R Torchio
email: torchio@esrf.fr

S Boccato

F Miozzi

N. Ishimatsu A D Rosa

I Kantor

Irifune

N Ishimatsu

N Sévelin-Radiguet

R Briggs

C Meneghini

T Irifune

G Morard

Melting curve and phase relations of Fe-Ni alloys: implications for the Earth's core composition

whether they are published or not. The documents may come

Melting curve and phase relations of Fe-Ni alloys:

implications for the Earth's core composition

Introduction

Constraining the thermal profile of planetary cores is mandatory to model their dynamics, from the generation of the magnetic field to the mechanism of differentiation.

Melting curves of materials constituting their interior provide a first constrain on their thermal profile. For instance, in the Earth, the crystallization temperature of liquid iron alloys, forming the solid inner core, represents an anchoring point for the geotherm through the Earth's core.

Nickel is the second most abundant element in planetary cores, after iron. However, as these two metals have a similar atomic number, the effects of nickel on the properties of iron are often assumed to be small in comparison to those of light elements (i.e. C, O, S, Si, H) [START_REF] Poirier | Light elements in the Earth's outer core : A critical review[END_REF]. Based on cosmochemical models and studies on iron meteorites, the Earth's core is believed to be composed by iron alloyed with 5-15 wt% of Ni (and other light elements) [START_REF] Birch | Elasticity and constitution of the Earth's interior[END_REF][START_REF] Hirose | Composition and State of the Core[END_REF], while iron meteorites have been found to contain up to 35 wt% of Ni [START_REF] Buchwald | Handbook of iron meteorites. Their history, distribution, composition and structure[END_REF].

While numerous investigations on pure Fe phase diagram under extreme conditions of pressure and temperature have been conducted, only few have been dedicated to Fe-Ni alloys. In particular, measurements of their melting curves are very scarce. To the best of our knowledge, there is only one study dedicated to the melting curve of the Fe-Ni alloy with 10 wt% of nickel, using Synchrotron Mössbauer Spectroscopy (SMS) in the LH-DAC [START_REF] Zhang | Temperature of Earth's core constrained from melting of Fe and Fe 0.9 Ni 0.1 at high pressures[END_REF]. In this study, no obvious effect of Ni was observed on the melting temperature of Fe up to 125 GPa.

Solid phase relations for Fe-Ni alloys at concentrations between 5 and 50 wt% of Ni have been previously investigated [START_REF] Huang | Phase relationships in Fe-Ni alloys at high pressures and temperatures[END_REF][START_REF] Huang | Phase diagram and elastic properties of Fe 30% Ni alloy by synchrotron radiation[END_REF][START_REF] Lin | Iron-nickel alloy in the earth's core[END_REF][START_REF] Mao | Phase relations of Fe-Ni alloys at high pressure and temperature[END_REF][START_REF] Kuwayama | Phase relations of iron and iron-nickel alloys up to 300 GPa: Implications for composition and structure of the Earth's inner core[END_REF][START_REF] Komabayashi | In situ X-ray diffraction measurements of the fcc -hcp phase transition boundary of an Fe -Ni alloy in an internally heated diamond anvil cell[END_REF][START_REF] Dubrovinsky | Body-Centered Cubic Iron-Nickel Alloy in Earth's Core[END_REF] up to 300 GPa and 3000 K showing that Ni alloying enlarges the fcc phase stability to higher pressures (P) and lower temperatures (T) with increasing Ni content. Ni alloy-ing has also proved to dramatically increase the strength of pure Fe [START_REF] Reagan | The effect of nickel on the strength of iron nickel alloys: Implications for the earth's inner core[END_REF].

On the other hand, the Fe equation of state (H. [START_REF] Mao | Static compression of iron to 300 GPa and Fe 0.8 Ni 0.2 alloy to 260 GPa: implications for composition of the core[END_REF] and c/a ratio of the hcp phase at high-P and high-T [START_REF] Lin | Iron-nickel alloy in the earth's core[END_REF][START_REF] Sakai | Equation of state of pure iron and Fe 0.9 Ni 0.1 alloy up to 3 Mbar[END_REF][START_REF] Komabayashi | In situ X-ray diffraction measurements of the fcc -hcp phase transition boundary of an Fe -Ni alloy in an internally heated diamond anvil cell[END_REF] have shown to remain practically unaffected. These studies have contributed to the formulation of hypotesis regarding the properties and structure of the Earth's inner core that include several extrapolations and assumption, one of those being the effect of Ni addition on the melting curve of Fe.

The purpose of this study is to clarify how Ni alloying affects the Fe phase diagram and in particular its melting curve. The melting temperature of this end-member is mandatory to constrain the liquidus shape.

Experimental methods

Fe-Ni samples with 20 wt% and 36 wt% of Ni were compressed and heated in Diamond Anvil Cells (DACs) equipped with nanocrystalline diamond anvils [START_REF] Rosa | Nano-polycrystalline diamond anvils: key devices for xas at extreme conditions: their use, scientific impact, present status and future needs[END_REF] in order to avoid diamond Bragg peaks. The cullet sizes range was from 150 to 400 microns in diameter. The sample chamber was made of pre-indented rhenium gaskets with holes of 70-150 microns in diameter and the sample was placed between two KCl disks, previously dried in vacuum oven, used both as thermal insulator and pressure transmitting medium. The samples were polycrystalline foils by Goodfellow with initial thickness of 6µm (Fe-20wt%Ni) and 8µm (Fe-36wt%Ni).

Fe K-edge (7.112 KeV) and Ni K-edge (8.333 KeV) EXAFS (Extended X-ray Absorption Fine Structure) measurements were performed at the energy dispersive beamline ID24 at the European Synchrotron Radiation Facility (ESRF) [START_REF] Pascarelli | The Time-resolved and Extreme-conditions XAS (TEXAS) facility at the European Synchrotron Radiation Facility: the energy-dispersive X-ray absorption spectroscopy beamline ID24[END_REF].

The X-ray spot size on the sample was 4x5 µm 2 FWHM.

The laser heating facility at ID24 [START_REF] Kantor | A laser heating facility for energy-dispersive X-ray absorption spectroscopy[END_REF] allows to measure EXAFS spectra of a compressed sample while it is heated from both sides of the DAC. The temperature is measured by spectral-radiometry also from both sides. The heating lasers are two infrared (IR) CW Nd:YAG fiber lasers (IPG photonics) with λ = 1064 nm, focused to a spot size of around 20 µm diameter on the sample. Once the sample is compressed to the desired pressure, a triggering system allows to launch the laser heating, the temperature measurement and the X-ray acquisition simultaneously, according to the scheme described in [START_REF] Boccato | The Melting Curve of Nickel Up to 100 GPa Explored by XAS[END_REF]. The error over the measured temperature is chosen as the maximum between the error obtained from the sliding two-colors fit [START_REF] Benedetti | Temperature gradients, wavelength-dependent emissivity, and accuracy of high and very-high temperatures measured in the laser-heated diamond cell[END_REF][START_REF] Giampaoli | Measurement of temperature in the laser heated diamond anvil cell: comparison between reflective and refractive optics[END_REF] and the difference in the temperature measurements from the two sides of the DAC. Temperature uncertainties are typically within 10% of the measured temperature but can reach 14% at low temperature because of low signal-to-noise ratio of the emission signal. The pressure was measured using the ruby fluorescence [START_REF] Dewaele | [END_REF] before and after the heating run, the pressure uncertainty typically accounts for around 10 % of the measured pressure. Thermal pressure was estimated as described in [START_REF] Morard | Solving controversies on the iron phase diagram under high pressure[END_REF]. Further details on the experimental procedure can be found in the supporting information.

Results and Discussion

Solid-solid and solid-liquid relations were investigated for Fe-Ni with Ni at 20 wt% and 36 wt% in the 0-120 GPa and 300-3500 K range.

At ambient conditions, Fe-20wt%Ni is stable with bcc structure, like pure iron. Up to 12 GPa all EXAFS oscillations shift to higher energies as a consequence of the interatomic distance compression (see Fig. sition is completed at 17 GPa and above this pressure only the energy shift due to compression is observed. The transition pressure and width are similar to that of pure iron, reported to occur around 13 GPa, with width variations depending on the transmitting medium [START_REF] Barge | Effect of non-hydrostaticity on the α-transition of iron[END_REF].

Upon heating, hcp Fe-20wt%Ni transforms into the fcc structure. The hcp to fcc transition is hard to observe in the EXAFS region because the oscillations are very similar for the two phases (see Fig. 1 right panel). This is not surprising since the hcp and fcc structures differ only in their stacking sequence of the planes. However significant modifications occur in the XANES region as it is shown in the left panel of Fig. 2. Temperature slightly modifies the XANES of the hcp structure. The subsequent transition to the fcc structure shows up in the appearance of a two peaks structure (B) and flattening of the post shoulder slope (A). The same transformation was observed at different pressures from 15 to 100 GPa. However below 40 GPa it is not possible to measure the transition temperature as the emission is too low for spectro-radiometry. At 70 GPa, the example shown in Fig. 2, the transition starts at 1990 K and is completed at 2210 K. A similar behaviour has been observed in pure iron for the T-induced hcp-fcc transition [START_REF] Morard | Solving controversies on the iron phase diagram under high pressure[END_REF]. Fe-36wt%Ni was found in the fcc structure at ambient conditions and in all the explored P/T range before melting.

We report hcp/fcc co-existence data in Fig. 3 in comparison with previous experimental works. Our results extend the hcp/fcc boundary of Fe-20wt%Ni up to 3000 K and 120 GPa. The Clapeyron slope (dT/dP) for the hcp/fcc boundary is found to be steeper with respect to previous studies at similar Ni content [START_REF] Kuwayama | Phase relations of iron and iron-nickel alloys up to 300 GPa: Implications for composition and structure of the Earth's inner core[END_REF] W. L. [START_REF] Mao | Phase relations of Fe-Ni alloys at high pressure and temperature[END_REF] and closer to previously reported boundary for Fe-10wt%Ni [START_REF] Dubrovinsky | Body-Centered Cubic Iron-Nickel Alloy in Earth's Core[END_REF]. Komabayashi and co-authors [START_REF] Komabayashi | In situ X-ray diffraction measurements of the fcc -hcp phase transition boundary of an Fe -Ni alloy in an internally heated diamond anvil cell[END_REF] claim that differences in the phase boundaries reported for Fe-10wt%Ni can be explained in terms of different evaluation or neglecting of the thermal pressure. This could also apply to the Fe-20wt%Ni case even though it does not explain all the discrepancies. In the work of [START_REF] Kuwayama | Phase relations of iron and iron-nickel alloys up to 300 GPa: Implications for composition and structure of the Earth's inner core[END_REF]) the pressure at high T was determined using the PVT equa- tion of MgO and could be overestimated by 8 GPa at most because of axial temperature gradients. In the work of (W. L. [START_REF] Mao | Phase relations of Fe-Ni alloys at high pressure and temperature[END_REF], the thermal pressure was neglected therefore a steeper slope would be expected.

The previous results on the hcp/fcc boundary in Fe rich Fe-Ni alloys shown in Fig. 3 have been used to formulate important hypothesis on the structure of the Earth's inner core (IC, 330-364 GPa and 4000-7000 K [START_REF] Anzellini | Melting of iron at Earth's inner core boundary based on fast X-ray diffraction[END_REF]), mostly proposing iron rich Fe-Ni alloys to crystallize in the hcp phase [START_REF] Lin | Iron-nickel alloy in the earth's core[END_REF]; W. L. [START_REF] Mao | Phase relations of Fe-Ni alloys at high pressure and temperature[END_REF][START_REF] Komabayashi | In situ X-ray diffraction measurements of the fcc -hcp phase transition boundary of an Fe -Ni alloy in an internally heated diamond anvil cell[END_REF][START_REF] Sakai | Equation of state of pure iron and Fe 0.9 Ni 0.1 alloy up to 3 Mbar[END_REF][START_REF] Tateno | The structure of Fe-Ni alloy in Earth's inner core[END_REF]. A simple extrapolation of our hcp/fcc boundary supports the hypothesis of the hcp structure for Fe-Ni with 20 wt% of Ni at IC conditions, and the same would apply to lower Ni contents.

The temperature-induced transition to the liquid phase can also be clearly distinguished in the XANES region. As temperature is increased the two peaks (B in Fig. 2, right panel) get suppressed while the shoulder shape flattens (A). Similar changes are observed at different pressures for the two alloys. The melting detection with XANES has been recently applied to determine the melting curves of pure Ni [START_REF] Boccato | The Melting Curve of Nickel Up to 100 GPa Explored by XAS[END_REF] and pure Fe [START_REF] Morard | Solving controversies on the iron phase diagram under high pressure[END_REF]. This method has been validated by scanning electron microscope (SEM) textural analyses, performed on exposed transverse sections of samples recovered from the in situ experiments and theoretical calculations in the case of pure Co [START_REF] Boccato | Local structure of liquid 3d metals under extreme conditions of pressure and temperature[END_REF].

In order to avoid any data misinterpretation due to modifications in the sample assembly after melting, i.e. sample diffusion and/or chemical reactions [START_REF] Boccato | The Melting Curve of Nickel Up to 100 GPa Explored by XAS[END_REF], only the first appearance of mix or full liquid phase was considered for the melting curve determination, and each heating run has been performed on a fresh portion of the sample. Chemical reactions with carbon and oxygen are clearly detectable through modifications in the XANES [START_REF] Aprilis | Comparative study of the influence of pulsed and continuous wave laser heating on the mobilization of carbon and its chemical reaction with iron in a diamond anvil cell[END_REF] and have been monitored by acquiring a quench (cold) spectrum in between each increase of laser power (see supporting information).

-5-manuscript submitted to Geophysical Research Letters The Fe-20wt%Ni melting curve, obtained using a Simon-Glatzel fit [START_REF] Simon | Bemerkungen zur Schmelzdruckkurve[END_REF] of the first liquid (or mixtures) data, reported in the phase diagram in Fig. 4, almost superimposes on the pure Fe one up to 100 GPa. The Fe melting curve reported by [START_REF] Morard | Solving controversies on the iron phase diagram under high pressure[END_REF] combines results of XANES, XRD [START_REF] Anzellini | Melting of iron at Earth's inner core boundary based on fast X-ray diffraction[END_REF] and results of synchrotron Mössbauer spectroscopy [START_REF] Jackson | Melting of compressed iron by monitoring atomic dynamics[END_REF][START_REF] Zhang | Temperature of Earth's core constrained from melting of Fe and Fe 0.9 Ni 0.1 at high pressures[END_REF].

The negligible effect of Ni is in agreement with a previous Fe-Ni study [START_REF] Zhang | Temperature of Earth's core constrained from melting of Fe and Fe 0.9 Ni 0.1 at high pressures[END_REF], the discrepancies of the absolute values, in fact, is given by a different estimate of the thermal pressure [START_REF] Morard | Solving controversies on the iron phase diagram under high pressure[END_REF]. A kink of the melting line of Fe-20wt%Ni can be also expected in correspondence to the triple point, as in pure Fe [START_REF] Morard | Solving controversies on the iron phase diagram under high pressure[END_REF].

Therefore, an extrapolation of this melting curve to IC boundary conditions would not be reliable and measurements above 120 GPa, where the melting occurs from the hcp phase, are needed. Three heating runs, at 30, 50 and 60 GPa were performed on the Fe-Ni alloy with 36 wt% of Ni. For sake of clarity, only the first melting signatures are reported on the phase diagram for this alloy. These three melting points nicely overlap on the Fe-20wt%Ni melting curve, indicating that even higher Ni content does not affect the melting curve of Fe, differently from the effect of light elements alloying [START_REF] Morard | Fe-FeO and Fe-Fe 3 C melting relations at Earth's core-mantle boundary conditions: Implications for a volatile-rich or oxygenrich core[END_REF].

The hcp/fcc boundary is fitted linearly. The extrapolation of the melting curve and of the hcp/fcc phase boundary from 120 GPa allows to locate the hcp/fcc/liquid triple point of Fe-20wt%Ni at 170±20 GPa and 4000±400 K. For pure Fe, the triple point has been recently found at 100 ±10 GPa and 3500±200 K [START_REF] Morard | Solving controversies on the iron phase diagram under high pressure[END_REF]. Therefore, while the melting curve of fcc Fe is substantially unaffected by the addition of 20 wt% of Ni, because of the shift of the hcp/fcc boundary, the triple point moves significantly to higher pressures and temperatures.

The position of the triple point is important for thermodynamic modeling [START_REF] Komabayashi | Internally consistent thermodynamic database for iron to the Earth's core conditions[END_REF] or to constrain entropy change upon melting related to heat flow at the coremantle boundary (CMB) [START_REF] Anderson | The high-pressure triple points of iron and their effects on the heat flow from the earth's core[END_REF]. Our results allow constraining the position of the triple point for a geophysical pertinent composition, Fe-10wt%Ni, by assuming melt- [START_REF] Morard | Solving controversies on the iron phase diagram under high pressure[END_REF] and pure Ni from [START_REF] Boccato | The Melting Curve of Nickel Up to 100 GPa Explored by XAS[END_REF] are also shown. Right: phase boundaries incertitude evaluated as described in SI Text7.

ing curve similar to pure Fe and Fe-20wt%Ni in the fcc phase, and a linear variation of the hcp/fcc boundary with Ni content, that is also in agreement with most recent measurements of the hcp/fcc boundary by (Komabayashi et al., 2012) (Fig. 5 left panel). The position of the triple point for Fe-10wt%Ni is then expected around 135 GPa and 3800 K, and indicates a reduction of the melting temperature at CMB conditions by around 400 K with respect to pure Fe. This impacts the liquidus for Fe alloys constituting the Earth's core, by shifting it toward lower temperature. As pure Fe has a melting temperature comparable to mantle silicates at CMB pressure (∼4200 K), Ni addition will reduce this to ∼3800 K.

In a previous discussion, we have shown that the presence of a notable amount of light elements is required to lower the crystallization temperature of core materials at CMB below 4150 K (Fig7 in [START_REF] Morard | Fe-FeO and Fe-Fe 3 C melting relations at Earth's core-mantle boundary conditions: Implications for a volatile-rich or oxygenrich core[END_REF]), an upper bound which corresponds to the mantle melting temperature at 136 GPa [START_REF] Fiquet | Melting of peridotite to 140 gigapascals[END_REF][START_REF] Andrault | Solidus and liquidus profiles of chondritic mantle: Implication for melting of the earth across its history[END_REF] (Fig. 5 right panel). The observation that the main constituting alloy (Fe-Ni) in the core exhibits already a reduced melting temperature, suggests that a lower fraction of light elements is required. Such a low fraction is in better agreement with the one estimated from geochemical observations and the one required to reduce the density (and seismic wave speed) of the core [START_REF] Badro | A seismologically consistent compositional model of Earth's core[END_REF].

Conclusions

In this study we present the first experimental determination of melting curves of Fe-Ni alloys at 20 and 36 wt% of Ni by means of x-ray absorption spectroscopy in the laser heated DAC, as well as their high-pressure, high-temperature phase diagram in the CMB for a core with Fe-X (dashed areas) and FeNi-X (full colored areas) composition, where X is C, S or O. The temperature at CMB is higher than the crystallization temperature of the outer-core alloy by 400-900 K [START_REF] Anzellini | Melting of iron at Earth's inner core boundary based on fast X-ray diffraction[END_REF]Komabayashi, 2014) since across the liquid outer core (from 135 to 330 GPa) the geotherm is expected to follow an adiabat with P-T slope that is less steep than the melting curve (otherwise the outer-core would not be liquid).

Therefore, this is estimated to be 4600-5100 K for pure Fe and 4200-4700 K for Fe-Ni.

solid phase in the 0-120 GPa and 300-3500 K range. Our data allow locating the position of the hcp/fcc/liquid triple point for Fe-20wt%Ni at 170±20 GPa and 4000±400 K.

Our results indicate that while Ni alloying with Fe strongly modifies the equilibrium relations of the hcp and fcc phases, by enlarging the fcc stability domain, the Pinduced bcc/hcp transition (at ambient T) and the melting curve up to 1 Mbar are substantially unaffected. On the other hand, the shift of the hcp/fcc/liquid triple point has important consequences for Fe-Ni alloys at concentrations relevant for Earth interior (10 wt% Ni) as it implies a reduction of the melting temperature of around 400 K at CMB with respect to pure Fe, thus shifting the whole liquidus for Fe alloys constituting the Earth's core toward lower temperature. This, is turn, has important consequences on the core composition requiring a lower amount of light elements than previously predicted.

Figure 1 .

 1 Figure 1. Left: selection of EXAFS spectra of Fe-20wt%Ni acquired under pressure and room temperature. The data are shifted in vertical for clarity. The bcc to hcp structural transition starts above 12 GPa (blue lines) and it is completed from 17 GPa (red lines). Right: example of heating run performed at a starting pressure of 52 GPa. A selection of EXAFS spectra have been chosen to show the subsequent transitions from hcp (black and blue line) to fcc (pink) to the liquid phase (red). The data are shifted in vertical for clarity (the temperature increases downwards).

Figure 2 .

 2 Figure 2. Left: selection of XANES spectra showing the temperature induced hcp-fcc phase transition in Fe-20wt%Ni at 70 GPa. The black, blue and pink solid lines represent the XANES signal from the hcp phase at room temperature, the hcp phase at high temperature and the fcc phase respectively. The inset shows spectra of mixed hcp-fcc phases (violet lines) along the transition. Right: selection of XANES spectra showing the melting of Fe-20wt%Ni at 50 GPa. The two smaller panels on the right are zooms over the regions where the modifications occur.

Figure 3 .

 3 Figure 3. Hcp/fcc boundary found in this study for Fe-20wt%Ni and comparison to other experimental works at close compositions (as indicated next to the corresponding shaded area).T and P errors are around 10% of the measured values.

Figure 4 .

 4 Figure 4. Left: Phase diagram obtained from the experimental data. Black, orange and cyan rotated squares are bcc, hcp and fcc solid phases respectively. The bcc/hcp and hcp/fcc co-existence range is indicated as two colors squares. Pink circles indicate liquid phases, and two colours (pink and green) hexagons are solid-liquid mixtures. The black triangle represents the predicted position for the hcp/fcc/liquid triple point of Fe-20wt%Ni. Black hexagonal symbols represent melting points for the Fe-36wt%Ni alloy. Black crosses represent P/T errors for the melting points in different pressure regions of the phase diagram and have been shifted in vertical for clarity. The melting curves of pure Fe from[START_REF] Morard | Solving controversies on the iron phase diagram under high pressure[END_REF] and pure Ni from(Boccato

Figure 5 .

 5 Figure 5. Left: schematic evolution of Fe-Ni phase diagram as a function of Ni content. The addition of Ni does not affect the melting curve in the fcc structure, but the triple point hcp-fccliquid is shifting toward higher pressure and temperature. Right: Expected temperature at the

Acknowledgments

The authors are thankful to Francesco Bianco for precious help in the error analysis, to Sakura Pascarelli for help in the beamline alignment, to Vera Cuartero for the reference measurements on BM23, to Jeroen Jacobs for technical support before the experiment and to Florian Occelli for provision and cutting of the Fe-36wt%Ni sample. The authors acknowledge the European Synchrotron Radiation Facility (ESRF) for provision of synchrotron radiation within Projects HC-3184, HC-3188 and HC1991. Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the U.S. Department of Energy, National Nuclear Security Administration under Contract DE-AC52-07NA27344. F. M. and G. M. have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation Programme (grant agreement ERC PlanetDive 670787). Data are available on Zenodo (Torchio et al., 2020) with free academic licence.


Yanzhang Luo

Shengqi Xiang

Peter Jan Hooikaas

Laura Van Bezouwen

A S Jijumon

Carsten Janke

Friedrich Förster

Anna Akhmanova
email: a.akhmanova@uu.nl

Marc Baldus
email: m.baldus@uu.nl

Direct observation of dynamic protein interactions involving human microtubules using solid-state NMR spectroscopy

Microtubules are important components of the eukaryotic cytoskeleton. Their structural organization is regulated by nucleotide binding and many microtubule-associated proteins (MAPs). While cryo-EM and X-ray crystallography have provided detailed views of interactions between MAPs with the microtubule lattice, little is known about how MAPs and their intrinsically disordered regions interact with the dynamic microtubule surface. NMR carries the potential to directly probe such interactions but so far has been precluded by the low tubulin yield. We present a protocol to produce [ 13 C, 15 N]-labeled, functional microtubules (MTs) from human cells for solid-state NMR studies. This approach allowed us to demonstrate that MAPs can differently modulate the fast time-scale dynamics of C-terminal tubulin tails, suggesting distinct interaction modes. Our results pave the way for in-depth NMR studies of protein dynamics involved in MT assembly and their interactions with other cellular components.

I

n eukaryotic cells, microtubules (MTs) are cytoskeletal polymers essential for many biological processes, including cell division, migration, polarization, and intracellular trafficking. MTs are assembled from α/β-tubulin heterodimers and are intrinsically polarized, with the highly dynamic, β-tubulinexposed plus end, which rapidly switches between growth and shrinkage in a process termed "dynamic instability" [START_REF] Desai | Microtubule polymerization dynamics[END_REF] . The dynamic instability of MTs is caused by GTP binding and hydrolysis on tubulin dimers.

Many MT-associated proteins (MAPs) regulate MT structure and function by interacting with MT lattices and/or MT ends [START_REF] Akhmanova | Tracking the ends: a dynamic protein network controls the fate of microtubule tips[END_REF][START_REF] Akhmanova | Microtubule minus-end-targeting proteins[END_REF] . Cryo-electron microscopy (EM) has made substantial progress to elucidate the interaction between MAPs and the MT lattice [START_REF] Alushin | High-Resolution microtubule structures reveal the structural transitions in αβ-tubulin upon GTP hydrolysis[END_REF][START_REF] Nogales | Visualizing microtubule structural transitions and interactions with associated proteins[END_REF] , including the cryo-EM reconstruction of the MAP tau binding to MTs [START_REF] Kellogg | Near-atomic model of microtubule-tau interactions[END_REF] . However, the direct observation of dynamic regions of tubulin, including the unstructured C-terminal tails that are critical for binding of different MT-associated proteins such as tau [START_REF] Kellogg | Near-atomic model of microtubule-tau interactions[END_REF] has remained challenging due to their intrinsic flexibility. To model such tubulin regions computational approaches were used, for example in the context of tau binding to MTs [START_REF] Kellogg | Near-atomic model of microtubule-tau interactions[END_REF] or, more recently, to determine the effect of α-tubulin acetylation on MT structure and stability [START_REF] Eshun-Wilson | Effects of α-tubulin acetylation on microtubule structure and stability[END_REF] . Given the wide-spread relevance of protein dynamics for MT function and, in particular, of tubulin tails for cellular processes and human disorders [START_REF] Gadadhar | The tubulin code at a glance[END_REF] , direct experimental insight into the dynamic interaction of MTs with MAPs is hence of significant interest.

Nuclear magnetic resonance (NMR) spectroscopy has been shown to provide unique structural insights into heterogeneous and dynamical systems at atomic resolution and on different time scales (see, e.g., refs. [START_REF] Peng | Exposing the moving parts of proteins with NMR spectroscopy[END_REF][START_REF] Wright | Intrinsically disordered proteins in cellular signalling and regulation[END_REF][START_REF] Renault | Solid-state NMR spectroscopy on complex biomolecules[END_REF][START_REF] Quinn | Structural biology of supramolecular assemblies by magic-angle spinning NMR spectroscopy[END_REF] ). Previously, solid-and solution-state NMR have been used to study the interactions between MTs and isotope-labeled MAPs or small drugs [START_REF] Kumar | Interaction of epothilone B (Patupilone) with microtubules as detected by two-dimensional solid-state NMR spectroscopy[END_REF][START_REF] Yan | Atomic-resolution structure of the CAP-Gly domain of dynactin on polymeric microtubules determined by magic angle spinning NMR spectroscopy[END_REF][START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF][START_REF] Kubo | A gel-encapsulated bioreactor system for NMR studies of protein-protein interactions in living mammalian cells[END_REF][START_REF] Kesten | The companion of cellulose synthase 1 confers salt tolerance through a Tau-like mechanism in plants[END_REF][START_REF] Kadavath | The binding mode of a tau peptide with tubulin[END_REF][START_REF] Atherton | Structural determinants of microtubule minus end preference in CAMSAP CKK domains[END_REF] . However, these studies were restricted to studying ligands that could be isotope labeled using bacterial expression systems. Thus far, the direct study of functional MTs from human cells that carry NMR-active labeling was precluded due to insufficient protein amounts. In addition, solution-state NMR studies on intact MTs are hampered by protein size and insufficient molecular tumbling. In the following, we describe a solid-state NMR (ssNMR) approach to directly study the interaction of labeled MTs with their binding partners. In particular, this method enables us to probe the dynamics of intact MTs. Moreover, we examine the influence of two different MT-associated proteins upon the C-terminal tail dynamics. We investigate the binding of the CKK domain that is important for the minus-end recognition of the calmodulin-regulated spectrinassociated protein (CAMSAP) [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF][START_REF] Atherton | Structural determinants of microtubule minus end preference in CAMSAP CKK domains[END_REF] . Furthermore, we examine the effect of the microtubule-binding domain (MTBD) of the MAP7 family of proteins, which play an important role in regulating kinesin-based intracellular transport and for which the structural details of MT binding are currently unknown [START_REF] Monroy | Competition between microtubule-associated proteins directs motor transport[END_REF][START_REF] Chaudhary | MAP7 regulates organelle transport by recruiting kinesin-1 to microtubules[END_REF][START_REF] Pan | MAP7D2 localizes to the proximal axon and locally promotes kinesin-1-mediated cargo transport into the axon[END_REF][START_REF] Hooikaas | MAP7 family proteins regulate kinesin-1 recruitment and activation[END_REF] . Our results suggest that MAP-tubulin tail interactions can involve both fast-time scale interactions between mobile chains as well as slowtime scale binding/unbinding events within stable MT-MAP complexes.

Results

Functional MTs for ssNMR studies. To obtain milligram quantities of human MTs we used HeLa S3 cells that not only grow as adherent culture but also in suspension, thereby increasing the efficiency of large-scale cultures [START_REF] Souphron | Purification of tubulin with controlled post-translational modifications by polymerization-depolymerization cycles[END_REF] . In addition, HeLa S3 cells express only a few tubulin isotypes [START_REF] Newton | Intrinsically slow dynamic instability of HeLa cell microtubules in vitro[END_REF][START_REF] Davis | A tubulin polymerization microassay used to compare ligand efficacy[END_REF] resulting in comparatively homogeneous samples. We isolated tubulin from cell lysates by using a polymerization and depolymerization cycle to remove contaminations (Fig. 1a,b). Subsequently, we polymerized tubulin into MTs with high concentration of 1,4-piperazinediethanesulfonic acid (PIPES) to remove MAPs binding and stabilized MTs with Taxol [START_REF] Weaver | How taxol/paclitaxel kills cancer cells[END_REF] . As demonstrated by sodium dodecyl sulfate (SDS) polyacrylamide gel electrophoresis, Taxol-stabilized MTs showed a purity of 90% (Fig. 1b). To check functionality, we incubated our prepared MTs with a fluorescently tagged MTBD of MAP7 domain-containing protein 3 (MAP7D3, in the following abbreviated by MAP7), which served as a MT-binding probe, and found that the purified MTs were decorated by this protein fragment (Supplementary Fig. 1A,B, left). Notably, the binding of MAP7 induced some bundling of MTs (Supplementary Fig. 1A,B). However, the MT bundling does not affect the structure and the dynamics of tubulin Cterminal tails of each individual MT [START_REF] Walczak | MAP for bundling microtubules[END_REF] , and hence did not interfere with our ssNMR experiments presented below. We also investigated whether HeLa S3-derived tubulin can polymerize without Taxol and shows dynamic instability by preparing an additional sample without Taxol, leading to soluble tubulin after a subsequent depolymerization. The resulting tubulin was used in an in vitro reconstitution assay where MTs are polymerized from stable MT seeds with GFP-tagged end binding protein 3 (EB3) as a marker for growing ends. The tubulin we prepared polymerized into MTs and showed phases of growth and shortening (Fig. 1c and Supplementary Fig. 1C, Movie 1), demonstrating that the purified tubulin remains polymerizationcompetent using our protocol. Taken together, this protocol allowed us to purify functional tubulin from mammalian cells that could form MTs, thus providing the basis for our NMR experiments described below.

To obtain isotope-labeled MTs for ssNMR studies, we grew HeLa S3 cells in 2L [ 13 C, [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N] labeled medium and obtained isotope-labeled, Taxol-MTs (in the following abbreviated by MTs) using the procedure described above. The sample was then packed into a 1.3 mm MAS NMR rotor and subjected to extended measurement periods using fast MAS rates. To ensure sample integrity under such conditions, we used transmission EM and TIRF microscopy that confirmed that our MT samples remained intact (Fig. 1d and Supplementary Fig. 1B).

MT samples as seen by [START_REF] Kumar | Interaction of epothilone B (Patupilone) with microtubules as detected by two-dimensional solid-state NMR spectroscopy[END_REF] C and 31 P ssNMR spectroscopy. To evaluate the sample quality, we first recorded a 2D 13 C- [START_REF] Kumar | Interaction of epothilone B (Patupilone) with microtubules as detected by two-dimensional solid-state NMR spectroscopy[END_REF] C dipolar-based correlation spectrum using radio frequency-driven recoupling (RFDR) [START_REF] Bennett | Homonuclear radio frequency-driven recoupling in rotating solids[END_REF] recoupling and compared our data to chemical-shift predictions for MTs (PDB ID: 5SYF) using FAN-DAS 2.0 [START_REF] Narasimhan | Rapid prediction of multi-dimensional NMR data sets using FANDAS[END_REF] . Overall, the spectrum agreed with in silico estimates (Fig. 2a, left). For example, in Cα-Cβ regions of serine, threonine and alanine residues, signals were observed in qualitative agreement with predictions for α-helical and β-strand conformations (Fig. 2a, right). Interestingly, alanine signals that were not observed (Fig. 2a, top right) resided in random-coil conformation and related to residues in tubulin loops. The latter observation would be consistent with the occurrence of loop motion as discussed elsewhere 7 at the experimental temperature (~298 K) in our dipolar-based experiments. While residue-specific analysis of such effects will require the extension to 3D ssNMR spectroscopy, possibly in combination with amino acid specific labeling [START_REF] Renault | Solid-state NMR spectroscopy on complex biomolecules[END_REF] , the spectral resolution observed in Fig. 2 for such a large complex hence speaks in favor of a homogenous sample of polymerized MTs.

This notion was further confirmed by [START_REF] Menéndez | Control of the structural stability of the tubulin dimer by one high affinity bound magnesium ion at nucleotide N-site[END_REF] P NMR signals stemming from nucleotides binding to MTs. In general, α/βtubulin dimers contain two nucleotide-binding sites. The GTP molecule bound to α-tubulin is non-hydrolysable, whereas, the nucleotide bound to β-tubulin is exchangeable, and GTP is hydrolyzed to GDP upon MT polymerization [START_REF] Menéndez | Control of the structural stability of the tubulin dimer by one high affinity bound magnesium ion at nucleotide N-site[END_REF] (Fig. 2b,left). Indeed, we observed ssNMR signals from both GTP and GDP in 1D [START_REF] Menéndez | Control of the structural stability of the tubulin dimer by one high affinity bound magnesium ion at nucleotide N-site[END_REF] P CPMAS spectrum (Fig. 2b, right) that were well resolved compared to previous results on lyophilized MTs [START_REF] Hyang | Solid-state 31P NMR investigation on the status of guanine nucleotides in paclitaxel-stabilized microtubules[END_REF] . The observed spectral resolution allowed us to distinguish NMR signals from both molecules (Supplementary Table 1) [START_REF] Hyang | Solid-state 31P NMR investigation on the status of guanine nucleotides in paclitaxel-stabilized microtubules[END_REF][START_REF] Spoerner | High pressure 31P NMR spectroscopy on guanine nucleotides[END_REF] . Integrated peak intensities (Supplementary Table 1) correlated well with the notion that the molar ratio of GDP:GTP was 1:1, which is in agreement with previous studies [START_REF] Alushin | High-Resolution microtubule structures reveal the structural transitions in αβ-tubulin upon GTP hydrolysis[END_REF][START_REF] Menéndez | Control of the structural stability of the tubulin dimer by one high affinity bound magnesium ion at nucleotide N-site[END_REF] further supporting the idea that our ssNMR preparations were well folded and functional. Interestingly, we also observed an additional broad peak at -2.7 ppm, which may result from co-purified lipids [START_REF] Kaur | Coupled ATPase-adenylate kinase activity in ABC transporters[END_REF] .

Probing tubulin tails by ssNMR. To probe mobile MT protein segments including the C-terminal tubulin tails (Fig. 3a), we carried out a series of scalar-based (J-based) ssNMR experiments [START_REF] Alam | 1H-13C INEPT MAS NMR correlation experiments with 1H-1H mediated magnetization exchange to probe organization in lipid biomembranes[END_REF] that previously revealed flexible parts within large biomolecules [START_REF] Andronesi | Determination of membrane protein structure and dynamics by magic-angle-spinning solid-state NMR spectroscopy[END_REF][START_REF] Ward | Proton detection for signal enhancement in solid-state NMR experiments on mobile species in membrane proteins[END_REF][START_REF] Xiang | Site-specific studies of nucleosome interactions by solid-state NMR spectroscopy[END_REF][START_REF] Damman | Atomic-level insight into mRNA processing bodies by combining solid and solution-state NMR spectroscopy[END_REF] . As discussed elsewhere [START_REF] Andronesi | Determination of membrane protein structure and dynamics by magic-angle-spinning solid-state NMR spectroscopy[END_REF][START_REF] Schmidt-Rohr | Multidimensional Solid-State NMR and Polymers[END_REF] , significant molecular motions with correlation times in the range of 10 -9 to 10 -7 s must be present to generate NMR signals in such ssNMR correlation experiments. Slower motions (in the range of milliseconds or slower) will, on the other hand, lead to signal loss (vide infra). In the current context, a 2D 15 N-HSQC spectrum contained several signals with a limited spectral dispersion (Fig. 3b), in line with the presence of a mobile unstructured protein region. Using additional 2D [START_REF] Kumar | Interaction of epothilone B (Patupilone) with microtubules as detected by two-dimensional solid-state NMR spectroscopy[END_REF] C-HSQC (Fig. 3c,d) [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] Nedited 1 H-1 H spin diffusion spectra (Fig. 3d), we could confirm that correlations observed in the [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N-HSQC spectrum are mainly due to glycine, glutamate, and alanine, which are the most abundant residues in the tubulin tails (Fig. 3a). Moreover, the corresponding resonance frequencies seen in the 2D [START_REF] Kumar | Interaction of epothilone B (Patupilone) with microtubules as detected by two-dimensional solid-state NMR spectroscopy[END_REF] C-HSQC reflected random-coil chemical shifts of these amino acids. Note that the latter spectrum contained additional signals from mobile side chains as well as correlations stemming from residual lipids (Fig. 2b) and buffer.

We could further identify correlations stemming from glutamate and alanine residues by tracing HN to Hβ or Hγ correlations. Interestingly, one glutamate NH signal showed correlations to the Hα of glycine, indicating that the corresponding glutamate residues are next to glycine residues (Fig. 3d, second strip). Such correlations are only expected for the αtubulin C-terminal tails (Fig. 3a). On the other hand, the other glutamate peak showed no contacts to glycine Hα (Fig. 3d, third strip), suggesting that these correlations most likely reflect glutamate residues of the β-tubulin C-terminal tail (Fig. 3a). In addition, we detected two glycine signals with an approximately 3:1 intensity ratio in line with three glycine residues in EGE motifs of the α-tubulin tail and one glycine representing the FGE motif of the β-tubulin. These tentative assignments were in good agreement with previous solution-state NMR studies [START_REF] Lefèvre | The C terminus of tubulin, a versatile partner for cationic molecules: Binding of tau, polyamines, and calcium[END_REF] of a peptide that contained C-terminal residues of human α-tubulin and enabled us to tentatively assign the most C-terminal residue of α-tubulin, i.e., Tyr451 (Fig. 3a). Moreover, we could identify one alanine correlation which most likely reflects the last residue of the β-tubulin based on its high [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N chemical-shift value, and the correlations from its amide proton to the Hβ of Ala and Glu.

Lastly, two correlations which may at least in part stem from the N-terminal residues (Fig. 3a) remained unassigned due to lack of cross peaks in the 3D spectrum (Fig. 3b, peaks indicated by asterisks). The corresponding resonance frequencies would speak against posttranslational modifications (PTMs) seen in previous solution-state NMR on Tetrahymena thermophila tubulin [START_REF] Wall | Molecular determinants of tubulin's C-terminal tail conformational ensemble[END_REF] . Indeed, earlier work showed that HeLa tubulin mostly lacks PTMs on tubulin tails [START_REF] Barisic | Microtubule detyrosination guides chromosomes during mitosis[END_REF] . Taken together, our results suggested that both αand β-tubulin tails are disordered and highly mobile on a nanosecond time scale.

Tubulin tail dynamics are modulated by the CKK domain. In our previous work we could decipher molecular properties that enable CKK domains of the CAMSAP protein family to preferentially associate with the transition zone between curved protofilaments and the regular MT lattice at MT minus ends [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF][START_REF] Atherton | Structural determinants of microtubule minus end preference in CAMSAP CKK domains[END_REF] . We found that the CKK domain that consists of folded protein core and disordered termini associates with the groove between two laterally attached tubulin dimers and discovered that CKKs can subtly differentiate specific tubulin conformations to enable MT minus-end recognition [START_REF] Atherton | Structural determinants of microtubule minus end preference in CAMSAP CKK domains[END_REF] . However, these studies did not reveal how tubulin tails, which are important for CKK binding [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] are involved in these events. Using our ssNMR protocol, we in the following investigated the influence of CKK binding upon the Cterminal tubulin tails. For this purpose, we purified the unlabeled CAMSAP1 CKK N1492A mutant that exhibits reduced minusend selectivity and binds with higher affinity to MTs compared to wild-type CKK [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF][START_REF] Atherton | Structural determinants of microtubule minus end preference in CAMSAP CKK domains[END_REF] . We then added unlabeled CKK to [ 13 C, [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N]-labeled MTs and repeated our [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N-HSQC experiments. Compared to free [ 13 C, [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N]-labeled MTs, we observed strong changes in the 2D correlation spectrum (Fig. 4a) that relate to arginine residues of MTs as well as to the C-terminal residues of α-tubulin and of β-tubulin. In the following, we discuss our ssNMR spectral findings and their relationship to previous results for each of these three aspects.

Firstly, signals for the side chains of arginine residues were strongly reduced compared to free MTs. This observation confirmed our previous findings that arginine residues of both αand β-tubulin tubulin are located in the binding region of the CKK domain [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] (Fig. 4b). Furthermore, our recent studies also showed that the binding of CKK induces protofilament skew leading to a reduced lateral space between tubulin dimers [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF][START_REF] Atherton | Structural determinants of microtubule minus end preference in CAMSAP CKK domains[END_REF] . Arginine residues located in regions distant from the CKK binding epitope but involved in these lateral interactions between tubulin may hence also become less dynamic [START_REF] Zhang | Mechanistic origin of microtubule dynamic instability and its modulation by EB proteins[END_REF] .

Secondly, several correlations including the last C-terminal residue of β-tubulin, A444, disappeared after CKK was bound to MTs and correlations appeared in the alanine, glycine and tyrosine regions (Fig. 4a). These spectral changes would be consistent with conformational exchange on the fast time scale 9 upon CKK binding. Interestingly, glycines in the FGE segment and alanine residues are only found in the C-terminal tail of βtubulin suggesting that the β-tubulin tail is involved in this dynamic interaction. Notably, the C-termini of both β-tubulin (17 residues, Fig. 4c) and of the CKK domain (13 residues, Fig. 4c) were not observed in the previous cryo-EM structure [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] . Most likely, the CKK C-terminus hence retains conformational variability upon binding to MTs. Assuming fully extended backbone conformations, both CKK and tubulin C-terminal tails could sample a distance range of at least 60 and 45 Å [START_REF] Ainavarapu | Contour length and refolding rate of a small protein controlled by engineered disulfide bonds[END_REF] , respectively, which would readily allow for such dynamic interactions between both mobile tails as indicated in Fig. 4d. Notably, previous EM and ssNMR experiments suggested that the N-terminus of CKK (9 residues) could interact with the C- terminal part of β-tubulin (Fig. 4c,e), which would be in line with our NMR data.

Y451 (α-tubulin) ω 1 -15 N (ppm) ω 1 -13 C (ppm) ω 2 -1 H (ppm) ω -1 H (ppm)
Thirdly, we also observed changes in ssNMR signal frequencies and intensities after CKK binding for glycine in EGE segments and residue Y451, respectively, that are both found in the Cterminal tail of α-tubulin (Fig. 4a). As shown in Fig. 4c,d, the Cterminal tail of α-tubulin with its 12 residues could hence also dynamically interact with the C-terminus of CKK.

Taken together, our results strongly suggest that that the Cterminal tubulin tails dynamically interact with CKK domain on the nano-to microsecond time scale. Combination of these results with our previous EM and ssNMR data further refines this notion, suggesting that the CKK C-terminus interacts with both αand β-tubulin while the CKK N-terminus engages in fast interactions with the C-terminus of β-tubulin. Future ssNMR experiments may allow us to further dissect the details of these dynamic interactions, including the more precise determination of motional time scales in a residue-specific manner.

MAP7-binding reduces MT tail dynamics. The MAP7 family of proteins plays an important role in regulating kinesin-based intracellular transport. However, the structural details of MAP7-MT interaction are currently unknown [START_REF] Monroy | Competition between microtubule-associated proteins directs motor transport[END_REF][START_REF] Chaudhary | MAP7 regulates organelle transport by recruiting kinesin-1 to microtubules[END_REF][START_REF] Pan | MAP7D2 localizes to the proximal axon and locally promotes kinesin-1-mediated cargo transport into the axon[END_REF] . A secondary-structure prediction of MAP7 on the basis of its amino acid sequence as well as preliminary NMR experiments on free MAP7 in solution suggest that the MAP7 domain adopts a highly α-helical structure separated by a short loop comprising R144 to T146 and flanked by unstructured termini (Fig. 5a).

To obtain insight into the interaction of MT tails with bound MAP7, we repeated our J-based experiments on [ 13 C, [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N]labeled MTs after adding unlabeled MAP7 in a 2:1 ratio ensuring full decoration of MTs (see Methods). Interestingly and unlike in the case of binding of the CKK domain to MTs, we did not detect any frequency changes in the 2D [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N-HSQC ssNMR correlation spectrum (Fig. 5b, cyan) compared to the case of free MTs. Instead, signals from both C-terminal tubulin tails, including the identified EGE and FGE segments as well as other E residues were strongly attenuated (Fig. 5c and Supplementary Fig. 2) compared to the most C-terminal residues of αand β-tubulin, Y451 and A444, respectively. These observations can be explained by a slow exchange process (millisecond time scale or longer) between freely mobile αand β-tubulin tail conformations (visible in the spectra) and C-terminal tails directly bound to MAP7. Note that the latter states would be invisible in our J-based experiments. In a simple two-state model, the relative amount of bound populations would be given by P bound = 1 -I bound /I free (see, e.g., refs. [START_REF] Peng | Exposing the moving parts of proteins with NMR spectroscopy[END_REF][START_REF] Lakomek | Structural dynamics and transient lipid binding of synaptobrevin-2 tune SNARE assembly and membrane fusion[END_REF] ) seen in Fig. 5c leading to values of up to a 80% bound tail residues around the EGE and FGE terminal segments in α and β tubulin tails, respectively, and decreasing to around to a 65% and 25% bound population for the most C-terminal residues of αtubulin (Tyr 451 ) and of β-tubulin (Ala 444 ), respectively. Unlike the case of CKK where dynamic tubulin C termini retain fast dynamics, these observations hence suggested that the MT termini directly bind to MAP7 at a time scale of milliseconds or longer. At the same time the formation of the MT-MAP7 complex also leads to the reduction of Arg side-chain dynamics which are apparent from our experimental data (Fig. 4b) and reminiscent of our findings in the case of CKK binding.

Discussion

Protein dynamics are critically involved in MT organization including the stochastic switching between growing and shrinking states as well as in the regulation of MTs by MAPs and other cellular factors. NMR carries the potential to directly probe such processes provided that functional and NMR-active MTs can be obtained. We have shown that high-resolution ssNMR spectra can be recorded on [ 13 C, [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N] labeled MTs obtained from human cells. The MTs were polymerized from tubulin in functional form [START_REF] Souphron | Purification of tubulin with controlled post-translational modifications by polymerization-depolymerization cycles[END_REF] , as confirmed by in vitro MT dynamics assays. In addition, our protocol allows obtaining purified, functional tubulin if Taxol is not included in the second polymerization (see Fig. 1c). Such preparations allow for NMR studies of human tubulin in solution (or after depolymerization), e.g., to study MT nucleation and its regulation by different MAPs and potentially related phase transitions [START_REF] Hernández-Vega | Local nucleation of microtubule bundles through tubulin concentration into a condensed tau phase[END_REF] . The narrow 31 P NMR lines indicated homogenous binding of nucleotides on tubulin subunits that resulted in correctly polymerized MTs. This notion was further confirmed by 2D dipolar-based correlation experiments that are in qualitative agreement with a MT lattice as seen in cryo-EM structures. The absence of loop signals in our 2D ssNMR dipolar based data possibly points towards enhanced dynamics in protein loop regions as expected for tubulin domains, which are critical for MT dynamic instability or involved in PTMs such as the α-tubulin loop of residues P37-D47 (also known as αK40 loop [START_REF] Eshun-Wilson | Effects of α-tubulin acetylation on microtubule structure and stability[END_REF] ). Further ssNMR studies, possibly using three-or higherdimensional ssNMR experiments may, in combination with tailored labeling, reveal the exact details of these motions. Complementary to these experiments, proton-detected scalarbased 2D and 3D ssNMR experiments allowed us to directly study the disordered, flexible tubulin tails that are critically involved in MAP binding [START_REF] Lefèvre | The C terminus of tubulin, a versatile partner for cationic molecules: Binding of tau, polyamines, and calcium[END_REF] and which are invisible in all available high-resolution structures. In the current context, we tracked the effect of binding of the CKK domain of CAMSAP and of MAP7 for the dynamics of αand β-tubulin C-terminal tails. Our data suggest that MAP-tubulin tail interactions can take place over a remarkably wide time scale. In the case of CKK, the dynamics of both αand β-tubulin C-terminal tails are rapidly (in the nano to microsecond scale) modulated by the CKK domain, confirming our previous finding that tubulin C-terminal tails are important for CKK binding. Combination of these experiments with results of our earlier cryo-EM and ssNMR studies [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF][START_REF] Atherton | Structural determinants of microtubule minus end preference in CAMSAP CKK domains[END_REF] provided further insight regarding the details of these dynamic interactions and suggest that the disordered termini of CKK are involved in these interactions. On the other hand, MAP7 binding to MTs is characterized by tubulin C-terminal tails that exchange between bound (major state) and free (minor state) conformations on a much slower (millisecond or longer) time scale.

The remarkable difference between CKK and MAP7 binding to the tubulin tails may be related in part to the structural and dynamical properties of the MAP itself. For example, the mobile CKK termini comprise several positively charged amino acids (Fig. 4c), whereas, in the case of MAP7, such residues are mostly found in the putatively structured core of MAP7 (Fig. 5a). In addition, the molecular details of the MAP binding epitope on MTs may play a role in defining tail interactions. As we have shown earlier [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF][START_REF] Atherton | Structural determinants of microtubule minus end preference in CAMSAP CKK domains[END_REF] , CKK binding takes place between protofilaments. On the other hand, MAP7 is known to compete for binding to MTs 20 with the protein tau and hence is likely to be associated with the protofilament crest as seen for tau [START_REF] Kellogg | Near-atomic model of microtubule-tau interactions[END_REF] . Further ssNMR studies may help to dissect these dependencies, including the exact CKK and MAP7 regions interacting with the C-terminal tails. Such studies may involve isotope labeled MAPs or mixed labeled [START_REF] Etzkorn | Probing molecular interfaces using 2D magic-angle-spinning NMR on protein mixtures with different uniform labeling[END_REF] MAP-MT preparations. Moreover, the presented approach could be readily extended to study the interactions of longer variants of MAPs that, in addition to the minimal MT binding region, comprise intrinsically disordered protein domains as well as the Kinesin-1 binding domain [START_REF] Pan | MAP7D2 localizes to the proximal axon and locally promotes kinesin-1-mediated cargo transport into the axon[END_REF] . As we have shown recently for the case of mRNA processing bodies [START_REF] Damman | Atomic-level insight into mRNA processing bodies by combining solid and solution-state NMR spectroscopy[END_REF] , such studies not only could target bona fide MTs but they could also reveal dynamic interactions leading to the compartmentalization of the MT lattice by condensation of tau or other MAPs [START_REF] Hernández-Vega | Local nucleation of microtubule bundles through tubulin concentration into a condensed tau phase[END_REF][START_REF] Siahaan | Kinetically distinct phases of tau on microtubules regulate kinesin motors and severing enzymes[END_REF][START_REF] Tan | Microtubules gate tau condensation to spatially regulate microtubule functions[END_REF] . Combination of such NMR experiments with data obtained from cryo-EM and fluorescence microscopy experiments could lead to a comprehensive view on the structural and dynamical aspects that define the interaction between MT and MAPs or other cellular players that regulate MT function.

Methods

Preparation of MTs for ssNMR experiments and in vitro assays. The HeLa S3 cell line (ATCC ® CCL2.2 ™ ) was used for culturing. [ 13 C, [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N] labeled DMEM medium was prepared in the same way as described in a previous study [START_REF] Kaplan | EGFR dynamics change during activation in native membranes as revealed by NMR[END_REF] except that we used 3.5 g/L glucose in order to maintain cell viability in suspension culture. The cells were first cultured in the labeled medium on two 150 mm cell culture dishes, and then transferred into 12 dishes with the same medium. When the culture reached a confluence of ~80% on the plates, cells were trypsinized and transferred into 2 L labeled medium and cultured in 7 1 L Erlenmeyer shaker flasks (Corning) until the cell density reached ~1.2-1.5 × 10 6 /mL. Cells were then harvested by centrifugation at 500 × g for 20 min at 4 °C. The cell pellet was collected and resuspended in phosphate-buffered saline and centrifuged again at 500 × g for 15 min at 4 °C and used for MT preparation. The purification of Taxol-stabilized MTs was performed based on the published protocols [START_REF] Jeffrey | α-Tubulin tyrosination and CLIP-170 phosphorylation regulate the initiation of dynein-driven transport in neurons[END_REF][START_REF] Guedes-Dias | Kinesin-3 responds to local microtubule dynamics to target synaptic cargo delivery to the presynapse[END_REF] with minor modifications. Harvested cells were first resuspended with 1 g cell/mL lysis buffer (80 mM PIPES pH 6.8, 1 mM EGTA, 1 mM MgCl 2 , 1 mM β-mercaptoethanol, 1 mM PMSF and protease inhibitors (Roche) and lysed on ice by passing through a French Press homogenizer 3 times at 1000 psi. Subsequently, lysed cells were spun down at 120,000 × g at 4 °C for 30 min and the supernatant was collected. The supernatant was centrifuged again at 5000 × g at 4 °C for 15 min to remove the remaining cell debris and then a half volume of glycerol and 1 mM GTP were added and mixed well. MT polymerization was carried out by incubating the mixture at 30 °C for 30 min. Subsequently, the crude MT pellet was spun down at 150,000 × g (Type 70.1 Ti, Beckman Coulter) at 30 °C for 30 min and placed on ice. The pellet was then resuspended in BRB80 buffer (80 mM PIPES pH 6.8, 1 mM EGTA, 1 mM MgCl 2 ) supplemented with protease inhibitors and kept on ice for 30 min to allow for MT depolymerization. For a more efficient depolymerization, the solution was resuspended frequently and then centrifuged at 150,000 × g (Type 70.1 Ti, Beckman Coulter) at 4 °C for 30 min, and the supernatant was collected. An equal volume of high concentration PIPES buffer (1 M PIPES pH 6.8, 10 mM MgCl 2 , 20 mM EGTA), together with an equal volume of glycerol and 1 mM GTP were then added to the supernatant and mixed well. MT polymerization was again performed at 30 °C for 30 min. Subsequently, 20 μM Taxol (Paclitaxel, Sigma) was added to the reaction and incubated for 20 min to generate Taxol-stabilized MTs. Taxol-stabilized MTs were then spun down at 150,000 × g (TLA-55, Beckman Coulter) at 30 °C for 30 min washed with BRB80 containing 20 μM Taxol and protease inhibitors.

For all in-vitro assays, Taxol-stabilized MTs were prepared in the same way as described above. Regarding the sample used in the in vitro dynamics assay, the preparation of tubulin was similar except that Paclitaxel was not included during the second MT polymerization. After the second MT polymerization, MTs were spun down and resuspended in ice cold BRB80 supplemented with protease inhibitors. The second depolymerization was done on ice for 30 min and then centrifuged at 150,000 × g at 4 °C for 30 min. Purified tubulin was aliquoted and snap-frozen in liquid nitrogen, stored at -80 °C until use.

In vitro assays. MT seeds were prepared by incubating 20 μM porcine tubulin mix containing 70% unlabeled, 18% biotin-tubulin and 12% HiLyte488-tubulin with 1 mM guanylyl-(α,β)-methylenediphosphonate (GMPCPP) at 37 °C for 30 min. Polymerized MTs were separated from the mix by centrifugation in an Airfuge for 5 min. MTs were subjected to one round of depolymerization and polymerization in 1 mM GMPCPP, and the final MT seeds were stored in MRB80 buffer (80 mM K-PIPES pH 6.8, 1 mM EGTA, 4 mM MgCl 2 ) containing 10% glycerol.

In vitro reconstitution assays were performed in flow chambers. Flow chambers were assembled by sticking plasma-cleaned glass coverslips on microscopic slides with double-sided tape. Assays with Taxol-stabilized HeLa MTs were performed in MRB80 prewashed chambers. The in vitro reaction mixture consisted of 15 μM HeLa MTs (stabilized by 20 μM Taxol) that were either before or after MAS at 44 kHz for 24 h, 150 nM MAP7D3-MTBD, 50 mM KCl, 0.1% Methylcellulose, 0.5 mg/ ml κ-casein, 1 mM GTP, oxygen scavenging system (20 mM glucose, 200 μg/ml catalase, 400 μg/ml glucose-oxidase, 4 mM DTT). After centrifugation in an Airfuge for 5 min at 119,000 × g, the reaction mixture was added to the flow chamber and sealed with vacuum grease.

Dynamic MT assays were performed in flow chambers that were functionalized by sequential incubation with 0.2 mg/ml PLL-PEG-biotin (Surface Solutions, Switzerland) and 1 mg/ml NeutrAvidin in MRB80 buffer for 5 min. MT seeds were attached to the biotin-NeutrAvidin links and incubated with 1 mg/ml κ-casein. The in vitro reaction mixture consisted of 15 μM HeLa tubulin (quantified using bovine serum albumin standard), 20 nM GFP-EB3 and 0.5 μM rhodamine-labeled porcine brain tubulin, 50 mM KCl, 0.1% methylcellulose, 0.5 mg/ml κ-casein, 1 mM GTP, oxygen scavenging system (20 mM glucose, 200 μg/ml catalase, 400 μg/ml glucoseoxidase, 4 mM DTT). After centrifugation in an Airfuge for 5 min at 119,000 g, the reaction mixture was added to the flow chamber containing the HiLyte-488 MT seeds and sealed with vacuum grease. HiLyte488-and rhodamine-tubulin were purchased from Cytoskeleton Inc.

All in vitro experiments were conducted at 30 °C. Data were collected using total internal reflection fluorescence (TIRF) microscopy on an inverted research microscope Nikon Eclipse Ti-E (Nikon) with the perfect focus system (Nikon), equipped with Nikon CFI Apo TIRF 100× 1.49 N.A. oil objective (Nikon, Tokyo, Japan), Photometrics Evolve 512 EMCCD (Roper Scientific) and Photometrics CoolSNAP HQ2 CCD (Roper Scientific) and controlled with MetaMorph 7.7 software (Molecular Devices, CA). The microscope was equipped with TIRF-E motorized TIRF illuminator modified by Roper Scientific France/PICT-IBiSA, Institut Curie. For excitation lasers we used 491 nm 100 mW Stradus (Vortran), 561 nm 100 mW Jive (Cobolt) and 642 nm 110 mW Stradus (Vortran). We used an ET-GFP 49002 filter set (Chroma) for imaging of proteins tagged with GFP and an ET-mCherry 49008 filter set (Chroma) for imaging X-rhodamine labeled tubulin amd mCherry-labeled MTBD of MAP7D3. For simultaneous imaging of green and red fluorescence we used an Evolve512 EMCCD camera (Photometrics), ET-GFP/ mCherry filter cube (59022, Chroma) together with an Optosplit III beamsplitter (Cairn Research Ltd.) equipped with double emission filter cube configured with ET525/50m, ET630/75m, and T585lprx (Chroma). To keep in vitro samples at 30 °C, we used a stage top incubator (model INUBG2E-ZILCS; Tokai Hit). Images were processed using ImageJ. All images were modified by linear adjustments of brightness and contrast. Kymographs were generated using ImageJ plugin KymoResliceWide v.0.4. https://github.com/ekatrukha/KymoResliceWide; copy archived at https://github.com/elifesciences-publications/KymoResliceWide).

Transmission EM. Taxol-stabilized MTs were prepared with and without MAS spinning as described above. The protein samples were negatively stained with 2% uranyl acetate on glow-discharged carbon coated copper grids. Images were recorded on a Tecnai 20 electron microscope with a LaB6 filament, operating at 200 kV with a BM Eagle 4 K CCD camera (ThermoFisher, Eindhoven, The Netherlands). Images were acquired with a defocus of approximately 5 μm The magnification used at 19,000 × g resulting in an effective pixel size of 1.14 nm on the specimen level.

Preparation of CAMSAP1 CKK N1492A in complex with MTs. [ 13 C, [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N] labeled MTs were prepared as described above. The purification of CKK domain and preparation of CKK-MT complexes were performed based on the method published in ref. [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] . CKK was first purified by a ÄKTA pure system with a POROS ™ MC column that was saturated with Ni 2+ . The column was first equilibrated using washing buffer (50 mM phosphate buffer, pH 8, 500 mM NaCl, 1 mM βmercaptoethanol and 20 mM imidazole). The protein was eluted with the same buffer but containing 400 mM imidazole. Subsequently, the protein was loaded onto a SEC HiLoad Superdex 75 26/60 column (GE Healthcare) equilibrated with 40 mM phosphate buffer, pH 7, supplemented with 150 mM NaCl and 1 mM DTT. The purified protein was then concentrated and used for ssNMR sample preparation. CKK N1492A was then added to a final concentration of 65.3 μM (4:1 CKK/tubulin) and incubated with labeled MTs at 37 °C for 30 min. The pellet was centrifuged down at 180,000 × g (Beckman TLA-55 rotor) at 30 °C for 30 min and washed with BRB80, without disturbing the pellet. The pellet was then transferred and packed into a 1.3 mm rotor.

Preparation of MAP7-MTBD and of MAP7-MTBD-MT complexes. The cDNA of human MAP7-MTBD (residues 59-170) was cloned into the pLICHIS vectors with the gene encoding a N-terminal His tag-Maltose-binding protein (MBP)thrombin cleavage site by using ligation independent cloning [START_REF] De Jong | Enzyme free cloning for high throughput gene cloning and expression[END_REF] .Transformation was done with Escherichia coli Rosetta 2 cells and grown in 1 L unlabeled M9 medium. Induction of the protein was done when OD 600 reached 0.6 with 0.3 mM IPTG at 20 °C for 16 h. The cultures were then centrifuged with 4000 × g at 4 °C for 20 min to harvest cells. Cell pellets were washed with 50 mM sodium phosphate buffer, pH 8, 500 mM NaCl, 1 mM β-mercaptoethanol and 20 mM imidazole and store at -80 °C.

For protein purification, cell lysis was done by sonication on ice and the cell lysate was collected by centrifugation of 40,000 × g at 4 °C for 30 min. Subsequently, the proteins were purified by a ÄKTA pure system with a POROS ™ MC column that was saturated with Ni 2+ . The column was first equilibrated with the same buffer as above mentioned. The cell lysate was then loaded onto the column and the column was washed with 20 column volumes with the same buffer. Proteins were eluted with 50 mM sodium phosphate buffer, pH 8, 150 mM NaCl, 1 mM β-mercaptoethanol and 400 mM imidazole supplemented with protease inhibitors. The protein was concentrated and then diluted with 40 mM sodium phosphate buffer, pH 6.5 to reach a final concentration of imidazole of 20-30 mM. Subsequently, a cation exchange purification was performed with the Hitrap HP SP chromatography column (GE Healthcare Life Sciences). The column was first equilibrated with buffer A (40 mM sodium phosphate buffer, pH 6.5). The sample was then loaded onto the column and washed 5 column volumes with buffer A. A gradient elution was used by combining buffer A and buffer B (40 mM sodium phosphate buffer, 1 M NaCl, pH 6.5) to elute the protein. The protein was then concentrated and stored at 4 °C. Finally, thrombin was used to cleave the MBP fusion and then supplemented with protease inhibitors.

A 10 mg/ml porcine brain tubulin was diluted in BRB80 buffer (80 mM K-PIPES, pH 6.8, 1 mM EGTA, 1 mM MgCl 2 ) to 2 mg/ml. After the addition of 1 mM GTP, the sample was incubated on ice for 5 min. MT polymerization was performed at 30 °C for 20 min. Subsequently, 20 μM taxol was added and incubated for 15 min at 30 °C. MT pelleting assays in the presence of MAP7-MTBD were performed by mixing with different molar ratios of MAP7-MTBD:MTs. As control treatments, taxol-stabilized MTs or MAP7-MTBD was applied alone. All the samples were then centrifuged at 180,000 × g for 30 min at 30 °C, an aliquot was taken from the supernatant. After removal of the supernatant, the pellet was resuspended in SDS sample buffer. Samples of supernatant and pellet fractions were loaded and analyzed on Coomassie-stained 12.5% SDS gels.

Before sample preparation for ssNMR, the purified unlabeled MBP-MAP7-MTBD was first incubated with 5 U thrombin at 4 °C for 16 h to cleave the fused MBP protein. Protease inhibitors were then added to the proteins. To prepare MAP7-MTBD-MT complexes, 2 mg of purified [ 13 C, [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N] labeled MTs were prepared and resuspended in warm BRB80 buffer with 20 μM taxol. MAP7-MTBD was then added to molar ratio of 2:1 for MAP7-MTBD:MT and incubated at 30 °C for 30 min. The pellet was centrifuged down at 180,000 × g (Beckman TLA-55 rotor) at 30 °C for 30 min and washed with warm BRB80 buffer with 20 μM taxol and protease inhibitors, without disturbing the pellet. The pellet was then transferred and packed into a 1.3 mm rotor. ssNMR experiments. NMR experiments of [ 13 C, [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N] labeled MTs (free MTs, CKK-bound MTs and MAP7-bound MTs) were performed on a standard-bore 700 MHz, a wide-bore 500 MHz (Bruker Biospin). SsNMR experiments 700 MHz included 2D 13 C-13 C RFDR [START_REF] Bennett | Homonuclear radio frequency-driven recoupling in rotating solids[END_REF] , 1 H-13 C/ [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N HSQC and 3D [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N-edited 1 H-1 H spin diffusion experiments [START_REF] Alam | 1H-13C INEPT MAS NMR correlation experiments with 1H-1H mediated magnetization exchange to probe organization in lipid biomembranes[END_REF] (set temperature 270 K, MAS rate 44 kHz). The actual temperature during the ssNMR experiments for both apo as well as MAPbound microtubular samples was 293 K. The 13 C- [START_REF] Kumar | Interaction of epothilone B (Patupilone) with microtubules as detected by two-dimensional solid-state NMR spectroscopy[END_REF] C mixing was 3 ms in the RFDR experiment. The PISSARRO decoupling [START_REF] Weingarth | Efficiency at high spinning frequencies of heteronuclear decoupling methods designed to quench rotary resonance[END_REF] scheme of 120 kHz was employed on the 1 H channel during the RFDR mixing and the detection of [START_REF] Kumar | Interaction of epothilone B (Patupilone) with microtubules as detected by two-dimensional solid-state NMR spectroscopy[END_REF] C. The proton spin diffusion time was 200 ms. In all proton-detected experiments, the PISSARRO decoupling scheme was applied at 11 kHz on 1 H, [START_REF] Kumar | Interaction of epothilone B (Patupilone) with microtubules as detected by two-dimensional solid-state NMR spectroscopy[END_REF] C and [START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N channels. [START_REF] Menéndez | Control of the structural stability of the tubulin dimer by one high affinity bound magnesium ion at nucleotide N-site[END_REF] P NMR experiment was conducted on the 500 MHz spectrometer (set temperature 290 K, MAS rate 11 kHz). The CP MAS experiment was recorded using a 100-50% ramp on 1 H-channel of 95.4 kHz, and 71.7 kHz on the 31 P-channel, with 1.2 ms CP contact time. A SPINAL decoupling [START_REF] Fung | An improved broadband decoupling sequence for liquid crystals and solids[END_REF] of 1 H during the acquisition of [START_REF] Menéndez | Control of the structural stability of the tubulin dimer by one high affinity bound magnesium ion at nucleotide N-site[END_REF] P was applied at 90 kHz. [START_REF] Menéndez | Control of the structural stability of the tubulin dimer by one high affinity bound magnesium ion at nucleotide N-site[END_REF] P chemical shifts were referenced externally using phosphate buffer, pH 7 and set the signal at 0 ppm. Reporting summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Fig. 1

 1 Fig. 1 MT preparation from HeLa S3 cells and sample characterization. a Schematic overview of the sample preparation. b SDS-PAGE analysis from each purification step. M: protein marker; S: supernatant; P: pellet; first poly: first polymerization; depoly: depolymerization; Taxol poly: polymerization with Taxol. The uncropped gel is provided as a Source Data file. c Functional characterization of purified HeLa S3 tubulin. Kymograph (left) and movie stills (right) of an in vitro polymerized MT imaged for 10 min on a TIRF microscope correspond to Fig. S1C. Time points and MT plus (+) and minus (-) ends are indicated. d Characterization of morphology of HeLa MTs before and after MAS NMR experiments by EM.

Fig. 2

 2 Fig.2SsNMR spectra of [ 13 C,[START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N]-labeled MTs. a The 2D 13 C-[START_REF] Kumar | Interaction of epothilone B (Patupilone) with microtubules as detected by two-dimensional solid-state NMR spectroscopy[END_REF] C radio frequency-driven recoupling (RFDR) experiment was performed at 270 K set temperature with a MAS rate of 44 kHz with zoom in's on serine, threonine and alanine Cα-Cβ regions. Crosses indicate the chemical shift predictions for MTs from SHIFTX2[START_REF] Han | SHIFTX2: significantly improved protein chemical shift prediction[END_REF] and FANDAS 2.0 30 based on the EM structure (PDB 5SYF). Red and green crosses represent predictions for α-tubulin and β-tubulin, respectively. b Schematic representation of the GTP/GDP binding to tubulin in MTs (left), and 1D H-31 P CP experiment at ambient temperature with MAS rate of 11 kHz allows to observe GTP and GDP bound to MTs.

Fig. 3

 3 Fig.3Flexible tubulin C-terminal investigated by J-based ssNMR. a The sequences of N-and C-termini of tubulin. Underlined residues showed sequential correlations in our ssNMR data sets. The protein sequences of α1 and β1 tubulin isotypes were used for analysis based on previous results[START_REF] Davis | A tubulin polymerization microassay used to compare ligand efficacy[END_REF] . b 2D 15 N-HSQC of [ 13 C,[START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N]-labeled MTs showed the flexible tubulin tails. c 2D 13 C-HSQC of [ 13 C,[START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N]-labeled MTs showing the residues present in the tubulin tails. Due to the high flexibility, the signals from side chains of leucine, lysine as well as buffer compounds and lipids were also observed. d Strips of a 3D 15 N-edited 1 H-1 H spin diffusion experiment showing the connections between[START_REF] Kumar | Interaction of epothilone B (Patupilone) with microtubules as detected by two-dimensional solid-state NMR spectroscopy[END_REF] C-HSQC and 15 N-HSQC.

Fig. 4

 4 Fig. 4 Tubulin C-terminal tail dynamics are modulated by the CKK domain. a Comparison of 2D[START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N-HSQC spectra obtained from [ 13 C,[START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N]-labeled MTs (black) and unlabeled CAMSAP1 CKK N1492A in complex with [ 13 C,[START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N]-labeled MTs (magenta). b Zoom-in on arginine residues found in the CKK-MT cryo-EM structure (PDB 5M5C), ref.[START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] ) that are located on α-tubulin (yellow) and β-tubulin (gray) and within 6 Å to CKK domain (magenta). c Top: aminoacid sequences of CKK termini with last residues observed in the cryo-EM structure (PDB 5M5C) indicated by stars. Bottom: C-terminal tails of α-tubulin and β-tubulin with last residues detected the cryo-EM structure (PDB 5M5C) are indicated by yellow and black stars, respectively. d Dynamic (indicated by double-headed arrows) C-terminal tubulin (dashed black and yellow lines) and CKK (magenta) tails. Blue lines measure the distance between the last residues observed in the cryo-EM structure of both tubulin tails (indicated by black and yellow stars) to the last CKK C-terminal residue observed in cryo-EM (magenta star). e Dynamic (indicated by double-headed arrows) CKK N-terminus (dashed magenta line) and β-tubulin C-terminus (dashed black line). The blue line indicates the distance between the last residue of β-tubulin and the first residue of CKK detected in the cryo-EM structure.

Fig. 5

 5 Fig.5Tubulin C-terminal tails interact with MAP7. a Secondary structure prediction of MAP7-MTBD by JPred[START_REF] Drozdetskiy | JPred4: a protein secondary structure prediction server[END_REF] . b Spectral comparison of 2D[START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N-HSQC spectra obtained from [ 13 C,[START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N]-labeled MTs (black) and unlabeled MAP7-MTBD in complex with [ 13 C,[START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N]-labeled MTs (cyan). c Signal intensity ratios of resolved peaks in[START_REF] Atherton | A structural model for microtubule minus-end recognition and protection by CAMSAP proteins[END_REF] N-HSQC between MAP7-MTBD bound MTs and free MTs. Error bars were calculated based on the NMR signal to noise ratio of each peak in the two spectra. Signal intensity ratios are provided as a Source Data file.

NATURE COMMUNICATIONS | (2020) 11:18 | https://doi.org/10.1038/s41467-019-13876-x | www.nature.com/naturecommunications

Acknowledgements

We thank Gert Folkers for helpful discussions and Johan van der Zwan for technical support. This work was supported by the Dutch Science Foundation NWO: VENI grant 722.016.002 to S.X., ALW Open program grant 824.15.017 to A.A., NWO-Groot (no. 175.010.2009.002) and TOP-PUNT (no. 718.015.001) grant to M.B. and by uNMR-NL, the National Roadmap Large-Scale NMR Facility of the Netherlands (grant 184.032.207). C.J. is supported by the grants ANR-10-IDEX-0001-02 PSL, ANR-11-LBX-0038, FRM DEQ20170336756. S.B. was supported by the FRM grant FDT201805005465, and CEFIPRA 5703-1, and J.A.S. by the European Union's Horizon 2020 Marie Skłodowska-Curie grant agreement No. 675737, and the FRM grant FDT201904008210.

Data availability

Data supporting the findings of this manuscript are available from the corresponding authors upon reasonable request. A reporting summary for this Article is available as a

Supplementary Information file. The source data underlying Figs. 1b and5c and Supplementary Figs.

Competing interests

The authors declare no competing interests.