Benoit Alary
email: benoit.alary@ircam.fr.

Archontis Politis

A DATASET FOR LOCATION-AND DIRECTION-DEPENDENT REVERBERATION ANALYSIS

Keywords: Anisotropy, inhomogeneity, auralization, directional reverberation, virtual reality

Measuring room impulse responses (RIRs) is fundamental to sound reproduction and acoustical research. For instance, these measurements play an essential role in building digital twins in virtual reality to preserve their cultural heritage. For sound reproduction, RIRs can be used directly through convolution, or a more complex timefrequency domain analysis may be used to characterize a parametric method. Measuring RIRs using microphone arrays, such as a spherical microphone array, is necessary to extend this reproduction to the spatial domain. Recent work has shown that reverberant sound fields have perceptually salient position-and direction-dependent characteristics which should be considered in six degrees of freedom (6DoF) sound reproduction. However, related psychoacoustics and signal processing research require complex datasets to measure to better understand these characteristics. In this article, we present an experiment carried out in the main auditorium of the Finnish National Opera and Ballet in Helsinki, where we measured spatial RIRs from the perspective of ninety-seven individual seats. We analyze key characteristics of the resulting anisotropic and inhomogeneous sound field using energy-based analysis methods and the dataset is shared publicly to allow for further research in this field, such as multi-slope decay analysis and 6DoF auralization.

INTRODUCTION

A measured room impulse response (RIR) contains information on the time-frequency behavior of sound waves in a room for a set of specific measurement conditions, such as a microphone and loudspeaker position. As such, an RIR may be used to detect the incident direction of early reflections [START_REF] Stewart | Statistical measures of early reflections of room impulse responses[END_REF], to study specific acoustics characteristics such as variable acoustics room [START_REF] Prawda | Calibrating the Sabine and Eyring formulas[END_REF][START_REF] Klein | The r3vival dataset: Repository of room responses and 360 videos of a variable acoustics lab[END_REF] or coupled volume [START_REF] Luizard | Coupled volume multislope room impulse responses: a quantitative analysis method[END_REF], and analyze properties of a late reverberant sound field [START_REF] Gover | Measurements of directional properties of reverberant sound fields in rooms using a spherical microphone array[END_REF][START_REF] Alary | Assessing the anisotropic features of spatial impulse responses[END_REF][START_REF] Hold | Resynthesis of spatial room impulse response tails with anisotropic multi-slope decays[END_REF]. Larger datasets of measured RIRs [START_REF] Piquet | Two datasets of room impulse responses for navigation in 6 degrees of freedom: a symphonic concert hall and a former planetarium[END_REF] find applications in speech recognition [START_REF] Szöke | Building and evaluation of a real room impulse response dataset[END_REF], conservation of acoustics [START_REF] Katz | Experience with a virtual reality auralization of Notre-Dame Cathedral[END_REF][START_REF] Katz | Exploring cultural heritage through acoustic digital reconstructions[END_REF], machine learning [START_REF] Götz | Neural network for multi-exponential sound energy decay analysis[END_REF][START_REF] Ratnarajah | Mesh2ir: Neural acoustic impulse response generator for complex 3d scenes[END_REF], and studying the perception of transitioning through coupled rooms [START_REF] Mckenzie | Acoustic analysis and dataset of transitions between coupled rooms[END_REF].

In virtual and augmented reality (VR/AR) applications, where reproduction accuracy and six degrees of freedom (6DoF) scene navigation are important, new challenges arise for acoustic reproduction [START_REF] Schissler | Efficient construction of the spatial room impulse response[END_REF][START_REF] Mccormack | Object-based six-degrees-of-freedom rendering of sound scenes captured with multiple ambisonic receivers[END_REF][START_REF] Neidhardt | Perceptual matching of room acoustics for auditory augmented reality in small rooms -literature review and theoretical framework[END_REF][START_REF] Garí | Room acoustic characterization for binaural rendering: From spatial room impulse responses to deep learning[END_REF][START_REF] Deppisch | Direct and residual subspace decomposition of spatial room impulse responses[END_REF]. For sound field reproduction, a spherical microphone array (SMA) is typically used to measure spatial room impulse responses (SRIR), which can be used for reproduction using convolution [START_REF] Gardner | Efficient convolution without inputoutput delay[END_REF], or spatial-time-frequency processing may be used to improve efficiency and accuracy of the reproduction [START_REF] Mccormack | Higher-order spatial impulse response rendering: Investigating the perceived effects of spherical order, dedicated diffuse rendering, and frequency resolution[END_REF][START_REF] Deppisch | Direct and residual subspace decomposition of spatial room impulse responses[END_REF].

While reverberation is often described as diffused in time, recent acoustics measurement research has demonstrated that reverberant sound fields are not necessarily isotropic [START_REF] Berzborn | Investigations on the directional energy decay curves in reverberation rooms[END_REF][START_REF] Nolan | A wavenumber approach to quantifying the isotropy of the sound field in reverberant spaces[END_REF][START_REF] Alary | Assessing the anisotropic features of spatial impulse responses[END_REF][START_REF] Nolan | Isotropy in decaying reverberant sound fields[END_REF], and may have perceptually salient position-and direction-dependent decay characteristics [START_REF] Alary | Perceptual analysis of directional late reverberation[END_REF], which should also be considered in 6dof auralization [START_REF] Alary | A method for capturing and reproducing directional reverberation in six degrees of freedom[END_REF]. However, since the perceptual effect of anisotropic reverberation will vary from one room to another and the perceptual threshold of such characteristics has not yet been fully established, more research is required to fully understand this aspect.

In the study of anisotropic and inhomogeneous sound fields, opera houses offer interesting characteristics. Indeed, while they are built to encourage a certain amount of reverberation in the audience section, they also contain large open spaces behind the stage as well as an orchestral pit and high ceilings, which all contributes to a non-uniform spatial distribution of sound energy throughout the decay. A previous experiment was performed in an opera hall to capture SRIRs from fifteen seats [START_REF] Alary | A method for capturing and reproducing directional reverberation in six degrees of freedom[END_REF] and propose the use of a directional feedback delay network reverberator for reproduction [START_REF] Alary | Directional feedback delay network[END_REF][START_REF] Alary | Frequency-dependent directional feedback delay network[END_REF]. However, a relatively large inhomogeneity was observed between adjacent measurement points, suggesting the necessity to reduce the distances between each measurement point.

In this article, we present an extended measurement campaign carried out in the main auditorium of the Finnish National Opera and Ballet in Helsinki, where SRIRs were measured from the perspective of ninetyseven individual seats in the parterre section. Using energy-based analysis methods, we analyze the sound field to confirm it contains both anisotropic and inhomogeneous characteristics. The dataset is shared publicly to allow its use in future research, including directional and multi-slope decay analysis, and 6DoF auralization. Since the stage curtain was raised during measurement, and the stage was left empty, the measurement conditions are not ideal for assessing the acoustics qualities of this opera hall, in a musical sense. Nonetheless, the dataset aims to offer an interesting set of sound field characteristics and challenges for future research in reverberation modeling and reproduction. The dataset, titled Op-eraRIR, is available publically at https://doi.org/ 10.5281/zenodo.8096639.

DATASET

Description

The main auditorium of the Finnish National Opera and Ballet (FNOB), located in Helsinki, Finland, is a modernshaped horseshoe opera hall that opened in 1993. The hall contains three balconies and a parterre, for a total of 1350 seats. The parterre contains 731 individual seats over 19 rows. In its widest section, the hall is approximately 27 m wide, and 25 m deep, from the center back of the hall to the beginning of the stage, including the orchestra pit.

In this measurement campaign, 210 SRIRs were measured. More specifically, 97 individual seats located on the parterre were measured sequentially using two different sound sources located on the stage (Fig. 1), for a total of 194 SRIRS. Among these measurement positions, four were selected as validation points, and two extra mea- surement sets were performed, using the same two sound sources, thus adding 16 SRIRs to the dataset. These validation points are intended for use in assessing the stability of the measurements and the background noise. The measurements were captured using an SMA, the Eigenmike ®1 , to obtain microphone signals that can be encoded as fourth-order ambisonic SRIRs. Two Genelec 8331A loudspeakers were used as sound sources and both were positioned at a depth of one meter, from the edge of the stage, on a 1.6 m stand. The first source was located 5.53 m from the lateral center, on the left side of the stage when looking from the parterre, and the second loudspeaker was located in the center 1. Other than the loudspeakers, the stage was left completely empty, the curtain was fully raised, and no audience was present. Therefore, in practice, the perceived reverberant sound field would be different during a live performance.

While the use of an omnidirectional sound source, such as a dodecahedron, is recommended to measure acoustic parameters and measurements [START_REF]Acoustics -Measurement of Room Acoustic Parameters[END_REF], we observed during the first experiment ( [START_REF] Alary | A method for capturing and reproducing directional reverberation in six degrees of freedom[END_REF]) that the deviation of omnidirectionality was unpredictable at mid-high frequencies, and that the loss of phase coherence due to their multi-driver operation was resulting in measurements that were sub-optimal for analysis and sound reproduction. Hence a high-quality, two-way studio monitor, was preferred as the excitation source, and its directivity is considered a property of the measurements. The SRIRs were measured using 30-second long exponential sine sweeps [START_REF] Griesinger | Beyond mls-occupied hall measurement with fft techniques[END_REF][START_REF] Farina | Simultaneous measurement of impulse response and distortion with a swept-sine technique[END_REF]. The loudness of each loudspeaker was adjusted using a sound pressure level (SPL) meter from an arbitrary position in the far field. However, after detecting some clipping in the output of the first source at high frequencies, the frequency range of the sweep used was restricted as a precaution. More specifically, we used a sweep covering a frequency range of 50 Hz to 16 kHz for the first sound source, and a sweep covering a frequency range 50 Hz to to 20 kHz for the second source. Nonetheless, spatial analysis in the 16 kHz-20 kHz frequency range are never recommended when using such an SMA due to physical limitations.

The locations of the measurement points were chosen to cover as much of the parterre given time constraints in the availability of the hall for measurements. For the first half of the parterre, closer to the stage, every second row was measured, and in the second half of the hall, every third row. For most measured rows, two non-measured seats were left between each measured one, and this was extended to four seats on the last row. The average lateral distance between two measured seats in the same row was 1.57 m, and the average depth distance between two measured rows was 1.58 m. Throughout the measurement campaign, the microphone was placed on the floor directly in front of a seat, using a 1.4 m tall stand. The location of each microphone position was obtained using a top-view architectural plan of the hall (Fig. 1). The coordinate system used here is in meters and the axis origin is located in the top left corner of the architectural plan, the two loudspeakers are positioned at y = 0. As such, the coordinates of the first source are (7.30, 0.0), and the second source is located at (12.83, 0.0).

In post-processing, the overall maximum amplitude value detected across the whole dataset was used to normalize the dataset while preserving the relative differences between measurements. The public dataset contains the deconvolved impulse responses, both as 32-channel microphone signals, as well as fourth-order Ambisonic files encoded with the ACN channel ordering and SN3D normalization. The SRIRs were measured at 48 hKz. The coordinates of each measurement position are provided in a separate data file (Table 1).

Alignment

One significant challenge of measuring a hall from many positions is ensuring a consistent alignment of the microphone for each measurement position. Since this hall contains no parallel walls to align with, and each seat has a slightly different rotation angle on the parterre, the front of the spherical microphone was aligned horizontally using a laser pointer, aiming at the loudspeaker located in the center of the stage. Therefore, each measurement of the dataset uses a different alignment which needs to be compensated during post-processing.

In the dataset's coordinate system, the alignment reference point is located at (12.83, 0). The exact orientation angle was obtained by a combination of geometrical prior knowledge and acoustical evidence from the measured SRIRs. More specifically, for each position a windowed SRIR was obtained by applying a rectangular window around the maximum peak of the omnidirectional RIR to all channels, hence isolating the direct path component. This windowed SRIR was then analyzed to detect the direction-of-arrival (DOA) of the direct path, using a plane wave decomposition approach, band-limited between 2-6 kHz, followed by peak finding on the plane wave amplitude distribution. The azimuth component of the obtained DOA combined with the azimuth of the line connecting the measurement position and the source was then used to obtain the azimuthal rotation of the Eigenmike in the global coordinate system. Based on the analyzed azimuthal rotation angle for each measurement position, the Ambisonic recordings were inversely rotated to face the back wall of the stage (Fig. 2). Compensation angles, original measured files, and rotated HOA files are all provided in the dataset.

Control points

In the context of sound reproduction, determining the optimal distance between measurement points remains an open question. In order to assess the homogeneity of the sound field at shorter distances, two pairs of seats were measured with a shorter distance between them. The first pair, measured on row 5, has a distance of 0.28 m between the two microphone positions, and the second pair, on row 7, has a distance of 0.55 m. These measurement points lie outside the main grid points used for the rest of the measurement campaign and may be of interest in the study of 6dof interpolation. These two pairs of seats were measured three times consecutively to study the stability of the measurement method.

ENERGY-DECAY ANALYSIS

In the context of sound reproduction, a common analysis approach for reverberant sound fields is to analyze the decay of energy over time [START_REF] Schroeder | New method of measuring reverberation time[END_REF]. While energy-decay analysis has some drawbacks, such as sensitivity to environmental noise, it provides useful measures in the context of artificial reverberation as they correspond well to our perception of sound decay. Additionally, time-frequency analysis of late reverberation in a measured RIR may be per- formed using a filter bank [START_REF] Jot | An analysis/synthesis approach to real-time artificial reverberation[END_REF]. For SRIRs, this analysis is extended to a set of angles to obtain direction-dependent characteristics [START_REF] Alary | Perceptual analysis of directional late reverberation[END_REF]. As such, directional room impulse responses (DRIRs) are obtained from a measured SRIR encoded in spherical harmonics (SHs) using plane wave decomposition for a set of angles distributed around the sphere y(n, ϕ, θ) = y T (ϕ, θ) s(n),

where s(n) = [s 1 (n), ..., s (L+1) 2 (n)] T is the L-th order ambisonic SRIR, and y = [Y 0,0 , Y 1,-1 ..., Y L,L ] T is a vector of SH values for a pair of azimuth and elevation angles (ϕ, θ). Directional, and frequency-dependent, decay curves are calculated from a DRIR using [START_REF] Alary | Assessing the anisotropic features of spatial impulse responses[END_REF][START_REF] Alary | Perceptual analysis of directional late reverberation[END_REF] EDC(n, ω, ϕ, θ) = 10 log 10

N i=n y(i, ω, ϕ, θ) 2 ,
(2) where ω is the center frequency of a band in a filter bank. As such, energy-decay analysis can be performed for different time segments (n), frequencies (ω), and directions (ϕ, θ). When visualizing results, we limit some of these parameters to allow comparison of specific timefrequency-directional aspects.

Energy-decay on the horizontal plane

Using the SRIR measured on seat 37, on the second row, and the first sound source, located on the left of the stage, the response was filtered using a bandpass between 1 kHz and 3 kHz. In Fig. 345, an energy-decay analysis is performed on a set of azimuthal angles around the sphere, for a fixed elevation angle (0 • ). On the analyzed plane, from the perspective of an audience member looking towards the stage, an azimuth angle 0 • is to the right, 90 • is towards the stage, 180 • is to the left, and 270 • is behind.

For any given time step, the directional decay analysis contains the sum of the remaining decay energy in that direction (Fig. 2). Figure 3 contains results for the first 25 ms of the measured SRIR. We observe that the direct sound is incident to 75 • , thus slightly to the right from the perspective of the parterre. We also observe that the decay energy is slightly stronger at 0 • and 235 • in the first 25ms of decay.

In Fig. 4, which contains analysis results for the first 1.5 seconds, more energy is centered around 335 • in the first 100 ms, before gradually migrating to 15 • and 175 • at around 0.5 seconds. In any SRIR measurements, some background noise will inevitably occur and the energy needs to be taken into consideration when interpreting decay analysis. In the later part of the measured sound field, the background noise is noticeably present towards 60 • and 250 • (Fig. 5), which appears to interfere with the analysis results already at 1 second. For sound reproduction, it is highly recommended to use denoising methods to avoid an unnatural reverberation effect when convolving with this noise [START_REF] Massé | Denoising directional room impulse responses with spatially anisotropic late reverberation tails[END_REF].

Energy-decay deviation

In a homogeneous sound field, sound energy is uniformly distributed to any point in space, and in an isotropic sound field, the energy incident to a point is uniformly distributed from any direction. In practice, these theoretical requirements for a diffuse sound field are never fully realized and it becomes interesting to quantify how much we deviate from this uniformity energy principle. The energy-decay deviation (EDD) [START_REF] Alary | Assessing the anisotropic features of spatial impulse responses[END_REF][START_REF] Alary | Perceptual analysis of directional late reverberation[END_REF], is a measure of the deviation between direction-dependent EDC(n, ϕ, θ) to a mean

EDD(n, ϕ, θ) = EDC(n, ϕ, θ) -EDC(n). (3)
where EDC(n) corresponds to the omnidirectional and location-independent mean. For the purpose of this dataset, we are interested in the study of both anisotropy and inhomogeneity and as such, the EDC(n) is calculated from a set of directions distributed on the top hemisphere, for every measurement point. Using this approach, we can analyze how the energy is distributed in the measured area, at different times. At time zero, time-aligned from the initial impulse for each seat, in Fig. 6, the location of the first sound source can clearly be identified as coming from the front left of the stage, represented in the top-left corner of the figure, while the overall reverberant energy decreases as the measuring point gets further away from the source.

In Fig. 7, we can observe that at 1 second, more reverberant energy between 3kHz and 5kHz originates from the ceiling compared to the first two and last measured rows. This may be explained by the presence of a different ceiling material directly above the first two measured rows.

In Fig. 8, representing the EDD of the reverberant sound field at six seconds, we observe the most prominent energy, which is caused by noise at this point in time, originates from the stage area. This energy is slightly less prominent in seats located on the right side of the parterre, suggesting that the source of the noise was either directional or obstructed in some way.

Reverberation Time

An important characteristic of a reverberant sound field is the reverberation time, T 60 . Here again, for spatial analysis, we favor a directional analysis from a set of DRIRs (T 60 (ϕ, θ)). The decay analysis time window used here starts after the mixing time and before the noise floor is reached [START_REF] Massé | Denoising directional room impulse responses with spatially anisotropic late reverberation tails[END_REF]. The mixing time is established using a spatial incoherence evaluation method to find the transition point between early and late reverberation ( [START_REF] Epain | Spherical harmonic signal covariance and sound field diffuseness[END_REF][START_REF] Massé | Denoising directional room impulse responses with spatially anisotropic late reverberation tails[END_REF]). In Fig. 9, we can observe the T 60 (ϕ, θ) of the middle seats in two different rows, 2 and 6. The shorter reverberation time coming from above seat 55 and longer T 60 (ϕ, θ) above Overall, through these energy-based analyses, we observe that the sound field should be considered both anisotropic and inhomogeneous. Further analysis also shows that the energy distribution during the early part of the reverberation is not a predictor of the behavior during late reverberation, which suggests that its reproduction would require direction-dependent decay characteristics.

CONCLUSION

This article introduced a dataset of measured SRIRs in the opera house of the FNOB located in Helsinki, Finland. Two directional sound sources were used on the stage along with 97 microphone positions distributed in the parterre section. A 32-channel SMA was used producing fourth-order Ambisonics SRIRs that allow further spatial analysis. Energy-based analysis methods confirmed that the reverberant sound field of the parterre area is nonuniform. This dataset is shared publicly and intended to help advance research on anisotropic and inhomogeneous reverberant field modeling and reproduction methods.

ACKNOWLEDGMENTS

The measurement campaign was part of a postdoctoral project funded by the Kaute Foundation (project "Conservation of the Acoustics of Historical Halls in Helsinki"). The authors would like to thank Jaakko Korkalainen and Timo Tuovila, from the Finnish National Opera and Ballet, for their help and invaluable support.

Figure 1 .

 1 Figure 1. Measurement layout.

Figure 2 .

 2 Figure 2. Lateral rotation angle of the SMA used during measurements.

Figure 3 .

 3 Figure 3. Directional EDC results on the horizontal plane, for the first 25 ms of an SRIR filtered between 1 kHz and 3 kHz, measured in front of seat 37, on the second row, using the first sound source.

Figure 4 .

 4 Figure 4. Directional EDC results on the horizontal plane, for the first 1.5 seconds of an SRIR filtered between 1 kHz and 3 kHz, measured in front of seat 37, on the second row, using the first sound source.

Figure 5 .

 5 Figure 5. Directional EDC results on the horizontal plane, for the first 4.5 seconds of an SRIR filtered between 1 kHz and 3 kHz, measured in front of seat 37, on the second row, using the first sound source.

Figure 6 .

 6 Figure 6. Top view analysis of each measured rows, at time 0 seconds.

Figure 7 .

 7 Figure 7. Top view analysis of each measured rows, at time 1 second.

Figure 8 .

 8 Figure 8. Top view analysis of each measured rows, at time 6 seconds.

Figure 9 .

 9 Figure 9. T 60 (ϕ, θ) analysis of the top hemisphere of two middle seats, located respectively on rows 2 and 6.

Table 1 .

 1 Microphone coordinates of the first two measured rows contained in the dataset.

	row seat	x	y	row seat	x	y
	2	37	3.51	7.80	4	112	3.00	9.56
		40	4.97	8.35		115	4.47	10.17
		43	6.52	8.87		118	5.97	10.71
		46	8.06	9.29		121	7.54	11.15
		49	9.60	9.58		124	9.12	11.44
		52	11.19 9.79		127	10.68 11.66
		55	12.81 9.86		130	12.28 11.72
		58	14.44 9.79		133	13.89 11.69
		61	16.02 9.60		136	15.48 11.59
		64	17.58 9.32		139	17.04 11.35
		67	19.14 8.91		142	18.62 11.03
		70	20.64 8.37		145	20.16 10.58
		73	22.11 7.72		148	21.69 10.01
						150	22.62	9.56

https://mhacoustics.com/


Annalisa D ' Urzo

Albert Konijnenberg

Giulia Rossetti

Johnny Habchi

Jinyu Li

Paolo Carloni

Frank Sobott

Sonia Longhi
email: sonia.longhi@afmb.univ-mrs.fr

Rita Grandori
email: rita.grandori@unimib.it

Molecular basis for structural heterogeneity of an intrinsically disordered protein bound to a partner by combined ESI-IM-MS and modeling

Intrinsically disordered proteins (IDPs) form biologically active complexes that can retain a high degree of conformational disorder, escaping structural characterization by conventional approaches. An example is offered by the complex between the intrinsically disordered N TAIL domain and the phosphoprotein X domain (P XD ) from measles virus (MeV). Here we detect distinct conformers of the complex by electrospray ionization-mass spectrometry (ESI-MS) and ion mobility (IM) techniques yielding estimates for the solvent-accessible surface area (SASA) in solution and the average collision cross section (CCS) in the gas phase. Computational modeling of the complex in solution, based on experimental constraints, provides atomicresolution structural models featuring different levels of compactness. The resulting models indicate high structural heterogeneity. The intermolecular interactions are predominantly hydrophobic, not only in the ordered core of the complex, but also in the dynamic, disordered regions. Electrostatic interactions become involved in the more compact states. This system represents an illustrative example of a hydrophobic complex that could be directly detected in the gas phase by native mass spectrometry. This work represents the first attempt to modeling the entire N TAIL domain bound to P XD at atomic resolution.

Introduction

The last decade has witnessed an extension to the protein structure-function paradigm, with the progressive understanding of the functional importance of intrinsically disordered proteins 3 (IDPs) or regions (IDRs). These proteins or protein regions lack ordered secondary and tertiary structure under physiological conditions and exist in solution as dynamic and heterogeneous conformational ensembles [START_REF] Habchi | Introducing Protein Intrinsic Disorder[END_REF][START_REF] Tompa | Intrinsically disordered proteins: a 10-year recap[END_REF][START_REF] Uversky | A decade and a half of protein intrinsic disorder: Biology still waits for physics[END_REF]. Approximately 40% of the human proteins are predicted to contain at least one disordered segment of at least 30 amino acids, with as many as 25% of them being likely disordered from start to end [START_REF] Oates | DP2)-P-2: database of disordered protein predictions[END_REF]. Predictions on representative genomes from the three kingdoms of life (i.e. bacteria, archaea and eukaryotes) confirmed the ubiquitous character of structural disorder, in spite of significant differences in its relative amount in the three domains [START_REF] Xue | Orderly order in protein intrinsic disorder distribution: disorder in 3500 proteomes from viruses and the three domains of life[END_REF]. The extent of protein structural disorder tends to increase with biological complexity. This trend could be related to the typical involvement of IDPs in signalling and regulation [START_REF] Schad | The relationship between proteome size, structural disorder and organism complexity[END_REF][START_REF] Dunker | The protein trinity -linking function and disorder[END_REF][START_REF] Uversky | Length-dependent compaction of intrinsically disordered proteins[END_REF].

The structural plasticity of IDPs allows for recognition and binding of multiple partners, resulting in pleiotropic roles of these proteins. Many cases have been described in the literature, in which IDPs acquire ordered conformations upon binding to partners or ligands. Folding coupled to binding can pertain either to specific segments or to the whole protein mettere qui [START_REF] Uversky | Unusual biophysics of intrinsically disordered proteins[END_REF]. Complete folding can lead to well-structured complexes that can be analysed by conventional techniques, such as X-ray crystallography [START_REF] Kovacs | Intrinsically disordered proteins undergo and assist folding transitions in the proteome[END_REF][START_REF] Fong | Intrinsic Disorder in Protein Interactions: Insights From a Comprehensive Structural Analysis[END_REF][START_REF] Lobanov | ComSin: database of protein structures in bound (complex) and unbound (single) states in relation to their intrinsic disorder[END_REF]. However, increasing evidence shows that many IDPs retain a high degree of structural disorder even in the bound state. These "fuzzy" complexes [START_REF] Tompa | Fuzzy complexes: polymorphism and structural disorder in proteinprotein interactions[END_REF] are stabilized by short, ordered recognition elements, referred to as molecular recognition elements (MoREs), and a large number of highly unstable contacts, leading to a cloud of interconverting conformations around a structured core [START_REF] Kovacs | Intrinsically disordered proteins undergo and assist folding transitions in the proteome[END_REF][START_REF] Tompa | Fuzzy complexes: polymorphism and structural disorder in proteinprotein interactions[END_REF][START_REF] Hazy | Limitations of Induced Folding in Molecular Recognition by Intrinsically Disordered Proteins[END_REF][START_REF] Uversky | Unusual biophysics of intrinsically disordered proteins[END_REF][START_REF] Fuxreiter | Fuzziness: linking regulation to protein dynamics[END_REF][START_REF] Meszaros | Disordered Binding Regions and Linear Motifs-Bridging the Gap between Two Models of Molecular Recognition[END_REF]. This staccato-type of interactions is much more difficult to characterize than stable interactions of folded complexes. Yet, it is thought to be relevant for biological function. Fuzzy regions within complexes can harbour regulatory post-translational modification sites, or can mediate interactions with additional partners. They can even directly or indirectly interfere with recognition elements, promoting or inhibiting binding. In addition, fuzziness provides a way to reduce entropic penalty, thereby affording enhanced affinity [START_REF] Fuxreiter | Fuzziness: linking regulation to protein dynamics[END_REF][START_REF] Fuxreiter | Fuzziness: Structural Disorder in Protein Complexes[END_REF].

Hence, description of the conformational ensembles characterizing fuzzy IDP complexes is essential to the understanding of the molecular processes by which IDPs establish their functional networks. However, the highly heterogeneous nature of IDPs and the fuzziness that is often observed in their bound state makes their structural characterization very challenging. Such investigation demands the combined application of various biophysical methods capable of capturing conformational heterogeneity and identifying metastable states.

In this regard, native mass spectrometry based on nano-ESI sources has emerged as a powerful approach, allowing detection of coexisting conformers with distinct global compactness [START_REF] Simmons | Characterization of transient protein folding intermediates during myoglobin reconstitution by time-resolved electrospray mass spectrometry with on-line isotopic pulse labeling[END_REF][ Kaltashov 2008]. The average charge state of each component yields an estimate of SASA for the structure in solution, at the moment of transfer to the gas phase [START_REF] Testa | Charge-Surface Correlation in Electrospray Ionization of Folded and Unfolded Proteins[END_REF][START_REF] Kaltashov | Estimates of protein surface areas in solution by electrospray ionization mass spectrometry[END_REF]. Hyphenation with IM measurements adds a further dimension to species separation and offers estimates of the CCS for each detected structure in the gas phase [START_REF] Konijnenberg | Native ion mobility-mass spectrometry and related methods in structural biology[END_REF][START_REF] Beveridge | Mass spectrometry methods for intrinsically disordered proteins[END_REF][START_REF] Lanucara | The power of ion mobility-mass spectrometry for structural characterization and the study of conformational dynamics[END_REF][START_REF] Woods | Advances in ion mobility spectrometry-mass spectrometry reveal key insights into amyloid assembly[END_REF]. These techniques conjugate the exceptional analytical power of mass spectrometry with structural description and, therefore, are particularly well suited to the challenges posed by conformational studies on IDPs [Chen 2014; Saikusa 2013; [START_REF] Beveridge | Mass spectrometry methods for intrinsically disordered proteins[END_REF]]. The development of atomic-resolution models requires, however, complementation of experimental data by computational simulations. Theoretical approaches have been improved to effectively model disordered conformational ensembles based on structural information derived from native mass spectrometry and other biophysical analyses [START_REF] Cong | Role of Prion Disease-Linked Mutations in the Intrinsically Disordered N-Terminal Domain of the Prion Protein[END_REF][START_REF] Dibenedetto | A Molecular Dynamics Simulation-Based Interpretation of Nuclear Magnetic Resonance Multidimensional Heteronuclear Spectra of alpha-Synuclein.Dopamine Adducts[END_REF][START_REF] Wang | Multiscaled exploration of coupled folding and binding of an intrinsically disordered molecular recognition element in measles virus nucleoprotein[END_REF].

We herein combine ESI-MS, ESI-IM-MS and computational methods to describe the N TAIL -P XD complex from measles virus (MeV). While N TAIL is an intrinsically disordered domain of 125 residues [START_REF] Longhi | The C-terminal domain of the measles virus nucleoprotein is intrinsically disordered and folds upon binding to the C-terminal moiety of the phosphoprotein[END_REF][START_REF] Bourhis | The C-terminal domain of measles virus nucleoprotein belongs to the class of intrinsically disordered proteins that fold upon binding to their physiological partner[END_REF][START_REF] Gely | Solution structure of the C-terminal X domain of the measles virus phosphoprotein and interaction with the intrinsically disordered C-terminal domain of the nucleoprotein[END_REF][START_REF] Jensen | Intrinsic disorder in measles virus nucleocapsids[END_REF], P XD is folded into an ordered three-helix bundle [START_REF] Johansson | Crystal structure of the measles virus phosphoprotein domain responsible for the induced folding of the C-terminal domain of the nucleoprotein[END_REF]. Interaction between N TAIL and P XD is crucial for MeV replication, as it allows recruitment of the viral RNA-dependent RNA polymerase onto the nucleocapsid template (Longhi, Curr Topics Microbiol Immunol 2009; Habchi and Longhi, Mol Biosysts 2012). Upon binding to P XD , N TAIL undergoes induced folding localized in an 18-residue -helical region. This -helical molecular recognition element (α-MoRE) [START_REF] Gely | Solution structure of the C-terminal X domain of the measles virus phosphoprotein and interaction with the intrinsically disordered C-terminal domain of the nucleoprotein[END_REF][START_REF] Jensen | Intrinsic disorder in measles virus nucleocapsids[END_REF][START_REF] Bourhis | The intrinsically disordered C-terminal domain of the measles virus nucleoprotein interacts with the C-terminal domain of the phosphoprotein via two distinct sites and remains predominantly unfolded[END_REF][START_REF] Belle | Mapping alpha-helical induced folding within the intrinsically disordered C-terminal domain of the measles virus nucleoprotein by site-directed spin-labeling EPR spectroscopy[END_REF] associates to P XD forming a four-helix bundle [START_REF] Johansson | Crystal structure of the measles virus phosphoprotein domain responsible for the induced folding of the C-terminal domain of the nucleoprotein[END_REF][START_REF] Kingston | Structural basis for the attachment of a paramyxoviral polymerase to its template[END_REF]. The N TAIL -P XD interaction mostly relies on hydrophobic contacts [START_REF] Gely | Solution structure of the C-terminal X domain of the measles virus phosphoprotein and interaction with the intrinsically disordered C-terminal domain of the nucleoprotein[END_REF][START_REF] Kingston | Structural basis for the attachment of a paramyxoviral polymerase to its template[END_REF][START_REF] Bernard | Interaction between the C-terminal domains of N and P proteins of measles virus investigated by NMR[END_REF] and is characterized by a K D in the sub-micromolar range, as consistently indicated by surface plasmon resonance (SPR) and isothermal titration calorimetry (ITC) experiments [START_REF] Bourhis | The intrinsically disordered C-terminal domain of the measles virus nucleoprotein interacts with the C-terminal domain of the phosphoprotein via two distinct sites and remains predominantly unfolded[END_REF][START_REF] Shu | Plasticity in Structural and Functional Interactions between the Phosphoprotein and Nucleoprotein of Measles Virus[END_REF][START_REF] Blocquel | Interaction between the C-terminal domains of measles virus nucleoprotein and phosphoprotein: A tight complex implying one binding site[END_REF]. Previous studies on the N TAIL -P XD complex by small-angle X-ray scattering (SAXS) and NMR showed that the majority of N TAIL remains disordered in the bound state, thus supporting the fuzzy and heterogeneous nature of this complex [START_REF] Gely | Solution structure of the C-terminal X domain of the measles virus phosphoprotein and interaction with the intrinsically disordered C-terminal domain of the nucleoprotein[END_REF][START_REF] Bourhis | The intrinsically disordered C-terminal domain of the measles virus nucleoprotein interacts with the C-terminal domain of the phosphoprotein via two distinct sites and remains predominantly unfolded[END_REF][START_REF] Kavalenka | Conformational Analysis of the Partially Disordered Measles Virus N-TAIL-XD Complex by SDSL EPR Spectroscopy[END_REF]. Although hydrophobic complexes could be expected to dissociate in the gas phase, detection of such complexes by MS has been reported in some instances [START_REF] Liu | Hydrophobic Protein-Ligand Interactions Preserved in the Gas Phase[END_REF][START_REF] Barylyuk | What Happens to Hydrophobic Interactions during Transfer from the Solution to the Gas Phase? The Case of Electrospray-Based Soft Ionization Methods[END_REF][START_REF] Marcoux | Mass spectrometry reveals synergistic effects of nucleotides, lipids, and drugs binding to a multidrug resistance efflux pump[END_REF].

The results of this study show that the MeV N TAIL -P XD complex is amenable to MS analysis and that distinct conformational states can be detected. Experimental data are used to validate structural modeling. The results highlight the conformational freedom of the complex and the hydrophobic nature of its interface.

Materials and methods

Expression and purification of MeV N TAIL and P XD proteins

The expression constructs in the pDEST14 vector, allowing expression of N-terminally (N TAIL ) or C-terminally (P XD ) hexahistidine tagged forms of the MeV proteins under the control of the T7 promoter, have already been described [START_REF] Bourhis | The intrinsically disordered C-terminal domain of the measles virus nucleoprotein interacts with the C-terminal domain of the phosphoprotein via two distinct sites and remains predominantly unfolded[END_REF]. Expression and purification of MeV N TAIL and P XD were carried out as described [START_REF] Bourhis | The intrinsically disordered C-terminal domain of the measles virus nucleoprotein interacts with the C-terminal domain of the phosphoprotein via two distinct sites and remains predominantly unfolded[END_REF], except that the final gel filtration step was carried out using 10 mM ammonium acetate pH 6.5 as elution buffer.

Mass spectrometry

Nano-ESI-MS analyses were performed on a hybrid quadrupole time of flight (Q-TOF) mass spectrometer (QSTAR Elite; ABsciex, Framingham, MA) equipped with a nano-electrospray ionization sample source. Metal-coated borosilicate capillaries (Proxeon, Odense, Denmark), with medium-length emitter tips of 1-μm internal diameter, were used to infuse the samples. The instrument was calibrated by the standard Renin-inhibitor solution (ABSciex, Framingham, MA) on the intact molecular ion [M+2H] 2+ (879.97 Da) and its fragment [M+H] 1+ (110.07 Da). Data were acquired with ion spray voltage 1,200 V and declustering potential 80 V, and were averaged over 2-min acquisitions. The interface was kept at room temperature (interface heater off). Pure preparations of the N TAIL and P XD protein fragments in 10 mM ammonium acetate pH 6.5 were stored at -20 °C and diluted to the indicated final concentrations in the same buffer before analyses. Samples were incubated at room temperature for 10 minutes before measurements.

Mass spectra from Figure 1A and Figure 2A were transformed from x = m/z to x = z as abscissa axis and data point were fitted by Gaussian functions. The analysis was performed by the software Origin7 (Originlab, Northampton,MA,USA) [START_REF] Dobo | Detection of multiple protein conformational ensembles in solution via deconvolution of charge-state distributions in ESI MS[END_REF][START_REF] Borysik | Co-populated conformational ensembles of beta(2)-microglobulin uncovered quantitatively by electrospray ionization mass spectrometry[END_REF].

Nano-ESI-IM-MS analyses were performed on a Synapt G2 HDMS instrument (Waters, Milford, MA, USA) by direct infusion, under non-denaturing conditions. The samples were injected at the indicated protein concentrations in 10 mM ammonium acetate pH 6.5 at room temperature.

Instrument parameters were carefully optimized to minimize disruption of non-covalent interactions. The following instrumental settings were applied: spray voltage 1,400 V, sampling cone voltage 50 V, trap collision energy 4 V, transfer collision energy 0 V, trap DC bias 45 V, backing pressure 2.98 mbar, trap pressure 5 × 10 -2 mbar, IMS pressure 3.09 mbar. Instrument calibration for CCS measurements was performed using concanavalin A, albumin, βlactoglobulin and cytochrome c as standards while referring to the absolute CCS values determined on a modified Synapt G1 as described by Bush et al. [START_REF] Bush | Collision Cross Sections of Proteins and Their Complexes: A Calibration Framework and Database for Gas-Phase Structural Biology[END_REF] Structural modeling. Homology modeling was performed to build an initial structure of the N TAIL -P XD complex for molecular simulations. The folded core was modeled on the crystallographic structure of the chimeric protein (PDB 1T6O) [START_REF] Kingston | Structural basis for the attachment of a paramyxoviral polymerase to its template[END_REF]. The missing regions (residues 401-485 and 505-525 of N TAIL ) were split into fragments and used to screen the structure database searching for suitable templates, following the approach by Bowie et al. [START_REF] Bowie | An Evolutionary Approach to Folding Small Alpha-Helical Proteins That Uses Sequence Information and an Empirical Guiding Fitness Function[END_REF][START_REF] Simons | Assembly of protein tertiary structures from fragments with similar local sequences using simulated annealing and Bayesian scoring functions[END_REF]. Ten templates (Figure S1), showing from a minimum of 28% sequence identity over 41 residues to a maximum of 56% over 17 residues to the target, were identified, reaching a cumulative 96.5% sequence coverage of the N TAIL disordered arms. These homology-derived restraints were used to generate 2000 models of the N TAIL -P XD complex by the MODELLER 9v9 package [START_REF] Marti-Renom | Comparative protein structure modeling of genes and genomes[END_REF]. Most (94.5%) of the resulting structures have favourable backbone conformations [START_REF] Ramachandran | Stereochemistry of polypeptide chain configurations[END_REF] for more than 80% of the residues, according to the Procheck program [START_REF] Laskowski | Procheck -a program to check the stereochemical of protein structures[END_REF]. The lowest-DOPE (discrete optimized protein energy) score [START_REF] Shen | Statistical potential for assessment and prediction of protein structures[END_REF] model was selected as the starting structure for the following molecular simulations.

Replica-exchange Monte Carlo (REMC) simulations were carried out by the PROFASI package (PROtein Folding and Aggregation SImulator) [START_REF] Irback | An effective all-atom potential for proteins[END_REF][START_REF] Li | Formation and Growth of Oligomers: A Monte Carlo Study of an Amyloid Tau Fragment[END_REF][START_REF] Jonsson | Distinct phases of free alpha-synuclein-A Monte Carlo study[END_REF], with 8 replicas performed at distinct temperatures between 298K and 348K. The energy distributions at these temperatures (Figure S2) show optimal overlap between consecutive temperatures of the explored range (Figure S2). Such an observation is relevant in order to guarantee a sufficient number of replica exchanges between neighbouring replicas, thus allowing an efficient sampling of the conformational space of the protein [START_REF] Fukunishi | On the Hamiltonian replica exchange method for efficient sampling of biomolecular systems: Application to protein structure prediction[END_REF]. Dihedral and distance restraints [START_REF] Irback | PROFASI: A Monte Carlo simulation package for protein folding and aggregation[END_REF] were applied to the regions represented in the crystallographic structure [START_REF] Kingston | Structural basis for the attachment of a paramyxoviral polymerase to its template[END_REF]. A total of 5.0  10 6 cycles of simulations were performed, according to a previously described protocol [START_REF] Cong | Role of Prion Disease-Linked Mutations in the Intrinsically Disordered N-Terminal Domain of the Prion Protein[END_REF]. Models obtained at 298K were extracted, constituting an ensemble of 2831 conformations.

The chemical shifts (CSs) of the N TAIL moiety for each conformation of the ensemble were calculated using the SHIFTX package [START_REF] Neal | Rapid and accurate calculation of protein H-1, C-13 and N-15 chemical shifts[END_REF] (Figure S3). The values of solvent accessible surface area (SASA) were calculated by the tools implemented in GROMACS 4.5.5 [START_REF] Van Der Spoel | Gromacs: fast, flexible, and free[END_REF]. The structures showing the best correlation with either experimental CSs or experimental SASA were identified. The circular dichroism (CD) spectra for each conformation were calculated by the DichroCalc webserver [START_REF] Bulheller | DichroCalc-circular and linear dichroism online[END_REF], using the parameters derived from both ab initio [START_REF] Besley | Theoretical studies toward quantitative protein circular dichroism calculations[END_REF] and semiempirical calculations [START_REF] Sreerama | Structural composition of beta(I)-and beta(II)-proteins[END_REF]. All the figures for structures visualization were drawn using PyMOL (Molecular Graphics System, Version 1.3, Schrödinger LLC).

Results and discussion

N TAIL . The MeV N TAIL protein was analyzed by nano-ESI-MS under non-denaturing conditions (Figure 1A). The spectrum shows a very broad, bimodal charge-state distribution (CSD), indicating structural heterogeneity consistent with the intrinsically disordered nature of this protein. Nonetheless, a compact conformation can be identified in the high m/z region of the spectrum, centered on the 9+ charge state. Such an extent of ionization approaches the behavior of normally folded proteins of the same size. The rest of the spectrum is characterized by a broad peak envelope that spans the region between the 10+ and the 24+ ions, with main charge state 16+. This component corresponds to disordered conformations, characterized by low compactness. Deconvolution by Gaussian fitting is shown in Figure 1B. The results indicate that, in addition to the compact and disordered conformations, a third component of intermediate compactness can be identified. Although the relative amounts of the distinct components depend somewhat on the type of instrument and the parameter settings (as generally true), the intermediate species was detected with good reproducibility under the conditions described here.

The compact and the intermediate conformations are depleted under acidic conditions (Figure 1C) and disappear upon further addition of 50% acetonitrile (Figure 1D), while the disordered component slightly shifts to higher charge states. This response to denaturing conditions suggests that the N TAIL protein populates collapsed and partially folded states that can be destabilized by acids and organic solvents. The isotopically averaged molecular weight by mass deconvolution (data not shown) yields a value of 14,630.94 ± 0.17 Da, in close agreement with the value calculated on the basis of the amino acid sequence, including the initial methionine (14631.7 Da). P XD . Figure 2 shows the nano-ESI-MS spectra of P XD preparations. Although P XD folds into a helical domain, it displays a bimodal CSD under non-denaturing conditions, with main charge states 6+ and 8+ (Figure 2A). Gaussian fitting of the two components is reported in Figure 2B. This result suggests that the three-helix bundle of the isolated P XD fragment tends to open to a less compact structure, at least under the here employed conditions. The 8+ component does not represent the fully denatured state, since it converts progressively into a more highly charged component (9+) by the addition of formic acid and acetonitrile (Figures 3C and3D). The experimental mass (6,554.28 ± 0.04 Da) corresponds to the value calculated from the amino acid sequence of the protein without the initial methionine (6,555.66 Da). The conformational heterogeneity adopted by MeV P XD is in agreement with previous biophysical and structural studies on the homologous phosphoprotein X domains from members of the closely related Rubulavirus genus, indicating that these domains span a structural continuum, ranging from compact to largely disordered states in solution [START_REF] Kingston | Structure of the nucleocapsidbinding domain from the mumps virus polymerase; an example of protein folding induced by crystallization[END_REF][START_REF] Yegambaram | Protein domain definition should allow for conditional disorder[END_REF].

N TAIL -P XD . The interaction between N TAIL and P XD was investigated by mixing equimolar amounts of the two proteins and infusing the sample after 10-min incubation at room temperature without agitation. The results obtained with concentrations of either 10 M or 20 M of both proteins are shown in Figure 3. The spectra are dominated by the peaks of the free proteins, but signals specific to the N TAIL -P XD complex become evident at the higher protein concentration.

The measured mass of the complex (21187.4 ± 0.61 Da) corresponds closely to the sum of the theoretical values expected for N TAIL with the initial methionine and P XD without the initial methionine (21,187.46 Da), indicating a 1:1 stoichiometry.

The complex disappears upon applying denaturing solvent conditions or high declustering potentials (data not shown). These results show that the MeV N TAIL -P XD complex, which is stabilized in solution by hydrophobic interactions, is preserved, at least partially, during the electrospray process and gas-phase ion separation, allowing detection by ESI-MS in a concentration-dependent manner. The expected fraction of bound protein at the concentrations shown in Figure 3B, based on solution affinity data [START_REF] Bourhis | The intrinsically disordered C-terminal domain of the measles virus nucleoprotein interacts with the C-terminal domain of the phosphoprotein via two distinct sites and remains predominantly unfolded[END_REF][START_REF] Shu | Plasticity in Structural and Functional Interactions between the Phosphoprotein and Nucleoprotein of Measles Virus[END_REF][START_REF] Blocquel | Interaction between the C-terminal domains of measles virus nucleoprotein and phosphoprotein: A tight complex implying one binding site[END_REF], is 93%. Although relative amounts of different species cannot be quantified by ESI-MS, and although the buffer conditions are not identical to previous solution studies, these results suggest that significant dissociation of the complex occurs under electrospray conditions.

The CSD of the complex-specific peaks is quite broad and, itself, bimodal, suggesting coexistence of at least two distinct conformational states of the bound species. This conformational heterogeneity likely reflects the persistence of a conspicuous degree of disorder in the complex [START_REF] Gely | Solution structure of the C-terminal X domain of the measles virus phosphoprotein and interaction with the intrinsically disordered C-terminal domain of the nucleoprotein[END_REF][START_REF] Jensen | Intrinsic disorder in measles virus nucleocapsids[END_REF][START_REF] Bourhis | The intrinsically disordered C-terminal domain of the measles virus nucleoprotein interacts with the C-terminal domain of the phosphoprotein via two distinct sites and remains predominantly unfolded[END_REF]. The high-charge component of the complex (18+) would then correspond to an "open" conformation, in which the disordered arms of N TAIL , upstream and downstream to the -MoRE, fluctuate maintaining high solvent accessibility. The low-charge component (11+), instead, likely represents a compact or "closed" conformation of the complex, in which the N TAIL arms collapse onto the surface of the folded partner, as suggested by the low extent of ionization, which approaches the expected value for folded globular proteins of the same mass (9.46+) [START_REF] Testa | Charge-Surface Correlation in Electrospray Ionization of Folded and Unfolded Proteins[END_REF]. The average SASA value of the "open" and "closed" states can be calculated from the empiric relation with the average charge state [START_REF] Testa | Charge-Surface Correlation in Electrospray Ionization of Folded and Unfolded Proteins[END_REF], resulting in estimated values of 16100 Å 2 and 9500 Å 2 , respectively.

It is worth noting that this dual nature of the N TAIL -P XD complex did not emerge from previous experimental studies Habchi and Longhi, Mol Biosysts 2012. Thus, the question arises as to whether this result reflects a real conformational heterogeneity in solution, captured only by the exquisite sensitivity of native MS, or an altered conformational ensemble induced by the electrospray conditions. To this regard, it should be noted that CSDs generally reflect structural compactness and conformational heterogeneity in solution, before or during the transfer to the gas phase. Thus, hypothetical conformational rearrangements leading to the low-charge component in the CSDs should take place at the level of ESI droplets. The fact that CSDs of IDPs detected by nano-ESI-MS and their response to solvent conditions are protein specific, as for instance indicated by opposite pH dependence and distinct effects of organic solvents, [START_REF] Testa | Charge-Surface Correlation in Electrospray Ionization of Folded and Unfolded Proteins[END_REF][START_REF] Testa | Extracting structural information from charge-state distributions of intrinsically disordered proteins by non-denaturing electrospray-ionization mass spectrometry[END_REF][START_REF] Natalello | Compact conformations of alpha-synuclein induced by alcohols and copper[END_REF][START_REF] Santambrogio | The role of the central flexible region on the aggregation and conformational properties of human ataxin-3[END_REF] Lambrughi Sic1 suggests that they reflect real conformational properties rather than artifacts induced by the experimental conditions. However, it could not be ruled out [START_REF] Uversky | Unusual biophysics of intrinsically disordered proteins[END_REF] spostare in intro that poorer kinetic trapping of disordered conformations compared to folded structures expose IDPs to more significant conformational changes inside ESI droplets, affecting in turn CSDs. Even more relevant structural rearrangements could be expected to take place in the gas phase, after electrospray and downstream to protonation reactions. Such structural rearrangements would not affect the CSDs but could be captured by ion-mobility measurements. In order to get further insight on the compact state of the complex, we further investigated the conformational space of the complex by ion mobility on a Waters Synapt G2 HDMS instrument under non-denaturing conditions comparable to the MS measurements reported above. The IM-MS spectrum obtained with a mixture of 20 M N TAIL and 20 M P XD is reported in Figure 4.

The CSDs are similar to those observed on the QSTAR Elite instrument, although with higher relative amounts of the compact form. The additional separation of analytes by IM allows detection of distinct structural species even at the same charge state. In this case, two slightly different conformations are found to populate the compact state of the N TAIL -P XD complex (charge states 8+ to 10+). Average CCS of 1326 and 1422 Å 2 can be derived for the two main peaks detectable for the 8+ charge state. This result suggests that the compact state of the complex is characterized by further structural heterogeneity. Thus, while its overall ionization suggests a collapsed structure, its arrival-time distribution reveals distinct peaks rather than the single peak typically observed for normally folded proteins. The presence of multiple conformers, although with different CCS values, is observed also for the 9+ and 10+ ions. The predominant conformer displays progressively larger CCS values (1422, 1466, 1607 Å 2 ) as the charge state increases from 8+ to 10+. This trend is consistent with the lowest charge state (8+ in this case) corresponding to the most compact species in the original ensemble and to the species with lowest interference of Coulomb repulsions upon transfer to the gas phase. Interestingly, at higher charge states (figure 4C), the structurally heterogenous nature of the complex is maintained, whereas for a fully disordered protein such as alpha-synuclein this converges into a single arrival time distribution for the higher charge states [ref]. Altogether, these results suggest that both the open and closed states of the complex should be described as conformational ensembles. The high variability of CCS values revealed by the IM profiles could represent a distinct feature of IDPs compared to normally folded, globular structures. Further studies will be needed to clarify to which extent this variability reflects solution and/or gas-phase properties.

Modeling the N TAIL -P XD complex. The structural models of the N TAIL -P XD complex were generated by combining homology modeling and an all-atom Monte Carlo based simulation tool, PROFASI [START_REF] Irback | An effective all-atom potential for proteins[END_REF][START_REF] Li | Formation and Growth of Oligomers: A Monte Carlo Study of an Amyloid Tau Fragment[END_REF][START_REF] Jonsson | Distinct phases of free alpha-synuclein-A Monte Carlo study[END_REF], which allows exploring the conformational ensemble of the complex in implicit solvent (see Methods for details). The quality of the conformational sampling was established by the agreement with available experimental data, namely NMR CSs of N TAIL bound to P XD [START_REF] Gely | Solution structure of the C-terminal X domain of the measles virus phosphoprotein and interaction with the intrinsically disordered C-terminal domain of the nucleoprotein[END_REF] and CD of the N TAIL -P XD complex [START_REF] Shu | Plasticity in Structural and Functional Interactions between the Phosphoprotein and Nucleoprotein of Measles Virus[END_REF]. Quite good agreement can be observed between calculated CSs and those measured by solution NMR measurements [START_REF] Gely | Solution structure of the C-terminal X domain of the measles virus phosphoprotein and interaction with the intrinsically disordered C-terminal domain of the nucleoprotein[END_REF] (Figure S3).

The calculated CD spectra of the conformational ensemble are similarly close to the experimental ones [START_REF] Shu | Plasticity in Structural and Functional Interactions between the Phosphoprotein and Nucleoprotein of Measles Virus[END_REF], reproducing the minimum at 208 nm, a shoulder at 222 nm and a positive maximum at 192 nm for the complex, although a well-defined local minimum at 222 nm is missing (Figure S4). Finally, the SASA mean value calculated from the models is 17920  690 Å 2 , indicating that the conformational ensemble well describes the open state of the complex detected by ESI-MS. Three models, namely Model 1, Model 2 and Model 3, were selected from the conformational ensemble, based on best agreement with the CSs from NMR or the SASA from ESI-MS (Figure 5, see Methods for selection criteria). Although these models are not representative of the entire N TAIL -P XD conformational ensemble, they are useful to inspect distinct interaction networks that could drive protein compaction and can also provide hints for targeting the complex in a conformation-specific manner by small molecules. Thus, contact analysis was performed, in order to investigate the nature of the interactions involving either the α-MoRE or the disordered regions that were missing from the crystallographic structure. Schematic diagrams of the interface between N TAIL and P XD are shown in Figure S5. The interface between the α-MoRE and P XD shows minor rearrangements relative to the X-ray structure, which could reflect structure dynamics in solution and/or differences between the chimeric protein and the intermolecular complex. Nevertheless, the interface within the four-helix bundle remains almost exclusively hydrophobic in Model 1 and Model 2, while it shows some additional electrostatic interactions in Model 3. Analysis of the contacts established by the fuzzy regions (see Figure S5) unveiled their prevalently hydrophobic nature, suggesting that the interactions between P XD and N TAIL are dominated by hydrophobic interactions, even outside the folded, globular core. A few hydrogen bonds and salt-bridges seem to give additional contribution to the binding of the two proteins. Thus, it seems that not only the helical core of the complex, but also the surrounding disordered cloud is dominated by hydrophobic interactions, although hydrogen bonding and electrostatic interactions seem to play a role in stabilizing the more compact states. The prevalently hydrophobic nature of the N TAIL -P XD complex is in agreement with previous reports highlighting that, although IDPs are characterized by a low content in hydrophobic residues, not sufficient to drive formation of a hydrophobic core, hydrophobic residues often play a dominant role in mediating physiologically relevant protein-protein interactions [START_REF] Meszaros | Molecular principles of the interactions of disordered proteins[END_REF].

Conclusions

This study combines information derived from biophysical investigation and molecular simulations, in order to develop high-resolution structural models for the fuzzy complex between N TAIL and P XD . The results show that the staccato-type interactions characterizing this molecular ensemble are mainly of hydrophobic nature. While previous atomic models focused only on the α-MoRE region of N TAIL , this study combines experimental data and computational modeling to generate models of the entire N TAIL -P XD complex at atomic resolution. By including the disordered arms in the molecular modeling, it was possible to extend interaction analysis to the dynamic regions of the complex, which are likely involved in biological function. The information that can be derived from this analysis sheds light onto the nature of the interactions that drive protein compaction and sets the basis for targeting specific conformations of the complex by small-molecules inhibitors.

The good agreement between SASA values derived from CSD analysis and solution models for the open state of the N TAIL /P XD complex suggests that the high-charge component of MS spectra reflects structural properties of the heterogeneous conformational ensemble and gives, in turn, further support to the structural details derived from the models. The MS results reported here also point out, for the first time, a compact state of the complex. IM/MS data indicate that this component is characterized by high structural heterogeneity in the gas phase. The broad arrival time distributions observed for the low charge-state component could be a distinct feature of collapsed states of IDPs, as opposed to natively folded, globular structures. Since compact conformations were not detected by previous experimental investigation, further studies will be required to tell whether they represent a minor population of the solution ensemble or a collapsed species induced by the electrospray process. Normally, charge states and CCS are closely linked to each other, but, if the protein can re-structure after the charge states are generated (i.e. after ESI), there can be a discrepancy between the two. Systematic comparison of solution and gasphase conformational ensembles of IDPs will be needed to clarify this point.

(

  Rebecca Beveridge, Kamila Parcholarz, Jason Kalapothakis, Cait MacPhee, Perdita Barran, 2014. "The Use of Mass Spectrometry to Determine the Disordered Content of Proteins". The Biophysical Society Meeting on Disordered Motifs and Domains in Cell Control. Dublin, Ireland).

Figure 1 .

 1 Figure 1. Nano-ESI-MS spectra of MeV N TAIL (ABSciex QSTAR Elite instrument).

Figure 2 .

 2 Figure 2. Nano-ESI-MS spectra of MeV P XD . (ABSciex QSTAR Elite instrument).

Figure 3 .

 3 Figure 3. Nano-ESI-MS spectra of MeV N TAIL and P XD mixtures. (ABSciex QSTAR Elite

Figure 4 .

 4 Figure 4. Nano-ESI-IM-MS spectrum of a MeV N TAIL and P XD mixture (Waters Synapt G2

Figure 5 .

 5 Figure 5. Structural models of the MeV N TAIL -P XD complex.

Figure

  Figure 2

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 2 Figure 2

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Figure 3 30 Figure 4 31

 304 Figure 3

Figure 5

 5 Figure 5

Acknowledgments

The authors thank Carlo Santambrogio for expert assistance and helpful discussions. This work was carried out with the financial support of the CNRS and of the Agence Nationale de la Recherche, specific programs "Physico-Chimie du Vivant" (ANR-08-PCVI-0020-01) and "ASTRID" (ANR-11-ASTR-003-01) to S.L. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. F.S. is a Francqui Research Professor at UA. The Synapt G2 mass spectrometer is funded by a grant from the Hercules Foundation -Flanders. 18