isotropic chemical shifts of sterols in solution and analysis of hydrogen-bonding effects[END_REF] The application of methods that require the interpretation of anisotropic NMR parameters, such as 2 H quadrupolar splitting and 31 P chemical shift anisotropy, is not possible in LCP, because the rapid reorientation of the lipid molecules within the isotropic phase leads to an averaging of these values. However, various laboratories have begun to extend and apply NMR methods that rely on parameters accessible in isotropic systems, such as polarization transfer rates, [START_REF] Nowacka | Polarization Transfer Solid-State NMR for Studying Surfactant Phase Behavior[END_REF] relaxation times [START_REF] Hakansson | Nuclear magnetic relaxation study of the microstructure of a bicontinuous cubic phase[END_REF] and line-shapes, [START_REF] Momot | Inhomogeneous NMR line shape as a probe of microscopic organization of bicontinuous cubic phases[END_REF] to LCP. There are certain advantages to conducting NMR experiments in LCP, because the rapid isotropic reorientation of the lipid components leads to almost liquid-like spectra in terms of line-width and intensity, and the NMR spectra of LCP samples have even been recorded in a solution state probe [START_REF] Boyle-Roden | High resolution HNMR of a lipid cubic phase using a solution NMR probe[END_REF] , although the use of an HR-MAS probe presents a definite advantage by removing inhomogeneous line broadening effects.

Here, we report the first quantification of H-bond partners of cholesterol in LCP, using cholesterol [START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] C isotropic chemical shifts. We use a methodology previously established to describe the hydrogen bonding of cholesterol in chain deuterated DMPC (DMPC-d 54 ) bilayers. [START_REF] Soubias | Understanding sterol-membrane interactions, Part II: Complete H-1 and C-13 assignments by solid-state NMR spectroscopy and determination of the hydrogen-bonding partners of cholesterol in a lipid bilayer[END_REF] This approach uses the exquisite and quantitative sensitivity of cholesterol carbon chemical shifts to the local environment and hydrogen bonding partners of the hydroxyl group. The results for four different systems are presented: DMPC-d 54 multi-lamellar vesicles (MLVs) with 10 mol% cholesterol at low (20 w/w%) and moderate (40 w/w%) hydration; and MO with 10 mol% cholesterol in a lamellar phase (20 w/w% hydration) and in an LCP (40 w/w% hydration). These hydration levels for MO were chosen because 40 w/ w% is the hydration typically used for forming LCP in X-ray crystallography of GPCRs, while 20 w/w% hydration of MO gives lamellar phases and allows a direct comparison with DMPC-d 54 and among the two MO major phases. These results are compared and discussed with reference to their implications for the in meso crystallization of membrane proteins.

Experimentals Materials

Cholesterol and 3,4-13 C 2 -cholesterol (used in parameter optimization) were purchased from Sigma-Aldrich Chemie Sarl, Saint-Quentin Fallavier, France and Euriso-Top-SA, Saint-Aubin, France, respectively. Monoolein (MO) was obtained from Nu-Chek Prep Inc, Elysian, MN, USA and 1,2-dimyristoyl(d 54 )-sn-glycero-3-phosphocholine (DMPC-d 54 ) from Avanti Polar Lipids Inc, Alabaster, AL, USA. D 2 O (99.85 atom%) and 2 H-depleted water were from Euriso-Top SA, Saint-Aubin, France, and chloroform (used in sample preparation) from VWR, Fontenay sous Bois, France. All materials were used without further purification.

Sample Preparation

MO or DMPC-d 54 and cholesterol were dissolved in excess chloroform and mixed in the desired molar ratio. Chloroform was evaporated to dryness under a constant flow of N 2 gas, and then under vacuum overnight. LCP samples containing MO and cholesterol at 40 w/w% hydration with D 2 O were prepared by mechanical mixing, according to the established protocol. [START_REF] Caffrey | Crystallizing membrane proteins using lipidic mesophases[END_REF] 40 w/w% hydration for the LCP sample was selected because this level of hydration is close to the full hydration capacity of LCP and frequently used in LCP crystallization studies, and therefore has practical relevance. In addition, in order to facilitate the preparation of homogeneous DMPC-d 54 MLVs for direct comparison, the use of a sample with as much D 2 O as could be incorporated without significantly disrupting the LCP was appropriate. It was verified that the [START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] C chemical shifts and line-widths of cholesterol and MO in LCP are not significantly altered by changes in hydration between 30 and 40 w/ w% (data not shown). Lamellar phase samples containing MO and cholesterol at 20 w/w% hydration were prepared by adding D 2 O to the dried lipids in the desired proportion and then mixing to homogeneity by centrifugation and freeze-thawing through at least five cycles. Lamellar phase samples containing DMPC-d 54 and cholesterol were prepared by hydrating the dried lipid film in excess water, lyophilizing overnight, and then re-hydrating with the desired quantity of 2 H-depleted water to obtain the 20 w/w% and 40 w/w% hydration levels. The samples were stored at 30 °C for 48 hours to reach the solvation equilibrium.

NMR Data Acquisition

Cubic phase experiments were performed on a Bruker DMX narrow bore spectrometer operating at a 1 H Larmor frequency of 500 MHz. Spectra were acquired using a 4 mm Bruker double resonance HR-MAS gradient probe with a deuterium lock, at a magic angle spinning (MAS) frequency of 2.5 kHz. Various rotational frequencies were tested to determine the optimal frequency to obtain narrow line widths from LCP without causing disruption of the phase (monitored by broadening/inhomogeneity in the proton peak from residual water in the sample). Frequencies between 1 and 5 kHz were acceptable, and 2.5 kHz was chosen as a reasonable speed to obtain adequate line widths while minimizing the presence of spinning side bands in 1 H and [START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] C spectra. Lamellar phase experiments were performed on a Bruker AVANCE standard bore operating at a 1 H Larmor frequency of 700 MHz and equipped with a 4 mm double resonance 1 H-[ 15 N- [START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] C] cross polarization (CP)-MAS probe. Lamellar phase samples containing MO and cholesterol were conducted at a MAS frequency of 5 kHz, and samples containing DMPC-d 54 at 10 kHz. For all experiments, the probe temperature was calibrated using ethylene glycol in d 6 -DMSO. [START_REF] Qiu | The phase diagram of the monoolein/water system: metastability and equilibrium aspects[END_REF] H NMR spectroscopy was used to check that the DMPC-d 54 chain lipid quadrupolar splittings at 303K had standard values for hydrated MLVs. Static 2 H spectra were recorded on a Bruker Avance narrow-bore spectrometer operating at a proton Larmor frequency of 500 MHz with a 5 mm single-resonance probe equipped with a solenoid coil oriented at 90° with respect to the magnetic field.

Cholesterol [START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] C chemical shifts for samples containing MO were obtained using a standard single-pulse experiment with power-gated 1 H decoupling (waltz16 with a decoupling field of 2.5 kHz). [START_REF] Shaka | Evaluation of a New Broadband Decoupling Sequence: WALTZ-16[END_REF] Typical π/2 pulse lengths were 7 μs for 1 H, and 7.65 μs for [START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] C. Cholesterol peaks were assigned with reference to published spectra of cholesterol in solution in CDCl 3 and DMPC bilayers. [START_REF] Soubias | Understanding sterol-membrane interactions, Part II: Complete H-1 and C-13 assignments by solid-state NMR spectroscopy and determination of the hydrogen-bonding partners of cholesterol in a lipid bilayer[END_REF] . For lamellar samples containing DMPC-d 54 , cholesterol [START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] C chemical shifts were obtained using a standard 1D CP-MAS sequence. A typical π/2 pulse length for 1 H was 2.9 μs. The 1 H- [START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] C CP magnetisation transfer step employed a linear ramp (80 to 100% field strength) on the 1 H channel with a contact time of 1.5 ms and a [START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] C radio frequency field of 55 kHz. High-power proton decoupling was obtained using the Spinal64 scheme [START_REF] Fung | An improved broadband decoupling sequence for liquid crystals and solids[END_REF] and a decoupling field of 86 kHz.

Calculations of rotamers, hydrogen bonding, and theoretical chemical shifts

Theoretical NMR chemical shifts were calculated using a Hartree-Fock strategy, as described in a previous publication. [START_REF] Jolibois | Understanding sterol-membrane interactions Part I: Hartree-Fock versus C-13 and H-1 NMR isotropic chemical shifts of sterols in solution and analysis of hydrogen-bonding effects[END_REF] The geometry of each of the supramolecular models, which combined the three major C3-O3 rotamer states of cholesterol (gauche (+), gauche (-), and anti, denoted as g+, g-, and anti, respectively) and the hydrogen-bonding partners of the hydroxyl group of cholesterol, was fully optimized at the HF/STO-3G level. Isotropic chemical shifts were determined for all atoms at the same theoretical level using a double-ζtype basis set with a polarization function [i.e., 6-31G(d,p)]. Note that previous calculations using a DFT approach with the same basis set did not lead to any improvement in the calculated cholesterol chemical shifts compared with the Hartree-Fock strategy. [START_REF] Jolibois | Understanding sterol-membrane interactions Part I: Hartree-Fock versus C-13 and H-1 NMR isotropic chemical shifts of sterols in solution and analysis of hydrogen-bonding effects[END_REF] The whole cholesterol molecule was used to perform calculations. To mimic the hydrogenbonding environment of the sterol (i.e., solvent water and either MO or DMPC-d 54 ), several hydrogen-bonding partners for the cholesterol hydroxyl group were considered: namely, the water molecules, the fatty acid ester bonds, and either the MO glycerol alcohol groups or the DMPC-d 54 phosphodiester. Water molecules and glycerol alcohol groups were considered as both donors and acceptors of hydrogen bonds. The glycerol alcohol groups were modeled by ethanol (primary alcohol) and propan-2-ol (secondary alcohol). The fatty acid ester bonds and the DMPC-d 54 head-group phosphate were modeled, as hydrogen-bond acceptors, by acetone and dimethyl phosphate, respectively. [START_REF] Soubias | Understanding sterol-membrane interactions, Part II: Complete H-1 and C-13 assignments by solid-state NMR spectroscopy and determination of the hydrogen-bonding partners of cholesterol in a lipid bilayer[END_REF][START_REF] Jolibois | Understanding sterol-membrane interactions Part I: Hartree-Fock versus C-13 and H-1 NMR isotropic chemical shifts of sterols in solution and analysis of hydrogen-bonding effects[END_REF] Following the procedure described in, [START_REF] Soubias | Understanding sterol-membrane interactions, Part II: Complete H-1 and C-13 assignments by solid-state NMR spectroscopy and determination of the hydrogen-bonding partners of cholesterol in a lipid bilayer[END_REF] the theoretical carbon chemical shift (CS) differences between the CS obtained for the different models and the averaged CS over the three rotamers of cholesterol with no hydrogen-bonding interaction were calculated; i indicates the carbon number of the sterol, j the C3-O3 rotamer conformation, and k the type of hydrogen-bonding partner. This difference reflects the theoretical effect of a specific hydrogen-bonding interaction with one conformation of cholesterol that occurs in the lipid phase compared with cholesterol in CCl 4 solution. For each carbon i (from 1 to 6), linear combinations of these CS variations were calculated in increments of 1% over each rotamer (%j, where j=g+,gor anti, is the percentage of each rotamer), and over the different types of hydrogen-bond partners (%k, where k=a specific hydrogen-bond partner is the percentage each type of interaction). The values are provided in Supplementary Information Table S1.

(eq. 1)

Each is then compared to the experimental values (eq. 2)

Two conditions must be fulfilled for each set of solutions: Σ j=g+,g-,anti %j = 100% and Σ k=H-bond partners %k ≤ 300%, which corresponds to a maximum of three simultaneous hydrogen-bonding interactions of the cholesterol hydroxyl group (one to the hydrogen of the hydroxyl group and two to the oxygen lone pairs).

The results were filtered to accept only values, for each carbon, for which the difference between the experimental and theoretical variations was less than 0.08ppm, to take into account both experimental accuracy and non-specific solvent effects on chemical shifts. [START_REF] Soubias | Understanding sterol-membrane interactions, Part II: Complete H-1 and C-13 assignments by solid-state NMR spectroscopy and determination of the hydrogen-bonding partners of cholesterol in a lipid bilayer[END_REF] The average value for the percentage of each rotamer and each H-bond partner was calculated over the 10% of solutions presenting the lowest value of root mean square deviation between theoretical and experimental CS variations.

Results and Discussion

Assignment of cholesterol 13 C chemical shifts in lipid environment

The [START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] C chemical shifts for cholesterol (10 mol%) in DMPC-d 54 and MO, each at 40 and 20 w/w% hydration, were recorded and assigned (see Table 1 and Figure 1). The use of cross polarization sequence, together with the perdeuterated chains of the DMPC-d 54 , enabled almost complete suppression of the lipid signal, facilitating the assignment of cholesterol carbon peaks. Only the two quaternary carbons were not assigned. The chemical shifts of cholesterol in DMPC-d 54 at these two hydration levels were similar to each other, and to values reported previously for samples containing 30 mol% cholesterol with 50 w/w% hydration. [START_REF] Soubias | Understanding sterol-membrane interactions, Part II: Complete H-1 and C-13 assignments by solid-state NMR spectroscopy and determination of the hydrogen-bonding partners of cholesterol in a lipid bilayer[END_REF] Despite the lack of perdeuterated acyl chains, and therefore the presence of large lipid signals in the spectra of the MO samples, the chemical shifts of all but two of the carbon atoms of cholesterol -C7 and C8 -could be resolved at both 40 and 20 w/w% hydration. These two unresolved carbons peaks were presumed to be situated underneath a strong lipid peak at ~32 ppm (based on their positions in the spectra in DMPC-d 54 and in CCl 4 ). A substantial difference between the intensity and line-width of the peaks in carbon spectra of the MO samples at 40 and 20 w/w% hydration was observed. At 40 w/w% hydration the sample is in an LCP, and the peaks are narrow (typical line widths of 6-12 Hz) with good signal-to-noise. Interestingly, the standard 'solution'-type INEPT-based NMR experiments, including DEPT and HSQC, which were used to corroborate the assignment of the cholesterol chemical shifts, gave good signal-to-noise and line-widths, demonstrating a practical effect of the rapid reorientation of the lipid molecules in LCPs. In the lamellar phase, at 20 w/w% hydration, the peaks are much broader (typically 12-24 Hz) and have poorer signal to noise. However, the chemical shifts of cholesterol in the two MO phases do not differ substantially.

Note that it was necessary to use perdeuterated DMPC but not perdeuterated MO in order to obtain full assignments because the increased complexity of the carbon spectra of the DMPC samples (with DMPC having two non-equivalent acyl chains) in comparison of the singlechained MO. Furthermore, the cross polarization based excitation of cholesterol [START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] C carbons filters out the deuterated DMPC resonances while increasing sensitivity.

Cholesterol chemical shift variations in the different lipid phases from NMR data

The differences between the chemical shifts of cholesterol dissolved in CCl 4 (isotropic environment) and of cholesterol incorporated in lipidic mesophases made of DMPC-d 54 or of MO are shown in Figure 2. These chemical shift differences can be divided into three broad groups. First, C7 to C19 (except C17) -that is the carbons found in rings B, C and D of the rigid sterol structure -are relatively insensitive to changes in their environment, reflecting their lack of conformational flexibility, and their distance from any potential hydrogen bonding or other electrostatic interaction of the cholesterol hydroxyl group. Second, the more flexible carbons of the cholesterol tail region -C17 and C20-27 -are more sensitive to their environment and show distinct variations between the CCl 4 , DMPCd 54 and MO phases. Interestingly, the chemical shifts of these carbons in the MO lamellar phase (at 20 w/w% hydration) are more similar to the chemical shifts in MO in the LCP (at 40 w/w% hydration) than to those in the DMPC-d 54 lamellar phases. The variations in the chemical shifts of C17 and C20-27 likely result predominantly from differences in side chain dynamics (i.e., the distribution of trans/gauche conformers along the side chain [START_REF] Quinn | The liquid-ordered phase in membranes[END_REF] ), implying that the dynamics of the chains in the center of the MO bilayer are different from the dynamics of the chains in the center of the DMPC-d 54 bilayer, and are more similar to the dynamics of the chains in the LCP. The middle part of the lipid bilayer is more 'isotropic' in both of the MO phases than in the DMPC-d 54 bilayer, as illustrated by the carbon chemical shifts of positions 25-27, which are closer to the values in CCl 4 ,(i.e., in an isotropic environment) than the corresponding chemical shifts in the DMPC-d 54 bilayer. Because chain deuterated DMPC is used, it should be noted that the deuteration of DMPC or the hydration with D 2 O has been shown to produce negligible effect on its lipid chain order parameters. [START_REF] Gross | Dipolar recoupling in MAS NMR: A probe for segmental order in lipid bilayers[END_REF][START_REF] Beranova | Effect of heavy water on phospholipid membranes: experimental confirmation of molecular dynamics simulations[END_REF] Similarly, we have controlled that DMPC-cholesterol samples give the same [START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] C chemical shifts when hydrated in H 2 O or in D 2 O (supplementary information, Fig S2). Finally, the chemical shifts of C1-6, in the A ring of the rigid sterol structure and in close proximity to the hydroxyl group at position 3, are most sensitive to their environment, and specifically to the nature and quantity of potential hydrogen-bonding partners for the hydroxyl group, as was established previously in [START_REF] Soubias | Understanding sterol-membrane interactions, Part II: Complete H-1 and C-13 assignments by solid-state NMR spectroscopy and determination of the hydrogen-bonding partners of cholesterol in a lipid bilayer[END_REF] . There are small variations in the chemical shift differences for C1, C2 and C4 in the four different samples. However, there is a significant reduction in the chemical shift differences of C3, C5 and C6 in the MO phases compared with the differences in the DMPC-d 54 phases. The fact that this reduction appears in the MO samples in both the cubic and lamellar phases implies that it is the result of some property of the MO itself, and not a function of the macromolecular organization (i.e., not an effect of curvature, lipid packing, lateral pressure, …). Determination of the distribution of hydrogen-bond partners: the chemical shift variations of cholesterol C1-6 were used to calculate the distribution of the rotameric states as described in the Materials and Methods section. The average values of the linear combination coefficients for the rotamers (%j) and hydrogen-bonding partners (%k) were calculated using only the 10% of solutions presenting the lowest rmsd values between the experimental and calculated CS variations (see below for discussion and full details in Table S2 in the Supplementary Information).

As a verification of the accuracy of the hydrogen-bonding calculations, these averaged values are combined with the variations (Table S2, in the Supplementary Information) to generate theoretical chemical shifts for carbons C1-6 in each sample using eq. 1. As seen in Supplementary Information Figure S1, there was excellent agreement between the experimental and theoretical chemical shifts for all six carbons in the two DMPC-d 54 samples, and for C1, C2, C4 and C5 in the MO samples. The discrepancy between the experimental and theoretical chemical shifts for C3 and C6 in the MO samples was within the experimental error, but was greater than for the other calculated chemical shifts. In all of the samples, the hydroxyl group was calculated to be approximately evenly distributed between the three rotameric states (Supplementary Information, Table S2). This calculated distribution of rotamers provides a good indication of the accuracy of the calculations, because the sample is isotropic and dynamic and the hydroxyl group expected to be free to flip between the rotamers, and none of the rotamers is expected to be favored over the others. The same observation had been made in our earlier work for cholesterol in DMPC bilayers ] . [START_REF] Soubias | Understanding sterol-membrane interactions, Part II: Complete H-1 and C-13 assignments by solid-state NMR spectroscopy and determination of the hydrogen-bonding partners of cholesterol in a lipid bilayer[END_REF]

Cholesterol/DMPC-d 54 hydrogen-bond partner distribution

The hydrogen-bond partners of cholesterol (10 mol%) in DMPC-d 54 at 40 and 20 w/w% hydration are similar to each other, and to those reported previously for cholesterol (30 mol %) in DMPC at 50 w/w% hydration. [START_REF] Soubias | Understanding sterol-membrane interactions, Part II: Complete H-1 and C-13 assignments by solid-state NMR spectroscopy and determination of the hydrogen-bonding partners of cholesterol in a lipid bilayer[END_REF] The average fraction of hydrogen bonding through the hydrogen of the cholesterol hydroxyl group to ester bond (0.28 ± 0.18, 0.27 ± 0.17 and 0.26 ± 0.19 for the samples with 40, 20 and 50 w/w% hydration, respectively), to head group phosphate (0.16 ± 0.02, 0.16 ± 0.02 and 0.18 ± 0.03, respectively) and to water (0.17 ± 0.10 for all three samples) were within one standard deviation of each other across the three samples (see Figure 3A and values in [START_REF] Soubias | Understanding sterol-membrane interactions, Part II: Complete H-1 and C-13 assignments by solid-state NMR spectroscopy and determination of the hydrogen-bonding partners of cholesterol in a lipid bilayer[END_REF] ). There was more variation in the results for hydrogen bonding to water through the oxygen of the cholesterol hydroxyl group, with average values of 0.89 ± 0.09, 0.70 ± 0.08 and 0.76 ± 0.14 for the samples with 40, 20 and 50 w/w% hydration, respectively (Figure 3A). Overall, these data suggest that cholesterol resides predominantly 'upright' in the DMPC bilayer, with its hydroxyl group participating in hydrogen bonds with the ester and phosphate region of the phospholipid and with water at the lipid-water interface. This conclusion is generally consistent with small-angle neutron scattering data and with molecular modeling results, which suggest the perpendicular orientation of cholesterol in PC bilayers. [START_REF] Harroun | Cholesterol is found to reside in the center of a polyunsaturated lipid membrane[END_REF][START_REF] Henin | Hydrogen-bonding patterns of cholesterol in lipid membranes[END_REF]

Cholesterol/MO hydrogen-bond partner distribution

The main differences between the hydrogen-bonding environment of cholesterol in the DMPC-d 54 and in the MO phases are the absence of the phosphodiester group and the addition of the primary and secondary alcohol groups in the MO system as donor of hydrogen to cholesterol (summarized graphically in Figure 4). In the MO samples, which contained secondary and primary alcohols as potential partners instead of phosphate, the preference for donating a hydrogen to the ester bond rather than to water or an alcohol was much stronger (e.g., 0.82 ± 0.03, 0.01 ± 0.01, 0.01 ± 0.01, and 0.01 ± 0.01 of 1 for the ester bond, water, secondary alcohol and primary alcohol, respectively, in the 40 w/w% hydration sample -Figure 3B). The average total donation of hydrogen was greater for the MO samples (e.g., 0.84 ± 0.03, in the 40 w/w% hydration sample -Figure 3D) than for the DMPC-d 54 samples (e.g., 0.62 ± 0.08, in the 40 w/w% hydration sample -Figure 3C). Similar to the situation with donation of hydrogen, the overall propensity of the oxygen of the cholesterol hydroxyl group to accept a hydrogen from a partner is greater in the MO phases (0.98 ± 0.04 and 0.96 ± 0.05 of 2 in the 40 and 20 w/w% hydration samples, respectively -Figure 3B) than in the DMPC-d 54 phase at the same hydration (0.89 ± 0.09, 0.70 ± 0.08 of 2, respectively -Figure 3A). In the same samples, the proportion of this interaction that is with water is less in the MO phase (0.06 ± 0.07 and 0.08 ± 0.05 in the 40 and 20 w/w% hydration samples, respectively -Figure 3B) compared with in the DMPC-d 54 phase at the same hydration (0.89 ± 0.09 and 0.70 ± 0.08, respectively -Figure 3A). The additional hydrogen-bonding interactions with the oxygen of the cholesterol hydroxyl group in the MO phases (Figure 3B) are predominantly with the secondary alcohol (0.81 ± 0.18 and 0.70 ± 0.23 in the 40 and 20 w/w% hydration samples) and a little with the primary alcohol (0.11 ± 0.16 and 0.17 ± 0.21, respectively). These changes in hydrogen-bonding partners have a significant effect on the overall distribution of hydrogen bonding, including increasing the preference of cholesterol to form hydrogen bonds with a lipid partner rather than with water in the MO phases (1.75 ± 0.11 and 0.06 ± 0.05 for MO and water in 40% hydration sample, respectively -Figure 3D) compared with in the DMPC-d 54 at the same hydration (0.45 ± 0.16 and 1.06 ± 0.15 for MO and water, respectively -Figure 3C). These data cannot be interpreted to report on the relative penetration of water at the polarapolar interface in the two systems, but raise an interesting question about the penetration of water at the different interfaces, and the extent of lipid-lipid hydrogen-bond formation that could be addressed by additional experiments and/or computer simulations. However, the hydrogen-bonding data do indicate that the cholesterol hydroxyl group interacts with the polar-apolar interfacial region of the MO lamellar and cubic phases to a comparable or greater extent than in the DMPC-d 54 lamellar phases, supporting the hypothesis that cholesterol maintains a conventional 'upright' position in these phases, as opposed to a 'horizontal' position at the center of the two lipid leaflets, as has been observed in certain systems with polyunsaturated phospholipids. [START_REF] Harroun | Cholesterol is found to reside in the center of a polyunsaturated lipid membrane[END_REF] A further demonstration of this predominant orientation of cholesterol in LCPs could be obtained using the elegant strategy developed by D. Huster and collaborators, which is based on 1 H MAS NOESY and the analysis of intermolecular cross relaxation rates. [START_REF] Huster | Influence of docosahexaenoic acid and cholesterol on lateral lipid organization in phospholipid mixtures[END_REF][START_REF] Scheidt | Investigating the membrane orientation and transversal distribution of 17 beta-estradiol in lipid membranes by solid-state NMR[END_REF] Taken together, the results presented in this paper have potential implications for using LCP as a membrane mimetic matrix for biophysical studies and crystallization of membrane proteins. The role of cholesterol in facilitating crystallization of GPCRs is well recognized although not fully understood on a molecular level [START_REF] Stevens | The GPCR Network: a large-scale collaboration to determine human GPCR structure and function[END_REF] . The exact nature of the lipid composition is known to play a role of the structure determination process, [START_REF] Li | Crystallizing Membrane Proteins in Lipidic Mesophases. A Host Lipid Screen[END_REF] both via specific lipid protein contacts and via global physical properties such as the spontaneous curvature and lateral pressure profiles [START_REF] Botelho | Conformational energetics of rhodopsin modulated by nonlamellar-forming lipids[END_REF][START_REF] Lindblom | Cubic Phase of Monoglyceride-Water Systems -Arguments for a Structure Based Upon Lamellar Bilayer Units[END_REF][START_REF] Kamo | Effects of an amphipathic alpha-helical peptide on lateral pressure and water penetration in phosphatidylcholine and monoolein mixed membranes[END_REF] . The greater extent of cholesterol-lipid hydrogen-bond formation in the MO membranes compared with the DMPC-d 54 membranes may affect the equilibrium between cholesterol-lipid and cholesterol-protein interactions in LCP in comparison with 'native' phospholipid membranes. Cholesterol's side chain [START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] C chemical shifts in MO were found to be close to those in an isotropic organic solvent solution, in contrast with those in DMPC-d 54 bilayers, suggesting a different lateral pressure profile at the acyl chain level. These considerations may be particularly important when studying membrane proteins for which significant conformational changes or flexibility in the transmembrane region of the protein are required for function. In such cases doping LCP with native lipids 8 may help to restore the specific protein conformation and function in LCP.

Conclusions

In summary, the experimentally determined [START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] C chemical shifts of cholesterol C1-6 were used to calculate the hydrogen-bonding partners of cholesterol in four lipid phases: DMPCd 54 MLVs with 10 mol% cholesterol at low (20 w/w%) and moderate (40 w/w%) hydration, and MO with 10 mol% cholesterol in MLVs (20 w/w% hydration) and in an LCP (40 w/w% hydration). This original methodology based on the combination of 13C chemical shifts and quantum chemistry, initially developed in DMPC-d 54 lipid bilayers, proves to be efficient in a completely different lipid phase and to afford a unique way of assessing the local environment around cholesterol. There were significant differences observed in the [START_REF] Mannock | The effect of variations in phospholipid and sterol structure on the nature of lipid-sterol interactions in lipid bilayer model membranes[END_REF] C chemical shifts, and hence in the hydrogen-bonding partners, of cholesterol in the MO phases in comparison with the DMPC-d 54 phases, with a slight increase in overall hydrogenbond formation, a decrease in cholesterol-water hydrogen bonding and an increase in lipidcholesterol hydrogen bonding in the MO phases. The properties characteristic of MO bilayers may also have implications for conformational equilibrium and crystallization of membrane proteins in LCP. They should be kept in mind when discussing cholesterol -GPCR interactions (or any other lipid -protein interaction) based on X-ray structures in LCP. The structure of cholesterol with carbon atom numbering

ABBREVIATIONS

  Figure 1.

Figure 2 .

 2 Figure 2. Plot of the differences between the 13C chemical shifts of assigned carbon positions in CCl4 and in various lipid phases Comparison of chemical shift differences (Δδ, defined as the chemical shift in CCl 4 minus the chemical shift in the conditions described) of assigned cholesterol carbons in DMPC-d 54 at 40 w/w% (black) and 20 w/w% (dark grey) hydration, and MO at 40 w/w% (white) and 20 w/w% (light grey) hydration. All DMPC-d 54 and MO samples contained 10 mol% cholesterol and data were recorded at 30°C. At 20 w/w% hydration the DMPC-d 54 and MO samples were both in a lamellar phase. At 40 w/w% hydration the DMPC-d 54 sample was in a lamellar phase whereas the MO sample was in a cubic phase. Chemical shifts were calibrated to C18 at 11.84ppm, and are accurate to ± 0.05ppm in DMPC-d 54 and ± 0.03ppm in MO.

Figure 3 .

 3 Figure 3.Calculated hydrogen-bonding partners of cholesterolA break-down of the interactions of cholesterol with specific hydrogen-bonding partners (fragments of the respective lipid modeled as small molecules) is provided in A) for DMPC-d54 and B) for MO at 40 w/w% (black) and 20 w/w% (dark grey) hydration. A summary of the calculated hydrogen-bonding interactions of cholesterol at 40 w/w% (black) and 20 w/w % (dark grey) hydration is provided in C) DMPC-d 54 and D) MO. In plots C and D, the data are expressed in two different ways: left, distinguished by whether the interaction is through the hydrogen of the cholesterol hydroxyl group -cholesterol-H -or through the oxygen of the cholesterol hydroxyl group -cholesterol-O; and right, distinguished by whether the interaction is with water or the lipid. The total probability of a hydrogen-bonding interaction is shown in the center. The vertical axes in these plots represent the probability of observing a hydrogen bond per cholesterol ± the standard deviation, where the standard deviation reflects the distribution of the results. The maximum number of hydrogen bonds per cholesterol hydroxyl group was normalized to 1 for bonds through the hydrogen of the hydroxyl (i.e., the hydrogen-bond partner acting as an H donor), and to 2 for bonds through the oxygen of the hydroxyl (i.e., the hydrogen-bond partner acting as an H acceptor). The three possible hydrogen bonds were considered independently in the calculations. The sum of the probability of a hydrogen bond occurring is always less than the maximum because the calculations did not constrain cholesterol to participate in a hydrogen-bonding interaction. The experimental data on which these calculations were based were obtained from DMPC-d 54 and MO samples containing 10 mol% cholesterol and data were recorded at 30°C. At 20 w/w% hydration, the DMPC-d 54 and MO samples were both in a lamellar phase. At 40 w/w% hydration, the DMPC-d 54 sample was in a lamellar phase whereas the MO sample was in a cubic phase.

Figure 4 .

 4 Figure 4. Summary of hydrogen-bonding interactions of cholesterol Graphical summary of the hydrogen-bonding interactions of cholesterol in DMPC-d 54 at A) 40 and B) 20 w/w% hydration, and in MO at C) 40 and D) 20 w/w% hydration. The values represent the percentage of interactions with the cholesterol of the different partners as either donor or acceptor of H-bond. The maximum number of hydrogen bonds per cholesterol hydroxyl group is three. Although all the figures indicate H atoms for clarity, the MO samples were hydrated with D 2 O.

Table 1 13

 1 C chemical shifts of cholesterol in DMPC-d 54 and in MO at different hydrations

	MO MO	40 20		37.45 37.46	30.81 30.89	70.97 71.00	41.55 41.62	141.09 141.07	120.94 121.00	--	--	50.24 50.27	36.07 36.43	21.18 21.19	39.99 39.98	42.32 42.33	56.82/56.50 56.85/56.47
	54 DMPC-d	20		37.39	30.82	70.42	41.63	141.89	119.88	31.85	31.85	50.07	-	20.98	39.91	-	56.68
	Sample CCl 4 54 DMPC-d	Hydration (w%) 0 40	Carbon	1 37.12 37.38	2 31.62 30.71	3 71.05 70.50	4 42.35 41.51	5 140.56 141.74	6 121.16 119.98	7 31.62 31.83	8 31.74 31.83	9 49.92 50.06	10 36.31 -	11 20.93 20.98	12 39.67 39.87	13 42.18 -	14 56.65 56.66

Acknowledgments

Funding sources

These studies and the IPBS NMR equipment were financed by the French Research Ministry, CNRS, Université Paul Sabatier, the Région Midi-Pyrénées and European structural funds. The research leading to these results has received funding from the EU's Seventh Framework Programme [FP7/2007-2013] under grant agreement # [211800], and by the NIH grant GM089857.

Supplementary Material

Refer to Web version on PubMed Central for supplementary material.