Julien Leclaire
email: julien.leclaire@univ-lyon1.fr

Guillaume Poisson

Fabio Ziarelli

Gerard Pepe

Frédéric Fotiadu

Federico M Paruzzo

Aaron J Rossini

Jean-Nicolas Dumez

Bénédicte Elena-Herrmann

Lyndon Emsleyf

Structure elucidation of a complex CO2-based organic framework material by NMR crystallography

A three-dimensional structural model of a complex CO 2 -based organic framework made from high molecular weight, self-assembled, flexible and multi-functional oligomeric constituents has been determined de novo by solid-state NMR including DNP-enhanced experiments. The complete assignment of the 15 N, 13 C and 1 H resonances was obtained from a series of two-dimensional through space and through bond correlation experiments. MM-QM calculations were used to generate different model structures for the material which were then evaluated by comparing multiple experimental and calculated NMR parameters. Both NMR and powder X-ray diffraction were evaluated as tools to determine the packing by crystal modelling, and at the level of structural modelling used here PXRD was found not to be a useful complement. The structure determined reveals a highly optimised Hbonding network that explains the unusual selectivity of the self-assembly process which generates the material. The NMR crystallography approach used here should be applicable for the structure determination of other complex solid materials.

Structure elucidation of a complex CO2-based organic framework material by NMR crystallography Introduction

The last decades have seen an explosive growth in the production of rationally designed supramolecular materials resulting from directed self-assembly of molecular building units. Among these selfassembled molecular networks displaying promising properties, one can cite metal organic frameworks (MOFs), 1 obtained by connecting metal containing secondary units with organic linkers, and organic supramolecular solids 2 resulting from the connection of carbon-based building blocks. Their synthesis is based on attractive one-pot self-assembly processes which illustrate the concept of molecular tectonics. [START_REF] Hosseini | Applications of supramolecular chemistry[END_REF][START_REF] Ferlay | Functional supramolecular architectures for organic electronics and nanotechnology[END_REF][START_REF] Hosseini | [END_REF] Self-organization results from the structure of and the interactions between the rigid building blocks. 6 Short-range, strong anisotropic interactions drive self-organization across length scales from the molecular and nano-scale level 7 up to the micro-and milli-scale levels. [8][9][10][11] The welldefined building units, coupled with the thermodynamic control of the self-assembly process, often lead to long range structural order i.e. to highly crystalline solids. 12 X-ray diffraction can frequently be used to characterize the structural features of these self-assembled networks if they are sufficiently regular.

Such supramolecular materials can have tunable physical and chemical properties, with cavities whose size and shape are easily manipulated. 13 However, the complete structural characterization of increasingly complex systems, that is essential to determine structure-activity relations and to then rationally improve properties, remains a considerable challenge. This notably often prevents exploration of molecular assemblies based on more flexible objects involving multiple functionalities.

In this context we have recently synthesized and described a self-assembled supramolecular solid which results from the one-pot thermodynamically controlled simultaneous reaction of two organic building blocks and CO 2 (Scheme 1). 14 Notably, this reversible CO 2 -based organic framework is produced by aggregation of flexible self-complementary oligomeric objects. As illustrated in Scheme 1 these oligomeric building blocks are themselves assembled in situ from the basic components, including CO 2 . The covalent assembly process of the oligomers consists in the simultaneous and reversible formation of 20 carbon-nitrogen bonds of three different chemical types (imine, aminal and carbamate). Since the final material results from the packing of oligomers that were themselves spontaneously assembled from elementary units through the reversible formation of covalent bonds, this supramolecular solid is in the class of what have been dubbed "dynamic materials" by Lehn. [START_REF] Lehn | polymeric material spontaneously obtained from monomers assembled with reversible covalent and non covalent bonds[END_REF][16][17] This particular dynamic material possesses original properties: both the material and its constitutive oligomers dissociate upon CO 2 departure in a cooperative manner, and the assembly process is found to be extremely selective in terms of building block incorporation. 18,19 Both features (reversibility and selectivity) are desirable in the context of CO 2 capture and use, as well as for selective extraction of valuable molecules from waste. 20 However, the material precipitates from solution as an insoluble nanocrystalline powder, which is not amenable to standard molecular level characterization. To address this problem we previously used solid-state Nuclear Magnetic Resonance (NMR) to propose basic structural features for this supramolecular system. 14 Scheme 1 Double self-assembly process leading to the discovery of a 3-component dynamic material based on CO 2 . (a) Elementary building blocks such as polyamines n (brown connector) and polyaldehydes X (orange hexagon) self-assemble in methanol at RT under air to yield 2-component oligomers (b), mainly X 2 n 3 capsules. In the case X = A and n = 2 in the same conditions, exposure to CO 2 (blue arch) as a third building block spontaneously yields the 3-component soluble "oligodynablock" A 4 2 9 (CO 2 ) 9 . This self-assembled species then itself spontaneously further selfassembles into the corresponding insoluble dynamic material DM A 2 (CO 2 ) as a nanocrystalline powder (electron micrograph, white bar: 100 nm) (c). Heating to around 50 °C induces CO 2 release and disassembly of the dynamic material which converts back into A 2 2 3 .

Here we further explore the three-dimensional molecular structure of the nano-crystalline dynamic material using an NMR crystallography approach, 21,22 and we evaluate the pertinence of powder X-ray diffraction (PXRD). Solid-state NMR spectroscopy complements diffraction methods and has recently developed into a versatile tool to determine the structures of both inorganic and molecular solids. [23][24][25][26][27][28][29][30][31][32][33][34] In combination with crystal structure prediction methods and DFT chemical shift calculations, NMR chemical shifts have recently been used to determined de novo crystal structures. 23 In particular in the context of supramolecular solids, solid-state NMR and DFT calculations have been used to explore hydrogen bonding and molecular structure in organic supramolecular systems 35,36 and to characterise structural features in MOFs, including determination of conformation changes upon adsorption or to observe the dynamic events that govern host-guest interactions. [37][38][39][40][41][42] Most recently, the superstructure of a substituted zeolitic imidazolate framework (ZIF) type MOF was elucidated by combining solidstate NMR, PXRD, and DFT calculations of NMR parameters from potential model structures. 43 Notably very rapid progress has recently been made by combining sophisticated spectral assignment strategies with state-of-the-art Density Functional Theory (DFT) chemical shift calculation methods.

Today, this provides a platform for analysis of both 13 C and [START_REF] Lehn | polymeric material spontaneously obtained from monomers assembled with reversible covalent and non covalent bonds[END_REF] N spectra, [44][45][46] as well as of 1 H shifts. 22- 24,47-51 Following this general approach, here MM-QM (molecular mechanics-quantum mechanics) calculations were used to generate several different model structures of the dynamic material. The model structures were then evaluated by comparing multiple experimental and calculated NMR and PXRD parameters. A detailed structural model is proposed for the individual oligomeric constituents of the material including their exact sequence, conformation, and potential packing.

Results and discussion

Synthesis of the dynamic material

Simple molecular building blocks such as polyamines and polyaldehydes are well-known to spontaneously interconnect with each other in mild conditions (room temperature, no catalyst, open air, undistilled solvents) through the formation of reversible C-N bonds (single: aminal; double: imine) to generate dynamic combinatorial libraries.

The objects assembled from these two classes of components using reversible or dynamic covalent bonds 52 are referred to as "oligo-dynablocks" [53][54][55] as they can themselves be building blocks (or dynamic tectons) to generate supramolecular structures. Here, this second level of assembly can be triggered by exposure to CO 2 which can post-functionalize the two-component oligomers. CO 2 reversibly reacts with primary or secondary amines yielding ammonium carbamate ion pairs. CO 2 exposure hence converts neutral objects into zwitterionic species. The CO 2 -postfunctionalization can perturb the pre-equilibrated 2-component system and induce a redistribution of the populations toward one or several stable 3-component objects. Formation of a solid network is then a potential driving force that can displace the equilibria and select a self-complementary post-functionalized species. 56 Twenty-eight libraries corresponding to the various combinations of polyamines n(2-8) and polyaldehydes X(A-D) were screened for the formation of a dynamic material induced by reversible CO 2 -postfunctionalization (Scheme 1). In the absence of CO 2 , the 2-component systems were dominated by low-molecular weight entropically favoured soluble oligomers (objects involving two aromatic units at most), with the capsule made from two aldehydes and three polyamine units noted X 2 n 3 being the major adduct as indicated by ESI-MS analysis (Scheme 1a and b). 57 For all combinations except one, this composition remained unchanged when CO 2 was introduced. In contrast, polyamine n = 2 and polyaldehyde X = A lead to the quantitative formation of a single 3-component dynamic material which precipitated upon CO 2 exposure as a nano-crystalline solid and re-dissolved upon gentle heating (Scheme 1b and c). As reversible linkages were used to assemble the building blocks, their average stoichiometry within the material was precisely determined by titration ( 1 H solution NMR for A and 2; volumetric analysis for CO 2 ) after acid hydrolysis of the dried powder. While 1D solid-state NMR confirmed that trialdehyde A and CO 2 were both covalently connected to the diethylenetriamine building block 2, the titration revealed that the oligo-dynablocks constituting the materials were mostly linear oligomers made of four aromatic units A condensed with nine diethylenetriamine chains 2 each bearing one molecule of CO 2 (noted A 4 2 9 (CO 2 ) 9 , Scheme 1b). Thermogravimetric analysis coupled to mass spectrometry measurements additionally revealed the presence of substantial amounts of water (15 percent in mass). The water is presumably adsorbed in layers rather than integrated into the framework of the zwitterionic material as it could be entirely expulsed by heating at 70 °C under atmospheric pressure for several minutes without modification of the solid-state 13 C CP-MAS solid-state NMR spectrum. No high molecular weight 3-component objects were detected in the mother liquor, nor was the A 4 2 9 precursor present in the parent 2-component library before CO 2 exposure. The oligodynablocks A 4 2 9 (CO 2 ) 9 are therefore clearly stabilized by their intermolecular packing within the solid network formed.

When the stoichiometry between the building blocks A and 2 was changed, their titration after cleavage of the resulting material revealed that the average measured length of the oligomers constituting the material changed correspondingly, in agreement with equilibrium displacement rules.

As a consequence, we conclude that the chain length in the objects that make up the dynamic material may display some degree of dispersity around the major chain length of 4. The analysis of the structure of these objects that are intrinsically unstable in solution (noted A 4 2 9 (CO 2 ) 9 ) and of their packing mode into the assembled dynamic material (noted DM A 2 (CO 2 )) can therefore only be performed in the solid state. 58 However, the precipitation of DM A 2 (CO 2 ) as a nano-crystalline solid with some disorder in chain length and water content makes it challenging to both perform basic molecular level characterization or to determine a crystal structure. It also hampers the understanding of the precise intra-and intermolecular interactions that drive the assembly of DM A 2 (CO 2 ). We have therefore used solid-state NMR spectroscopy, which is not necessarily hampered by this type of disorder, in combination with quantum chemical calculations to propose a three-dimensional structural model of the dynamic material DM A 2 (CO 2 ).

Determining constitutional isomers

We have previously identified 14 some of the functional groups borne by the oligo-dynablocks A 4 2 9 (CO 2 ) 9 from basic one-dimensional magic angle spinning [START_REF] Lehn | polymeric material spontaneously obtained from monomers assembled with reversible covalent and non covalent bonds[END_REF] N and13 C solid-state NMR spectroscopy (Fig. 1a). It is worth noting at this stage that the 13 C CP-MAS NMR spectrum of DM A 2 (CO 2 ) remained unchanged when the stoichiometry of the molecular constituents was varied by tuning the initial ratio between building blocks A and 2, strongly suggesting that variations in the chain length can be accommodated by the crystal structure of the material. In order to explore the connectivity between individual heavy atoms (carbon and nitrogen), a partially 13 C and fully [START_REF] Lehn | polymeric material spontaneously obtained from monomers assembled with reversible covalent and non covalent bonds[END_REF] N enriched dynamic material (referred to as DM A 2 (CO 2 )*) was produced by using fully 13 C-labeled CO 2 (to label carbamates) and [START_REF] Lehn | polymeric material spontaneously obtained from monomers assembled with reversible covalent and non covalent bonds[END_REF] N-labeled diethylenetriamine for the assembly process. 59 A 2D double crosspolarization (DCP) [START_REF] Lehn | polymeric material spontaneously obtained from monomers assembled with reversible covalent and non covalent bonds[END_REF] N- 13 C HETCOR 60 spectrum of DM A 2 (CO 2 )* allowed us to assign most of the carbon nuclei directly bonded to nitrogen centers (Fig. 1c, black/nitrogen to red/carbon labels) by analogy with known shifts (N1′ and N2′ are characterized by broad peaks of low intensity and failed to provide detectable correlations with neighboring carbons except for N1′-C14). This experiment confirmed the presence of unusual chemical functionalities stabilized by the solid environment, such as the aminal carbamate moiety (carbon atom 11 and nitrogen 3′, Fig. 1b). However, the similarity of the . Carbon resonances are numbered on the spectra and assigned to the proposed structure of DM A 2 (CO 2 ). The 13 C- 13 C refocused INADEQUATE spectrum (Fig. 1d ande) indicates the direct connections between the neighboring sp 2 carbon atoms (C1-C10 region) of the polyaldehyde building block, including the carbonyl groups engaged in three chemically distinct types of linkages (imine, enamine and aminal). Note that we used high field dynamic nuclear polarization (DNP) 62,63 to enhance the sensitivity of the solid-state NMR experiments to enable acquisition of a refocused INADEQUATE 13 C- 13 C correlation spectrum in a reasonable experimental time. 64,65 In order to perform DNP experiments the powdered DM A 2 (CO 2 ) was impregnated with a solution of the nitroxide biradical polarizing agent TEKPol 66 in 1,1,2,2-tetrachloroethane (TCE). 67 TCE was chosen since it is a nonsolvent for DM A 2 (CO 2 ). In these experiments the protons within the DM A 2 (CO 2 ) crystallites are remotely polarized by proton spin diffusion. 64,68,69 DNP provides a spectacular increase in the signal-tonoise ratio as compared with analogous room temperature experiments (ESI, Fig. S6 †), revealing well resolved individual scalar coupling correlations between all the carbons in the 13 C- 13 C refocused INADEQUATE spectrum. This leads to the full assignment of the carbon nuclei (C13-C19) in the aliphatic region (Fig. 1e). In conclusion, this analysis allows us to propose the chemical structure for DM A 2 (CO 2 ) shown in Fig. 1b.

Determining tautomers

2D 1 H- 13 C dipolar HETCOR (Fig. 2a) and 1 H-15 N solid-state refocused INEPT 70 (Fig. 2b) experiments were performed in order to identify hydrogen atoms bound to carbon and nitrogen atoms on the monomeric unit. These experiments also allowed us to explore intermolecular connections between oligo-dynablocks. By determining the protonation state of heteroatoms it was possible to identify the tautomeric forms of the various possible carbamic acid-amine and/or ammonium carbamate and imine-phenol or enamine-quinone combinations. The 1 H-15 N solid-state refocused INEPT spectrum (Fig. 2b) clearly shows that of all the nitrogen atoms, only N1′ and N6′ are protonated. Comparison of the 1 H- 13 C and 1 H- [START_REF] Lehn | polymeric material spontaneously obtained from monomers assembled with reversible covalent and non covalent bonds[END_REF] N 2D correlation spectra indicates that both N6′ (likely an ammonium nitrogen) and C11 (a carbamate carbon) show correlations to the same 1 H nuclei with a shift of 9 ppm typical of ammonium protons. This suggests that the aminoethylaminal N6′-C11 side chain exists as an ammonium -aminal carbamate ion pair (Fig. 2c).

In contrast, the diethylenetriamine central spacer is involved on its extremities in enamine and imine linkages with the aromatic units. N5′ can only be post-functionalized into a neutral carbamic acid. The 1 H- 13 C dipolar HETCOR experiment also provided some information about the intermolecular bonding between oligo-dynablocks. In this spectrum, both C10 and C11 showed correlations to 1 H nuclei with a chemical shift of ca. 13.7 ppm. This suggests that the anionic carbamate (C11) site engages in hydrogen bonds with the neutral carbamate sites (C10). Considering that C11 also engages in a hydrogen bond to the ammonium group, we can conclude that it is a pivotal anchoring group, acting as a hydrogen bond acceptor both with the ammonium center and with the carbamic acid groups of two different neighboring oligo-dynablock within the solid network (Fig. 2c).

Determining conformers

To explore the conformation of the flexible zones (namely the dihedral angles C12-C13, C14-C15, C16-C17 on the main chain and the C4-C9 dihedral angle on the bicyclic aminal-phenol system), a DNP-enhanced Lee-Goldberg (LG) CP HETCOR experiment 72 was conducted to probe short range contacts between 1 H and 13 C nuclei (Fig. 3a). This experiment confirmed the regioisomeric assignment and the intermolecular pairing mode through the observation of correlations between C4-C5; C6-C5; C6-C3; C2-C3; C2-C7; C1-N1; C11-C19; C11-C5 and C10-C19 (Fig. 3b). Besides a C4-C9 contact, two correlations (C1-C9) and (C11-C5) between the aminal carbamate side chain and the central aromatic core could be observed (Fig. 3a andb). A statistical analysis of the Cambridge structural database indicates that for benzylic aminal structures the planes of the six and five membered rings are systematically almost perpendicular in such molecular patterns. 14 While this orientation fulfills the requirements for the inter-molecular ionic pairing between oligo-dynablocks, the aforementioned contacts between nuclei from these adjacent rings additionally tend to indicate that C9-H and C1-O bonds are almost coplanar. The perpendicular orientation of the primary and side chains, which are both non-symmetrical, results in axial chirality around the C4-C9 linkage. As C9 is itself a stereogenic center, both axial and central chirality are inter-related. In the present case, only (S,P) or (R,M) combinations of configuration and conformation are in agreement with the LG-CP HETCOR experiment (Fig. 3c).

Elucidation of tacticity and crystal structure

From the above, for a given oligomeric primary chain, two opposite absolute configurations corresponding to reversed orientations of the N3′-carbamated diethylenetriamine can be envisaged, leading to structures of varying tacticity.

To proceed further to an atomic-level model of the structure, we modelled six different trial structures of the oligo-dynablocks (shown schematically in Scheme 2 (1-6)), which differed in terms of stereochemistry. For each type of structure trial crystal structures were generated using the direct-space genetic algorithm (GA) technique incorporated in the program Genmol. [START_REF]A statistical analysis has shown that there is a strong correlation between the geometrical feature of the molecules and the space group of their crystalline phases. For more details[END_REF][START_REF] Pepe | [END_REF][75] Among these six trial architectures, objects 4, 5 and 6 were true potential candidates whose sequence and structure were in full agreement with the data from the previous solid-state NMR experiments. Objects 1, 2 and 3 were reference compounds with erroneous configurations and/or conformations on part or all of the monomeric units which were deliberately included (all disagree with the analysis of the LG-CP HETCOR spectrum, in Fig. 3a). They were included to validate the ability and sensitivity of the chemical shifts to discriminate diastereoisomers on high molecular weight multi-component architectures and simultaneously elucidate their packing. Scheme 2 Crystal structure prediction process on oligo-dynablocks 1-6 with their Cahn-Ingold-Prelog configurations.

In more detail, 6 consists of isotactic (S,P) 4 oligo-dynablocks, while 5 and 4 are their syndiotactic [(S,P)-(R,M)] 2 and block (made of meso dyads) (S,P) 2 -(R,M) 2 diastereoisomer respectively. 3 is also syndiotactic [(S,P)-(S,M)] 2 but displays erroneous configurations (with respect to 5) or conformations (with respect to 6) on non-adjacent monomeric units. 2 is isotactic (R,P) 4 with erroneous configurations/conformations on every unit. Finally, 1 is the regioisomer of 2 where all phenol groups are localized in para position with respect to the aminal ring (configuration referred to as: [p-(R,P)] 4 ) and corresponds to the structure previously suggested for DM A 2 (CO 2 ). 14 DM A 2 (CO 2 ) is well beyond the scope of comprehensive crystal structure prediction today, as it has 130 heavy atoms and each of the four monomeric units of the oligo-dynablocks has at least 13 degrees of conformational freedom. In addition the models we use here neglect the presence of water in the structure, and do not consider disorder in the chain lengths. We are therefore looking for structural models that will certainly not be exact, but which will reproduce the qualitative features of the conformation and intermolecular packing in the crystal structure. The models used to generate the trial crystal structures were thus built from tetramers whose configuration and conformation agreed with most or all NMR experiments (anti conformation was chosen for the main chain and the bicyclic dihedral angle set to 90°, in agreement with NMR data). These structures were then treated as rigid bodies during the process of crystal generation and preliminary minimization. Candidate crystal structures for each of the six oligodynablock structures 1-6 were generated in the P 1 space group. For each candidate the three hundred most stable lattices were selected from a randomly generated pool and then pre-optimized by energy minimization with MM + QM calculations (see Section S1.5.1. in ESI for details †).

In the case of 2 and 6, respectively, two and three hits (labelled a-c) having a high predicted stability (lattice energy lower than -180 kcal mol -1 ) were obtained and conserved. 1, 3, and 5 all yielded a most stable predicted structure with lattice energies lower than -105 kcal mol -1 . Block oligomers 4 (made of meso dyads) failed to yield stable crystal packing (lattice energies were all higher than -100 kcal mol -1 ) and were therefore excluded.

All-atom DFT geometry optimization was performed on the eight candidates obtained (1, 2a,b, 3, 5, 6a-c) and the chemical shift tensors of the resulting leads were calculated using the GIPAW (Gauge Including Projector Augmented Wave) 44,76,77 method in CASTEP. 78 To assess the quality of the proposed structures 1-3 and 5-6, they were ranked based on the combination of predicted lattice energy and four different NMR chemical shift parameters (Fig. 4; ESI, Table S18 †). For the chemical shifts, root-mean-squared deviations (rmsd) between experimental and calculated values of isotropic chemical shifts ( 1 H, [START_REF] Lehn | polymeric material spontaneously obtained from monomers assembled with reversible covalent and non covalent bonds[END_REF] N and 13 C), as well as 13 C chemical shift anisotropy (Fig. 4; ESI, Table S18 †) were computed. 24,27 Experimental 13 C chemical shift tensor parameters were determined from a DNPenhanced 13 C magic angle turning (MAT) spectrum of DM A 2 (CO 2 ) (Fig. S9 †). experimental and calculated [START_REF] Lehn | polymeric material spontaneously obtained from monomers assembled with reversible covalent and non covalent bonds[END_REF] N isotropic chemical shifts (blue) and 13 C chemical shift anisotropy (green).

Computed crystal energy, 1 H and 13 C isotropic chemical shift are today reasonably well understood, and were hence chosen as quantitative indicators (Fig. 4a-c). In the particular case of 1 H chemical shifts the "cut-off value" of rmsd under which a virtual crystal is considered to be in good agreement with the experiment is usually around 0.6 ppm. 23,49 Since they have so far been less frequently used, [START_REF] Lehn | polymeric material spontaneously obtained from monomers assembled with reversible covalent and non covalent bonds[END_REF] N isotropic chemical shift and 13 C chemical shift anisotropy were considered in Fig. 4c as qualitative indicators of potential discrepancy when abnormally high values of rmsd were obtained.

The results of the comparisons are summarized in Fig. 4a-c, and ESI Table S18. † Structures 1, 3 and 5 are predicted to be significantly less stable than the others, with 1 and 5 also showing significant deviations in the chemical shift parameters, and can be discounted. The case of oligo-dynablock 1 highlights the difference between the molecular and the supramolecular point of view: the C O positioning on C 3 obviously induces a decrease in steric hindrance locally with the five-membered aminal ring but globally yields a packing of poor stability. Similarly, syndiotactic oligo-dynablocks 3 and 5 with alternate conformations and configurations on adjacent monomeric units, respectively yield structures with higher predicted energy compared to isotactic oligo-dynablocks 6. Structures 2a and 2b, which differ in the conformation of the flexible side chains of their constituents and their relative position in the structures, display contrasted scores for qualitative NMR indicators. Lattices, 2 and 6 which are formed from isotactic oligo-dynablocks are indeed predicted to be significantly more stable. Structure 2b can be discounted since it has an abnormal disagreement in the 13 C CSA parameters. When comparing structures 2a, 6a, 6b and 6c, we see that 6c has overall only qualitative agreement. 2a, 6a and 6b all have better agreement, but we see that among them only 6b is in good agreement with the 1 H chemical shifts, with a 1 H rmsd value below 0.6 ppm. At this point we recall that structure 2 does not agree with the NMR correlation data. We therefore tentatively conclude that structure 6b, which is predicted to be the most stable, is the structure that is in best overall agreement with the ensemble of experimental data from NMR, including chemical shifts and correlation spectra. While we are certain that this is not an exact representation of the lattice (due to the disorder in chain length and solvation discussed above), we hypothesise that it is likely to contain the essential structural features of the solid.

Note that candidates 6b and 6c were the only model structures in the series whose constituents have a zwitterionic protonation state (ammonium carbamate) on the C11-N6′ chain, in agreement with experimental observations. Although the other model crystal structures were systematically generated from zwitterionic oligo-dynablocks, proton exchange during all atom DFT optimization resulted in neutral structures. The correct protonation state on the hetero-nuclei partially accounts for the lower rmsd of the 1 H chemical shift values in the structures 6b and 6c. As mentioned above, when 6b and 6c are compared on the basis of the other major structural parameters, 6b appears to be the best candidate. Note that, 6b is not in the best agreement among the set in terms of calculated and experimental isotropic [START_REF] Lehn | polymeric material spontaneously obtained from monomers assembled with reversible covalent and non covalent bonds[END_REF] N chemical shifts. This is particularly true for the sp 2 nitrogen centers N1′ and N2′ (with rmsd of 47 and 32 ppm respectively). However, these nuclei systematically yielded poor correlation for all candidate structures (the average difference along the series 5 and 6 being 35 and 33 ppm respectively). While the chemical shift of sp 3 nitrogens seem to display little sensitivity to their protonation state (a 10 ppm shift on average was observed when comparing candidates 1, 2a, 2b, 5 and 6a with 6b and 6c), sp 2 nitrogens in salicylic systems are reported to be extremely sensitive to the proton transfer from the phenol group (from -50 to -220 ppm) and to the exact position of the proton between the oxygen and the nitrogen N1′ centers, 79 and other work has shown strong sensitivity of nitrogen shifts to the migration of protons across hydrogen bonds. 80 It is therefore expected that a very slight discrepancy in the calculated position of the N1′-⋯O proton could results in large shifts in the resonance of the N1′ and to a lesser extent on N2′ which is directly conjugated to N1′ through the aromatic ring. As a result we choose the disregard these shifts in the evaluation. We note that recent reports of calculated [START_REF] Lehn | polymeric material spontaneously obtained from monomers assembled with reversible covalent and non covalent bonds[END_REF] N isotropic chemical shifts in the literature include both cases of excellent agreement 81,82 or systematic overestimation with respect to experimental data. 83

Intermolecular H-bonding drives selectivity

Structure 6b, which appears as the most credible model from among the idealised structures proposed here, is characterized by a significantly lower calculated energy than the other potential candidates 5, 6a and 6c. Examination of the inter-molecular binding modes in the lattice of 6b (Fig. 5b andc) reveals an optimized network of hydrogen bonds. 6b is the only structure whose ammonium and carbamate/carbamic acid moieties are engaged in three and two hydrogen bonds (Fig. 5d), respectively (vs. one and two at most in all other structures). This optimization of the hydrogen bond network not only provides subsequent stabilization to the molecular network but also presumably accounts for the significantly improved agreement between calculated and experimental data for structure 6b with respect to the remaining candidates. Importantly, this hydrogen bond network would appear to strongly depend on the nature of the constituent building blocks. In fact, polyamines of increased length or steric hindrance would compromise this optimal pairing. Therefore, the choice of the building block incorporated into the DM A 2 (CO 2 ) controls the packing efficiency, which in turn drives the self-assembly process. The new picture that emerges here from a simplified model appears to explain the singular selectivity previously observed for the formation of DM A 2 (CO 2 ).

Powder X-ray diffraction

Powder X-ray diffraction and solid-state NMR are both powerful techniques which have been used independently or in tandem for crystal structure solution. 21,24,29,31,35,[84][85][START_REF] Harris | RSC[END_REF] We therefore did assess the possible contribution of PXRD to the structural modelling developed here in parallel to the NMR measurements. Fig. 6 shows the PXRD pattern obtained from the nanocrystalline material, and which is found to have quite high resolution with reflections beyond 30° indicative of a structure that has long range periodicity and well defined regular structural features. At first sight, it may thus be possible to index this pattern and determine the structure. Indexing of the experimental PXRD spectrum was first attempted using the McMaille program. Despite a thorough screening of the possible Bravais lattices and cell parameters, the procedure failed, leading to several possible solutions, even when combining two polymorphic structures. The main reason for failure appeared to be the lack of well-resolved peaks at large angles.

Fig. 6 Comparison between the experimental PXRD pattern and the simulated spectra for structures 1-6 after all-atom DFT optimization. PXRD spectra were then simulated for all the candidate 1-6. It can be seen from Fig. 6 that the resulting patterns displayed very little similarity with the experimental spectrum, whether the oligomeric constituents were true candidates or not. Furthermore, the changes observed in the PXRD patterns predicted for structures before and after DFT geometry optimisation (Fig. S2 †) are of the same order of magnitude as the difference between the candidate structures even though the structural changes induced by optimisation are relatively minor.

This highlights the fact that PXRD patterns are sensitive to very small structural changes, such that if the candidate structure is not within a few fractions of an angstrom in rmsd from the correct structure then poor agreement will always be obtained. 85 Notably, changes in the unit cell parameters induce large changes in the PXRD line positions and intensities, and since indexing failed here it is unlikely that the candidate structures have exactly correct cell parameters. This is especially true if we recall that that the materials here may have some dispersion in the chain lengths and the hydration states that would almost certainly induce changes with respect to the model cells predicted here. We have seen that removing some empty space (which may contain water) from the structures by changing the unit cell dimensions while keeping the atomic coordinates fixed produces large changes in the predicted PXRD patterns (Fig. S24 †), while including water molecules in the same empty space in the candidate structures also changes the predicted PXRD intensities.

For well ordered crystalline materials perfect agreement with PXRD can often be obtained and would be the gold standard in validating a final structure. However, in this case of a well ordered but slightly disperse material, and where indexing fails, we see that PXRD is not a useful indicator, whereas high resolution NMR data can still be obtained and directly related to the average properties of the structures. This is an excellent example of the complimentary nature of the two methods.

Conclusions

Structural elucidation of organized nano-crystalline powdered solids made of complex molecular ingredients represents an unresolved challenge to date. Here we have applied state of the art NMR crystallography methods to obtain a proposal for the structure of a complex three-component dynamic oligomeric material by using a series of solid-state MAS NMR experiments, including DNP enhanced spectroscopy. It has allowed to obtain the complete assignment of 1 H, 13 C and [START_REF] Lehn | polymeric material spontaneously obtained from monomers assembled with reversible covalent and non covalent bonds[END_REF] N resonances, and to determine a number of spatial proximities between atoms thereby providing strong constraints on possible structures. We used comparisons between experimental and calculated NMR chemical shifts to select the best model structures. This is one of the most complex systems for which solid-state NMR has been able to provide a de novo structure, starting only with the molecular formula, to date.

Since the material contains disorder both in chain length and solvation the structure proposed here is certainly not exact (for example in terms of the predicted unit cell parameters), but we suggest it does capture the essential structural features. Dispersity in terms of oligomer length, and the integration of hydration, is well beyond the current scope of the prediction tools used here. However, this did not hamper the application of NMR and the extraction of quantitative constraints on the structure, whereas they did render comparison with PXRD of no use.

These results highlight the increasing capabilities of the combination of solid-state NMR, crystal structure prediction, periodic DFT plane wave calculations (and powder X-ray diffraction) for the determination of crystal structures when single crystal X-ray diffraction is not possible. The structure determined from NMR notably suggests the presence of an optimised intermolecular hydrogen bonding network that explains why the self-assembly of the material is so selective in terms of building blocks. Small changes in the building blocks would prevent formation of the H-bond network.

Fig. 1

 1 Fig. 1 (a) Building block content and molecular patterns previously identified. 14 (b) Structure of the oligo-dynablock proposed here based upon solid-state NMR analysis. (c) 2D DCP 15 N-13 C HETCOR spectrum for partially 13 C and fully 15 N enriched DM A 2 (CO 2 )*. Correlations between nitrogen atoms (black labels) and carbon atoms (red labels) are indicated by dashed lines. (d) 100 K DNP-enhanced 2D refocused INADEQUATE 13 C-13 C correlation spectrum (aromatic region only) acquired from natural isotopic abundance DM A 2 (CO 2 ) impregnated with a 16 mM solution of TEKPol in 1,1,2,2tetrachloroethane. Correlations/connectivity are indicated by solid orange lines and provide iterative assignment of green labels. (e) Aliphatic region of the 2D refocused INADEQUATE 13 C-13 C correlation spectrum (provides unambiguous assignments of purple labels). By combining the information in the 2D DCP 15 N-13 C HETCOR spectrum and the 2D refocused INADEQUATE 13 C-13 C correlation spectrum it is possible to completely assign the spectra and propose the model chemical

Fig. 2

 2 Fig. 2 Heteronuclear correlation (HETCOR) spectra for assignment of 1 H chemical shifts and determination of the protonation state and intermolecular binding modes of the oligodynablocks. (a) The carbonyl region of the 1 H-13 C dipolar HETCOR spectrum of DM A 2 (CO 2 ). (b) Full 1 H-15 N solidstate refocused INEPT spectrum of DM A 2 (CO 2 )*; eDUMBO-1 22 1 H homonuclear decoupling was applied during t 1 evolution to obtain high 1 H resolution. 71 (c) Corresponding identified intermolecular binding modes.By determining the protonation state of heteroatoms it was possible to identify the tautomeric forms of the various possible carbamic acid-amine and/or ammonium carbamate and imine-phenol or enamine-quinone combinations. The 1 H-15 N solid-state refocused INEPT spectrum (Fig.2b) clearly shows that of all the nitrogen atoms, only N1′ and N6′ are protonated. Comparison of the 1 H-13 C and 1 H-15 N 2D correlation spectra indicates that both N6′ (likely an ammonium nitrogen) and C11 (a carbamate carbon) show correlations to the same 1 H nuclei with a shift of 9 ppm typical of ammonium

Fig. 3

 3 Fig. 3 Coupled configurational/conformational exploration of the junction between main and side chain around the connective center C 9 through (a) a short range (τ CP = 500 μs) DNP-enhanced 1 H-13 C LG-CP HETCOR spectrum revealing spatial contacts. (b) Structural model with black arrows indicating correlations observed within the rigid backbone, and red arrows indicating observed correlations between flexible parts. This analysis leads to two possible enantiomeric monomeric units with opposite absolute coupled configuration/conformation on the C 9 center (c).The perpendicular orientation of the primary and side chains, which are both non-symmetrical, results in axial chirality around the C4-C9 linkage. As C9 is itself a stereogenic center, both axial and central chirality are inter-related. In the present case, only (S,P) or (R,M) combinations of configuration and conformation are in agreement with the LG-CP HETCOR experiment (Fig.3c).

Fig. 4

 4 Fig. 4 Comparison of agreement between calculated and experimental data for the predicted crystal structures 1-6. (a) Predicted crystal lattice energies; (b) root-mean-square deviation (rmsd) between experimental and calculated 1 H (red) and 13 C (yellow) isotropic chemical shifts; (c) rmsd between

Fig. 5

 5 Fig. 5 Crystal structure 6b which shows the best overall agreement with the experimental data. (a) Comparison of the structure of oligomer 6b in the crystal before (blue) and after all-atom geometry optimization with CASTEP (red). Packing between nearest neighbours along (b) z axis and (c) x axis. (d) Partial view of the intermolecular main and side chain binding.

C chemical shifts of several carbon atoms in the ethyl bridges prevented complete13 C assignment (Fig.1c, purple labels). A DNP enhanced13 C-13 C refocused INADEQUATE spectrum61 (Fig.1d and e) was then recorded on the natural abundance DM A 2 (CO 2 ) to complete the carbon-13 assignment and to elucidate the substitution pattern of the three carbamate-diethylenetriamine side arms borne by the phenolic core of the monomeric unit.

This journal is © The Royal Society of Chemistry 2016

Acknowledgements

We are grateful to Prof. P. Tordo, Dr O. Ouari and Dr G. Casano (Aix-Marseille Université, France) for providing the biradicals used in the DNP NMR experiments. Financial support from the Agence Nationale de la Recherche (ANR-12-JS07-0011-01), the TGIR-RMN-THC FR3050 CNRS, and Swiss National Science Foundation grant no. 160112 for conducting the research is gratefully acknowledged. This work was supported by the LABEX iMUST (ANR-10-LABX-0064) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).


PhD. Mohamed Tachrount
email: mohamed.tachrount@univmed.fr

Guillaume Duhamel

Jérôme J Laurin

Tanguy Marqueste

André Maues De Paula

Patrick Decherchi

Patrick J Cozzone

Virginie Callot

Andre Maues De Paula

MR spectroscopy of mouse cervical spinal cord at very high magnetic field (11.75T

Introduction

Proton Magnetic Resonance Spectroscopy ( 1 H MRS) allows for in vivo non-invasive assessment of cerebral biochemistry. In addition, 1 H MRS reveals physiological alterations that are not attainable with MRI, thus contributing to its increasing application in central nervous system (CNS) studies. Whereas almost all the 1 H MRS studies of CNS have been conducted in the brain [START_REF] Soares | Magnetic resonance spectroscopy of the brain: review of metabolites and clinical applications[END_REF][START_REF] Van Der Graaf | In vivo magnetic resonance spectroscopy: basic methodology and clinical applications[END_REF][START_REF] Marino | 1H-MR spectroscopy in traumatic brain injury[END_REF][START_REF] Morita | Clinical Application of MR Spectroscopy and Imaging of Brain Tumor[END_REF], it is clear that 1 H MRS could also be of interest in the study of several pathologies affecting the spinal cord (SC) and revealed by MRI (e.g. multiple sclerosis (MS) and amyotrophic lateral sclerosis (ALS) [START_REF] Losseff | Spinal cord atrophy and disability in multiple sclerosis. A new reproducible and sensitive MRI method with potential to monitor disease progression[END_REF][START_REF] Thorpe | Spinal MRI in patients with suspected multiple sclerosis and negative brain MRI[END_REF], spinal cord ischemia [START_REF] Kumral | Spinal ischaemic stroke: clinical and radiological findings and short-term outcome[END_REF], spinal tumors [START_REF] Sahgal | Stereotactic body radiotherapy for spinal metastases: current status, with a focus on its application in the postoperative patient[END_REF], and spinal cord injury (SCI) [START_REF] Cadotte | Spinal cord injury: a systematic review of current treatment options[END_REF]). However, very few 1 H MRS SC studies have been reported so far, in humans [START_REF] Blamire | Axonal damage in the spinal cord of multiple sclerosis patients detected by magnetic resonance spectroscopy[END_REF][START_REF] Cooke | Quantitative proton magnetic resonance spectroscopy of the cervical spinal cord[END_REF][START_REF] Edden | Proton MR spectroscopic imaging of the medulla and cervical spinal cord[END_REF][START_REF] Gomez-Anson | In vivo 1H-magnetic resonance spectroscopy of the spinal cord in humans[END_REF][START_REF] Henning | Quantitative magnetic resonance spectroscopy in the entire human cervical spinal cord and beyond at 3T[END_REF] and in rats [START_REF] Balla | In vivo intermolecular zero-quantum coherence MR spectroscopy in the rat spinal cord at 17.6 T: a feasibility study[END_REF][START_REF] Bilgen | In vivo magnetic resonance microscopy of rat spinal cord at 7 T using implantable RF coils[END_REF][START_REF] Erschbamer | 1H-MRS in spinal cord injury: acute and chronic metabolite alterations in rat brain and lumbar spinal cord[END_REF][START_REF] Qian | Neuronal and axonal degeneration in experimental spinal cord injury: in vivo proton magnetic resonance spectroscopy and histology[END_REF][START_REF] Silver | In vivo 1H magnetic resonance imaging and spectroscopy of the rat spinal cord using an inductively-coupled chronically implanted RF coil[END_REF][START_REF] Zelaya | Localized 1H NMR spectroscopy of rat spinal cord in vivo[END_REF]. This could be explained by challenging experimental difficulties caused by the small size of the SC structure, the important physiological motion and the increased magnetic field heterogeneity due to surrounding bony structures. To the best of our knowledge, this study is the first account of the use of in vivo 1 H MRS for the quantification of SC metabolites in healthy or pathological mice, although transgenic mouse models are widely used to understand pathological mechanisms and to explore therapeutic approaches.

The present work demonstrates the feasibility of an optimized short TE proton spectroscopy sequence based on the Point REsolved SpectroScopy (PRESS) sequence for the investigation of the mouse spinal cord at very high magnetic field (11.75T). The shimming strategy and the acquisition method have been adapted and optimized in order to improve the static field homogeneity, and to reduce motion effects and lipid signal contamination arising from surrounding tissues. The robustness of the optimized SC protocol was evaluated and compared to results obtained in the thalamus area. Finally, the optimized sequence was applied to preliminarily investigate the feasibility of detecting SC metabolic alterations following a SC injury (SCI).

Materials and Methods

MRI and MRS experiments were carried out on a Bruker Avance 11.75 T/89 mm vertical wide bore imager (Bruker, Ettlingen, Germany) equipped with actively shielded gradients (maximum gradient strength of 1 T/m, maximum slew rate of 9 kT/m/sec). A birdcage coil (diameter 2 cm, homogenous length 3 cm; Micro 2.5 probe; Bruker) was used for the transmission and the reception of signals.

MR Spectroscopy

MRS acquisitions were performed using a PRESS sequence with the following parameters: TE/TR = 10/4000 ms, BW = 4960 Hz, number of samples = 512, and number of averages = 16/256 without/with water suppression. Hermitian excitation pulses (0.8 ms, BW = 6750 Hz) and Shinnar-Le Roux refocusing pulses (0.8 ms, BW = 6250 Hz) were applied for the volume of interest (VOI) selection. The voxel sizes, in the dorsal-ventral, left-right, and caudal-rostral directions, were 2.0x1.8x1.1 mm 3 (VOI sc ~4µl) for the spinal cord and 1.5x4.5x1.5 mm 3 (VOI Thalamus ~10µl) for the thalamus. Phase cycling (8 steps) was applied to suppress signal from unwanted coherence orders. Water suppression (WS) was achieved using the VAPOR (variable power RF pulses with optimized relaxation delays) module which was interleaved with three outer volume suppression (OVS) blocks to improve localization performance [START_REF] Tkác | In vivo 1H NMR spectroscopy of rat brain at 1 ms echo time[END_REF].

VAPOR consisted of seven frequency selective Hermitian RF pulses with a bandwidth of 300 Hz (~ 0.6 ppm). Each OVS block contained six spatial selective hyperbolic secant RF pulses (2.0 ms, BW ~ 10.1 kHz). The water suppressed signal and navigator signal acquisitions were interleaved. Navigator signal, which was used as reference signal, was acquired using the same VOI selection module but with a lower excitation flip angle (α=15°).

Animal Preparation

Healthy and injured male C57BL/6 mice (weight 29-36 g) were cared for and used according to a protocol approved by our institutional Committee on Ethics in animal research, in conformity with the European convention for the protection of vertebrate animals used for experimental purposes and institutional guidelines (no. 86/609/CEE November 24, 1986).

After isoflurane induction in an anesthetic chamber, the animals were kept anesthetized at a respiratory frequency of 50-70 breaths per minute by spontaneous respiration of a mixture of air and isoflurane (1.5%; mean flow rate 255 mL/min; Univentor 400 anesthesia unit, Zejtun, Malta) delivered through a dedicated nose cone. Respiration was monitored throughout the experiment, using a pressure sensor placed under the abdomen of the mouse and connected to an MR-compatible monitoring and gating system (SA Instruments, Inc., Stony Brook, NY, USA). Physiological temperature was maintained by heating the gradient cooling system to 39°C. The animals were positioned head up on an animal bed and maintained by a teeth holder and by taping their pelvis to the cradle.

In order to illustrate the potential of MRS optimized sequence, one mouse with spinal cord injury was studied. The animal was anesthetized by an intraperitoneal injection of a mixture of 100 mg/Kg of ketamine (Panpharma Laboratories, France) and 10 mg/Kg of xylazine (Bayer HealthCare, France). After a midline longitudinal skin incision over the C1-C4 spinous processes, vertebral muscles were dissected to expose the dorsal laminae and spinal processes of C3. A partial dorsolateral laminectomy on the left side of the spinal cord was performed to expose the segment C3. Perpendicular to the rostral-caudal axis of the spine, a 2-French Fogarty catheter (Edwards Lifesciences SAS, Maurepas, France) connected to an air syringe was inserted between the C2-C3 vertebra and advanced caudally for 3 mm, so that the center of the balloon rested at the C3 epidural space of the spinal cord. The balloon was then rapidly inflated during 5 sec (10 mm 3 , 25 kPa) to induce cervical spinal cord compression. MR data acquisitions were performed in two separate steps at the cervical spinal cord level and in the thalamus. The region of interest was aligned with the coil center and placed at the magnet isocenter in order to obtain the optimal sensitivity. Following standard spectrometer adjustments (coil tuning/matching, RF gain calibration) and fast localization imaging, the MRS VOI positioning was performed using sagittal and axial high spatial resolution T 1weighted images for SC location (C3 level, Fig. 1a and Fig. 1b), and T 2 -weighted images for thalamus location (Fig. 1c and Fig. 1d). T 1 -weighted images were acquired using a FLASH sequence [START_REF] Haase | FLASH imaging. Rapid NMR imaging using low flip-angle pulses[END_REF] (flip angle = 15°; TE/TR = 1.7/30.0 ms; TA = 1min 5s/3min 50s [axial/sagittal]; spatial resolution = 0.08x0.15 mm 2 ; slice thickness = 0.5 mm; number of slices = 6/12 [axial/sagittal]). T 2 -weighted images, which provide a better delineation of the brain structures, were acquired with a RARE sequence (23) (TE/TE eff /TR = 9.1/19.4/2000 ms; NA = 2; RARE Factor = 4; TA = 4min16s; number of slices = 30; slice thickness = 0.5 mm; FOV = 20x20 mm 2 ; Matrix = 256x256). Shimming was optimized prior the MRS acquisition, using fast localized automatic adjustment of all first-and second-order shims (FASTMAP manufacturer sequence [START_REF] Gruetter | Automatic, localized in vivo adjustment of all first-and second-order shim coils[END_REF]). The best shim quality, evaluated by measuring the Full Width at Half Maximum (FWHM) of a reference water spectrum, was obtained by taking shim voxels centered on the spectroscopic VOI and a volume size of about 4.2 mm 3 in the SC (i.e. including vertebra bone) and 4.7 mm 3 in the thalamus. Localized adjustments of both resonance frequency and reference gain were additionally performed to reduce the VOI location errors and to achieve the correct effective flip angle, respectively. MRS data acquisition was synchronized with breath motion to reduce artifacts arising from movement. Spectra acquisition time was about 25 minutes per location and the total protocol duration was 90 minutes.

Data processing and quantification

MRS data were processed using the jMRUI tool (version 3.0, http://www.mrui.uab.es/mrui) [START_REF] Naressi | Java-based graphical user interface for the MRUI quantitation package[END_REF] and in-house developed software running under Matlab (The Mathworks Inc, USA).

Navigator signals were applied to normalize and to correct separately each acquired water suppressed signal for eddy currents and B 0 frequency drift effects before adding them all.

Following a zero filling of a factor 4, the signals acquired in SC and thalamus were multiplied by a 10-Hz and 3-Hz exponential line-broadening window function, respectively. After Fourier transform, the phases of the spectra were corrected manually and the residual water signal was subsequently removed using the HLSVD procedure (Hankel-Lanczos Singular Value Decomposition) (26) of jMRUI. Model fitting was performed in the time domain using the QUEST (quantification based on semi-parametric quantum estimation) ( 27) procedure of jMRUI. The metabolite basis set was quantum-mechanically simulated using GAMMA (General Approach to Magnetic resonance Mathematical Analysis) [START_REF] Smith | Computer Simulations in Magnetic Resonance. An Object-Oriented Programming Approach[END_REF] based on published chemical-shift and J-coupling values [START_REF] Govindaraju | Proton NMR chemical shifts and coupling constants for brain metabolites[END_REF]. The basis sets, simulated for the pulse sequence parameters used in this study, included 16 metabolites: alanine (Ala), aspartate (Asp), creatine (Cr), phosphocreatine (PCr), gamma-amino-butyric acid (GABA), glucose (Glc), glutamate (Glu), glutamine (Gln), glutathione (GSH), glycerophosphocholine (GPC), phosphocholine (PCho), lactate (Lac), myo-inositol (Ins), N-acetyl aspartate (NAA), N-acetylaspartyl glutamate (NAAG), and taurine (Tau) in accordance with the literature [START_REF] Ratiney | Time-domain semi-parametric estimation based on a metabolite basis set[END_REF][START_REF] Gottschalk | Short-TE localised (1)H MRS of the human brain at 3 T: quantification of the metabolite signals using two approaches to account for macromolecular signal contributions[END_REF][START_REF] Posse | Proton echo-planar spectroscopic imaging of J-coupled resonances in human brain at 3 and 4 Tesla[END_REF].

For SC (thalamus respectively) spectra fitting, the modeled signals chemical shift correction was limited to 25 Hz (20 Hz respectively) and the line broadening was limited to 50 Hz (40 Hz respectively). The significant macromolecular (MM) signals were estimated from initial acquired samples using QUEST. In our study, the optimal number of truncated samples was fixed to five. This number estimation was based on prior SC and thalamus metabolite nulled spectra measurements performed using an inversion recovery preparation (TR = 2.5s, TI = 700 ms) with a secant hyperbolic RF pulse of 4ms duration (data not shown) and a previous study [START_REF] Ratiney | Short Echo Time H1 Chemical Shift Imaging data quantification in the mouse brain at 11.7T using a constrained parametric macromolecular model[END_REF].

Finally, the metabolites quantified with Cramér-Rao lower bound (estimated error of metabolite quantification) lower than 50% were included in the final neurochemical profile whereas those with lower bounds greater than 50% were classified as not detected.

Metabolites with similar and strongly correlated overlapping resonances were summed (tNAA = NAA+NAAG, tCr = PCr+Cr, and tCho = PCho + GPC) and the corresponding CRBs were accordingly corrected. The Signal to Noise Ratio (SNR) was calculated using the real part of the spectrum and by dividing the NAA peak intensity by the standard deviation of the noise between 6.0 and 7.5 ppm.

Reproducibility and inter-subject variability

The reproducibility R of the quantified spectra was evaluated for both SC and thalamus, by repeating measurements at three time points on 3 mice. R was estimated for each metabolite by calculating the value of (1-SD/M)×100, where M and SD represent the normalized metabolite amplitude mean value and standard deviation obtained over the 3 measurements and the 3 mice. The inter-subject variability, V, defined by the relation V=SD/M×100, was estimated for each metabolite in the spinal cord and the thalamus using 7 and 9 healthy mice, respectively.

Spinal cord post-injury 1 H MRS

The preliminary investigation of metabolic alterations arising within the spinal cord following experimental injury was performed with the same protocol at days 3, 7, and 42 post-injury.

The MRS VOI was located at the C3 level and included the lesion site (Fig. 4a and Fig. 4b).

Statistical analysis

All data were presented as mean ± SD. An unpaired t-test was applied for comparing spinal cord and thalamus main metabolite normalized amplitudes and results with p<0.005 were considered significant.

Results

Healthy mouse SC 1 H MRS

The averaged reference water signal FWHMs were found equal to 25.3±2.4 Hz, range 21.8 to 26.6 Hz within the spinal cord (n=7) and 22.9±3.2 Hz, range 17.0 to 26.6 Hz within the thalamus (n=9). The averaged SNR was measured to 11.9 ± 1.4 (VOI = 4 µl) for SC and 27.7 ± 4.3 (VOI = 10 µl) for thalamus. Typical 1 H MR spectra acquired in the SC and the thalamus of healthy mouse are presented in Fig. 2a and Fig. 2b, respectively, along with the QUEST quantification results that include estimated spectra and baseline (Fig. 2c and Fig. 2d) as well as residue (Fig. 2e and Fig. 2f). The mean normalized amplitudes of detected metabolites in both SC and thalamus are presented in Fig. 3 along with their corresponding CRBs. The principal discernable metabolites in SC were tNAA, tCr, tCho, mI, and Glu (Fig. 3a). In thalamus, Ala, Asp, Gln, Tau, GABA, GSH, Glc, and Lac were additionally observed (Fig. 3b). In SC, tNAA, tCr, mI and Glu were detected with CRBs < 8% whereas tCho was quantified with CRBs < 15% (Fig. 3c). In thalamus, tNAA, tCr, tCho, mI, Glu, Tau, Gln, GABA, Ala, GSH, and Asp were quantified with CRBs < 10% whereas Glc, and Lac were quantified with CRBs < 30% (Fig. 3d). The tNAA, tCr, tCho, and Glu normalized amplitudes were significantly lower in the spinal cord than in the thalamus (p< 0.005). There was no significant difference between mI normalized amplitudes in the spinal cord compared to thalamus. Table 1. Healthy mice 1 H MR spectra quantification reproducibility (R) and inter-subject variability (V) in the spinal cord (SC) and the thalamus (Tha). (nd: not detected) Spinal cord spectra quantification reproducibility (R) and inter-subject variability (V) are presented in Table 1 for each of the detected metabolites. The mean reproducibility regarding tNAA, tCr, tCho, mI and Glu quantification was 76.5 ± 12.1 % for the spinal cord and 90.0 ± 2.4 % for the thalamus. The averaged inter-subject variabilities of these metabolites within the spinal cord and thalamus were 15.0 ± 5.0 % and 11.4 ± 4.4 %, respectively. When averaging the 13 detected metabolites for the thalamus, the mean reproducibility and inter-subject variability were equal to 78.0 ± 16.2 % and 21.0 ± 12.2 %, respectively. The 1 H MRS VOI was located at the C3 level and included the lesion epicenter, as depicted on Fig. 4a and4b. 1 H MR spectra acquired at 3, 7, and 42 days post-injury (dpi) are shown in Fig. 4d-f, along with a reference spectrum (Fig. 4c). The difference within the metabolites amplitude highlighted (i) the metabolic alterations and changes that occurred between healthy and injured SC, and (ii) occurring within the post-injury days. Quantitative analyses of these variations are presented on Fig. 5.

Injured mouse 1 H MRS

FIG. 4. Location of the selected voxel for in vivo

During the first week post-injury, decreases of about 50%, 15%, 8%, 13% and 49% in the tNAA, tCr, tCho, mI and Glu amplitudes were noticed compared to averaged healthy control measurements. Following the first seven days post-injury, a progressive recovery of these metabolites was observed with time. At day 42 post-injury, mI amplitude returned to the control value whereas the tNAA and the Glu presented an incomplete recovery (-15% and -18%, respectively). In contrast, the tCr and tCho presented higher amplitudes than the control value (+15% and +13%, respectively). The variations of the tNAA, tCr, mI and Glu amplitudes were higher than the healthy mice averaged inter-subject variability whereas the tCho amplitude variations were lower. FIG. 5. SC normalized metabolite amplitudes obtained in one injured mouse at 3, 7 and 42 dpi. The mean values at -1 day post-injury (i.e before injury) correspond to the averaged healthy mice measurements (n=7) and the error bars to the mean variability.

Discussion

H MRS acquisition of the mouse spinal cord

This study reports the successful acquisition of 1 H MR spectra of the mouse SC despite various challenges including low sensitivity, susceptibility effects and physiological motion.

To overcome the low sensitivity inherent to the small size of the cord, several studies, performed on rats, have used implanted or surface RF coils to increase the SNR [START_REF] Balla | In vivo intermolecular zero-quantum coherence MR spectroscopy in the rat spinal cord at 17.6 T: a feasibility study[END_REF][START_REF] Bilgen | In vivo magnetic resonance microscopy of rat spinal cord at 7 T using implantable RF coils[END_REF][START_REF] Qian | Neuronal and axonal degeneration in experimental spinal cord injury: in vivo proton magnetic resonance spectroscopy and histology[END_REF][START_REF] Silver | In vivo 1H magnetic resonance imaging and spectroscopy of the rat spinal cord using an inductively-coupled chronically implanted RF coil[END_REF][START_REF] Erschbamer | 1) H-MRS in spinal cord injury: acute and chronic metabolite alterations in rat brain and lumbar spinal cord[END_REF]. Although the implanted RF coil strategy would optimize the sensitivity, this approach necessitates a particular know-how and its invasiveness may preclude early MRI/MRS measurements due to possible hemorrhage following implantation. Then, the use of an implanted coil is not worthy for cervical SC applications. At this level, the cord is largely surrounded by skeletal muscles. In this work, SNR limitations were partially overcome by the use of a very high magnetic field strength system (11.75T) and a small volume coil well adapted to the SC morphology, allowing good quality SC and thalamus spectra acquisition with reasonable SNR value and within an acquisition time of 25 minutes.

Then, despite the large susceptibility differences between vertebral bodies, intervertebral discs, and the surrounding tissues expected at high magnetic field, the automatic shimming adjustments performed in the mouse SC allowed to obtain a shim quality (FWHM = 0.05 ppm) similar to that reported at lower field strength in rats or humans [START_REF] Bilgen | In vivo magnetic resonance microscopy of rat spinal cord at 7 T using implantable RF coils[END_REF][START_REF] Qian | Neuronal and axonal degeneration in experimental spinal cord injury: in vivo proton magnetic resonance spectroscopy and histology[END_REF][START_REF] Erschbamer | 1) H-MRS in spinal cord injury: acute and chronic metabolite alterations in rat brain and lumbar spinal cord[END_REF]. The combination of the PRESS sequence with a series of OVS RF pulses interleaved with VAPOR RF pulses minimized both contamination by signals arising from outside the VOI and residual water signal. The spatially selective RF pulses transmit frequency used in our study was centered between lipids and water resonance frequencies in order to reduce the chemical shift displacement errors (CSDE), which may cause MRS VOI mislocation, complicated J-modulation patterns [START_REF] Edden | Optimized detection of lactate at high fields using inner volume saturation[END_REF], and lipid contamination arising from surrounding tissues. The CSDE corresponding to our PRESS excitation and refocusing RF pulses were about of 14% and 15%, respectively. These displacement errors effects on acquired spectra were further reduced by using large bandwidth factor OVS RF pulses (CSDE ≈ 9%).

As physiological motion of the mouse spinal cord at the cervical level is dominated by respiration, the MRS data acquisitions were synchronized to the breathing cycle. The preparation (WS and OVS) and the VOI selection modules as well as the signal sampling were synchronized with the respiratory quiescent period to reduce these motion artifacts. To minimize the longitudinal relaxation effects that may arise when the respiratory cycle varies, relatively long repetition times, compared to metabolite longitudinal relaxation times at 11.75T [START_REF] De Graaf | High magnetic field water and metabolite proton T1 and T2 relaxation in rat brain in vivo[END_REF], were additionally used. Furthermore, navigator signals acquisitions were interleaved with water suppressed signals sampling in order to be used as reference signals.

Since the double signal excitation during a single repetition time saturates the available signal and reduces the sensitivity, navigator signals were excited using a low flip angle (α=15°) and acquired after the metabolite signals acquisition. The estimated water signal loss due to the navigator acquisition was about 5%.

Mouse SC 1 H MRS quantification

There are only sparse reports of in vivo SC 1 H MRS quantification. The absolute metabolite concentration quantification has been reported in the case of human studies which mainly concerned cervical spinal cord, and the results presented an important variability among different groups [START_REF] Blamire | Axonal damage in the spinal cord of multiple sclerosis patients detected by magnetic resonance spectroscopy[END_REF][START_REF] Cooke | Quantitative proton magnetic resonance spectroscopy of the cervical spinal cord[END_REF][START_REF] Edden | Proton MR spectroscopic imaging of the medulla and cervical spinal cord[END_REF][START_REF] Gomez-Anson | In vivo 1H-magnetic resonance spectroscopy of the spinal cord in humans[END_REF]. In other studies, relative amplitudes to unsuppressed water signal [START_REF] Qian | Neuronal and axonal degeneration in experimental spinal cord injury: in vivo proton magnetic resonance spectroscopy and histology[END_REF] or to total creatine [START_REF] Erschbamer | 1) H-MRS in spinal cord injury: acute and chronic metabolite alterations in rat brain and lumbar spinal cord[END_REF] have been reported. In this study, we have used a navigator signal to normalize the metabolite amplitudes. Five metabolites were quantified within healthy mouse spinal cord with the advantage of glutamate quantification compared to studies on rats [START_REF] Balla | In vivo intermolecular zero-quantum coherence MR spectroscopy in the rat spinal cord at 17.6 T: a feasibility study[END_REF][START_REF] Bilgen | In vivo magnetic resonance microscopy of rat spinal cord at 7 T using implantable RF coils[END_REF][START_REF] Qian | Neuronal and axonal degeneration in experimental spinal cord injury: in vivo proton magnetic resonance spectroscopy and histology[END_REF][START_REF] Silver | In vivo 1H magnetic resonance imaging and spectroscopy of the rat spinal cord using an inductively-coupled chronically implanted RF coil[END_REF][START_REF] Zelaya | Localized 1H NMR spectroscopy of rat spinal cord in vivo[END_REF][START_REF] Erschbamer | 1) H-MRS in spinal cord injury: acute and chronic metabolite alterations in rat brain and lumbar spinal cord[END_REF]. The increased spectral resolution obtained at higher magnetic field might explain these results.

Given that 1 H MRS of the mouse spinal cord had never been performed before, thalamus spectra were acquired with the same protocol for quality comparison. Thalamus 1 H MRS provided thirteen metabolites which could be quantified with results in agreement with reported rodent brain studies at very high magnetic field [START_REF] Lei | Neurochemical profile of the mouse hypothalamus using in vivo 1H MRS at 14.1T[END_REF][START_REF] Mlynárik | 1H NMR spectroscopy of rat brain in vivo at 14.1Tesla: improvements in quantification of the neurochemical profile[END_REF]. Although thalamus and spinal cord are likely to present different neurochemical profiles, the comparison was primarily performed to characterize the robustness and sensitivity of the optimized 1 H MRS PRESS sequence for mouse spinal cord studies. Then, MRS studies at the thalamus level are also of particular interest in the case of SC injury since metabolic changes are expected [START_REF] Likavcanova | Metabolic changes in the thalamus after spinal cord injury followed by proton MR spectroscopy[END_REF] and since the thalamus plays an important role in the transmission of pain and in the sensorimotor pathways involved in the locomotor activity.

The robustness and the sensitivity of the technique to experimental measurement fluctuations (VOI positioning, physiological motion) and quantification errors were estimated by calculating the averaged reproducibility which was found in the order of 77 % and lower than for the same metabolites within the thalamus (90%). The inter-subject variability, which bears individual differences but also experimental measurement fluctuations, was slightly lower in the thalamus (11%) than in the spinal cord (15%) mainly due to reduced motion effects. The inter-subject variability observed in the SC was comparable or better than the values reported in human studies on healthy [START_REF] Cooke | Quantitative proton magnetic resonance spectroscopy of the cervical spinal cord[END_REF][START_REF] Edden | Proton MR spectroscopic imaging of the medulla and cervical spinal cord[END_REF] or multiple sclerosis control subjects [START_REF] Blamire | Axonal damage in the spinal cord of multiple sclerosis patients detected by magnetic resonance spectroscopy[END_REF][START_REF] Gomez-Anson | In vivo 1H-magnetic resonance spectroscopy of the spinal cord in humans[END_REF]. The estimated reproducibility and inter-subject variability allow confident measurements and longitudinal follow-ups. When looking at the individual metabolites, tCho, mI, and Glu quantified amplitude presented lower reproducibility and higher variability than NAA or tCr. These quantification result variations could be attributed to baseline distortions due to residual eddy current effects and/or residual water signal as well as the macromolecular signals estimation. These signals were estimated based on a semi-parametric approach using the initial part of the acquired signal [START_REF] Ratiney | Time-domain semi-parametric estimation based on a metabolite basis set[END_REF]. The acquisition of metabolite-nulled spectra (containing only contributions from macromolecules and lipid) would provide higher precision [START_REF] Gottschalk | Short-TE localised (1)H MRS of the human brain at 3 T: quantification of the metabolite signals using two approaches to account for macromolecular signal contributions[END_REF]. However the technique drastically increases the total acquisition time, which precludes its use in routine.

Finally, although our primary purpose in this study was not to characterize SC pathologies, the method has been applied to a preliminary model of mouse spinal cord injury. The observed initial decreases in metabolites normalized amplitudes could be attributed to axonal and neuronal damage as well as to cell population decrease due to primary cell disintegration and secondary perturbations. The progressive increases that followed could correspond to progressive axonal recovery as well as glial activation and proliferation. Variations greater than the inter-individual variability and reproducibility have been observed, demonstrating that our optimized protocol is a potential tool to study pathological mouse SC metabolism.

Although a strict comparison with reported studies is complicated by the use of different models of injury and reference signals (Cr or unsuppressed water), the results obtained in this first study are in general agreement with reported SC and brain injury studies [START_REF] Qian | Neuronal and axonal degeneration in experimental spinal cord injury: in vivo proton magnetic resonance spectroscopy and histology[END_REF][START_REF] Schuhmann | Metabolic changes in the vicinity of brain contusions: a proton magnetic resonance spectroscopy and histology study[END_REF]. Further studies that are beyond the scope of this feasibility demonstration study would be required.

Conclusion

In this study, the feasibility of an optimized short TE 1 H MRS sequence for the mouse spinal cord investigation at very high magnetic field (11.75T) has been demonstrated. The protocol described for both acquisition and quantification allowed reliable SC metabolite amplitudes collection at the cervical level with good reproducibility and limited inter-subject variability.

To the best of our knowledge, 1 H MRS of the mouse spinal cord has never been reported so far. This work demonstrates that the challenges of mouse SC 1H MRS can be overcome. It may therefore open new perspectives to study various pathological conditions provided by transgenic mouse models and deepen the understanding of the diseases by providing quantitative information complementary to MRI.

Finally, muscles

  FIG. 1. Location of the selected voxels for in vivo 1 H MRS measurements (white rectangle) in the spinal cord (VOI sc ~4µl), using axial (a) and sagittal (b) T 1 -weighted images, and in the thalamus (VOI Thalamus ~10µl), using axial (c) and sagittal (d) T 2 -weighted images. The voxel size, in the dorsal-ventral, left-right, and caudal-rostral directions, were 2.0x1.8x1.1 mm 3 for the spinal cord and 1.5x4.5x1.5 mm 3 for the thalamus. The dashed line rectangles represent the shim voxels in the spinal cord (18 µl) and in the thalamus (22 µl).

FIG. 2 .

 2 FIG. 2. (a) Typical in vivo healthy mouse 1 H spectra acquired at 11.75T from spinal cord and (b) thalamus with PRESS sequence (TR = 4s, TE = 10 ms, and NA = 256), with indication of the detected metabolite resonances. (c) Spinal cord and (d) thalamus estimated spectra and baseline (dashed line) obtained using QUEST. (e) Quantification residue corresponding to spinal cord and (f) thalamus.

FIG. 3 .

 3 FIG. 3. Histograms of healthy mice normalized metabolite amplitude detected in SC (a) and thalamus (b) with corresponding normalized CRBs (c) and (d), respectively.

  FIG. 4. Location of the selected voxel for in vivo 1 H MR spectroscopy of injured spinal cord in sagittal T 1 -weighted images (a) and axial T 2 * -weighted images (b). The VOI included the lateralized lesion (b). Acquired spectra before injury (c) and 3 (d), 7 (e), and 42 (f) days postinjury. Lipid signal amplitude was observed to be more pronounced in the injured mouse than in the healthy controls, with maximum amplitude at 7 days post-injury.

Acknowledgments

This work received the support of the CNRS (Centre National de la Recherche Scientifique, UMR 6612), and ANR (Agence Nationale de la Recherche, ANR-09-BLAN-0295-01). We thank Yann Le Fur and Hélène Ratiney for advice with spectra processing and quantification.

Figure legends

Tables

ANR-09-BLAN-0295-01 (TRAUMATISM project) and CNRS