Piotr Paluch

Tomasz Pawlak

Karol Lawniczak

Julien Trebosc

Olivier Lafon

Jean-Paul Amoureux

Marek J Potrzebowski

Karol Ławniczak

Julien Trébosc

∥⊥ Jean- Paul Amoureux

Simple and Robust Study of Backbone Dynamics of Crystalline Proteins Employing H-1-N-15 Dipolar Coupling Dispersion

published or not. The documents may come   L'archive ouverte pluridisciplinaire

INTRODUCTION

To understand in detail the biological functions of proteins, knowledge of their dynamics is crucial. Indeed, it is well-known that protein motions occurring on the pico-to millisecond time scales play important functional roles, [START_REF] Krushelnitsky | Solid-state NMR approaches to internal dynamics of proteins: from picoseconds to microseconds and seconds[END_REF] and that dynamics modulates the interactions between physiological partners. [START_REF] Torchia | Dynamics of biomolecules from picoseconds to seconds at atomic resolution[END_REF] A large amount of experimental and computational methods have been developed and applied to study protein dynamics at different time and length scales. As an example fluorescence techniques, [START_REF] Ding | Infrared and fluorescence assessment of protein dynamics: from folding to function[END_REF] atomic force microscopy, [START_REF] Tndo | High-speed AFM and applications to biomolecular systems[END_REF] and optical or magnetic tweezers, [START_REF] Capitanio | Interrogating biology with force: Single molecule highresolution measurements with optical tweezers[END_REF] usually analyze dynamics on length scales of a few tens of Å and time scales longer than milliseconds. Nuclear magnetic resonance (NMR), [START_REF] Kleckner | An introduction to NMR-based approaches for measuring protein dynamics[END_REF] neutron scattering, [START_REF] Zaccai | Neutron scattering perspectives for protein dynamics[END_REF] and Molecular Dynamics (MD) simulations, [START_REF] Adcock | Molecular dynamics: Survey of methods for simulating the activity of proteins[END_REF] are among the techniques that allow direct analyses of atomic motions from pico-seconds to seconds.

The unique feature of NMR spectroscopy is the possibility to analyze the dynamics of biomolecules at atomic resolution both in the liquid and solid states. Study of proteins in solids seems particularly attractive because the overall tumbling, which interferes in the liquid phase with the small local motions is eliminated. Several NMR analyses of dynamics, such as measurements of relaxation rates, 9 , 10 CPMG or T1 relaxation dispersion profiles, 11 , 12 , 13 pioneering high resolution T1 relaxation dispersion [START_REF] Charlier | Nanosecond Time Scale Motions in Proteins Revealed by High-Resolution NMR Relaxometry[END_REF] and magnetization or hydrogen exchange rates, [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] can be carried out in liquid and solid states. Solid-state NMR (ssNMR) methodologies mostly exploit the analysis of anisotropic tensorial interactions, such as dipolar coupling 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 and CSA (chemical shift anisotropy). 24 , 25 , 26 However, these anisotropic interactions are averaged to zero by a fast sample spinning at the magic angle (MAS) in terms of the first order Average Hamiltonian Theory (AHT). To date, a large number of techniques have been developed to reintroduce these anisotropic interactions with pulse sequences that are often based on symmetry rules introduced by Levitt. 27 , 28 These sequences are called CN  n and RN  n where the symbols N, n, and  are small symmetry integer numbers that depend on the rotation properties of the spin angular moment during the rotor-synchronized train of radio-frequency (rf) pulses. In this strategy the relationship between spins, space, rotation and rf-pulses is used to amplify the desired and suppress the unwanted interactions. As an example, the recently published RN-CSA symmetry schemes are suitable for CSA recoupling at fast spinning speeds (R ≥ 40 kHz). [START_REF] Ge | Measurement of amide proton chemical shift anisotropy in perdeuterated proteins using CSA amplification[END_REF] Other important sequences designed to measure dipolar couplings are based on REDOR [START_REF] Gullion | Rotational-Echo Double-Resonance NMR[END_REF][START_REF] Schanda | Quantitative Analysis of Protein Backbone Dynamics in Microcrystalline Ubiquitin by Solid-State NMR Spectroscopy. Local Structure and Relaxation in Solid-State NMR: Accurate Measurement of Amide N-H Bond Lengths and H-N-H Bond Angles[END_REF] T-MREV 20,[START_REF] Helmus | Conformational Flexibility of Y145 Stop Human Prion Protein Amyloid Fibrils Probed by Solid-State Nuclear Magnetic Resonance Spectroscopy[END_REF] and CPPI [START_REF] Chevelkov | Accurate Determination of Order Parameters from 1 H, 15 N Dipolar Couplings in MAS Solid-State NMR Experiments[END_REF] approaches.

In this paper, we report a method named cross-polarization with variable-contact (CPVC), [START_REF] Paluch | Simple and accurate determination of H-X distances under ultra-fast MAS NMR[END_REF] which is based on a different philosophy and which allows for a simple, accurate and robust way to analyze local molecular motions in the solid state via the analysis of heteronuclear dipolar couplings. The main advantage of this method is that it offers a three times larger scaling factor compared to sequences based on CN  n or RN  n schemes. Moreover, the application of these two symmetry based recoupling schemes is problematic under ultrafast MAS (R  60 kHz) due to rf-field limitations. Another motivation to design CPVC approaches is the fact that REDOR type of experiments may be difficult to use in the case of ultra-fast MAS due to finite pulse durations. On the other hand, ultra-fast MAS is more and more frequently used in ssNMR, and presently probe-heads allowing sample spinning rates over 110 kHz are commercially available. [START_REF] Nishiyama | Fast magic-angle sample spinning solid-state NMR at 60-100 kHz for natural abundance samples[END_REF][START_REF] Wickramasinghe | Evolution of CPMAS under fast magic-angle-spinning at 100 kHz and beyond[END_REF] The power of this CPVC approach is demonstrated here with a GB-1 protein. We employed a sample doped with a paramagnetic Na2CuEDTA salt (called GB-1Cu) to reduce the relaxation delay between two accumulations in order to save experimental time, a procedure frequently used, for which a detailed analysis has been provided by Linser et. al. [START_REF] Linser | Sensitivity enhancement using paramagnetic relaxation in MAS solid-state NMR of perdeuterated proteins[END_REF] Since one of the purposes of our work is to develop proton-detected sequences to analyze the H-N dipolar couplings, we have used a 2 H, [START_REF] Tollinger | Site-Resolved Measurement of Microsecond-to-Millisecond Conformational-Exchange Processes in Proteins by Solid-State NMR Spectroscop[END_REF] C, [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N labeled GB-1Cu sample with backexchanged labile (N-H) protons. Indeed, the 2 H labeling greatly increases the spectral resolution in the 1 H domain, especially at fast MAS. However, it must be mentioned that the [START_REF] Krushelnitsky | Solid-state NMR approaches to internal dynamics of proteins: from picoseconds to microseconds and seconds[END_REF] H linewidths still decrease when the spinning speed increases over R = 110 kHz. [START_REF] Paepe | Is protein deuteration beneficial for proton detected solid-state NMR at and above 100 kHz magic-angle spinning? Solid State[END_REF] GB-1Cu is often used to develop and test new methodological approaches, e.g. by Ishii's group. [START_REF] Wang | Nano-mole scale sequential signal assignment by 1H-detected protein solid-state NMR[END_REF] Nevertheless, it is rather surprising that a full site specific assignment for this GB-1Cu sample

had not yet been published when we started this project.

METHODOLOGY NMR measurement

The 2 H/ 13 C/ [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N GB-1Cu sample with back-exchanged labile (N-H) protons was purchased as an already filled 1.3 mm rotor from Giotto-Biototech/Cortecnet and was used as received. All experiments were performed at 14.1 T on a Bruker Avance III 600 spectrometer equipped with a 1.3 mm 1 H/ 13 C/ [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N CPMAS probe-head operated at frequencies of: 600.1, 150.9 and 60.8 MHz for 1 H, [START_REF] Tollinger | Site-Resolved Measurement of Microsecond-to-Millisecond Conformational-Exchange Processes in Proteins by Solid-State NMR Spectroscop[END_REF] C and 15 N, respectively. In all cases, the sample was spun at R = 60 kHz and the recycling delay was equal to RD = 200 ms. For assignments, we used series of 1 Hdetected experiments, either 2D (hNH) or 3D (hCONH, hCANH, hcaCOcaNH, hcoCAcoNH, hcaCBcaNH, hcaCBcacoNH) as described by Pintacuda et al. [START_REF] Barbet-Massin | Rapid proton-detected NMR assignment for proteins with fast magic angle spinning[END_REF][START_REF] Marchetti | Backbone assignment of fully protonated solid proteins by 1 H detection and ultrafast magic-angle-spinning NMR spectroscopy[END_REF] All experiments started from the proton, which is indicated with the h at the beginning of their names, following Pintacuda's convention. [START_REF] Schanda | Quantitative Analysis of Protein Backbone Dynamics in Microcrystalline Ubiquitin by Solid-State NMR Spectroscopy. Local Structure and Relaxation in Solid-State NMR: Accurate Measurement of Amide N-H Bond Lengths and H-N-H Bond Angles[END_REF] For the benefit of non-experts in ssNMR of proteins, these sequences are shortly described in the ESI. Moreover, we also collected two [START_REF] Tollinger | Site-Resolved Measurement of Microsecond-to-Millisecond Conformational-Exchange Processes in Proteins by Solid-State NMR Spectroscop[END_REF] C-detected 2D correlations (hNCA and hNCO) based on the double CP scheme. Detailed information about rf-fields, number of points, spectral widths, number of scans, etc. are presented in ESI. Spectra were processed using TopSpin 3.1. In case CPVC experiment RF were near to 20 and 40 for 1 H and [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N respectively, actual power were precisely calibrated on each experiments.

In the case of 3D CPVC experiments, after two standard FTs along the two chemical shift dimensions, the imaginary part of the spectrum was set to zero with a Python script calling the "dd" Unix commend, and then a real FT was performed along the dipolar dimension, without any apodization. To remove the strong peak at the center of the dipolar spectrum, the 'qfil' baseline correction implemented in TopSpin was used. For analyses of 2D and 3D spectra, we used Sparky 3.115 with NMRFAM-Sparky extensions. Strip plots from 3D datasets were prepared using NMR Glue. 38,39

RESULTS AND DISCUSSION

Assigning GB-1Cu

The literature reporting structural studies of [START_REF] Tollinger | Site-Resolved Measurement of Microsecond-to-Millisecond Conformational-Exchange Processes in Proteins by Solid-State NMR Spectroscop[END_REF] C and/or 15 N labeled GB-1 proteins by means of ssNMR is very extensive. A survey of the published works clearly shows that most of the results come from the Rienstra's group. [START_REF] Franks | Magic-angle spinning solid-state NMR spectroscopy of the β1 immunoglobulin binding domain of protein G (GB1): 15 N and 13 C Chemical shift assignments and conformational analysis[END_REF] In the cited papers, authors have employed different multi-dimensional ssNMR techniques for the assignments of GB-1, including 2D 13 C- [START_REF] Tollinger | Site-Resolved Measurement of Microsecond-to-Millisecond Conformational-Exchange Processes in Proteins by Solid-State NMR Spectroscop[END_REF] C DARR/SPC-5, 2D/3D N(CO)CX and N(CA)CX, and 3D CONCA. The same group has shown the first application of the 4D CANCOCX sequence for the chemical shifts assignment and thus performed a more accurate structural analysis of GB-1. [START_REF] Franks | Four-dimensional heteronuclear correlation experiments for chemical shift assignment of solid proteins[END_REF] In these articles, the [START_REF] Tollinger | Site-Resolved Measurement of Microsecond-to-Millisecond Conformational-Exchange Processes in Proteins by Solid-State NMR Spectroscop[END_REF] C/ 15 N isotopes were directly detected. To the best of our knowledge, the first approach utilizing the inverse mode via 1 H detection for the assignment of GB-1 (and other proteins) in the solid state has been presented by Zhou et al., [START_REF] Zhou | Protondetected solid-state spectroscopy of fully protonated proteins at 40 kHz magic-angle spinning[END_REF][START_REF] Zhou | Solid-state protein structure determination with proton-detected triple resonance 3D magic-angle spinning NMR spectroscopy[END_REF] and this methodology was tested with R = 40 kHz. With current hardware developments, the reduction of rotor diameters allows for an increase of the spinning rate up to R = 150 kHz presently, and this inverse detection approach has found a large number of spectacular applications. Recent articles of Pintacuda et al., [START_REF] Barbet-Massin | Rapid proton-detected NMR assignment for proteins with fast magic angle spinning[END_REF] Shanda et al., [START_REF] Fraga | Solid-state NMR H-N-(C)-H and H-N-C-C 3D/4D correlation experiments for resonance assignment of large proteins[END_REF] and others, [START_REF] Agarwal | De novo 3D structure determination from sub-milligram protein samples by solid-state 100 kHz MAS NMR spectroscopy[END_REF][START_REF] Penzel | Protein resonance assignment at MAS frequencies approaching 100 kHz: a quantitative comparison of J-coupling and dipolar-coupling-based transfer methods[END_REF] provide straightforward evidences showing the power of 1 H inverse detection based on very fast MAS techniques. As a consequence, novel spectral editing methods, which permit drastic spectral simplifications, have been recently proposed. [START_REF] Wang | Nano-mole scale sequential signal assignment by 1H-detected protein solid-state NMR[END_REF] Despite the large number of papers published so far, the structural refinement of our GB-1Cu crystalline sample is not trivial, even if the assignment of signals is unambiguous. The first problem is related to the polymorphism of GB-1. Indeed, it is well known that this protein exists at least in 5 different polymorphic forms, which are characterized by slightly different chemical shifts. [START_REF] Schmidt | Crystal polymorphism of protein GB1 examined by solid-state NMR spectroscopy and X-ray diffraction[END_REF] It should be noted that other proteins exhibit such polymorphism, e.g. ubiquitin, [START_REF] Ma | Observing the overall rocking motion of a protein in a crystal[END_REF] and thus this problem is quite general. Moreover, differences in experimental chemical shifts can be caused by a tiny miss-calibration, use of different external standards (e.g. TSP vs. glycine) or other factors including substitution of protons by deuterons. Indeed, deuteration may affect the [START_REF] Tollinger | Site-Resolved Measurement of Microsecond-to-Millisecond Conformational-Exchange Processes in Proteins by Solid-State NMR Spectroscop[END_REF] C chemical shifts, changing their values in the range of 0.2-1.5 ppm for each directly bonded position due to secondary 1 H/ 2 H isotopic effects. [START_REF] Cavanagh | Protein NMR Spectroscopy: Principles and Practice[END_REF] However, such changes are much lower for adjacent 2 H/ [START_REF] Tollinger | Site-Resolved Measurement of Microsecond-to-Millisecond Conformational-Exchange Processes in Proteins by Solid-State NMR Spectroscop[END_REF] C pairs and they rarely exceed 0.1 ppm.

Additionally, we used a 2 H/ 13 C/ [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N enriched protein doped with paramagnetic additives in order to reduce the relaxation time. Such an approach, called PACC (Paramagnetic-Assisted Condensed data Collection) 50 has found a large number of impressive applications in structural studies of crystalline proteins. When using PACC, ultrafast MAS and Non-Uniform Sampling, it has recently been shown that [START_REF] Krushelnitsky | Solid-state NMR approaches to internal dynamics of proteins: from picoseconds to microseconds and seconds[END_REF] H inverse detection 1 H- [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N HETCORs can be recorded as fast as in 9 seconds on GB-1Cu. [START_REF] Ishii | Progress in proton-detected solid-state NMR (SSNMR): Super-fast 2D SSNMR collection for nano-mole-scale proteins[END_REF] However, it must be stressed that paramagnetic additives can disturb all chemical shifts due to the pseudo-contact shift (PCS), [START_REF] Bertini | Paramagnetic constraints: an aid for quick solution structure determination of paramagnetic metalloproteins[END_REF] or the direct Fermi contact shift (FCS), and that the changes strongly depend on the distance and angular position between the observed nuclei and the paramagnetic center. In the case of Cu 2+ , the PCS could be neglected due to the isotropic magnetic susceptibility tensor. On the contrary, the FCS could be observed even in such case, in particular for the closest nuclei to the paramagnetic centers. Such FCS interaction should not be neglected in general, as it can lead to significant chemical shift changes due to the interaction between the protein and Cu 2+ . Following these difficulties (polymorphism, deuteration and interaction with the paramagnetic center), and to be sure of our refinement, we decided to carry out a de novo assignment of signals for our GB-1Cu sample.

Our assignment strategy is very similar to the scheme proposed by Bax and coworkers for structural analyses of proteins in the liquid state. [START_REF] Bax | Triple resonance three-dimensional protein NMR: Before it became a black box[END_REF][START_REF] Sattler | Heteronuclear multidimensional NMR experiments for the structure determination of proteins in solution employing pulsed field gradients[END_REF][START_REF] Cavanagh | Protein NMR Spectroscopy: Principles and Practice[END_REF] In these articles, different variants of 3D HNCA/HN(CO)CA experiments were employed. In our current project, series of 2D (hNH, hNCO, hNCA) and 1 H-detected 3D (hCONH, hCANH, hcaCOcaNH, hcoCAcoNH, hcaCBcaNH, hcaCBcacoNH) experiments were carried out. [START_REF] Barbet-Massin | Rapid proton-detected NMR assignment for proteins with fast magic angle spinning[END_REF] Comparing the liquid and solid-state NMR approaches, it has to be emphasized that for the hCANH experiment performed on condensed matter, only correlations between H(i)-N(i)-Ca(i) are seen, whereas both H(i)-N(i)-Ca(i) and H(i)-N(i)-Ca(i-1) correlations are visible in HNCA experiment in the liquid phase. This is due to the fact that in the liquid state the magnetization is transferred via scalar coupling, and that 1 JNCa and 2 JNCa have very similar values. In ssNMR experiments, the magnetization is transferred via CPMAS, exploiting the dipolar interactions, which are strongly distance dependent, D  rij -3 , and hence the transfer of magnetization between not directly bonded atoms is very ineffective. It should be noted that J-coupling based protein experiments also exist in ssNMR, and such strategy was proposed e.g. by Rienstra and Mueller. [START_REF] Chen | Backbone Assignments in Solid-State Proteins Using J-Based 3D Heteronuclear Correlation Spectroscopy[END_REF] In such cases, both intra-and inter-residual correlations are visible on some of the residues. A more extended description of assignments with a Table giving the chemical shifts is presented in the ESI. 2D spectra and some representative strip plots from 3D spectra are presented in Fig. 1,2 and S14-S18. In addition, structure calculations using CS-ROSETTA and comparison with previous data are also included in the ESI. In addition chemical shift data have deposited in BioMagResBank at reference number 27562.

Dynamic process analysis

ssNMR is one of the most powerful techniques to study dynamic processes in condensed matter. This ability is related to the very large sensitivity of the various NMR observables to dynamics over large time-scale ranges, and it is possible to observe microscopic motions occurring between pico-to hundreds of seconds. Such methods can be classified into five different groups based on: (i) relaxation (R1, R2, R1 etc), 56 , 57 , 58 (ii) dipolar and (iii) quadrupolar couplings, [START_REF] Pawlak | Computed and experimental chemical shift parameters for rigid and flexible YAF peptides in the solid state[END_REF][START_REF] Dvinskikh | Measurements of motionally averaged heteronuclear dipolar couplings in MAS NMR using R-type recoupling[END_REF] (iv) chemical shift anisotropy, [START_REF] Hou | Recoupling of chemical shift anisotropy by R-symmetry sequences in magic angle spinning NMR spectroscopy[END_REF] and (v) chemical exchange. [START_REF] Krushelnitsky | Superslow backbone protein dynamics as studied by 1D solid-state MAS exchange NMR spectroscopy[END_REF][START_REF] Krushelnitsky | Solid-State NMR Approaches to Internal Dynamics of Proteins: From Picoseconds to Microseconds and Seconds[END_REF] These methods, which are sensitive to very different time scales, are applicable to small molecules, [START_REF] Piślewski | Spin-lattice relaxation study of the methyl proton dynamics in solid 9,10-dimethyltriptycene (DMT)[END_REF] polymers, [START_REF] Leisen | Multidimensional 2 H NMR studies of the nonexponential chain relaxation of polystyrene above the glass transition[END_REF] and biomolecules. [START_REF] Schanda | Studying dynamics by magic-angle spinning solid-state NMR spectroscopy: Principles and applications to biomolecules[END_REF] In the case of biomolecules, relaxation and dipolar coupling-based methods have wider uses.

Quantitative relaxation studies often require either a definition of the model of dynamics or a usage of a model-free approach based on the formalism proposed by Lipari and Szabo. [START_REF] Lipari | Model-free approach to the interpretation of nuclear magneticresonance relaxation in macromolecules: 1. Theory and range of validity[END_REF][START_REF] Jaremko | The quest for simplicity: Remarks on the free-approach models[END_REF] In both cases, numerical calculations are required and it is necessary to collect a large amount of high quality spectra to precisely determine the various relaxation parameters.

However, these methods allow an accurate determination of the motional timescales, which is not really possible with other methods. Conventional qualitative or semi-quantitative analyses, e.g. by direct comparison of T2 values, only require the determination of relaxation rates. However, this type of analysis can become problematic when a paramagnetic doping is used. Indeed, in such case the relaxation rates change, and these changes are related to specific interactions of the protein with the paramagnetic center. Therefore, these paramagnetic relaxation changes are not uniform around the whole protein molecule. This strongly complicates the analysis of relaxation data in the case of paramagnetic doping and such data must be treated very carefully. Nevertheless, it should be noted that these paramagnetic relaxation changes should not always be considered as drawbacks, and they can also be used as valuable restrains for structure calculation. [START_REF] Jaroniec | Structural studies of proteins by paramagnetic solid-state NMR Spectroscopy[END_REF] On the contrary, dipolar-based methods usually do not require complicated data treatments, and they often only necessitate collecting a single spectrum. More importantly, the interactions with paramagnetic centers do not change the dipolar couplings, which leads to an easy interpretation of data in the case of the PACC strategy. 50 It is important to remember that the PACC approach decreases by a factor of 5 to 10 the recycling delay with respect to the conventional approach. Therefore, even if we consider that for the dipolar dimension we need more points than for the "relaxation" dimension, the total experiment time is comparable or even lower than with relaxation measurements. Unfortunately, the full information of the time-scales is lost. Indeed, if we consider the two most typical 1 H- [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N and 1 H- [START_REF] Tollinger | Site-Resolved Measurement of Microsecond-to-Millisecond Conformational-Exchange Processes in Proteins by Solid-State NMR Spectroscop[END_REF] C dipolar couplings for biomolecules, these methods only allow one to know if a process with a timescale smaller than 10 s exists or not. Occasionally, some motional models can be proposed from the reduced dipolar tensor parameters. In this article, we use one of these dipolar-based methods for a fast analysis of the backbone dynamics in GB-1Cu. Since the dynamics of the GB-1 protein is well known, with a large number of datasets mostly based on relaxation measurements, [START_REF] Lamley | Unravelling the complexity of protein backbone dynamics with combined 13 C and 15 N solid-state NMR relaxation measurements[END_REF][START_REF] Lamley | Intermolecular interactions and protein dynamics by solid-state NMR spectroscopy[END_REF] the purpose of this work is to perform a comparative analysis of CPVC results with the existing data and to demonstrate that our results are in good agreement with the literature, and at the same time obtained with a methodology easily applicable under veryfast MAS.

Recently, we proposed a new 2D approach, called CPVC (Cross-Polarization with Variable-Contact), to measure the 1 H- [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N or 1 H-13 C dipolar couplings. [START_REF] Paluch | Simple and accurate determination of H-X distances under ultra-fast MAS NMR[END_REF] This simple method consists of a controlled 1 H → 15 N or 1 H → 13 C CP transfer under very fast MAS (R  60 kHz). The F2 dimension corresponds to the 15 N or [START_REF] Tollinger | Site-Resolved Measurement of Microsecond-to-Millisecond Conformational-Exchange Processes in Proteins by Solid-State NMR Spectroscop[END_REF] C chemical shifts (15N or 13C) and the F1 dimension is the 1 H → 15 N or 1 H → 13 C dipolar recoupled spectrum. This spectrum presents two symmetrical narrow peaks, the separation of which is called the dipolar splitting, . The dipolar coupling is described by a second rank tensor with a null trace. When there is no motion, one eigenvalue is equal to D = μ0γiγj/4π 2 rij 3 and the two others to -D/2, and hence the dipolar asymmetry parameter is equal to  = 0. In this case, the dipolar value can directly be determined from the dipolar splitting,  = D/2. When a molecular motion exists, an averaging occurs over the different orientations of the H-N or H-C vector. This motion leads to a decrease of the D value and an increase of the  parameter in the 0-1 range. [START_REF] Schanda | Solid-State NMR Measurements of Asymmetric Dipolar Couplings Provide Insight into Protein Side-Chain Motion[END_REF] The D and  values depend on the amplitude of the motion and on its topology, but they are independent on its time-scale, at least when this motion is fast enough. The CPVC method allows for the measurement of the D and  dipolar coupling parameters, averaged by the molecular motions, but a fitting of the dipolar spectrum may be required to obtain accurate values for these two parameters. We have shown that the 1 H → 15 N, 1 H → 13 C or 1 H→ 31 P CPVC schemes are very useful in the case of small molecules, [START_REF] Paluch | 1 H-31 P CPVC NMR method under Very Fast Magic Angle Spinning for analysis of dipolar interactions and dynamics processes in the crystalline phosphonium tetrafluoroborate salts[END_REF] or peptides, [START_REF] Dudek | A multitechnique experimental and computational approach to study the dehydration processes in the crystals of endomorphin opioid peptide derivative[END_REF] and we have fully validated their use for quantitative analyses of dynamics with numerical simulations. [START_REF] Paluch | Theoretical study of CPVC: a simple, robust and accurate MAS NMR method for analysis of dipolar C-H interactions under rotation speeds faster than ca. 60 kHz[END_REF] In addition, we have shown that such analyses can be run in inverse-detected mode ( 1 H → 15 N → 1 H or 1 H → 13 C→ 1 H with two CPMAS transfers), [START_REF] Nishiyama | Accurate NMR determination of C-H or N-H distances for unlabelled molecules[END_REF] and have used this inverse detection to study not only dynamic processes but also hydrogen bonding phenomena. [START_REF] Rajput | Exploring the salt-cocrystal continuum with solid-state NMR using natural-abundance samples: implications for crystal engineering[END_REF] Opella has demonstrated that such an approach is also useful to study the protein backbone dynamics, when it is developed into a 3D inverse-detected experiment for 1 H- [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N dipolar coupling measurements. [START_REF] Park | Resolution and measurement of heteronuclear dipolar couplings of a non-crystalline protein immobilized in a biological supramolecular assembly by proton-detected MAS solid-state NMR spectroscopy[END_REF] Simultaneously, we have proposed another 3D method, called CPVC-RFDR, with [START_REF] Tollinger | Site-Resolved Measurement of Microsecond-to-Millisecond Conformational-Exchange Processes in Proteins by Solid-State NMR Spectroscop[END_REF] C detection (D1H-13C-13C-13C), for dynamics studies of protein side-chains aromatic rings. [START_REF] Paluch | Analysis of local molecular motions of aromatic side chains in proteins by 2D and 3D fast MAS NMR spectroscopy and quantum mechanical calculations[END_REF] To the best of our knowledge, it was the first attempt to study such process with atomic resolution.

In the current project, we focused our attention on the backbone dynamics using inverse-detected 3D experiments. In the first part, we used the 3D inverse-detected 1 H- [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N-1 H CPVC method to measure the D1H-15N values with 1 H and [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N chemical shift editing (15N-D1H-15N-1H). The CPVC sequence is an adaptation to our method modified by inverse-detected approach described by Pruski. [START_REF] Wiench | Chemical shift correlation NMR spectroscopy with indirect detection in fast rotating solids: studies of organically functionalized mesoporous silicas[END_REF][START_REF] Mao | Conformations of silica-bound (pentafluorophenyl)propyl groups determined by solid-state NMR spectroscopy and theoretical calculations[END_REF][START_REF] Kobayashi | Study of intermolecular interactions in the corrole matrix by solid-state NMR under 100 kHz MAS and theoretical calculations[END_REF] In our modification, only one change is required: the second CPMAS transfer must be performed with constant rf-fields (Fig. 3).

Figure 3. Such an approach has been previously described in a 2D version. [START_REF] Lamley | Relaxation-Based Magic-Angle Spinning NMR Approaches for Studying Protein Dynamics[END_REF][START_REF] Pawlak | Computed and experimental chemical shift parameters for rigid and flexible YAF peptides in the solid state[END_REF] This approach allows for an easy determination of the H-N vectors that have enough mobility to partially average their dipolar interactions. The 2D (15N-D1H-15N) projection from the full 3D cube (Fig. 4) shows that some residues have lower dipolar splitting values, , and hence lower dipolar couplings. However, it is clear that such simple 2D analysis is not sufficient to precisely determine the dynamics processes for proteins, due to limited resolution along the [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] One observes that for small asymmetry parameters,  < 0.2, D/2 and  are identical within 5%, which means that it is possible to use the  value to calculate D instead of a full simulation of dipolar spectra. For larger asymmetry values,  is much smaller than D, and so a global dipolar lineshape fitting is required, which necessitates the usage of a model for dynamics (Fig. S9 andS10). This is a very useful property of CPVC, because in the case of backbone analysis we do not predict large motions that could lead to large  values. This fact strongly decreases the time and effort needed to determine the dipolar couplings. Indeed, when the S/N ratio is low or when several species overlap in the dipolar 1D slice, it is much easier to determine directly the  values than to simulate the D ones. We have also compared in Table S2 the results obtained from direct splitting measurements (scaled up by 1.41) and from the lineshape fitting across the GB-1Cu backbone. Both values are in good agreement, except that the D values determined from lineshape fitting are slightly higher than those obtained from direct splitting measurements. When   0.2, which can be the case of sidechains aromatics, it is possible to use the  value for a first qualitative analysis of the dynamics process. This observation is consistent with our previous simulations, [START_REF] Paluch | Theoretical study of CPVC: a simple, robust and accurate MAS NMR method for analysis of dipolar C-H interactions under rotation speeds faster than ca. 60 kHz[END_REF] where several full lineshapes were compared with various D and  values. In the simulations we used the equations published in ref [77] and presented in the ESI. For different D values, it must be noted that the dipolar lineshapes are only scaled by the D value (Fig. S10).

One of the major drawbacks of the 3D inverse-detected1 H-15 N-1 H CPVC approach is the impossibility to determine the D value when 1H and 15N are very close for two or more residues. In such case, a large overlap in the 1D dipolar slice occurs, and the true D or  values are difficult to extract, even in the case of the small GB-1Cu protein. As an example, this overlapping occurs for Gly-38 and Gly-41, for which 1H and 15N values are almost the same, as observable in a strip plot from hCANH (Figure 2). In such a case, other edition methods of the dipolar coupling must be considered. One possibility is to use C as an editing nucleus instead of [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N. To that purpose, in this work, we have developed a new 3D hCA(N)H-CPVC method, as an extension of the existing Pintacuda's sequence (Fig. 6). [START_REF] Barbet-Massin | Rapid proton-detected NMR assignment for proteins with fast magic angle spinning[END_REF] Figure 6. 3D hCA(N)H-CPVC sequence. Most parameters (phase cycling, delays, etc) are the same as in Pintacuda's paper. [START_REF] Barbet-Massin | Rapid proton-detected NMR assignment for proteins with fast magic angle spinning[END_REF] The only differences are that (i) there is no 15N evolution, and (ii) the last [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N → 1 H CP transfer uses constant rf amplitudes for CPVC.

It is obvious that a CO editing is also possible, giving the hCO(N)H-CPVC method, but C species have a higher chemical shift range than CO. More generally, in the case of very high overlapping spectra, this approach could by further extended to a 4D sequence with three chemical shift axes (1H, 15N, 13C) and one dipolar dimension (D1H-15N). In Fig. 7 we present the 1D dipolar slices extracted for Gly-38 and Gly-41 from two 3D experiments, Fig. 7. 1D dipolar slices from 1 H-15 N-1 H-and hCA(N)H-CPVC extracted for a) Gly-38 and b) Gly-41.

The 1 H- [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N-1 H CPVC signals of the two residues present two well defined maxima (Fig. 7 top), but it is not easy to attribute them to Gly-38 or to Gly-41. The same problem probably exists in the case of relaxation measurements with 1 H/ [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N editing. In contrast, hCA(N)H-CPVC experiment leads to an unambiguous determination of the two dipolar coupling values for both Gly-38 and Gly-41 (Fig. 7 bottom). The chemical shift differences for [START_REF] Krushelnitsky | Solid-state NMR approaches to internal dynamics of proteins: from picoseconds to microseconds and seconds[END_REF] H, [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N and [START_REF] Tollinger | Site-Resolved Measurement of Microsecond-to-Millisecond Conformational-Exchange Processes in Proteins by Solid-State NMR Spectroscop[END_REF] C of these two residues are equal to 0.03, 0.2 and 1.67 ppm (18, 12 and 250 Hz), respectively. These differences are very small for 1 H and [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N, hence leading to the dipolar doublets with similar peak amplitudes observed with 1 H- [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N-1 H CPVC on the first line. For [START_REF] Tollinger | Site-Resolved Measurement of Microsecond-to-Millisecond Conformational-Exchange Processes in Proteins by Solid-State NMR Spectroscop[END_REF] C this shift difference is much higher, allowing a clear separation of the two contributions in Fig. 7 bottom. Signal overlap for these residues is also clearly visible in the case of hNH 2D spectra (Fig. S11), whereas resolved peaks are observed in the cases of 2D hNCO (Fig. S13) and especially hNCa (Fig. S12).

Theoretically, 1 H- [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N-1 H and hCA(N)H CPVC experiments should provide the same dipolar values. However, small non-systematic differences between the values obtained from these two experiments exist in both cases of direct measurements of  and numerical fitting of D and  values. On the other hand, in most cases these differences are smaller than the digital resolution, defined as SW/number of FID points, here 400 Hz (30 kHz/75), and they can be related to the limited resolution and different S/N ratios in the two experiments. Therefore, in the following part, whenever it is possible, we use the average value from the two experiments. The dipolar values from these two experiments, obtained from the  values or by lineshape analyses, are presented in Table S2. Finally, it should also be noted that the relaxation measurements using our triple resonance editing, with 13C instead of 15N, should be possible and very useful in a full detailed analysis of protein dynamics.

One of the best and simplest way to perform a dipolar coupling analysis across the backbone chain is to determine the so-called dipolar order parameter. This simple factor is defined as S 2 DD,i = (Di/Dref) 2 , where Di is the observed dipolar coupling for i-th residue, and Dref is a reference value calculated for some reference rigid system with known distance between interacting spins. It should be noted that for such analysis it is necessary to assume that the distances between interacting spins are constant over the backbone. Otherwise, a modification of S 2 DD,i could mean a change of either Di or the reference distance (Dref). Fortunately, in the case of directly bonded H-N nuclei this assumption is generally true in the protein backbone. When S 2 DD,i is equal or close to 1 this means that i-th residue is rigid or has few motions. A much lower value of this parameter means that the analyzed residue exhibits intrinsic motions. In the case of GB-1Cu, only a few residues have a S 2 DD,i value much lower than 1 (Fig. 8), namely: Lys-10, Thr-11, Leu-12, Thr-17, Glu-19, Asp-40 and Gly-41. Except for residue Thr-17, all of them are localized in the unstructured loop and it is easy to understand that such residues exhibit much higher motions than residues located in the helices or -sheets. In the 'structure calculations section' in ESI employing the CS Rosetta method, we show the higher order structure and the site-specific assignment for each individual amino acid in the GB-1Cu sequence. As previously revealed, a β-hairpin is formed, stabilized by residues Trp43, Tyr45, and Phe52. Residue contacts between residue Phe30 in an α-helix and the β-hairpin strengthen the nucleation of the β-sheet starting from residues Leu5 and Phe52.

The last nucleation residue, Tyr3, assists in forming the central part of the β-sheet, resulting in a globular protein. Analyzing the structure in terms of molecular dynamics, we can conclude that in the well-organized fragment of protein with strong hydrogen bonding and insufficient voids for molecular reorientation, the H-N backbone is rigid. Larger amplitude motions can be expected in loops joining the helixes and sheets. Fig. 10 displays in pictorial form the position of the amino acids under discussion in the structure of GB-1Cu. It is apparent from these results that local molecular motions are strongly correlated with higher order structure of the protein. Our data are in good agreement with results published by Lewandowski and coworkers for a GB-1 sample without paramagnetic doping. [START_REF] Lamley | Unravelling the complexity of protein backbone dynamics with combined 13 C and 15 N solid-state NMR relaxation measurements[END_REF][START_REF] Lamley | Intermolecular interactions and protein dynamics by solid-state NMR spectroscopy[END_REF] Authors employing relaxation experiments have proved that straightforward correlation between secondary structure and molecular dynamics of protein exists. We have also a good agreement with the MD simulations and the very detailed relaxation studies in solution and solid states provided by Mollica. [START_REF] Mollica | Atomic-Resolution Structural Dynamics in Crystalline Proteins from NMR and Molecular Simulation[END_REF] In this article, the average order parameters, <S 2 >  0.9, is in good agreement with our data. For the most mobile residue (Gly41), the authors provide a value of S 2  0.6, whereas we find 0.72 for this residue, which can be still considered as a good agreement. The behaviors of Lys10 and Thr11 are also in good agreement between our and Mollica's data and S 2  0.8 in both cases. Our approach complements these studies and offers a simpler methodology.

CONCLUSIONS

In this work, we report two new CPVC pulse sequences with 1 H detection, 1 H-15 N-1 H and hCA(N)H, to measure the dynamics of H-N vectors. Both 3D methods are applicable in proteins and other complex structures. The hCA(N)H CPVC experiment utilizes C instead of [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N edition, which is very useful in the case of large signal overlap in the 1 H and 15 N dimensions. These two experiments are complementary and their simultaneous use provides much more information than the classical approaches with only 1 H/ [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N chemical shift editions. They have a good sensitivity due do proton detection and they may be an alternative to relaxation measurements. It should be noted that dipolar coupling analyses are simpler to analyze, at least in a semi-quantitative way, than relaxation data. These dipolar methods are also very promising in the case of proteins with paramagnetic doping, because short relaxation delays can then be used to speed up measurements. We have demonstrated the utility of this method on a small GB-1 protein doped with Na2CuEDTA. Moreover, for the first time to the best of our knowledge, we have presented 1 H, [START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N, CA, CB and CO assignments of such samples, and we have compared our results with those previously published for the same protein without paramagnetic doping. Based on this chemical shift data we have determined the structure of this labeled protein, which is in good agreement with those previously reported without doping.

Figure 1 .

 1 Figure 1. hNCO (a), hNCA (b), hNH (c) 2D spectra for GB-1Cu. Larger size spectra with assignments are presented in ESI.

Figure 2 .

 2 Figure 2. Strip plots from 3D hCANH, hcoCAcoNH, hCONH, hcaCOcaNH for residues from 34Ala to 47Asp. Full sets of strip plots are given in ESI.

  N dimension. Indeed, the F1 dipolar slices may be the sum of several overlapping signals, as shown in Fig.4for 15N = 105 and 108 ppm.

Figure 4 .Fig. 5 ,

 45 Figure 4. GB-1Cu: 15N-D1H-15N projection from the 1 H-15 N-1 H-CPVC 3D spectrum with two extracted 1D slices.To have site specific information about the dipolar couplings, D1H-15N, one can either only scale up by 2 the dipolar splittings () measured on the 1D dipolar slices extracted from the 3D cube, or perform full dipolar lineshape analyses using AHT equations to determine the correct dipolar values. We have compared the two methods with numerical simulations. In Fig.5, S9 and S10, we have presented the CPVC dipolar spectra observed for 10 different 

Figure 5 .

 5 Figure 5. Dipolar doublets calculated for D = 10.5 kHz and 10 various  values.In the simulations we used the equations published in ref[77] and presented in the ESI. For different D values, it must be noted that the dipolar lineshapes are only scaled by the D value (Fig.S10).

Figure 8 .

 8 Figure 8. Dipolar 1 H-15 N order parameters defined as S 2 DD,i = (Di/Dref) 2 across the GB-1Cu chain. The reference value (Dref = 11.35 kHz) corresponds to a rigid 1 H-15 N spin system with bond length of 1.02 Å. The average order parameter is <S 2 > = 0.89.

Fig. 10 .

 10 Fig.10. Model of GB-1Cu obtained by means of CS Rosetta with labeled amino acids in loops joining helixes and sheets. Solid lines (orange) represent hydrogen bondings.

H-[START_REF] Kuwata | NMRdetected hydrogen exchange and molecular dynamics simulations provide structural insight into fibril formation of prion protein fragment[END_REF] N-1 H-and hCA(N)H-CPVC.

ACKNOWLEDGMENTS

The authors are grateful to the Polish National Science Centre (NCN) for financial support under Grant No. UMO-2014/13/B/ST4/03050. The computational resources were partially provided by the Polish Infrastructure for Supporting Computational Science in the European Research Space (PL-GRID). Chevreul Institute (FR 2638), Ministère de l'Enseignement Supérieur et de la Recherche, Région Hauts-de-France and FEDER are acknowledged for supporting and funding partially this work. Financial support from the TGIR-RMN-THC FR 3050 CNRS for conducting the research is gratefully acknowledged. Authors also acknowledge contract CEFIPRA n°85208-E, PRC CNRS-NSFC, ANR-14-CE07-0009-01 and ANR-17-ERC2-0022 (EOS).

AUTHOR INFORMATION

Corresponding Authors

Piotr Paluch

email: ppaluch@cbmm.lodz.pl or piotr.paluch@gmail.com Marek J. Potrzebowski email: marekpot@cbmm.lodz.pl § Present Address Univ. Lille, UMR 8181, UCCS: Unit of Catalysis and Chemistry of Solids, F-59000 Lille,

France

Notes

The authors declare no competing financial interests.


Guillaume Rousseau

Lionel Montagne

François Mear

François O Méar

Further insights on the Thermal degradation of aluminum metaphosphate prepared from aluminum dihydrogen phosphate solution

published or not. The documents may come

Further insights on the thermal degradation of aluminum metaphosphate prepared from aluminum dihydrogen phosphate solution

Introduction

Aluminum metaphosphate materials have been used for years as binding agents in the refractory materials industry [START_REF] Kingery | Fundamental Study of Phosphate Bonding in Refractories : I, Literature Review[END_REF][START_REF] Vippola | Structural Characterization of Aluminum Phosphate Binder[END_REF], as an acid compound for acid-base cements [START_REF] Shubow | Bonded Aggregate Structures and Production Thereof[END_REF][START_REF] Tomic | Phosphate cement and mortar[END_REF] and as precursors for protective coating against oxidation for Carbon/Carbon composite materials [START_REF] Balhadere | Procédé pour la protection contre l'oxydation de pièces en matériau composite contenant du carbone[END_REF][START_REF] Lu | Oxidation protection of carbon materials by acid phosphate impregnation[END_REF].

These materials are generally obtained by heating solutions of aluminum dihydrogen-phosphate Al(H2PO4)3, which are characterized by their P/Al atomic ratio. It was shown that solutions with a P/Al atomic ratio above 3 are stable for long time, while solutions with a ratio between 2 and 3 are subjected to precipitation of AlH3(PO4)2.3H2O after few weeks, thus limiting their use in industrial processes [START_REF] D'yvoire | Phosphates of Aluminium and Trivalent Iron[END_REF].

The heating of an aluminum dihydrogen-phosphate solution at a temperature between 600 and 700°C leads to the formation of an aluminum metaphosphate Al(PO3)3 binding agent. The different steps of formation of the aluminum metaphosphate from solutions of aluminum dihydrogenphosphate with ratios between 2 and 3.5 have already been studied [START_REF] Chen | Study on aluminum phosphate binder and related Al2O3-SiC ceramic coating[END_REF][START_REF] Han | Studies on Curing Chemistry of Aluminum-Chromium-Phosphates as Low Temperature Curable Binders[END_REF][START_REF] O'hara | Studies in phosphate bonding[END_REF][START_REF] Tricot | New insights into the thermal evolution of aluminophosphate solutions: A complementary XRD and solid state NMR study[END_REF][START_REF] Tsuhako | Formation of aluminum phosphates at low temperatures[END_REF][START_REF] Vippola | Thermal analysis of plasma sprayed oxide coatings sealed with aluminium phosphate[END_REF]. The heating of the solutions induces a polymerization of Al(H2PO4)3 into AlH2P3O10,xH2O and then into Al(PO3)3. A higher P/Al ratio of the initial solution increases the rate of the polymerization so the Al(PO3)3 is formed at lower temperatures. Al(PO3)3 was indeed already observed at 350°C after heating a solution with a ratio P/Al of 3.5. If the P/Al ratio is beyond 3, the excess of phosphorus leads to the presence of residual phosphoric acids after the heat treatment.

Since most applications of aluminophosphate materials are at high-temperatures, some authors studied the degradation of Al(PO3)3 with temperature [START_REF] Kniep | Orthophosphates in the Ternary System Al2O3-P2O5-H2O[END_REF][START_REF] Maier | The influence of aluminum phosphates on graphite oxidation[END_REF][START_REF] Rickles | The effect of heat upon inorganic cements[END_REF]. They showed that after heating the Al(PO3)3 phase above 1000°C, a weight loss is observed because Al(PO3)3 is degraded into AlPO4 and P2O5, the latter being volatile for temperatures above 600°C [START_REF] Haynes | CRC Handbook of Chemistry and Physics 97[END_REF]. At 1400°C, Al(PO3)3 melts and forms an aluminophosphate glass after quenching [START_REF] O'hara | Studies in phosphate bonding[END_REF][START_REF] Tsuhako | Formation of aluminum phosphates at low temperatures[END_REF].

In this contribution, we report further insights in the thermal degradation of aluminum metaphosphate. A solution of aluminum dihydrogen-phosphate with a P/Al ratio of 3.2 was used. This specific P/Al ratio solution was selected for its better stability,. After a heat treatment of the solution at 700°C (which allows the formation of the aluminum metaphosphate according to the literature), we conducted a study of the evolution of the aluminum metaphosphate at temperatures between 700 and 1000°C. Indeed, this range of temperatures can be of interest in some applications of the aluminum metaphosphate [START_REF] Balhadere | Procédé pour la protection contre l'oxydation de pièces en matériau composite contenant du carbone[END_REF][START_REF] Mazany | Oxidation inhibition of Carbon-Carbon composites[END_REF] and it has not been particularly investigated in the literature. Nowadays, the tendency is to decrease the elaboration temperature of the aluminophosphate materials at lower temperature such as 700°C, in order to decrease the associated energy cost. Thus, it is of importance to analyze the behavior of the aluminum metaphosphate between its temperature of elaboration and utilization. For instance, the presence of hydroxyl groups inside the aluminum metaphosphate after its elaboration can influence its properties when the material is used as a seal for electrical insulation (Berard, 2008;Norelli, 2016;Vetrivendan, 2017).

Thermogravimetric analyses coupled with mass spectroscopy were performed to study the degradation of the Al(PO3)3 until 1200°C. Structural data and new investigation on the presence and the localization of residual hydroxyls groups in the aluminum metaphosphate was performed by 31 P, 27 Al, 1 H and 31 P{ 1 H} cross polarization MAS NMR.

Experimental procedures

The aluminum metaphosphate (Al(PO3)3) sample has been prepared by the conventional procedure consisting in heating a solution of aluminum dihydrogen-phosphate (Al(H2PO4)3), which has been purchased to Budenheim Gmbh (Mainz). Since some variability of the P/Al atomic ratio of the commercial solution has been observed, it was checked by inductively coupled plasma method (ICP) on an ICP-OES Agilent 5100 machine. The measured P/Al ratio of the solution used was measured to be 3.2 ± 0.06. The heat treatment of the solution consisted in a first step of 2h at 220°C and a final step at 700°C for 1h. The heating rates between ambient temperature and 220°C is 1°C/min and the one between 200 and 700°C is 3°C/min. Thermogravimetric analysis coupled with mass spectroscopy (TGA-MS) analyses have been performed on a TG 92 from Setaram coupled with an Omnistar MS from Pfeiffer. The sample was placed in a platinum crucible and was heated at 5°C/min until a temperature of 1200°C under air.

For the gravimetric analyses, the aluminum metaphosphate powder has been placed in a platinum crucible, which was introduced in an oven at 1000 or 1200°C for different durations. The crucible was then taken out of the oven, cooled at ambient air and weighted with a 0.1mg precision.

The Magic Angle Spinning Nuclear Magnetic Resonance (MAS NMR) for 31 P, 1 H and cross polarization 31 P{ 1 H} experiments were performed at 9.4T on a Bruker spectrometer with a 3.2 mm triple channel probe operating at spinning frequency of 20 kHz. The relaxation delays/high power pulse for the 31 Pand 1 H were 300s/2µsand 120s/2.425µ,s respectively. The relaxation delay for the cross polarization 31 P{ 1 H} experiment, which permits the detection of the spatial proximity between the proton and the phosphorus nuclei, was 120s with a contact time of 2ms. . The 27 Al MAS NMR spectra were recorded at 18.8T on a Bruker spectrometer equipped with a 3.2 mm rotor spinning at 20 kHz.

The relaxation delay/high power pulse was 2s/1 µs.

Results

The 27 Al and 31 P (Figure 1 The gravimetric analyses achieved at temperatures of 1000 and 1200°C are shown in Figure 2.

A first weight loss of around 1% is observed after 5 min at 1000 and 1200°C. To make sure that this weight loss was not caused by adsorbed water on the surface of the sample, two samples were dried one night in an oven at 120°C, and the same weight loss of around 1% after 5 minutes at 1000 and 1200°C was found. This thus indicates that a specie is eliminated from the sample at a temperature bellow 1000°C. After the first 5 minutes, the weight loss increases linearly for both temperatures.

To investigate the first weight loss, thermogravimetric analysis coupled with mass spectroscopy of the aluminum metaphosphate was performed (Figure 3). Thermogravimetric analyses doesn't show any weight loss until 875°C. At this temperature, 1% of the mass is suddenly lost, which correlates with the 1% weight loss observed after the 5 first minutes in the previous gravimetric study.

Mass spectroscopy analysis of H2O shows a bump at 875°C, which corresponds to the first mass loss, and indicates the presence of -OH groups inside the sample. At 1000°C, a weight loss starts, which rate increases with temperature. As reported by Maier et al., this second weight loss corresponds to the decomposition of Al(PO3)3 into AlPO4 and P2O5 [START_REF] Maier | The influence of aluminum phosphates on graphite oxidation[END_REF].

The presence of -OH groups was investigated using 1 H (Figure 4) and 31 P{ 1 H} cross-polarization (Figure 5) MAS NMR. The 1 H spectrum (Figure 4) shows several resonances. The resonances at 1 and 7 ppm are attributed to the rotor signal and adsorbed water on the sample [START_REF] Ratcliffe | NMR Chemical shifts of dilute 1H in inorganic solids[END_REF][START_REF] Yesinowski | Hydrogen Environments in Calcium Phosphates : 1H MAS NMR at High Spinning Speeds[END_REF], respectively. The resonances at 11 and 16 ppm are attributed to -OH groups [START_REF] Mastikhin | 1H NMR and catalytic studies of surface hydroxyl groups in aluminium phosphate catalysts[END_REF][START_REF] Ratcliffe | NMR Chemical shifts of dilute 1H in inorganic solids[END_REF]. On the 31 P{ 1 H} CP MAS-NMR spectrum (Figure 5), a resonance centered at -31 ppm and a shoulder centered at -45ppm are observed, which indicate the presence of P-OH groups. The small signal on noise ratio of this CP experiment indicates that only a small amount of P-OH groups is present. It is worth noting that a HMQC 27 Al{ 1 H} MAS NMR experiment was also performed, but no signal was measured.

Further MAS NMR analyses were recorded to observe the evolution of the aluminum metaphosphate samples after the gravimetric analysis (2h at 1000 and 1200°C). 1 H MAS NMR spectra shows that there was less and no more -OH groups at 1000 and 1200°C, respectively (Figure 6).

Discussion

The gravimetric analyses show a first sudden weight loss that occurs after 5 minutes at 1000°C or 1200°C and then a continuous weight loss is observed for the two temperatures. Since the latter weight loss increases linearly with time, it has a zero order kinetic and can thus be attributed to a decomposition reaction of the aluminum metaphosphate. The NMR analyses of the sample heated 2h at 1200°C shows the formation of AlPO4, which confirms the decomposition of the Al(PO3)3 into P2O5 and AlPO4 [START_REF] Haynes | CRC Handbook of Chemistry and Physics 97[END_REF]. The formation of AlPO4 is hardly detectable at 1000°C as the amount of Al(PO3)3 that has been decomposed is negligible.

The first weight loss was never detected nor investigated in the literature. TGA-MS indicates that, despite the preparation temperature at 700°C seems high enough to obtain a full dehydration of the initial solution, some hydroxyls groups (-OH) remain in the sample after the heat treatment since H2O is detected for temperatures between 875 and 900°C. 1 H NMR confirms the presence of the -OH and the CP MAS NMR indicates that the -OH groups are localized on the PO4 3-cycles of the Al(PO3)3. Furthermore, the lack of HMQC 27 Al{ 1 H} MAS NMR indicates that these hydroxyl groups are not present as Al-OH groups. These hydroxyls groups are thus present only as P-OH bonds, and despite the weak CP intensity, the resonances are found at chemical shifts close to those of [A] and [B] aluminum metaphosphate forms, thus indicating that P-OH groups are present on both forms. These P-OH groups are thus probably present as defects on the metaphosphate cycles. It is worth noting that the presence of such residual hydroxyl groups has also been detected in other phases like silica [START_REF] Merle | 17O NMR Gives Unprecedented Insights into the Structure of Supported Catalysts and Their Interaction with the Silica Carrier[END_REF]. When heated at a temperature above 875°C, these hydroxyl groups are decomposed and evaporate as H2O, causing the weight loss on the TGA

Conclusion

We conclude that the conventional heat treatment reported in the literature used to prepare aluminum metaphosphate from aluminum dihydrogen-phosphate solution is efficient, but some residual hydroxyls groups are still present in the product. TGA-MS and NMR analyses indeed show the presence of P-OH groups in the aluminum metaphosphate heated at 700°C. These hydroxyl groups are decomposed into H2O at a temperature above 875°C. A heat treatment of 2h at 1200°C enables to prepare P-OH-free aluminum metaphosphate.

  ) MAS NMR results indicate the presence of the [B] form of Al(PO3)3 (-15 ppm resonance on the 27 Al spectrum and -36, -37, -43 ppm resonances on the 31 P spectrum [ref]) and also of the [A] form (-21.5 ppm resonance on the 27 Al and -50.6 ppm resonance on the 31 P spectrum [ref] ). D'Yvoire (D'Yvoire, 1960) reported that 6 forms of Al(PO3)3 (denominated [A], [B], [C], [D], [E] and [F]) can be obtained. After a heat treatment of an aluminum dihydrogen-phosphate solution at 700°C, [A] and [B] forms have been observed, with ratios depending on the P/Al ratio [ref]. The higher the ratio is, the higher the quantity of [A] formed is. Al(PO3)3 [A] is a tetrametaphosphate composed of cycles of 4 tetrahedral PO4 3-, while Al(PO3)3 [B] is a hexametaphosphate composed of cycles of 6 PO4 3-. The [B] form of Al(PO3)3 is metastable and is converted into the [A] form above 800°C (O'Hara, 1972).

  27 Al and 31 P (Figure 7) MAS NMR spectra exhibit two resonances, at -21.5 and -50.6 ppm on the 27 Al and 31 P spectra, respectively, which show that only the [A] Al(PO3)3 form remains at these temperatures. In addition, resonances at 40 and -28 ppm on the 27 Al and 31 P spectra, respectively, are attributed to AlPO4 [ref].

Figures

  Figures

Figure 1 :

 1 Figure 1 : 27 Al (a) and 31 P (b) MAS NMR spectra of aluminum metaphosphate.

  Figure 1 : 27 Al (a) and 31 P (b) MAS NMR spectra of aluminum metaphosphate.

Figure 2 :

 2 Figure 2 : Gravimetric analysis of aluminum metaphosphate.

Figure 3 :

 3 Figure 3 : Thermogravimetric analysis (top) and MS detection of H2O (m=18) (bottom) of aluminum metaphosphate.

Figure 4

 4 Figure 4 : 1 H MAS NMR spectrum of aluminum metaphosphate.

Figure 5 :

 5 Figure 5 : 31 P{ 1 H} CP MAS NMR spectrum of aluminum metaphosphate

Acknowledgements

The authors would like to thank Bertrand Doumert for the NMR spectra acquisition.

The authors thank the Chevreul Institute (FR 2638), Ministère de l'Enseignement Supérieur, de la Recherche et de l'Innovation, Hauts-de-France Region and FEDER are acknowledged for supporting and funding partially this work.