Elise Delaforge

Tiago N Cordeiro

Pau Bernadó

Nathalie Sibille
email: nathalie.sibille@cbs.cnrs.fr

Conformational Characterization of Intrinsically Disordered Proteins and Its Biological Significance

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Introduction

During the last decades, intrinsically disordered proteins (IDPs) have been revealed as pivotal actors in diverse biological processes. Indeed, it has been demonstrated that the characterization of intrinsically disordered proteins (IDPs) or domains is needed as more than 30 % of eukaryotic proteins have disordered regions of length equal or superior to 50 consecutive residues. These proteins, that lack stable tertiary and/or secondary structures, are more common in Eukaryota than in Bacteria and Archaea [START_REF] Ward | Prediction and Functional Analysis of Native Disorder in Proteins from the Three Kingdoms of Life[END_REF], probably due to their biological complexity. IDPs have a very specific amino acid composition that is rich in charged, structure-breaking residues (proline and glycine), and in alanine, while they are depleted in order-promoting amino acids such as hydrophobic and aromatic residues [START_REF] Habchi | Introducing Protein Intrinsic Disorder[END_REF].

IDPs are associated to distinct and complementary functions and localizations to these of their globular counterparts. Order is found in enzymes performing catalytic functions, whereas disordered is linked to signalling, regulation, and transport. A key aspect to explain this preponderance is linked to how disordered chains recognize their partners. Partner recognition of IDPs is normally performed through short linear motifs (SLiMs) that are embedded in disordered poorly conserved regions. A crucial feature of IDPs lies on the entropic cost associated to the disorder-to-order transitions observed in SLiMs upon partner recognition. This entropic cost very often implies low to moderate affinities. This particularity in combination with the high specificity of the interactions, make IDPs very well suited agents for signalling processes [START_REF] Tompa | Intrinsically disordered proteins: emerging interaction specialists[END_REF]. It also explains the capacity of many IDPs to present one-to-many and many-to-one interactions, or binding promiscuity, explaining the enrichment of disorder in interactome hubs [START_REF] Dunker | Flexible nets. The roles of intrinsic disorder in protein interaction networks[END_REF] [START_REF] Uversky | Intrinsically disordered proteins in human diseases: introducing the D2 concept[END_REF]. Moreover, many IDPs are submitted to additional regulation processes governed by alternative splicing and posttranslational modifications (PTMs) (i.e. phosphorylation, acetylation, N-or O-linked glycosylation, methylation, ubiquitination…), which are facilitated by the accessibility of modifying enzymes to disordered chains. Given the important number of above-mentioned sensitive biological processes linked with disorder, it is not surprising that the vast majority of proteins involved in cancer, cardiovascular diseases or neurodegeneration are predominantly disordered.

The relevance of disorder in biology and disease has fostered and intensified research aiming at deciphering the structural basis of their function. In that context, Nuclear Magnetic Resonance (NMR) is the most adapted structural biology technique to address these questions. In this chapter, we describe how NMR can probe the structural and dynamic properties of IDPs at residue level. Its sensitivity to changes in the chemical environment enables NMR to monitor partnerrecognition processes or the incorporation of PTMs [START_REF] Landrieu | NMR analysis of a Tau phosphorylation pattern[END_REF][START_REF] Sugase | Mechanism of coupled folding and binding of an intrinsically disordered protein[END_REF][START_REF] Sibille | Structural characterization by nuclear magnetic resonance of the impact of phosphorylation in the proline-rich region of the disordered Tau protein[END_REF]. We also address the technical and conceptual challenges associated to ensemble representations, and how the combination of multiple NMR parameters and/or information from other techniques can help to obtain more accurate conformational ensembles of IDPs and their complexes.

Frequency Assignment

Several features of IDPs complicate their NMR frequency assignment. First, they display low amide proton dispersion (7.5 to 8.5 ppm), resulting in crowded spectrum, which has been a bottleneck to frequency assignment in the past [START_REF] Dyson | Unfolded proteins and protein folding studied by NMR[END_REF]. However, the availability of spectrometers of increasingly high magnetic field (up to 1 GHz), and the possibility to record high dimensional NMR spectra in reasonable time thanks to non-uniform sampling have led to a significant improvement of the capacity to resolve this crowding [START_REF] Yao | A six-dimensional alpha proton detection-based APSY experiment for backbone assignment of intrinsically disordered proteins[END_REF]. Alternatively, in the case of very large proteins, a "divideand-conquer" approach is often used to reduce the complexity of the spectra [START_REF] Mark | Characterization of segments from the central region of BRCA1: an intrinsically disordered scaffold for multiple protein-protein and protein-DNA interactions?[END_REF].

Second, the amino acid composition found in IDPs, which can be highly repetitive and enriched in prolines, often cause difficulties for frequency assignment [START_REF] Uversky | Why are "natively unfolded" proteins unstructured under physiologic conditions?[END_REF],13]. Prolines can be either in cis or trans conformation, and they interconvert on a slow timescale, leading to the existence of a second population of resonances in the spectrum [START_REF] Biasio | P15PAF Is an intrinsically disordered protein with nonrandom structural preferences at sites of interaction with other proteins[END_REF]. To overcome this issue, Hα and carbon detection are increasingly used, allowing to find chain connectivities independently to the presence of prolines [START_REF] Bermel | Protonless NMR Experiments for Sequence-Specific Assignment of Backbone Nuclei in Unfolded Proteins[END_REF].

An especially difficult case for the assignment is the presence of Low-Complexity Regions (LCRs), which correspond to protein segments with a very high amino acid composition bias. Homorepeats, long stretches of the same amino acid, are specially eye-catching examples of LCRs and often linked to human diseases [START_REF] Jorda | Protein homorepeats sequences, structures, evolution, and functions[END_REF]. LCRs in general and homorepeats in particular represent especially difficult case for NMR assignment due to the similar chemical environment of these residues; the result is a more crowded spectrum that prevents conventional assignment. A recent study on a N-terminal region of the androgen receptor containing 25 consecutive glutamines demonstrated that in some circumstances the assignment of homorepeats can be achieved [START_REF] Eftekharzadeh | Sequence Context Influences the Structure and Aggregation Behavior of a PolyQ Tract[END_REF].

Finally, the exchange rate of amide protons with water molecules in IDPs is fast due to large solvent exposition of their backbone. Fortunately, IDPs are usually stable at a wide range of pH, which allows one to work at pH below 7, typically pH 6, to reduce the exchange rate [START_REF] Kim | Fast hydrogen exchange affects 15N relaxation measurements in intrinsically disordered proteins[END_REF]. Moreover, due to their high flexibility, IDPs give rise to narrow high intensity resonances. Lowering temperature can thus also be used to reduce the exchange whilst retaining a good quality spectrum.

A significant research effort has also been devoted in recent years to automate the assignment of IDPs, and several software packages have been developed to speed-up this tedious but unavoidable process [START_REF] Baran | Automated Analysis of Protein NMR Assignments and Structures[END_REF]. One of the most striking recent achievements was the automated assignment of Tau protein (441 amino acids) using 5D and 7D spectra, GAPRO for cross-peaks picking, and MARS for automated assignment, resulting in 92 % of assigned residues within 5 days -including the time to record spectra [START_REF] Narayanan | Automatic assignment of the intrinsically disordered protein Tau with 441-residues[END_REF].

NMR Observables

NMR is a rich source of structural and dynamic information for IDPs. Multiple NMR observables can be measured and they can probe local and global characteristics of disordered proteins. Importantly, NMR parameters correspond to time-and ensemble-averaged values due to the fact that the interconversion rate between different co-existing conformations is faster than the chemical shifts time-scale (ms). This averaging process must be considered when using these parameters to built structural models (see below). In this section, we succinctly describe the most relevant NMR parameters that are used for the structural and dynamic characterization of IDPs by NMR.

Chemical shifts

The chemical shift (CS) is the most directly accessible parameter of a NMR spectrum, and given its sensitivity to the chemical environment of the nucleus, it contains information relative to the presence of secondary structure. Using the secondary chemical shift (SCS), i.e. the difference between the observed chemical shift and the chemical shift of the same amino acid in a random coil conformation, it is possible to determine the structural propensities within an IDP [START_REF] Wishart | The chemical shift index: a fast and simple method for the assignment of protein secondary structure through NMR spectroscopy[END_REF]. Indeed, the SCS of a carbon alpha (CA) or carbonyl (CO) will be positive in the case of helical propensity and negative in the case of β-strand or extended propensity, whereas a carbon beta (CB), nitrogen (N), aliphatic (HA), and amide (HN) proton chemical shifts will display the opposite behaviour. However, since IDPs are not -fully -structured, the SCS values obtained are small, and require the use of reliable databases for the random coil values. Several databases have been created to obtain these reference chemical shifts following different rationale. The earliest database was created using the chemical shifts of individual amino acids inserted in the middle of a glycine peptide (GGXGG) in 8 M Urea at pH 2, and using a correction for residues following prolines [START_REF] Wishart | 1H, 13C and 15N random coil NMR chemical shifts of the common amino acids. I. Investigations of nearest-neighbor effects[END_REF]. More recently, other databases were created, including correction factor for all amino-acids [START_REF] Schwarzinger | Sequencedependent correction of random coil NMR chemical shifts[END_REF] and using QQXQQ peptides, with the rationale that glycines were not representative amino acids, using a lower denaturant concentration, and at neutral pH to better represent physiological conditions [START_REF] Kjaergaard | Sequence correction of random coil chemical shifts: correlation between neighbor correction factors and changes in the Ramachandran distribution[END_REF]. Following a different approach, Tamiola and Mulder created a random coil database (ncIDP) [START_REF] Tamiola | Sequence Specific Random Coil Chemical Shifts of Intrinsically Disordered Proteins[END_REF]. In their study, the CSs of 14 native IDPs were used to parameterize a database that uses both leftand right-neighbour correction factors, improving considerably the accuracy of chemical shift prediction for natively unfolded proteins. As the deviation from random coil behaviour can be subtle in the case of IDPs, one further step of analysis of SCSs was the addition of the contributions coming from CA and CB, which are insensitive to errors from chemical shift referencing [START_REF] Zhang | RefDB: a database of uniformly referenced protein chemical shifts[END_REF]. For example, the SSP algorithm developed by Julie Forman-Kay's laboratory calculates the SCS using the RefDB random coil chemical shifts (which uses all CS from the BioMagResBank (BMRB)), and computes a secondary structure propensity (SSP) score using a smoothing function over five residues of the CA and CB SCS (Figure 1A) [START_REF] Marsh | Sensitivity of secondary structure propensities to sequence differences between alpha-and gamma-synuclein: implications for fibrillation[END_REF].

CSs are also a powerful tool to study PTMs, which often participate in the regulation of IDPs interactions. The most commonly studied PTM by NMR is phosphorylation, but it is also possible to follow glycosylation, acetylation, methylation, oxidation, propionylation… [START_REF] Theillet | Cell signaling, post-translational protein modifications and NMR spectroscopy[END_REF]. NMR allows not only to identify the presence of a PTM on a protein, to locate it at the sequence level, but also to follow its kinetics [START_REF] Landrieu | NMR analysis of a Tau phosphorylation pattern[END_REF][START_REF] Cordier | Ordered phosphorylation events in two independent cascades of the PTEN C-tail revealed by NMR[END_REF] and the structural changes it causes [START_REF] Sibille | Structural characterization by nuclear magnetic resonance of the impact of phosphorylation in the proline-rich region of the disordered Tau protein[END_REF][START_REF] Baker | CFTR regulatory region interacts with NBD1 predominantly via multiple transient helices[END_REF], which are key to understand the role of PTMs in the context of partner recognition [START_REF] Okuda | Real-time and simultaneous monitoring of the phosphorylation and enhanced interaction of p53 and XPC acidic domains with the TFIIH p62 subunit[END_REF].

Scalar Couplings (J)

Another parameter that contains backbone structural information is the scalar coupling. In particular, the relation between the 3 JHNHA and the dihedral torsion angle Φ of the peptide bond is described by the Karplus equation [START_REF] Karplus | Vicinal Proton Coupling in Nuclear Magnetic Resonance[END_REF]: 𝐽 ! (ϕ) = A cos " 𝜙 + B cos 𝜙 + C . Several parameterizations of this equation have been made over the years, the most recent one is A=7.97 Hz, B=-1.26 Hz, and C=0.63 Hz [START_REF] Vögeli | Limits on Variations in Protein Backbone Dynamics from Precise Measurements of Scalar Couplings[END_REF]. Traditionally, the measurement of 3 JHNHA couplings in proteins can be obtained using a 3D 15 N-separated quantitative J-correlation spectrum [START_REF] Vuister | Quantitative J correlation: a new approach for measuring homonuclear three-bond J(HNH.alpha.) coupling constants in 15N-enriched proteins[END_REF]. Recently, the accurate measurement of these couplings, directly from splittings in the 1 H dimension of a WATERGATE-optimized 1 H-15 N TROSY-HSQC spectrum, have been reported for IDPs [START_REF] Roche | Accurate measurement of (3)J(HNHalpha) couplings in small or disordered proteins from WATERGATE-optimized TROSY spectra[END_REF]. Secondary structure propensities are reflected in the measured 3 JHNHA coupling values. Residues in helices display couplings below 5 Hz, in random coil between 6 and 8 Hz, and in extended structures more than 8 Hz. An advantage of 3 JHNHA compared to CSs is that it is possible to distinguish type II polyproline helix (PPII) structures from β-strands. Indeed, residues in PPII have a 3 JHNHA coupling value slightly higher than those of helices, between 5 and 6 Hz, due to the fact that PPII is a relatively open structure and has no intramolecular hydrogen bond [START_REF] Oh | A comprehensive library of blocked dipeptides reveals intrinsic backbone conformational propensities of unfolded proteins[END_REF]. As all the other NMR parameters, 3 JHNHA scalar couplings are time-and ensemble-averaged values, thus transiently populated secondary structures are difficult to identify. One solution could be, as for CSs, to subtract the value of a random coil 3 JHNHA coupling from the experimental data to locate deviations due to the presence of transient secondary structures. However, the only random coil 3 JHNHA databases that exist were either measured in the presence of a chemical denaturant (guanidinium chloride), or predicted from coil regions of crystallographic structures, and may thus not be representative of native IDPs [START_REF] Plaxco | The effects of guanidine hydrochloride on the "random coil" conformations and NMR chemical shifts of the peptide series GGXGG[END_REF][START_REF] Smith | Analysis of main chain torsion angles in proteins: prediction of NMR coupling constants for native and random coil conformations[END_REF].

Residual Dipolar Couplings (RDCs)

The most sensitive and accurate parameters reporting on IDP conformation are residual dipolar couplings (RDCs) measured by partially aligning the studied protein in solution [START_REF] Tjandra | Direct measurement of distances and angles in biomolecules by NMR in a dilute liquid crystalline medium[END_REF]. RDCs have been widely used to study the structure of multi-domain molecules but their use for IDPs has increased over the past few years and robust tools for predicting their values for both globular and disordered proteins have been developed [START_REF] Prestegard | Residual dipolar couplings in structure determination of biomolecules[END_REF][START_REF] Huang | Direct prediction of NMR residual dipolar couplings from the primary sequence of unfolded proteins[END_REF][START_REF] Kosol | Structural Characterization of Intrinsically Disordered Proteins by NMR Spectroscopy[END_REF]. In the case of IDPs, measured RDCs report on the orientation of the measured bond vector averaged over all existing conformers co-existing in solution. Although resulting RDCs are small due to the averaging process, they are measurable due to the inherent elongated structure of disordered chains [START_REF] Louhivuori | On the origin of residual dipolar couplings from denatured proteins[END_REF]. However, secondary structure elements have a statistically averaged preferential orientation with respect to the magnetic field. For helices, the N-H bond vectors tend to be parallel to the magnetic field giving rise to more positive RDC values, whereas for extended structures, such as PPII or β-strands, the N-H bond vectors are on average orthogonal to the magnetic field yielding to more negative RDC values (Figure 1B) [START_REF] Jensen | Quantitative conformational analysis of partially folded proteins from residual dipolar couplings: application to the molecular recognition element of Sendai virus nucleoprotein[END_REF]. In addition to local conformational bias, RDCs also report on long-range intramolecular interactions by modulating the RDC profile along the chain [START_REF] Bernado | Defining longrange order and local disorder in native alpha-synuclein using residual dipolar couplings[END_REF]. However, decomposing both contributions is difficult. Many alignment media have been developed so far: PEG-alcohol, bicelles, stretched or compressed acrylamide gels, filamentous phages… [START_REF] Prestegard | Partial alignment of biomolecules: an aid to NMR characterization[END_REF] When measuring RDCs, one has to be extremely careful that the studied protein does not interact with or is not disturbed by the alignment medium: constant line width of the signal and no significant chemical shift differences with respect to a non-aligned sample must be observed. Indeed, strong electrostatic interaction can intervene decrease the tumbling rate of the protein concomitantly causing increased signal line-widths, as for example with filamentous phages, which are negatively charged and can thus interact with positively charged parts of a protein.

Dynamics via Relaxation parameters

The combination of the longitudinal (R1), transverse (R2) relaxation rates and heteronuclear cross relaxation effect -or Nuclear Overhauser Effect (het-NOE) -of 15 N nuclei has been extensively used to study protein dynamics in solution (Figure 1C,D) [START_REF] Korzhnev | NMR studies of Brownian tumbling and internal motions in proteins[END_REF]. These rates report on motions faster than the correlation time of the protein (in the range of tenths of picoseconds to tenths of nanosecond). In the case of IDPs, the interpretation of relaxation rates is highly complex and is most often used in a qualitative manner applying the reduced spectral density mapping [START_REF] Bracken | NMR spin relaxation methods for characterization of disorder and folding in proteins[END_REF][START_REF] Peng | Mapping of the spectral densities of N-H bond motions in eglin c using heteronuclear relaxation experiments[END_REF]. This approach translates the relaxation rates in the probability function of finding motions at specific angular frequencies, J(ω), thereby allowing the qualitative assessment of flexibility at residue level and thus permitting the localization of secondary structure formation segments. More recently, a specific mathematical framework has been proposed for the interpretation of relaxation rates in disordered proteins. It has been demonstrated in an extensive study of relaxation rates in Sendai virus' archetypal IDP, NTAIL, showed that three dynamic modes are involved in IDPs dynamics: librational motions, local backbone sampling of the Ramachandran space, and segmental motions [START_REF] Abyzov | Identification of Dynamic Modes in an Intrinsically Disordered Protein Using Temperature-Dependent NMR Relaxation[END_REF].

Paramagnetic Relaxation Enhancement (PRE)

Long-range contacts influence the NMR parameters such as RDCs and need to be taken into account to get a more realistic structural description of IDPs [START_REF] Uversky | Seven lessons from one IDP structural analysis[END_REF]. By attaching a paramagnetic probe such as nitroxide spin label or a lanthanide to a specific residue on a protein, one can measure its influence on residues that are close -transiently or not -in space -up to 25-30 Å to the label [START_REF] Gillespie | Characterization of long-range structure in the denatured state of staphylococcal nuclease. I. Paramagnetic relaxation enhancement by nitroxide spin labels[END_REF]. Depending on the paramagnetic probe used, the effect on the surrounding residues is different. Some probes, such as lanthanides, induce a change of the chemical shift of nearby nuclei. These pseudo contact shifts (PCS) give information on the orientation between the observed nucleus and the paramagnetic center relative to the magnetic susceptibility tensor induced to the protein [START_REF] Yagi | Three-dimensional protein fold determination from backbone amide pseudocontact shifts generated by lanthanide tags at multiple sites[END_REF]. Other useful probes are stable free radicals, which increase the relaxation of nearby nuclei proportionally to the inverse sixth power of the distance to the probe (Figure 1E). This second type of probes is the most commonly used for IDPs as it only induces a line shape broadening of the signal corresponding to nuclei in the proximity of the paramagnetic center, due to a transverse paramagnetic relaxation enhancement (PRE). Common probes include MTSL spin label or 3-(2-iodoacetamido)-proxyl (PROXYL), which can be attached to a cysteine residue via a disulphide bond or a C-S bond, respectively [START_REF] Berliner | A novel reversible thiol-specific spin label: papain active site labeling and inhibition[END_REF][START_REF] Ramos | A New Method To Detect Long-Range Protein-RNA Contacts: NMR Detection of Electron-Proton Relaxation Induced by Nitroxide Spin-Labeled RNA[END_REF]. The latter is often preferred due to of its stability in presence of reducing agents that are needed, for example for interaction experiments with a cysteine containing protein. These probes can easily be reduced, commonly using ascorbic acid. Therefore, the same sample can the be used for the measurement of both the paramagnetic and diamagnetic conditions, allowing simple analysis of the data using the intensity ratio Ipara/Idia extracted from 1 H-15 N HSQC spectra, avoiding normalization issues and sample preparation imprecisions.

From NMR Parameters to Conformational Ensembles

As described in previous sections, NMR represents an especially rich source of information to structurally and dynamically characterize IDPs. Importantly, through different observables, NMR offers information at the local (residue) level, but also on the overall size, and the presence of longrange interactions between remote positions of the chain [START_REF] Jensen | Exploring free-energy landscapes of intrinsically disordered proteins at atomic resolution using NMR spectroscopy[END_REF][START_REF] Jensen | Describing intrinsically disordered proteins at atomic resolution by NMR[END_REF]. However, NMR structural parameters are ensemble-and time-averaged observables, and therefore they have to be interpreted in a framework accounting for the coexistence of multiple conformations [START_REF] Kruschel | Conformational averaging in structural biology: issues, challenges and computational solutions[END_REF]. Although this feature is general for all kinds of biomolecules, IDPs represents an especially significant challenge due to their vast and flat conformational landscape. The number of degrees of freedom required to accurately describe disordered proteins is much larger than the amount of information that can be recorded experimentally. During the last decade multiple approaches have appeared to alleviate this intrinsic problem. The common feature of all these strategies is the application of sophisticated computational approaches that use previous knowledge on the chemical nature of peptide chains to reduce the number of degrees of freedom. The final aim is to have a description of the protein of interest that identifies its structural features and to link them with a specific biological function [START_REF] Eliezer | Biophysical characterization of intrinsically disordered proteins[END_REF]. In the following paragraphs we will succinctly describe the different approaches used to derive structural ensembles of IDPs using NMR data.

Two general approaches have been developed in order to derive conformational ensembles from NMR data. The first one uses restrained Molecular Dynamics (MD) simulations by running in parallel multiple copies of the same molecule that collectively provide a good description of the experimental data used as restraints [START_REF] Vendruscolo | Determination of conformationally heterogeneous states of proteins[END_REF]. This approach combines an empirical energy force field with experimental information, and it is philosophically equivalent to the classical simulated annealing approaches for the structural determination of globular proteins by NMR. Restrained MD simulations have been applied to describe CSs [START_REF] Robustelli | Interpreting protein structural dynamics from NMR chemical shifts[END_REF], PREs [START_REF] Allison | Determination of the free energy landscape of alpha-synuclein using spin label nuclear magnetic resonance measurements[END_REF][START_REF] Ganguly | Structural interpretation of paramagnetic relaxation enhancementderived distances for disordered protein states[END_REF], and RDCs [START_REF] Esteban-Martin | Refinement of ensembles describing unstructured proteins using NMR residual dipolar couplings[END_REF] or their combination [START_REF] Huang | Ensemble calculations of unstructured proteins constrained by RDC and PRE data: a case study of urea-denatured ubiquitin[END_REF][START_REF] Wu | Structural reorganization of alpha-synuclein at low pH observed by NMR and REMD simulations[END_REF]. In these approaches, it remains unclear how the introduction of experimental restrains affects the exploration of the conformational space, which is key point for solving underdetermined problems. To ensure a more extensive sampling, some authors use Replica Exchange Molecular Dynamics (REMD), where conformations are exchanged between parallel simulations according to a Monte Carlo criteria [START_REF] Cavalli | Molecular dynamics simulations with replicaaveraged structural restraints generate structural ensembles according to the maximum entropy principle[END_REF]. Another inherent limitation of the approach is the potential inaccuracy of present force fields to describe disordered protein conformational fluctuations and solvent behaviour. The improvement of force fields to adapt them to study IDPs is a very active field of research [START_REF] Henriques | Molecular Dynamics Simulations of Intrinsically Disordered Proteins: Force Field Evaluation and Comparison with Experiment[END_REF][START_REF] Mercadante | Kirkwood-Buff Approach Rescues Overcollapse of a Disordered Protein in Canonical Protein Force Fields[END_REF].

The second approach is based on the selection from a large ensemble of a subset of conformations that collectively describe the experimental data. This approach aims at enriching the ensemble with the conformations containing the structural features that are coded in the experimental data [START_REF] Jensen | Describing intrinsically disordered proteins at atomic resolution by NMR[END_REF]. The generation of the initial pool is a key aspect of the approach, and it should explore as broadly as possible the conformational landscape of the protein. To achieve this aim, enhanced sampling approaches based on MD simulations have been used [START_REF] Mukrasch | Highly populated turn conformations in natively unfolded tau protein identified from residual dipolar couplings and molecular simulation[END_REF][START_REF] Fisher | Modeling intrinsically disordered proteins with bayesian statistics[END_REF]. Alternatively, the conformational space can be sampled using simpler approaches based on statistical coil models derived from the backbone dihedral angle of loop regions of crystallographic structures [START_REF] Smith | Analysis of main chain torsion angles in proteins: prediction of NMR coupling constants for native and random coil conformations[END_REF][START_REF] Fitzkee | The Protein Coil Library: a structural database of nonhelix, nonstrand fragments derived from the PDB[END_REF][START_REF] Jha | Statistical coil model of the unfolded state: resolving the reconciliation problem[END_REF][START_REF] Bernado | A structural model for unfolded proteins from residual dipolar couplings and small-angle xray scattering[END_REF][START_REF] Ozenne | Flexible-meccano: a tool for the generation of explicit ensemble descriptions of intrinsically disordered proteins and their associated experimental observables[END_REF]. In the absence of secondary structural elements or long-range contacts, Flexible-Meccano (FM), which is the most widely used statistical coil model, can describe conformational fluctuations at residue level probed by RDCs and the overall dimensions of the ensemble reported by SAXS [START_REF] Bernado | A structural model for unfolded proteins from residual dipolar couplings and small-angle xray scattering[END_REF]. Importantly, the presence of scarcely populated secondary structure or transient long-range contacts can be validated by comparing conformationally biased FM ensembles with experimental RDCs, CSs or PREs [START_REF] Biasio | P15PAF Is an intrinsically disordered protein with nonrandom structural preferences at sites of interaction with other proteins[END_REF][START_REF] Bernado | Defining longrange order and local disorder in native alpha-synuclein using residual dipolar couplings[END_REF][START_REF] Wells | Structure of tumor suppressor p53 and its intrinsically disordered N-terminal transactivation domain[END_REF][START_REF] Perez | Structural characterization of the natively unfolded N-terminal domain of human c-Src kinase: insights into the role of phosphorylation of the unique domain[END_REF].

In IDPs, the need to simultaneously describe both local conformations and overall features has prompted strategies with the capacity to integrate multiple NMR observables in combination with other biophysical measurements. Among these approaches, the programs ENSEMBLE [START_REF] Choy | Calculation of ensembles of structures representing the unfolded state of an SH3 domain[END_REF][START_REF] Krzeminski | Characterization of disordered proteins with ENSEMBLE[END_REF] and ASTEROIDS [START_REF] Salmon | NMR characterization of long-range order in intrinsically disordered proteins[END_REF][START_REF] Nodet | Quantitative description of backbone conformational sampling of unfolded proteins at amino acid resolution from NMR residual dipolar couplings[END_REF][START_REF] Ozenne | Mapping the potential energy landscape of intrinsically disordered proteins at amino acid resolution[END_REF] are the two most popular ones. The combination of RDCs and PREs is especially useful as PREs probe long-range intramolecular contacts whereas RDCs probe both local and long-range features but both contributions are difficult to deconvolute [START_REF] Huang | Direct prediction of NMR residual dipolar couplings from the primary sequence of unfolded proteins[END_REF]. When applying this combination to α-synuclein, it was unambiguously proven that an interaction between the N-and C-termini of the protein [START_REF] Salmon | NMR characterization of long-range order in intrinsically disordered proteins[END_REF]. Residue-specific NMR information can also be complemented with information reporting on the fluctuations of the overall properties of the ensemble such as SAXS [START_REF] Sibille | Structural characterization of intrinsically disordered proteins by the combined use of NMR and SAXS[END_REF][START_REF] Cordeiro | Smallangle scattering studies of intrinsically disordered proteins and their complexes[END_REF] or smFRET [START_REF] Delaforge | Large-Scale Conformational Dynamics Control H5N1 Influenza Polymerase PB2 Binding to Importin alpha[END_REF].

It is widely recognized that a conformational ensemble that is in agreement with experimental data is not necessarily a proof of its accuracy [START_REF] Jensen | Exploring free-energy landscapes of intrinsically disordered proteins at atomic resolution using NMR spectroscopy[END_REF][START_REF] Kruschel | Conformational averaging in structural biology: issues, challenges and computational solutions[END_REF]. The reliability of an ensemble is increased when multiple experimental parameters reporting with different sensitivity on similar features are integrated in the same minimization. Some strategies have bee developed to assess the accuracy of data-driven ensembles. Cross-validation represents a very useful strategy to assess model accuracy, although it requires extensive experimental information. In cross-validation, a fraction of the experimental data is not used for the minimization and the capacity of the final model to describe these non-used data is evaluated. This strategy has been applied for the characterization of longrange interaction in Tau protein using 11 PRE datasets [START_REF] Bibow | Structural impact of proline-directed pseudophosphorylation at AT8, AT100, and PHF1 epitopes on 441-residue tau[END_REF], and for the same protein and αsynuclein using an extensive NMR dataset including CSs, RDCs, PREs and SAXS [START_REF] Schwalbe | Predictive Atomic Resolution Descriptions of Intrinsically Disordered hTau40 and α-Synuclein in Solution from {NMR} and Small Angle Scattering[END_REF]. An alternative to cross validation is the use of Bayesian statistics [START_REF] Fisher | Constructing ensembles for intrinsically disordered proteins[END_REF]. In this approach, the relative population of all members of the initial ensemble and (importantly) their uncertainty are defined based on the experimental data [START_REF] Fisher | Modeling intrinsically disordered proteins with bayesian statistics[END_REF][START_REF] Ullman | Explaining the structural plasticity of alpha-synuclein[END_REF]. The development of robust strategies to derive and validate ensemble models of IDPs is one of the future directions of the field. In that context, databases collecting experimental data and derived ensembles can be highly valuable [START_REF] Varadi | pE-DB: a database of structural ensembles of intrinsically disordered and of unfolded proteins[END_REF].

NMR Studies of Disordered Proteins Complexes

With their flexibility and inherent plasticity, IDPs play an important role in protein-protein interactions in many cellular processes, such as signalling and regulation of gene expression. Providing a comprehensive description of the biomolecular recognition processes for IDPs is thus of great importance for the understanding of key biological functions that are orchestrated by this family of proteins. Despite their relevance, detailed experimental evidence of binding mechanisms employed by disordered proteins is still scarce. In this regard, NMR has been used to establish and characterize the vital role of protein disorder in the formation of biomolecular complexes. These highly flexible complexes are challenging or even impossible to study by crystallography. Although the study of these flexible complexes can be nicely complemented by other structural techniques, such as SAXS, the ability to build structural ensembles and to map dynamics of IDPs within complexes at the atomic scale makes NMR a unique tool.

Many IDPs present conformational bias at specific regions of the chain, which very often are associated to protein-protein interaction sites. An example of IDP that has been structurally characterized studied in its free state and in complex with its natural partner is the proliferatingcell-nuclear-antigen-associated factor (p15 PAF ), which is overexpressed in several types of human cancer. Although highly flexible, this protein populates a complex equilibrium of conformations in its free state, comprising partially structured states at specific segments of the protein. NMR relaxation and RDC analysis revealed that those segments coincide with functional binding sites, such as the PCNA interacting protein motif (PIP-box) and the KEN-box, which is recognized by the ubiquitin ligase to target p15 PAF for degradation [START_REF] Biasio | P15PAF Is an intrinsically disordered protein with nonrandom structural preferences at sites of interaction with other proteins[END_REF]. In complex with Proliferating Cell Nuclear Antigen (PCNA), p15 PAF remains highly flexible with the exception of the PIP-box that binds with moderate affinity to PCNA adopting a conformation close to that found in its free state [START_REF] Biasio | Structure of p15(PAF)-PCNA complex and implications for clamp sliding during DNA replication and repair[END_REF][START_REF] Cordeiro | Disentangling polydispersity in the PCNA-p15PAF complex, a disordered, transient and multivalent macromolecular assembly[END_REF].

As in the case of p15 PAF , many IDPs present pre-formed structures in the free state that resemble theses of the bound state ("conformational selection"), which influence the binding affinity and the interaction kinetics. In other cases, the binding site undergoes a conformational transition only after association with the target ("induced fit"). These are two extreme cases, and generally both mechanisms co-exist and proteins present a disorder-to-order transition upon binding to their partner, referred to as the coupled folding and binding mechanism [START_REF] Wright | Linking folding and binding[END_REF].

NMR relaxation dispersion probes protein dynamics in the microsecond to millisecond time range providing atomic resolution insights into coupled folding and binding processes of IDPs. This is exemplified in the of the folding upon binding process of the phosphorylated kinaseinducible activation domain (pKID) of the transcription factor CREB upon binding to its target, the KIX domain of the transcriptional co-activators CBP/p300 [START_REF] Sugase | Mechanism of coupled folding and binding of an intrinsically disordered protein[END_REF]. pKID is largely disordered in the free state and binds through a dynamic encounter complex, stabilized primarily by non-specific hydrophobic contacts, and ultimately folds into the fully bound state without dissociation from KIX. Unlike pKID, the disordered protein c-Myb binds KIX without formation of observable intermediates and its association strongly depends on the residual helical structure present in the N-terminal portion of c-Myb [START_REF] Arai | Conformational propensities of intrinsically disordered proteins influence the mechanism of binding and folding[END_REF]. Akin to c-Myb, the unbound disordered domain of Sendai virus nucleoprotein (NTAIL) has a helix-forming propensity that affects its binding to the C-terminal domain of the phosphoprotein (PX). However, the interaction of NTAIL with its folded partner stabilizes a preformed helical state in an initial dynamic encounter complex docked to PX, previously to the formation of the final bound state [START_REF] Schneider | Visualizing the molecular recognition trajectory of an intrinsically disordered protein using multinuclear relaxation dispersion NMR[END_REF]. In general, NMR and binding kinetics data show clearly that coupled folding and binding reactions of IDPs do not follow a single, general mechanism. Rather, binding occurs by a variety of mechanisms, depending on the inherent conformational propensities of the IDP, as well as the conformational dynamics of their partners.

The coupled folding-binding process might give the impression that IDPs are in fact proteins "waiting for a partner to fold" [START_REF] Janin | Protein flexibility, not disorder, is intrinsic to molecular recognition[END_REF], and subsequently, to adopt its conformational unambiguous functional state. This might be true for some IDPs, but cannot be generalized for all of them. In this sense, NMR has allowed to put in evidence that the preservation of protein disorder by experiencing transient contacts in the bound state is an essential property of some functional IDP complexes. Similarly to fuzzy logics in mathematics, such flexible assemblies are termed as fuzzy complexes [START_REF] Miskei | FuzDB: database of fuzzy complexes, a tool to develop stochastic structure-function relationships for protein complexes and higher-order assemblies[END_REF]. Disorder in fuzzy complexes can be local or global, and it is often tuneable by environmental or PTMs. Fuzziness in IDP complexes alleviates the entropic cost of binding and enables an ultra-sensitive response to signals, as well as the adaptability of disordered region to bind multiple partners.

The application of NMR to study fuzzy complexes of IDPs with local or global disorder is illustrated for G-actin bound to β-thymosin/WH2 domains and the signalling protein Sic1 interacting with Cdc4. β-thymosin/WH2 (β-t/WH2) domains are widespread short disordered regions (25-50 residues) able to recognize G-actin and regulate actin-assembly. When bound to Gactin, the N-terminal half of β-t/WH2 adopts a well-ordered amphipathic helix, whereas the Cterminal part remains highly dynamic, but tuneable by electrostatic interactions. NMR analyses showed that at low ionic strength β-t/WH2 sequesters G-actin in a polymerization incompetent state, where the dynamic interactions of the C-terminal part restrain it to a single main conformational and functional state [START_REF] Didry | How a single residue in individual beta-thymosin/WH2 domains controls their functions in actin assembly[END_REF]. NMR has also uncovered the example of a fuzzy complex while studying the interaction of cyclin-dependent kinase inhibitor Sic1 and the SCF subunit of Cdc4 [START_REF] Mittag | Dynamic equilibrium engagement of a polyvalent ligand with a single-site receptor[END_REF]. Sic1 is a disordered protein comprising nine phosphorylation sites that can bind to Cdc4 in a phosphorylation dependent manner [100]. Interestingly, Cdc4 has only one high-affinity binding pocket for a phosphate group. NMR indicates that Sic1 remains largely disordered also when bound to Cdc4, forming a high affinity fuzzy complex only after six phosphorylations. The conformational plasticity of Sic1 allows the interchange between phosphorylation sites, which are in constant equilibrium with each other to occupy the single Cdc4 binding site. Along the orderdisorder continuum, Sic1 remains on the disorder extreme of the spectrum even upon binding, exemplifying a clear case where structural disorder and multiplicity are used to perform a highly specialized function.

A successful structural and dynamic elucidation of highly plastic complexes requires the integration of information derived from complementary techniques. Indeed, since NMR is limited in the size of the particle under study, and by its sensitivity to heterogeneous chemical environments, structural characterisation of flexible complexes can become unmanageable by NMR. However, as illustrated in Figure 2, the disappearance of NMR signals for residues directly involved in the formation of the complex can be used to localize the interacting region, to then isolate and co-crystallize it in order to get the detailed crystallographic structure of the complex. On top of that, SAXS provides the overall envelope of the entire system, and can be used to integrate in a common model both the NMR and the crystallographic information.

Outlook

In this chapter, we have described how NMR has contributed to the conformational characterization of intrinsically disordered proteins and their complexes, and to decipher the structural bases of their biological function.

During the last two decades, tremendous efforts that have been undertaken to link structural features in disordered regions with the specific tasks performed in vivo. One of the most striking observations has been the evolutionary conservation of functional stretches in IDPs, which is in contrast to the non-functional parts that exhibit much lower sequence conservation due to the lack of structural or functional requirements [START_REF] Habchi | Introducing Protein Intrinsic Disorder[END_REF]. In the vast majority of cases, these observations arise from bioinformatics studies, and therefore require experimental validation, which necessarily must come from NMR. It has been shown that NMR is the tool of choice to highlight the structural hot spots within disordered chains. Moreover NMR enables the localization of residues directly implicated in PTMs and recognition events. The identification of functional elements within an IDP is an essential information to guide the rational design of small molecules or peptide mimics able to modulate specific signalling cascades for pharmacological applications. Les connaissances actuelles sur les bases moléculaires de la régulation l'expression des gènes par RAR sont basées sur des structures aux rayons X de NRs en présence de certains ligands et/ou peptides dérivés des motifs de liaison de NCoR ou SMRT (le Maire et al., 2010). Cependant, ces images statiques ne peuvent expliquer que partiellement ces phénomènes puisque les protéines co-régulatrices sont intrinsèquement désordonnées.

Caractérisation de NCoR en complexe avec RAR/RXR

Pour tenter de répondre aux questions ci-dessus, nous avons récemment réalisé la caractérisation de NCoR et de son complexe par l'intégration simultanée d'informations de RMN, de SAXS, cristallographique, bioinformatique et de modélisation informatique.

Along this chapter we have detailed the enormous technical and conceptual progress that NMR has experienced that nowadays enables the structural and dynamic characterization of IDPs and their complexes. Despite this progress there are multiple aspects that still require the attention of the NMR community. Probably the most urgent need is to develop robust and statistically meaningful methods to derive conformational ensembles from NMR data. Researchers still differently address the definition of the best combinations of experimental observables, and the integration of parameters with different information content or averaging properties. Even more fundamental is the assessment of the reliability of conformational ensembles, and how their accuracy depends on the experimental data used or the strategy applied. It will be also necessary to better define conformational transitions in IDPs. This dynamic phenomenon is poorly understood due to the vast and flat energy landscape explored by IDPs. Here, the development of computational approaches enabling to explore this landscape will be required. Reliable force fields and strategies to integrate relaxation rates into these simulations seem to be of fundamental relevance to understand how IDPs exchange from one conformation to another. The abovementioned technical and conceptual improvements will be necessary to address the next biological challenges of the field. Low-complexity regions presenting high degeneracy of chemical shifts are an especially relevant one. To disentangle their spectroscopic complexity, either novel highdimensional pulse sequences or tailored isotopic labelling schemes will have to be developed.

The formation of biomolecular complexes is on the origin of many biological functions of IDPs. Understanding the molecular bases of these interactions is therefore crucial but remains challenging in many instances, as they are fuzzy and/or only formed transiently. The combination of multiple relaxation rates probing a broad range of time-scales (from ps to ms) can deliver a kinetic perspective of these interactions. Very often IDPs can simultaneously interact with multiple partners, or similar regions of the same disordered chain compete for a single binding site. Subtle perturbations in these equilibriums can drive to different signalling or metabolic pathways. By exploiting its atomic resolution, NMR is the most suited tool to study these complex and polydisperse scenarios.

IDPs were discovered two decades ago. Since then, our understanding of these proteins and their role in fundamental biological processes has enormously grown. However, we are convinced that there are still many structural and functional aspects of disordered proteins that remain unknown. NMR, as the sole structural biology technique able to probe these proteins at atomic level, has the unique opportunity to unveil new facets of this fascinating family of proteins.

Fig. 1 .

 1 Fig. 1. Illustration of the sensitivity of NMR parameters to the presence of residual secondary structure and long-range contacts in IDPs. A. The secondary structure propensity (SSP) calculated from experimental CA and CB chemical shifts using the software SSP is close to zero when no structure is present and increases in the helical element. B. 1 DNH residual dipolar couplings are negative in the disordered chain, where the bond vectors are on average perpendicular to the field; whereas in the helical region they are positive due to the tendency of the bond vector to be aligned with the field. C. The 15 N R2 relaxation rates also show an increase in the region of the helical element. D. The { 1 H}-15 N steady state heteronuclear Overhauser effects displays a value close to zero in the disordered chain and is more positive in the helical element. E. Paramagnetic relaxation enhancement intensity ratio: the presence of the probe affects the relaxation of residues close to it in the primary sequence, but also residues further apart, which are making transient contact with the region of the probe. The black line represents the data in the case where there are no transient contacts in the chain. Reproduced with permission from Communie G, et al. PLoS Pathog. 2013;9:e1003631 (A,C,D), reproduced with permission from Schneider R, et al. Mol. Biosyst. 2012;8:58-68 (B,E).

Fig. 2 .

 2 Fig. 2. Role of integrative structural biology to study plastic complexes.

- 16 -

 16 rétinoïque), dont l'activité dépend d'un groupe diversifié de protéines appelé co-régulateurs (Lonard & O'Malley, 2012). Les hétérodimères RXR/RAR peuvent agir soit en tant que répresseurs ou activateurs de la transcription des gènes. En effet, leur état de ligation détermine leur capacité à recruter soit des co-répresseurs, soit des co-activateurs(Gronemeyer et al., 2004). Les co-répresseurs des récepteurs nucléaires (NCoR et SMRT) agissent comme des plates-formes pour recruter des complexes de haut poids moléculaire qui présentent une activité épigénétique (histone déacétylase) (Perissi et al., 2010). Trois motifs d'interaction co-répresseur/NR conservés définis par la séquence protéique LXXI/HIXXXI/L ont été identifiés dans SMRT et NCoR (Hu & Lazar, 1999). En parallèle, les co-activateurs tels que ceux de la famille p160 (TIF-2/SRC-1/RAC3), qui accueillent également de multiples motifs de liaison aux NRs, interviennent dans l'interaction des NRs avec des complexes co-activateurs, de poids moléculaire élevé. Ces complexes acétylent des résidus spécifiques des queues N-terminales des histones, permettant d'ouvrir la chromatine pour l'activation de la transcription (Chen et al., 1999).Les objectifs de notre étude sont les suivants : Caractérisation des perturbations que les différents ligands (agoniste, inverse agoniste, etc) exercent sur les NRs Bases moléculaires de l'interaction entre les protéines très plastiques (co-répresseurs et coactivateurs) et les NRs, et le rôle que jouent les différents ligands sur cette reconnaissance Rôle biologique des multiples motifs d'interaction consécutifs hébergés par les protéines corépressives et co-activatrices Comprendre le mécanisme transformant les NRs de l'état répressif à l'état actif.

Acknowledgments

Financial support by the French Infrastructure for Integrated Structural Biology (FRISBI -ANR-10-INSB-05-01) and the Structural Biology RIO/IbiSA platform (Centre de Biochimie Structurale) is gratefully acknowledged. Keywords (Intrinsically disordered proteins, conformational ensemble, disordered complexes, integrative methods)


Nathalie Sibille
email: nathalie.sibille@cbs.cnrs.fr

Mariano Dellarole

Catherine A Royer

Christian Roumestand

Measuring Residual Dipolar Couplings at High Hydrostatic Pressure: Robustness of Alignment Media to High Pressure

Keywords: High Hydrostatic pressure NMR spectroscopy, Residual Dipolar Couplings, Alignment Media, folding/unfolding under pressure

Measuring residual dipolar couplings at high hydrostatic pressure: robustness of alignment media to high pressure

Defining the physical-chemical determinants of protein folding and stability, under normal and pathological conditions has constituted a major subfield in biophysical chemistry for over 50 years [START_REF] Dill | The protein-folding problem, 50 years on[END_REF][START_REF] Wolynes | Chemical physics of protein folding[END_REF]. Although a great deal of progress has been made in recent years towards this goal, a number of important questions remain. These include characterizing the structural, thermodynamic and dynamic properties of the barriers between conformational states on the protein energy landscape, understanding the sequence dependence of folding cooperativity, defining more clearly the role of solvation in controlling protein stability and dynamics, investigating the structural and dynamic properties of unfolded and partially folded ensembles and probing the high energy thermodynamic states in the native state basin and their role in misfolding and aggregation. Fundamental to the elucidation of these questions is a complete structural, dynamic and thermodynamic description of protein folding landscapes.

Since the first pressure-temperature phase diagrams of protein folding were published in the early 1970's [START_REF] Brandts | Thermodynamics of protein denaturation. Effect of pressu on the denaturation of ribonuclease A[END_REF][START_REF] Hawley | Reversible pressure--temperature denaturation of chymotrypsinogen[END_REF][START_REF] Zipp | Pressure denaturation of metmyoglobin[END_REF], the community of protein physical chemists has succeeded in providing a rather complete molecular and thermodynamic understanding of the effect of temperature on protein stability and structure (D 'Aquino et al. 1996;[START_REF] Fu | On the origin of the enthalpy and entropy convergence temperatures in protein folding[END_REF][START_REF] Gomez | The heat capacity of proteins[END_REF][START_REF] Hilser | Structure-based statistical thermodynamic analysis of T4 lysozyme mutants: structural mapping of cooperative interactions[END_REF][START_REF] Kauzmann | Some factors in the interpretation of protein denaturation[END_REF][START_REF] Murphy | Common features of protein unfolding and dissolution of hydrophobic compounds[END_REF][START_REF] Privalov | Stability of protein structure and hydrophobic interaction[END_REF]. In contrast to this rather satisfying and highly useful physical understanding of temperature effects on protein structure, the physical basis for the effects of pressure on protein structure and stability has remained poorly understood. Recently, thanks to the analysis of the folding properties of model proteins (Nank [START_REF] Rouget | Size and sequence and the volume change of protein folding[END_REF] Staphyloccocal nuclease (SNase) [START_REF] Kitahara | Structural plasticity of staphylococcal nuclease probed by perturbation with pressure and pH[END_REF]Roche et al. 2012a;Roche et al. 2012b;Roche et al. 2012c)), we have identified internal solvent excluded void volume as a major determining factor in the value of the decrease in protein molar volume upon unfolding, and hence of the magnitude of the pressure effect. In contrast to the large contribution of internal voids to pressure effects, differences in solvent density upon hydration of exposed protein surface were not found to make a significant contribution. In these recent studies of SNase, a residue-per-residue quantification of pressure effects was obtained by coupling 2D NMR spectroscopy with pressure perturbation. A drawback of this approach is the paucity of information gained concerning the structural properties of the unfolded state. Pressure unfolded states are of interest because, due to the specific effect of pressure on cavities, they are thought to be less disrupted than unfolded states obtained at high temperature or high concentrations of chemical denaturant. Hence, they may more closely resemble the unfolded state accessed by proteins under native conditions all information on the unfolded state of the protein can be obtained only indirectly.

Precise characterization of the unfolded state is necessary to fully describe the folding pathways and mechanisms. NMR spectroscopy is well adapted to describe this disordered state: chemical-shift and/or residual dipolar coupling (RDC) measurements have provided detailed descriptions of the structural and dynamic features of intrinsically disordered proteins (IDPs) [START_REF] Dyson | Unfolded proteins and protein folding studied by NMR[END_REF]. Investigation of conformational sampling using orientational restraints such as residual dipolar couplings (RDC) has been carried out under denaturing conditions at high urea concentrations [START_REF] Meier | Mapping the conformational landscape of ureadenatured ubiquitin using residual dipolar couplings[END_REF]). Nevertheless, urea is suspected to greatly disturb the hydrogen bond network within the denatured state of the protein, including H-bonds that involve water molecules. The use of high pressure to induce protein unfolding in non-denaturing buffer conditions will provide complementary information about the unfolded state manifold.

Having access to the crucial structural information given by RDCs under extreme conditions, such as high pressure, is not a new idea. Attempts in that direction has been already made by Kalbitzer and col. [START_REF] Brunner | Pressure-stability of phospholipid bicelles: measurement of residual dipolar couplings under extreme conditions[END_REF] who have characterized the pressure/temperature dependence of DMPC/DHPC bicelles (doped with hexadecyl(cetyl)trimethylammonium bromide (CTAB)). They have shown an amazing strong stabilizing effect of temperature under pressure:

although bicelles collapsed at pressure below 400 bar at ambient temperature, the oriented phase remained stable up to ca. 2000 bar at high temperature (102 °C). The aim of the present study is to identify and characterize among the most common ordering media, used under standard conditions for protein study (pH, temperature…), those that are able to resist high pressures (up to 2500 bar).

We have tested the pressure effect on four dilute liquid crystal media: Pf1 filamentous phage (10 mg/mL) [START_REF] Hansen | Tunable alignment of macromolecules by filamentous phage yields dipolar coupling interactions[END_REF], n-alkyl-poly(ethylene glycol)/n-alkyl alcohol mixture (the molar ratio r of C12E5 to n-hexanol was 0.85 and the C12E5/water ratio was 5 wt % (PEG/Hex)) [START_REF] Ruckert | Alignment of biological macromolecules in novel nonionic liquid crystalline media for NMR experiments[END_REF], phospholipid bicelles (5% (w/v) total DLPC and CHAPSO in water in a ratio of 4.2) [START_REF] Wang | A liquid crystalline medium for measuring residual dipolar couplings over a wide range of temperatures[END_REF], and DNA nanotubes (DNA of 400-nm-long 6-helix bundle nanostructure (6HB), 18 mg/mL) [START_REF] Bellot | Recovery of intact DNA nanostructures after agarose gel-based separation[END_REF]. All media were dissolved in a 10 mM BisTris buffer (H2O:D2O; 95:5) pH 6.5. To monitor the behavior of the commonly used alignment media under high pressure, we measured first the 2 H quadrupolar splitting of D2O as a function of pressure in different liquid crystal media. 2 H quadrupolar splitting of D2O were used as a sensor of the liquid crystalline state to check the constancy of the degree of alignment with increasing pressure. Quadrupolar splittings were measured at 25 °C and 600 or 700 MHz Bruker Avance III spectrometers equipped with either a conventional ambient-temperature or a cryogenic tripleresonance probe, respectively. A commercial high-pressure NMR ceramic cell and an automatic pump system (Daedalus Innovations, Philadelphia, PA) were used to vary the pressure in the 1-2500 bar range.

Pressure had no effect on the 2 H quadrupolar splitting of D2O measured in a C12E5/Hex mixture in the 1-2500 bar range, whereas a transition was observed for Pf1 phage and 6HB nanotubes: the value of the quadrupolar splitting decreased by approximately 50 and 25% for the two media, respectively, between 300 and 900 bar, then remained virtually constant up to 2500 bar (Fig. 1). A similar transition was observed after a 2-fold dilution of the Pf1 sample: 2 H quadrupolar splitting decreased by approximately 30%. In all cases, this transition was fully reversible, demonstrating that pressure does not alter irreversibly Pf1 phage or DNA nanotubes structure. In contrast, phospholipid bicelles did not tolerate high hydrostatic pressure: the effective alignment was abolished as the pressure was increased beyond 400 bar (Fig. S1), as shown by the disappearance of the quadrupolar splitting in the 2 H spectra and the concomitant appearance of a narrow singlet resonance indicating the onset of isotropic reorientation of the lipid molecules (Fig. S1). These results are in general agreement with those recently published [START_REF] Fu | Partial alignment and measurement of residual dipolar couplings of proteins under high hydrostatic pressure[END_REF].

However, neither the reversibility nor the apparent transition observed in Pf1 media were reported in that previous work. This is probably due to smaller pressure jump increments (of 200 bar instead of 500 bars) used in the present study. Similar to what was observed for DMPC/DHPC bicelles [START_REF] Brunner | Pressure-stability of phospholipid bicelles: measurement of residual dipolar couplings under extreme conditions[END_REF], the pressure stability of the DLPC/CHAPSO bicelles was found to increase with the temperature: at 45°C, the oriented phase remains stable up to ca. 600 bar. But this is far beyond the stabilization observed for CTAB-doped DMPC/DHPC bicelles, where the oriented phase remained stable up to 2000 bar for temperature above 62°C. The addition of CTAB to the solutions has been suggested as the most likely reason for the extraordinarily high temperature stability of DMPC/DHPC bicelles. Due to its robustness and its stability over a large pressure range, the neutral alcohol mixture, which forms an α lamellar crystalline phase, appeared to be the most promising medium for pressure dependent RDC measurements on proteins. The Pf1 phage and DNA nanotubes, which usually form a nematic crystalline phase under the standard conditions used for RDC measurements, underwent a reversible pressure-induced 2 H quadrupolar transition. This medium can be used nonetheless for studies under pressure with this qualification in mind. Given their high cost and a pressure response similar to that of the Pf1 phage, DNA nanotubes were not considered further.

To further explore the utility of Pf1 phage and the PEG/Hex mixture as suitable weak alignment media for high pressure studies of proteins, we measured the pressure dependence of the which depends on the alignment of the protein along the magnetic field direction [START_REF] Tjandra | Direct measurement of distances and angles in biomolecules by NMR in a dilute liquid crystalline medium[END_REF]. Around neutral pH and in absence of denaturant SNase ∆+PHS neither unfolds nor experiences substantial conformational changes up to 2500 bar [START_REF] Kitahara | Structural plasticity of staphylococcal nuclease probed by perturbation with pressure and pH[END_REF]) (Fig. S2).

The lack of pressure effect is particularly apparent in the OB-fold sub-domain (SubD1, FigS2A) (Roche et al. 2012c) encompassing the ß-barrel and helix 1. Focusing on the pressure dependence of the 1 DN-H RDCs measured on this sub-domain, and more especially on the ß-barrel, allowed characterization of the pressure dependence of the alignment frame without any interference from possible conformational rearrangements in the protein. All the experiments were performed at 20 °C with the same experimental set up as for quadrupolar splitting measurements. Uniformly 15 N labeled SNase Δ+PHS (1 mM) was dissolved in 10 mM BisTris buffer at pH 6.5. 5% C12E5/Hex = 0.85 alcohol mixture or 10 mg/mL of Pf1 filamentous phage (plus 200 mM NaCl) were added for 1 DN-H RDCs measurements. In the Pf1 phage sample, 2 H quadrupolar splitting measurements revealed a transition over the 300-900 bar pressure range, as already observed in absence of the protein (Fig. 1). The alignment strength is lower (8 Hz instead of 14 Hz, Figure 1B), due to the high concentration of salt added to screen strong electrostatic interactions between the basic protein and the acidic phage and possibly due to some Pf1 aggregation during salt addition [START_REF] Hansen | Tunable alignment of macromolecules by filamentous phage yields dipolar coupling interactions[END_REF]. At each pressure, 1 DN-H RDCs were extracted from the difference between the 1 JN-H couplings measured with 1 H -15 N TROSY and semi 1 H -15 N TROSY experiments [START_REF] Weigelt | Single scan, sensitivity-and gradient-enhanced TROSY for multidimensional NMR experiments (vol 120, pg 10778[END_REF] in the isotropic sample and the 1 JN-H + 1 DN-H couplings measured with 1 H-15 N IPAP-HSQC experiments [START_REF] Cordier | A doublet-separated sensitivity-enhanced HSQC for the determination of scalar and dipolar one-bond J-couplings[END_REF] in the anisotropic samples.

A preamble to this study was to ensure that the protein behaved equivalently with pressure when dissolved in an isotropic medium or diluted in a slightly anisotropic medium.

Pressure is known to perturb protein NMR spectra, even at non-denaturing values. For instance, amide chemical shifts are pressure sensitive, their variation has been mostly associated to protein compressibility [START_REF] Li | Pressure alters electronic orbital overlap in hydrogen bonds[END_REF] (Fig. S2). A good sensor of this compressibility is the average difference in chemical shift between 2500 and 1 bar, calculated for each amide group as Δ∂ (2500-1)bar = [(Δδ 2 HN + Δδ 2 N/25] 1/2 [START_REF] Grzesiek | The solution structure of HIV-1 Nef reveals an unexpected fold and permits delineation of the binding surface for the SH3 domain of Hck tyrosine protein kinase[END_REF].

The values of the amide resonance chemical shift variation ∆∂ (2500-1)bar measured for SNase ∆+PHS in each medium versus the protein sequence are reported on Fig. S3. Fig. 2 highlights the chemical shift behavior of the amide group of residues belonging to the ß-barrel of the protein. While Pf1 diluted phage have no effect on the protein compressibility, in particular in the ß-barrel domain, significant variations are observed in the alcohol mixture. This later medium apparently destabilizes the protein, as already suggested by the poor quality of spectra recorded in this medium at atmospheric pressure (Fig. S4), and the protein is even further destabilized with pressure. This is probably due to a specific interaction between PEG and the protein, already detectable in the HSQC spectra of SNase ∆+PHS at C12E5 concentrations far below those used in the anisotropic medium composition. Note that addition of n-hexanol alone up to similar concentrations did not give rise to any spectral modification (data not shown). Thus, in the following, we focused on the 1 DN-H extracted from the diluted Pf1 phage sample to follow the pressure dependence of the alignment tensor parameters. To investigate the behavior of the phage alignment medium under pressure, we characterized the alignment tensor parameters (relative to an arbitrary molecular frame) of the protein dissolved in this anisotropic medium by following the pressure dependence of the axis orientation defined by the Euler angles (α, β, γ) and the eigenvalues of the tensor (axial and rhombic component, Aa and Ar, respectively, and R = Ar/Aa as the rhombicity). Depending on the pressure-affected parameter, these measurements should indicate whether the decrease of the 2 H quadrupolar splitting of D2O was related to reversible changes at the surface of the phage Pf1, responsible for changes in the interaction between the protein and the particle, (R), or to a decrease in the order of magnitude of the alignment (Aa).

The correlation between back calculated and experimental RDCs and the alignment tensor parameters were determined with the Module software [START_REF] Dosset | A novel interactive tool for rigid-body modeling of multi-domain macromolecules using residual dipolar couplings[END_REF]), using the SNase Δ+PHS X-ray structure (3BDC PDB code) and the experimental 1 DN-H data measured on the SNase Δ+PHS upon pressure. Hydrogens were added to the X-ray structure using the program CNS and a distance of 1.04 Å has been used for the internuclear distance of the N-H vectors. Aa is referred to as the magnitude of the residual dipolar coupling tensor, and Ar to as the rhombic component, both normalized to the N-H dipolar interaction [START_REF] Dosset | A novel interactive tool for rigid-body modeling of multi-domain macromolecules using residual dipolar couplings[END_REF]). Thus, Aa and Ar, described in [START_REF] Dosset | A novel interactive tool for rigid-body modeling of multi-domain macromolecules using residual dipolar couplings[END_REF]) are the unit-less axial and rhombic components of the molecular alignment tensor A, and are on the order of 10 -4 .

The global fitting of all the 1 DN-H RDCs measured on the SNase Δ+PHS X-ray structure (3BDC PDB code) is shown on Fig. S5. The relatively low agreement between back calculated and measured 1 DN-H RDCs on the entire protein could come from a slightly different relative orientation of the different sub-domains in the X-Ray structure when compared to the protein in the NMR sample. In addition, the agreement slightly decreases when the pressure increases (R 2 = 0.90 at 1 bar and 0.87 at 2500 bar), suggesting subtle reorganization of the different sub-domains of the protein under pressure. This low agreement between back calculated and measured RDCs on the entire protein could prevent precise estimation of the global alignment tensor and add noise to the extracted tensor parameters. So we decided to focus only on the ß-barrel of this protein, part of subD1 domain (Table S6), in order to have a more accurate determination of the alignment tensor.

Alignment tensor parameters were determined at each pressure (1 to 2500 bar, with 200 and 400 bar step below and above 900 bar, respectively) using 20 1 DN-H values (Fig. 3, Fig. S5). The pressure dependence of the Euler angles and eigenvalues of alignment tensors revealed an increase in the rhombicity (R = Ar/Aa) (Fig. 3B), but there was no change in the eigenvectors defined by the Euler angles (Fig. 3A), and the eigenvalue Aa revealed that the alignment strength remained virtually constant (Fig. 3C). The absence of variation upon pressurization of the axial component (Aa) is confirmed by the overall fitting of 1 DN-H to the X-Ray structure at 1 bar (Aa = 10.3×10 -4 , Ar = 1.7×10 -4 , R = Ar/Aa = 0.16) and 2500 bar (Aa = 10.5×10 -4 , Ar = 2.8×10 -4 , R = Ar/Aa = 0.26) (Fig. S5).

Highly charged liquid-crystalline media, such as the popular Pf1 phage particles, form nematic phases. However, just below the nematic phase boundary the behavior of the system is paranematic [START_REF] Zweckstetter | Characterization of molecular alignment in aqueous suspensions of Pf1 bacteriophage[END_REF]. Given the low phage concentrations and high salt concentration used in the present work, the phase of the alignment medium should be paranematic.

According to Le Chatelier's Principle, pressure will shift equilibrium between multiple states towards those states that occupy the smallest molar volume. Thus, the transition observed on the pressure dependence of the quadrupolar splitting could possibly arise from a "pseudo"-phase transition shifting the initial ordering of the Pf1 at ambient pressure to a more compact one at highpressure. If this is the case, the alignment strength of the protein should scale proportionately to that of the deuterium quadrupole splitting. Since in our work the value of the axial component (Aa) remains constant with pressure, the change observed in the 300-900 bar range in the 2 H quadrupolar splitting does not appear to be associated with a loss of alignment degree in the sample.

Alternatively, although protein alignment results from a coarser steric and electrostatic combination of forces, 2 H quadrupolar splitting results from D2O molecule alignment, and water alignment results from the hydration distribution of the molecules on the atomic surface of the Pf1.

Increasing hydrostatic pressure should provoke only subtle and reversible rearrangement of the Pf1 phage surface proteins, yielding concomitantly a decrease of 2 H quadrupolar splitting of D2O, and an increase of the rhombicity of the alignment tensor of the co-dissolved protein. In our study, the change observed in the 300-900 bar range in the 2 H quadrupolar splitting must reflect modification of the Pf1 particle hydration that could induce a slight change in the interaction between the protein and the Pf1's surface, which, in turn, is reflected in a constant variation of the rhombicity (R = Ar/Aa) of the alignment tensor. Thus, in this case, the 2 H quadrupolar splitting only senses the hydration of the proteins at the surface of the Pf1. Such an interpretation is analogous to that of [START_REF] Ottiger | Characterization of magnetically oriented phospholipid micelles for measurement of dipolar couplings in macromolecules[END_REF] for DHPC/DMPC bicelles. In that system, the 2 H quadrupolar splitting was strongly temperature dependent, but the protein alignment was not, and the temperature dependence of 2 H quadrupolar splitting simply reflects a change in hydration characteristics of the phospholipids. NMR is an exquisite experimental approach to detect and characterize folding intermediates at the individual residue level. For instance, hydrogen/deuterium exchange experiments, relaxation dispersion have already been used to identify intermediate states during unfolding process, both at atmospheric [START_REF] Boehr | The dynamic energy landscape of dihydrofolate reductase catalysis[END_REF][START_REF] Englander | Protein folding intermediates and pathways studied by hydrogen exchange[END_REF] or at high hydrostatic pressure [START_REF] Korzhnev | Probing the transition state ensemble of a protein folding reaction by pressuredependent NMR relaxation dispersion[END_REF][START_REF] Nisius | Key stabilizing elements of protein structure identified through pressure and temperature perturbation of its hydrogen bond network[END_REF]Roche et al. 2012c;[START_REF] Fuentes | Local stability and dynamics of apocytochrome b562 examined by the dependence of hydrogen exchange on hydrostatic pressure[END_REF]. However, the use of long-range structural restraints to characterize pressure-induced folding intermediates or denatured states were still missing. Here we demonstrate the feasibility of high pressure RDCs measurements on proteins in several alignment media. Indeed, we have identified and characterized three pressure stable and resistant alignment media, that can orient the co-dissolved bio-molecules via steric (alcohol mixture) and electrostatic (filamentous bacteriophage and DNA nanotubes) interactions. Fu and Wand have also observed the stability of alcohol mixture and Pf1 phage in slightly different conditions [START_REF] Fu | Partial alignment and measurement of residual dipolar couplings of proteins under high hydrostatic pressure[END_REF]. In their study, they have shown that RDCs measured at 2500 bar exhibited significant deviations from those backcalculated on the ubiquitin structure at atmospheric pressure, especially in regions where pressure-induced structural changes were previously highlighted in a solution structure determined using classical NMR restraints at 3000 bar [START_REF] Kitahara | NMR snapshots of a fluctuating protein structure: ubiquitin at 30 bar-3 kbar[END_REF]. We have chosen to focus on a different model: the ultra-stable ∆+PHS SNase, and more precisely on its ß-barrel sub-domain that do not experience structural changes within the pressure range used for this study. This allowed us to focus only on alignment media properties, discarding any contribution from protein conformational changes. Thus, in the case of Pf1 alignment medium, we were able to safely conclude that the sigmoidal pattern exhibited by the variation of 2 H quadrupolar splitting with pressure can be solely related to alignment media perturbations: probably to reversible changes at the phage surface, affecting their hydration properties.

In addition, Fu and Wand found another stable medium composed of dinucleotides.

Thus, four different alignment media appear suitable for high pressure studies. Moreover, our study has shown the pressure reversibility of three of these commonly used media making them useful for folding/unfolding studies. Thus, depending on the pI of the bio-molecule under study and its compatibility with the diluted liquid crystal, alternative alignment media can be chosen for RDC measurements under high hydrostatic pressure. In addition, the accessibility to several liquid crystal media with different alignment properties will allow the detailed investigation of the protein structure and dynamics. For instance, it will allow the refinement of structure of intermediate states during folding [START_REF] Blackledge | Recent progress in the study of biomolecular structure and dynamics in solution from residual dipolar couplings[END_REF], the accessibility to the dynamics over a broad time-scale [START_REF] Bouvignies | Identification of slow correlated motions in proteins using residual dipolar and hydrogenbond scalar couplings[END_REF], the study of domain rearrangement along the folding pathways of multi-domain proteins. Thus, measurement of RDCs under pressure will complete the toolbox for the characterization of these intermediate states, but can also bring unique information on the unfolded state. Indeed, RDCs contain both local and long range structural information that allow to establish the existence of transient and/or stable α helices, β extended or PPII (PolyProline II helix) elements of folded and unfolded states and thus to calculate an ensemble of relevant conformations. Consequently, the broad range of structural information afforded by measurement of RDCs [START_REF] Bax | Weak alignment NMR: a hawk-eyed view of biomolecular structure[END_REF][START_REF] Tjandra | Direct measurement of distances and angles in biomolecules by NMR in a dilute liquid crystalline medium[END_REF][START_REF] Tolman | Nuclear magnetic dipole interactions in field-oriented proteins: information for structure determination in solution[END_REF] can be now extended to the analysis of protein folding under pressure.

Fig. S2.

Overlay of the 1 H-15 N HSQC spectra of SNase Δ+PHS recorded at 25°C in a 10 mM BisTris buffer at pH 6.5 over a pressure range spanning from 1 to 2500 bar. Even at the higher pressure, the spectrum remains well resolved and characteristic of a structured protein. Chemical shift variations of the amide group nuclei have been mostly attributed to Hbond compression [START_REF] Li | Pressure alters electronic orbital overlap in hydrogen bonds[END_REF]. Insert: SNase Δ+PHS X-ray structure (3BDC PDB code) with the ultra stable subdomain (subD1) in dark blue. Sub-domain 2 consists on the C-terminal helix α3 (green), and helix α2 (light blue) forms the inter-domain (Roche et al. 2012).

Fig. S3

. Difference between amide average chemical shift variations Δ∂ (2500-1)bar measured on the protein dissolved in an isotropic medium and (blue) the protein dissolved in Pf1 filamentous phage (10 mg/mL), or (green) the protein dissolved in 5% C 12 E 5 /Hexanol = 0.85 alcohol mixture. Table S6. Extracted values on residues mentioned in column 1 of the β-barrel of the SNase ∆+PHS: 1 J N-H , 1 D N-H in Pf1 phage at 1, 300, 500, 900, 1300, 1700, 2100 and 2500 bar, and the amide average chemical shift variations between 2500 and 1 bar (∆∂ (2500-1)bar ) measured on the protein dissolved in an isotropic medium, in Pf1 filamentous phage (10 mg/mL), or in 5% C12E5/Hexanol = 0.85 alcohol mixture

Fig. 1 2

 2 Fig. 1 2 H quadrupolar splitting of D2O (Hz) measured in (A) C12E5/n-hexanol system, r was 0.85 and the C12E5/water ratio was 5 wt %; (B) Pf1 filamentous phage (10 mg/mL); (C) DNA nanotubes of 400 nm 6-helix bundle (18 mg/mL); (left) spectra; (right) values as a function of pressure (blue diamonds: positive P-jumps, from 1 to 2500 bar; pink squares: negative P-jumps, from 2500 to 1 bar).

Fig. 2

 2 Fig. 2 Pressure effects sensed by the amide chemical shift variations Δ∂ (2500-1)bar measured for residues belonging to the ßbarrel (Sub-Domain 1, SubD1) of SNase Δ+PH. In both panels, the pink curve corresponds to Δ∂ (2500-1)bar values measured in an isotropic medium and has to be compared to values measured (A) in Pf1 phages (10 mg/mL) (blue curve) and (B) in 5% C12E5/Hexanol = 0.85 alcohol mixture (green curve).

Fig. 3

 3 Fig. 3 Alignment tensor parameters extracted from 20 residues belonging to the SNase ∆+PHS ß-barrel: (A) Euler angles (α, β, γ); (B) rhombicity: R = Ar/Aa (C) axial (Aa) and rhombic (Ar) component. Errors in these alignment tensors (+/-0.2 for Aa and Ar) are mainly influenced by uncertainties in the reference structure and were estimated using the Monte Carlo method included in the Module software.

Fig. S4 .

 S4 Fig. S4. 1 H-15 N IPAP spectra of SNase Δ+PHS in (A) 5% C 12 E 5 /Hexanol = 0.85 alcohol mixture, and (B) Pf1 filamentous phage (10 mg/mL), at 1 bar (left) and 2500 bar (right)

DN-H RDCs for an ultra-stable variant of Staphylococcal Nuclease protein (SNase ∆+PHS)(Kitahara et al.

2011;Roche et al. 2012a; Roche et al. 2012b; Roche et al. 2012c), dissolved in these media. RDCs measured on the backbone nuclei allows to calculate an alignment tensor

Acknowledgements

We gratefully acknowledge support from the Agence National de la Recherche, grant PiriBio 09-455024. High pressure NMR work was supported by the French Infrastructure for Integrated Structural Biology (FRISBI) ANR-10-INSB-05-01 and the Structural Biology RIO/IbiSA platform (Centre de Biochimie Structurale).

Measuring Residual Dipolar Couplings at High

Hydrostatic Pressure: Robustness of Alignment Media to High Pressure

Supporting Information

Authors: Nathalie Sibille 1,2,3,* Mariano Dellarole 1,2,3 , Catherine Royer