Franc Üois Devred

Pascale Barbier

Soazig Douillard

Octavio Monasterio

Manuel Andreu

Vincent Peyrot

Tau Induces Ring and Microtubule Formation from Râ-Tubulin Dimers under Nonassembly Conditions ² |

Tau is a neuronal microtubule-associated protein that plays a central role in many cellular processes, both physiological and pathological, such as axons stabilization and Alzheimer's disease. Despite extensive studies, very little is known about the detailed molecular basis of tau binding to microtubules. We used the four-repeat recombinant htau40 and tubulin dimers to show for the first time that tau is able to induce both microtubule and ring formation from 6S Râ tubulin in phosphate buffer without added magnesium (nonassembly conditions). The amount of microtubules or rings formed was protein concentration-, temperature-, and nucleotide-dependent. By means of biophysical approaches, we showed that tau binds to tubulin without global-folding change, detectable by circular dichroism. We also demonstrated that the tau-tubulin interaction follows a ligand-mediated elongation process, with two tau-binding site per tubulin dimer. Moreover, using a tubulin recombinant R-tubulin C-terminal fragment (404-451) and a â-tubulin C-terminal fragment (394-445), we demonstrated the involvement of both of these tubulin regions in tau binding. From this model system, we gain new insight into the mechanisms by which tau binds to tubulin and induces microtubule formation.

The microtubule cytoskeleton is a very dynamic network that plays a crucial role in many cellular processes such as cellular architecture, cell division, and intracellular traffic. Microtubule dynamic instability and functions are regulated by microtubule-associated proteins (MAPs). 1 Tau is a MAP that stabilizes axonal microtubules and maintains neuronal processes [START_REF] Cleveland | Purification of tau, a microtubule-associated protein that induces assembly of microtubules from purified tubulin[END_REF]. Tau is also known to play a major role in Alzheimer's disease (see ref 2 for review). Detached from microtubules by phosphorylation, tau may aggregate to form pathological paired helical filaments (PHFs) upon further hyperphosphorylation (see ref 3 for review). Recently, it has also been suggested that tau could play a role in Alzheimer's disease long before it detaches from microtubules and aggregates [START_REF] Mandelkow | Clogging of axons by tau, inhibition of axonal traffic, and starvation of synapses[END_REF][START_REF] Panda | Differential regulation of microtubule dynamics by threeand four-repeat tau: Implications for the onset of neurodegenerative disease[END_REF]. Thus, tau binding to microtubules plays a pivotal role in both pathological and physiological processes.

Tau-microtubule interactions have been investigated intensively, leading to the identification of tau and tubulin regions implicated in this interaction. Each tau isoform contains three to four microtubule-binding repeats, located in its C-terminal part. The first inter-repeat [START_REF] Lee | The primary structure and heterogeneity of tau protein from mouse brain[END_REF][START_REF] Goode | Identification of a novel microtubule binding and assembly domain in the developmentally regulated inter-repeat region of tau[END_REF], as well as the flanking domains [START_REF] Gustke | Domains of tau protein and interactions with microtubules[END_REF][START_REF] Goode | Functional interactions between the proline-rich and repeat regions of tau enhance microtubule binding and assembly[END_REF], enhances the binding affinity of these repeats. For tubulin, except for one study that showed that the N-terminal peptide R(1-75) was able to bind tau [START_REF] Littauer | Common and distinct tubulin binding sites for microtubule-associated proteins[END_REF], most of the studies showed that tau, just like the others MAPs, binds in the C-terminal region of tubulin [START_REF] Serrano | Localization of the tubulin binding site for tau protein[END_REF][START_REF] Marya | Kinesin and tau bind to distinct sites on microtubules[END_REF][START_REF] Maccioni | Differential interaction of synthetic peptides from the carboxyl-terminal regulatory domain of tubulin with microtubule-associated proteins[END_REF]. Recently, it was shown that tau binds to two distinct sites on the C-terminal part of tubulin, one of which is located within the 12 C-terminal amino acids of both R and â tubulin [START_REF] Chau | The microtubule-associated protein tau cross-links to two distinct sites on each alpha and beta tubulin monomer via separate domains[END_REF]. Using taxol-stabilized microtubules, Al-Bassam et al. [START_REF] Al-Bassam | MAP2 and tau bind longitudinally along the outer ridges of microtubule protofilaments[END_REF] concluded that tau binds longitudinally along the outer ridges of protofilaments, probably on tubulin H11 and H12 helices. More recently, in a study performed in the presence of TMAO, known to enhance tau activity on tubulin assembly, Kar et al. [START_REF] Kar | Repeat motifs of tau bind to the insides of microtubules in the absence of taxol[END_REF] proposed that tau would also bind to the inside of the microtubule wall. It has also been suggested that tau undergoes a complex intramolecular rearrangement upon binding to microtubules [START_REF] Goode | Functional interactions between the proline-rich and repeat regions of tau enhance microtubule binding and assembly[END_REF][START_REF] Devred | First tau repeat domain binding to growing and taxol-stabilized microtubules, and serine 262 residue phosphorylation[END_REF].

On the basis of these results, several models have been proposed to explain how tau proteins interact with microtubules. According to the most prevailing model, tau would overlap along several tubulin dimers or across the protofilaments [START_REF] Gustke | Domains of tau protein and interactions with microtubules[END_REF][START_REF] Butner | Tau protein binds to microtubules through a flexible array of distributed weak sites[END_REF][START_REF] Novella | Chemically synthesized 182-235 segment of tau protein and analogue peptides are efficient in vitro microtubule assembly inducers of low apparent sequence specificity[END_REF][START_REF] Ichihara | Visualization of the stop of microtubule depolymerization that occurs at the high-density region of microtubule-associated protein 2 (MAP2)[END_REF]. This model presumes that each repeat and * To whom correspondence should be addressed. Telephone and fax: [START_REF] Bloomfield | Frictional coefficients of multisubunit structures. II. Application to proteins and viruses Biopolymers[END_REF] 491835505. E-mail: vincent.peyrot@pharmacie.univ-mrs.fr.

³ Faculte  de Pharmacie. § Universidad de Chile.

| Consejo Superior de Investigaciones Cientificas. 1 Abbreviations: AUC, analytical ultracentrifugation; CD, circular dichroism; Cr, critical concentration; EM, electron microscopy; MAP, microtubule-associated protein; MES, 2-(N-morpholino)ethanesulfonic acid; PEMGT buffer, 3.4 M Glycerol, 20 mM sodium phosphate, 1 mM EGTA, 10 mM Mg 2+ , 0.1 mM GTP, and 1 mM TCEP at pH 6.5; PGT buffer, 20 mM sodium phosphate, 10 -4 or 10 -5 M GTP, and 1 mM TCEP at pH 6.5; PIPES, piperazine-N,N -bis(ethanesulfonic acid); PT buffer, 20 mM sodium phosphate and 1 mM TCEP at pH 6.5; SDS-PAGE, sodium dodecyl sulfate polyacrylamide gel electrophoresis; SEC, size-exclusion chromatography; TCEP, tris(2-carboxyethyl)phosphine; TFA, trifluoroacetic acid; TFE, trifluoroethanol; TMAO, trimethylamine-N-oxyde.

inter-repeat region interacts with a separate but adjacent tubulin monomer within the microtubule wall. However, some studies suggest that tau would not necessarily need to overlap several tubulin dimers to stabilize microtubules [START_REF] Chau | The microtubule-associated protein tau cross-links to two distinct sites on each alpha and beta tubulin monomer via separate domains[END_REF][START_REF] Devred | First tau repeat domain binding to growing and taxol-stabilized microtubules, and serine 262 residue phosphorylation[END_REF][START_REF] Ennulat | Two separate 18-amino acid domains of tau promote the polymerization of tubulin[END_REF][START_REF] Aizawa | A common amino acid sequence in 190-kDa microtubule-associated protein and tau for the promotion of microtubule assembly[END_REF].



Many studies addressed the issue of stoichiometry, binding affinity, and geometry of tau binding to microtubules; however, results obtained in different conditions lead to different conclusions, and so far no unifying scheme was proposed. Furthermore, the question whether tau acts as a stabilizing agent by binding to the microtubules wall or as a true assembly inducer from tubulin dimers remains unresolved. To investigate the mechanisms by which tau binds to microtubules and/or to Râ-tubulin dimers, we used an environment depleted of assembly promoters such as taxol, TMAO, or Mg 2+ . For the first time, we showed that fourrepeat tau is a true microtubule assembly inducer. In nonassembly conditions, tau was able to induce either microtubule or tubulin ring formation depending on the temperature and GTP concentration. We showed that microtubule formation follows a ligand-mediated elongation process and gave an estimation of the tau-tubulin binding constant, the elongation constant, and the stoichiometry. Using two tubulin C-terminal peptides R(404-451) and â-(394-445), from the main tubulin vertebrate isotypes [START_REF] Jimenez | Helicity of alpha(404-451) and beta(394-445) tubulin C-terminal recombinant peptides[END_REF], we also demonstrated the interaction of tubulin H12 and newly described H11 (24) C-end regions in tau binding. Finally, we showed that tau binds to tubulin without globalfolding change, detectable by circular dichroism (CD). These results provide new insight into the tau mechanism of action, which is a central issue for both neurodegenerative processes and neuron stabilization.

EXPERIMENTAL PROCEDURES

Tubulin Purification and Expression of R and â C-Terminal Domains. Tubulin was purified from lamb brains by ammonium sulfate fractionation and ion-exchange chromatography and stored in liquid nitrogen as described [START_REF] Jimenez | Helicity of alpha(404-451) and beta(394-445) tubulin C-terminal recombinant peptides[END_REF][START_REF] Weisenberg | The colchicine-binding protein of mammalian brain and its relation to microtubules[END_REF][START_REF] Andreu | Interaction of tubulin with bifunctional colchicine analogues: an equilibrium study[END_REF]. Tubulin concentration was determined spectrophotometrically at 275 nm with an extinction coefficient of 109 000 M -1 cm -1 in 6 M guanidine hydrochloride. R tubulin fragment RL52R3 (termed CR throughout) consists of the 48 C-terminal residues of R tubulin (404-451) (isotype hkR1), whereas the â tubulin construct RL33â6 (termed Câ throughout) consists of the 52 C-terminal residues of â tubulin (394-445) (isotype câ2), preceded by the amino acid sequence ARIRAP from the plasmid construction. Expression, purification, and peptide concentration determination using an extinction coefficient of 9530 M -1 cm -1 at 280 nm was performed as previously described [START_REF] Jimenez | Helicity of alpha(404-451) and beta(394-445) tubulin C-terminal recombinant peptides[END_REF].

Tau Expression and Purification. The four-repeat 441 amino acids isoform of tau, htau40 (termed tau throughout), was expressed from a pET vector (kindly provided by M. Goedert) introduced into Escherichia coli BL21(DE3). Tau expression was induced by the addition of 0.5 mM isopropyl 1-thio-â-D-galactopyranoside (IPTG) to cells when A600nm reached 0.6. A total of 3 h after induction at 37 C, cells were pelleted and resuspended in purification buffer [50 mM MES, 1 mM DTT, 1 mM PMSF, and 5 mM EDTA (pH 6.5)]. After two runs in the French press (6 tones), the lysate was cleared by a centrifugation 25 000 rpm for 30 min at 4

C and then precipitated with 45% ammonium sulfate for 10 min at 4 C. It was then recentrifuged, and the pellet was resuspended in purification buffer and dialyzed against a buffer containing 50 mM MES, 1 mM TCEP, 1 mM EGTA, and 5 mM EDTA (pH 6.5) overnight. After the solution was cleared by centrifugation, the supernatant was loaded onto a HiTrap SP Sepharose HP cation exchange column (Amersham Pharmacia) pre-equilibrated with a buffer containing 50 mM MES at pH 6.5 and then eluted at 0.5 mL min -1 with a buffer containing 50 mM MES and 0.5 M NaCl at pH 6.5. Further purification was achieved using a SourceTM 15RPC PE 7.5/150 (Amersham Pharmacia) reverse-phase column equilibrated with H 2 O TFA (0.065%), on which fractions containing tau were loaded and eluted with Acetonitrile TFA (0.05%). Fractions containing tau were then pooled and dry-lyophilized. Tau was weighted and resuspended before use. The tau concentration was measured at 280 nm using an extinction coefficient of 7700 M -1 cm -1 as calculated with antheprot [START_REF] Deleage | Protein structure prediction. Implications for the biologist[END_REF] and then checked by amino acid composition.

Tau and Tubulin/Tubulin Peptide Interaction. In nonassembly conditions, tubulin was prepared by equilibrating the tubulin on a cold Sephadex G25 medium (1 1 20 cm) equilibrated with an appropriate buffer. Experiments were performed in a PT buffer (20 mM sodium phosphate and 1 mM TCEP at pH 6.5) with 10 -4 or 10 -5 M GTP, when needed (in the presence of tubulin). In assembly conditions, tubulin was prepared as described previously [START_REF] Barbier | In vitro effect of cryptophycin 52 on microtubule assembly and tubulin: molecular modeling of the mechanism of action of a new antimitotic drug[END_REF] in a PEMGT buffer (3.4 M glycerol, 20 mM sodium phosphate, 1 mM EGTA, 10 mM Mg 2+ , 0.1 mM GTP, and 1 mM TCEP at pH 6.5).

Cosedimentation Assay and Gel Analysis. Samples (125 íL) were centrifuged using a TL-100 Beckman ultracentrifuge with a TLA 100.2 rotor during 15 min at 50 000 rpm at 37 C to pellet microtubules. Polyacrylamide gel electrophoresis in denaturing conditions (SDS-PAGE) was performed using 15% acrylamide in the separating gel and Amersham Pharmacia low-weight calibration kit (97, 66, 45, 30, 20.1, and 14.4 kDa) for standards. Gels were stained with Coomassie Brilliant Blue. The protein quantification and molar ratio of tubulin dimer to tau were performed using Traitima.exe, image-analysis software provided by Dr. Sarrazin (marcel.sarrrazin@pharmacie.univ-mrs.fr). The assay was performed 3 times. In the absence of tubulin, tau never sedimented to more than a few percents and neither did tubulin in the absence of tau.

Spectroscopic Measurements. Light absorption spectra were obtained with a Perkin-Elmer Lambda 800 UV-vis spectrometer. Fluorescence measurements were obtained with a Kontron SFM 25 luminescence spectrometer 50, with slit widths of 5/5 nm, using 0.2 (excitation direction) 1 1 cm (emission direction) cells (Hellma), thermostated at 25 C. The excitation was done at 275 nm or at 295 nm to specifically excite tryptophans. Note that, at the concentrations used, spectra gave no appreciable inner-filter effect (A < 0.05).

CD Spectra. CD spectra of tau, tubulin, and peptides were acquired with a Jasco 720 spectropolarimeter using cuvettes from 0.1 to 1 mm optical path. Spectra of the tau-tubulin mixture were recorded with a 0.5 nm step at 20 nm min -1 speed, as an average of 5 scans, and corrected for the baseline. Spectra of the tau-tubulin peptide mixture were recorded with a 1.0 nm step at a 20 nm min -1 speed, as an average of 4 scans, and corrected for the baseline. All of these measurements are reported as ellipticity õ (millidegrees). The secondary structure analysis of the CD data was performed as previously described using Dicroprot [START_REF] Deleage | Protein structure prediction. Implications for the biologist[END_REF].

Exclusion Chromatography. Size-exclusion chromatography experiments were performed at room temperature using an AKTA-HPLC system (Amersham Pharmacia Biotech). Samples were loaded on a Superdex 200 HR10/30 column (Amersham Pharmacia Biotech) pre-equilibrated in the same buffer as the samples, except for the measurement of the Stokes radius of tau, where the PT buffer was supplemented with 500 mM NaCl. Fractions of 0.2-1 mL were collected at a flow rate of 0.5 mL min -1 , and absorbances were measured at 280 and 215 nm. For calibration, we used proteins with known Stokes radii and molecular masses. The standards were ferritin (MW ) 232 kDa, Rs ) 61 Å), catalase (MW ) 232 kDa, Rs ) 52.2 Å), aldolase (MW ) 158 kDa, Rs ) 48.1 Å), albumin (MW ) 67 kDa, Rs ) 35.5 Å), chymotrypsinogen A (MW ) 25 kDa, Rs ) 20.9 Å), and RNase A (MW ) 13.7 kDa, Rs ) 16.4 Å).

Analytical Ultracentrifugation: Sedimentation Equilibrium. Experiments were performed with a Beckman Optima XL-A analytical ultracentrifuge equipped with absorbance optics, using an An55Ti rotor. A short column sedimentation equilibrium experiment was performed on 60 íL of tau, with a loading concentration ranging from 1.5 to 4.5 mg/mL in the six-channel centerpieces of charcoal-filled Epon. Measurement was done at three successive speeds (8000, 10 000, and 14 000 rpm) by taking scans at the appropriate wavelength (275 and 250 nm) when sedimentation equilibrium was reached. The temperature was 20 C. High-speed sedimentation was conducted afterward for baseline correction. Average molecular masses were determined by fitting a sedimentation equilibrium model for a single sedimenting solute to individual data sets with XLAEQ and EQASSOC supplied by Beckman [START_REF] Minton | Modern Ultracentrifugation[END_REF]. Data analysis was also performed by global analysis of several data sets obtained at different loading concentrations using MULTEQ3B [START_REF] Minton | Modern Ultracentrifugation[END_REF] and NONLIN [START_REF] Johnson | Analysis of data from the analytical ultracentrifuge by nonlinear least-squares techniques[END_REF]. The partial specific volume of tau was 0.721 mL/g, calculated from the amino acid composition by SEDNTERP [START_REF] Laue | Computer-aided interpretation of analytical sedimentation data for proteins in Analytical Ultracentrifugation in Biochemistry and Polymer Sciences[END_REF].

Sedimentation Velocity: Tau Characterization. Experiments were carried out at 55 000 rpm and 20 C in the same XL-A instrument, using 12 mm aluminum double-sector centerpieces. Data were acquired in continuous mode at 275 nm. Apparent sedimentation coefficients were determined using SEDFIT [START_REF] Schuck | Determination of the sedimentation coefficient distribution by least-squares boundary modeling[END_REF] and were corrected to standard conditions using SEDNTERP [START_REF] Laue | Computer-aided interpretation of analytical sedimentation data for proteins in Analytical Ultracentrifugation in Biochemistry and Polymer Sciences[END_REF].

The frictional coefficient ratio (f/f0) was calculated using f/f0 ) smax/s, where f0 and smax are the frictional and sedimentation coefficients of a smooth unhydrated sphere corresponding to the given protein mass, s is the experimental sedimentation coefficient obtained by UCA, and f is the frictional coefficient of the protein [START_REF] Bloomfield | Frictional coefficients of multisubunit structures. II. Application to proteins and viruses Biopolymers[END_REF].

Tau-Tubulin Interaction. Experiments were carried out at 30 000 and 40 000 rpm at 20 C using 12 mm charcoalfilled Epon centerpieces. Data were acquired in continuous mode at 275 nm. The distributions g(s*) were generated by least-squares boundary modeling of sedimentation velocity data by DCDT + [START_REF] Stafford | Modern Applications of Analytical Ultracentrifugation in Analytical Ultracentrifugation in Biochemistry and Polymer Science[END_REF][START_REF] Philo | A method for directly fitting the time derivative of sedimentation velocity data and an alternative algorithm for calculating sedimentation coefficient distribution functions Anal[END_REF]. These distributions were then fitted with Gaussian curves, and the areas and maximum, which represent the sediment coefficient of the sample, were calculated. We used this analysis to qualitatively characterize the tau-tubulin interaction; the boundaries do not represent individual species but interacting zones.

In AUC, experiments were performed in 10 -5 M GTP. The nucleotide composition of the tubulin was determined to be mainly GTP tubulin (87%), which is not significantly different from the GTP tubulin equilibrated with 10 -4 M GTP buffer (90%).

The solvent density and the viscosity were calculated with SEDNTERP; they were 1.000 58 g/cm 3 and 0.010 469 poise, respectively (at 20 C).

Models of Ligand-Induced Macromolecular Self-Association. Ligand-induced tubulin assembly may proceed by two different pathways [START_REF] Diaz | Thermodynamics of ligand-induced assembly of tubulin[END_REF]: either a ligand-facilitated elongation pathway, in which the elongation precedes the binding of the ligand (eq 1) or a ligand-mediated elongation pathway, in which the binding of tau (noted X), to either tubulin or microtubule, precedes the elongation (eq 2 and 2 ). Equation 1is characterized by an apparent elongation constant Kapp ) K2(1 + K1X). Equations 2 and 2 are not thermodynamically discernible and are characterized by an apparent elongation constant Kapp ) K1K2X/(1 + K1X) (for more details, see the appendix of ref 37). In the case of a two-ligand-mediated elongation process, the apparent elongation constant becomes Kapp ) K1 K2 X 2 /(1 + K1 X 2 ). All of the fittings were done using a graphics-fitting program (Sigmaplot 4.0, Jandel Scientific).

Miscellaneous. Residual Mg 2+ concentration was determined by atomic absorption spectroscopy [START_REF] Martin | Atomic absorption spectrometry of magnesium[END_REF][START_REF] Rivas | Magnesium-induced linear self-association of the FtsZ bacterial cell division protein monomer. The primary steps for FtsZ assembly[END_REF].

Nucleotide content measurement was performed as previously described [START_REF] Barbier | The active GTP-and ground GDP-liganded states of tubulin are distinguished by the binding of chiral isomers of ethyl 5-amino-2-methyl-1,2-dihydro-3-phenylpyrido[3,4-b] pyrazin-7-yl carbam-ate[END_REF] with minor modifications. Samples of 900 íL, precipitated with perchloric acid (3%) in the presence of an additional 1 íM GMP as an internal standard, were centrifuged in a Heraeus Sepatech Biofuge A at maximum speed (13 000 rpm) for 10 min at 4 C. Supernatants were then neutralized to pH 8.0 using 3 M NaOH and loaded on a Nucleosil 4000.7 PE column pre-equilibrated with 10 mM Tris/HCl at pH 8.2. Nucleotides were then eluted with 20 mM Tris/HCl at pH 8.0 and 1.5 M NaCl. The GTP and GDP ratio was then measured by peak integration.

Electron Microscopy. Samples were adsorbed onto 200 mesh, Formvar carbon-coated copper grids, stained with 2% (w/v) uranyl acetate, and blotted to dryness. Grids were observed using a JEOL JEM-1220 transmission electron microscope operated at 80 kV. Magnifications used ranges from 20001 to 500001. To ensure that microtubules do not disassemble during adsorption, this step was performed in a thermostated room at 37 C, unless stated otherwise.

RESULTS

Characterization of Purified Recombinant hTau40. Recombinant tau was purified without heat treatment because

K K 2 1
MT + Tub 7 98 MT -Tub + X 7 98 MT -Tub -X (1)

7 K K 1 2
X + Tub 98 Tub -X + MT 7 98 MT -Tub -X (2)

7 K K 1 2
MT + X 98 MT -X + Tub 7 98 MT -Tub -X ( 2)

it has been shown that boiling affects the tau structure [START_REF] Ruben | Alzheimer disease hyperphosphorylated tau aggregates hydrophobically[END_REF].

Because tau has a high tendency to oligomerize in nonreducing conditions [START_REF] Wille | Alzheimer-like paired helical filaments and antiparallel dimers formed from microtubule-associated protein tau in vitro[END_REF], we conducted the whole study in the presence of a stable reducing agent (1 mM TCEP). As evidenced by SDS-PAGE analysis (data not shown), the protein was 98% homogeneous and behaved as an apparent 66 500 Da species, in agreement with what has been reported [START_REF] Cleveland | Purification of tau, a microtubule-associated protein that induces assembly of microtubules from purified tubulin[END_REF]. Using mass spectrometry, we found a single sharp peak at 45 718 ( 50 Da (theoretical 45 850 Da), indicating that the first methionine residue had been cleaved because of the bacterial expression, which was confirmed by N-terminal sequencing.

Tau is known to promote tubulin assembly into microtubules [START_REF] Weingarten | A protein factor essential for microtubule assembly[END_REF]. To check the functionality of our tau preparation, we tested its activity on tubulin assembly in vitro, in PEMGT buffer [START_REF] Barbier | In vitro effect of cryptophycin 52 on microtubule assembly and tubulin: molecular modeling of the mechanism of action of a new antimitotic drug[END_REF]. In these conditions, the critical concentration (Cr) under which no tubulin assembly occurs is 7.0 íM [START_REF] Devred | First tau repeat domain binding to growing and taxol-stabilized microtubules, and serine 262 residue phosphorylation[END_REF]. Figure 1 shows that, in the presence of tau, tubulin polymerizes below this threshold. The turbidity generated by the assembly of tubulin increases in the presence of tau at 37 C and decreases when the sample was cooled to 9 C, indicating the reversibility of the process. At the plateau, electron microscopy revealed the presence of morphologically normal microtubules (inset of Figure 1). Tau induced and stabilized microtubule formation; therefore, it is functional and can be further characterized in solution.

By far-UV CD, we found that tau had little secondary structure compatible with 6% helix, 15% sheet, and 12% turn. This is consistent with the earlier studies revealing a mostly random-coil conformation of tau [START_REF] Cleveland | Purification of tau, a microtubule-associated protein that induces assembly of microtubules from purified tubulin[END_REF][START_REF] Schweers | Structural studies of tau protein and Alzheimer paired helical filaments show no evidence for beta-structure[END_REF]. Nevertheless, this could also be due to some unusual secondary structure elements such as poly(L-proline) II helical conformation [START_REF] Syme | A Raman optical activity study of rheomorphism in caseins, synucleins and tau. New insight into the structure and behavior of natively unfolded proteins[END_REF].

To characterize the quaternary structure of tau in solution, we performed Superdex S200 size-exclusion chromatography (SEC) and analytical ultracentrifugation (AUC) experiments. Results are summarized in Table 1. SEC analysis showed that the protein was eluted as a single sharp peak with a Stokes radius of 44 Å. This radius is too large for a globular monomer with a molecular mass of 45 719 Da. It could either correspond to a tetramer or to a extended protein, because estimation of molecular weight from SEC is only suitable for globular protein [START_REF] Le Maire | Use of gel chromatography for determination of size and molecular weight of proteins: further caution Anal[END_REF]. Thus, to determine the association state of tau, sedimentation equilibrium experiments were performed using three initial loading concentrations of tau and three rotor speeds (Figure 2A). Fitting the three The symbols show the experimental radial distribution of tau at sedimentation equilibrium at 1.5 mg mL -1 (4), 3 mg mL -1 (0), and 4.5 mg mL -1 (O). The solid lines represent the best fit curves of global analysis of multiple sedimentation equilibrium data with the single, ideal species model. Of nine fitted data sets (the three protein concentrations indicated above at three speeds: 10 000, 12 000, and 16 000 rpm) only three (the ones at 16 000 rpm) are shown. The r m is the radial distance at the meniscus, with the residuals representing the variation between the experimental data and those generated by the fit with single species. (B) Continuous sedimentation coefficient distribution C(s) of tau at 1.9 mg mL -1 at 20 C. Inset shows the dependence of the apparent sedimentation coefficient at 20 C in water. concentration data sets simultaneously at one speed (16 000 rpm) showed that the best residual distribution, and the minimum square root of variance was obtained for a single ideal species model (Figure 2A). We found a value of 44 000 ( 5000 Da, in agreement with the theoretical molecular mass of the monomer of tau. Sedimentation velocity experiments confirmed the monodisperse nature of tau in solution by the presence of a single sharp boundary, at any concentration used. The sedimentation coefficient distribution C(s) showed a single symmetrical peak centered at 2.57 S (Figure 2B), indicating the presence of a single species.

The tau sedimentation coefficient decreased with concentration, as expected for a nonassociative single particle (inset of Figure 2B). A s 0 20,w of 2.5 ( 0.1 S was obtained at infinite dilution in water. Using this sediment coefficient value, we calculated (see the Experimental Procedures) the frictional coefficient ratio (f/f0) of tau to be 1.81 and the Stokes radius, 42 Å (Table 1). This frictional coefficient ratio is higher than 1.6, which corresponds to a moderately elongated protein [START_REF] Bloomfield | Frictional coefficients of multisubunit structures. II. Application to proteins and viruses Biopolymers[END_REF]. Indeed, the sedimentation coefficient of tau 2.5 S is larger than the value expected for a random-coil polypeptide chain of the same length, s 0 20,w 1.4 S (47), implying some residual restriction to a complete unfolding of tau in a buffer.

After concluding that tau was pure, functional, and monomeric in reducing conditions, we were able to study tau interaction with R-â tubulin dimers.

Analysis of Tau-Tubulin Interaction at 20 C. Most of the previous experiments to study tau binding to microtubules or tubulin were performed either with stabilized microtubules or with peptides corresponding to small constructs of tau and/or tubulin. To observe the binding of tau to unpolymerized tubulin and to measure potential changes in either tau or tubulin structures, we studied the binding of the entire tau protein to tubulin dimers by AUC under nonassembly conditions. The sedimentation velocity of tubulin was examined at 20 C in the presence of tau. In our conditions, control tubulin sedimented as a single species as indicated by the single Gaussian distribution of the g(s*) plot. This distribution was centered on 5.43 ( 0.03 S for 15 íM tubulin (inset of Figure 3A).

Figure 3A shows a trimodal pattern resulting from the interaction of 15 íM tubulin and 7.5 íM tau. The g(s*) distribution, which is very sensitive to the presence of multiple species, was fitted with 3 Gaussian curves centered on 6 S, 30-35 S, and 40-50 S, respectively. To test the nature of the equilibrium, similar experiments were performed at a different speed. They led to the same sedimentation pattern, indicating that this self-associating system was in rapid equilibrium [START_REF] Lee | Studies of macromolecular interaction by sedimentation velocity in Modern Analytical Ultracentrifugation[END_REF]. Note, however, that the peaks observed by AUC are not individual species but sediment boundaries of this reversible associating system. Apparent sedimentation coefficients (inset of Figure 3B) and amount of the different sediment boundaries (Figure 3B) were calculated by integrating the Gaussian curves obtained for the different peaks (see the Experimental Procedures) for different tau/tubulin molar ratios and different tubulin concentrations. The proportion of the slow peak centered on 6 S decreased in favor of a rapid sedimenting peak centered on 30 S, and then, when the tau/tubulin ratio was raised even more, a third peak centered on 45 S appeared. As we increased the tau/tubulin ratio, the area of the second sedimenting boundary (30 S) increased until it reached 20% and remained constant from the tau/tubulin ratio of 0.5, which corresponds to one tau for two tubulin dimers. The most rapid sedimenting peak (45 S), which was absent for a tubulin concentration of 5 íM, appeared at a tau/tubulin ratio of 0.5 for a tubulin concentration of 10 íM (âââ) and at tau/tubulin ratio of 0.25 for a tubulin concentration of 15 íM (s). The formation of these different species is an equilibrium system, tubulin and tau concentration dependent.

To gain insight into the nature of the self-association process, we examined the samples by EM. They consisted of circular polymers that were mostly single wall rings with an average external diameter of about 45 ( 5 nm and an internal diameter of 30 ( 5 nm, corresponding to about 14 (---). The inset shows the variation of the apparent sedimentation coefficient in the function of the tau/tubulin ratio with tubulin 15 íM. This coefficient was obtained by analysis of the S* distribution described above. Tau by itself does not contribute to the signal. Note that for 5 íM tubulin there is no 45 S boundary. tubulin dimer rings (Figure 4A). Nevertheless, the EM observation also revealed the presence of other circular polymers, such as thick wall rings and possibly spirals (Figure 4B), as well as partial rings. This structural heterogeneity could explain the spread profile of the peaks of the g(s*) distribution of the fast sedimenting species in the sedimentation velocity experiment (Figure 3A).

Because tau is unordered in solution, it has been frequently suggested that it might acquire some folding upon interaction with tubulin [START_REF] Al-Bassam | MAP2 and tau bind longitudinally along the outer ridges of microtubule protofilaments[END_REF][START_REF] Kotani | Interaction mechanism between microtubule-associated proteins and microtubules. A proton nuclear magnetic resonance analysis on the binding of synthetic peptide to tubulin[END_REF]. Our results showed that tau interacted with tubulin and promoted tubulin oligomerization. To check for potential changes in the secondary structure accompanying these interactions, we performed CD measurements. Spectra obtained for tau without TFE (line 1 of the inset of Figure 5A) showed a minimum around 200 nm, which is characteristic of largely random-coil structures. In the presence of TFE, tau spectrum (line 2 of the inset of Figure 5A) presented a maximum at 190 nm and two minima at 208 and 222 nm, characteristic of R-helical structures. However, the tau interaction with tubulin did not change the spectra of the mixture substantially, arguing that the randomcoil structure dominated in all cases. Indeed, the observed CD spectrum of a mixture of tau and tubulin (line 3 of Figure 5A) is almost superimposable on that obtained by a linear combination of the individual CD spectra of tau and tubulin in the same ratio (line 4 of Figure 5A). This indicates that there is no change in the overall helical-structure content of either tau or tubulin, resulting from the interaction. However, this does not rule out local changes at tau-tubulin or tubulin-tubulin binding interfaces.

Because tubulin and tau have aromatic residues, we also performed fluorescence experiments to further characterize their interaction. During complex formation, the fluorescence emission spectrum can shift in the wavelength of its maximum or in fluorescence intensity. These shifts can therefore be used to follow interactions. Figure 5B shows the uncorrected emission spectra of tau (line 1) and of tubulin (line 2). The fluorescence emission spectrum of a mixture of tau and tubulin (line 3) was shifted toward the lower wavelengths with a slight modification in its intensity as compared to the summed emission spectra of the two individual components (line 4 and inset of Figure 5B). This small change in fluorescence is compatible with a minor modification in the environment of tryptophan residues of tubulin. We conducted the same measurements with an excitation wavelength of 295 nm (data not shown). At this wavelength, the emission fluorescence signal was only due to tubulin, because tau has no tryptophan residues. Nevertheless, it did not improve the result significantly, nor did it permit any quantitative analysis of the interaction. Thus, at 20 C, tau binds to tubulin with no apparent R-helical structure induction and induces tubulin assembly into rings.

Tau-Tubulin Interaction at 37 C. Having shown that tau decreased the critical concentration in PEMGT buffer at 37 C and that tau was able to induce the assembly of tubulin into rings at 20 C in PGT buffer, we investigated tautubulin interactions at 37 C in PGT buffer. PGT is a magnesium less buffer that normally supports neither tubulin association nor microtubule assembly in our range of tubulin 4) Linear combination of the separate spectra of tau and tubulin (4 ) 1 + 2). The difference between (3) and ( 4) is drawn in [START_REF] Panda | Differential regulation of microtubule dynamics by threeand four-repeat tau: Implications for the onset of neurodegenerative disease[END_REF]. Spectra were recorded in a 0.1 mm cuvette. The inset represents 2 íM tau spectra without TFE [START_REF] Cleveland | Purification of tau, a microtubule-associated protein that induces assembly of microtubules from purified tubulin[END_REF] or with 40% TFE [START_REF] Trojanowski | The role of tau in Alzheimer's disease[END_REF]. Spectra were recorded with a 1 mm cuvette with 2 íM tau. (B) Fluorescence spectra of 15 íM tau (1), 15 íM tubulin (2), and 15 and 15 íM tau-tubulin mixture (3). ( 4) Linear combination of the separate spectra of tau and tubulin (4 ) 1 + 2). The excitation wavelength is 275 nm. The inset represents an enlarged view of the peak area of ( 3) and (4). To clarify the inset, tubulin spectrum (2) was omitted. concentration (3-30 íM). However, at 37 C, we observed an immediate increase in turbidity upon addition of tau, which implied the formation of polymers (line 1 of Figure 6A). Assembly was reversed by cooling the samples to 9 C, which indicated the absence of irreversible aggregation. Disassembly was rapid and reached a new baseline within 5 min, slightly higher than the original baseline. From EM, we confirmed that these polymers observed at 37 C were microtubules (Figure 6B). Upon cooling, the samples presented depolymerizing microtubules with ends pealing outward and even some rings (Figure 6C). At 9 C, rings and a few residual cold-resistant microtubules were observed by EM, explaining the remaining turbidimetry. With 10 -4 M GTP, tubulin was able to undergo several cycles of assembly-disassembly (two are shown in Figure 6A), whereas at 10 -5 M GTP, only one cycle of assemblydisassembly was observed (data not shown). This indicated that GTP hydrolysis occurred during tau-induced microtubule formation and that tau was unable to induce microtubule formation from GDP-tubulin. Furthermore, to show the specificity of the tau effect in PGT buffer, we compared it to taxol in the same conditions. Line 2 of Figure 6A shows that equimolar taxol is not able to induce tubulin assembly in PGT buffer.

Titration of tubulin assembly by tau revealed interesting features. Upon increasing the concentration of tau to a 1:1 molar ratio, we observed a gradual increase of the turbidity plateau (Figure 7A). When tau concentration was greater than tubulin concentration, the turbidity signal increased dramatically to an absorbance greater that 2 (line 6 of Figure 7A). This drastic increase of turbidity correlated with the presence of bundles of microtubules as evidenced by EM (parts B and C of Figure 7). Turbidity is known to be a function of the total weight concentration of scattering particles only when the particles have small diameters compared to the wavelength of incident light [START_REF] Berne | Interpretation of the light scattering from long rods[END_REF][START_REF] Gaskin | Techniques for the study of microtubule assembly in vitro Methods Enzymol[END_REF]. Bundles do not match these conditions, which explains the observed turbidimetric behavior of microtubules in these conditions.

To study the linkage of tau binding to tubulin isodesmic self-association, we thus used cosedimentation assays (see the Experimental Procedures) rather than turbidimetric measurements (Figure 7D). It enabled us to measure the concentration of microtubules and tau bound to microtubules in the pellet.

Analysis of Tau-Tubulin Interaction at 37 C. We assumed in first approximation that tau concentration in the supernatant was equal to [taufree], tau concentration in the pellet, equal to [taubound], and tubulin concentration in the supernatant, equal to [tubulinfree], thus neglecting the quantity of potential small tau-tubulin complexes. This enabled us to quantitatively analyze tau binding. A number of theoretical studies have shown that in linked self-association systems, the shape of the ligand-binding isotherm depends on the a longitudinal bridging of the tubulin dimers. Indeed, several studies have shown that tau would form oligomers or aggregates upon binding to microtubules, which is consistent with the hypothesis of an accumulation of tau on the microtubule surface [START_REF] Ackmann | Nonsaturable binding indicates clustering of tau on the microtubule surface in a paired helical filament-like conformation[END_REF][START_REF] Makrides | Microtubule-dependent oligomerization of tau. Implications for physiological tau function and tauopathies[END_REF].

It has been suggested that tau gets structured upon binding to its ligand. Kotani et al.,by NMR (49), presented evidence of a disordered to ordered transition upon microtubule binding, suggesting also a particular involvement of tyrosines, which might be located in H12. We showed that unstructured tau was able to interact with CR(404-451), Câ(394-445), or tubulin dimers, causing a slight shift in fluorescence intensity and wavelength, suggesting a small modification in the tryptophan environment. The specificity of the interaction of the C-terminal tubulin fragments was confirmed by the inhibition and disassembly of tau-induced microtubules. Maccioni et al. [START_REF] Maccioni | A discrete repeated sequence defines a tubulin binding domain on microtubule-associated protein tau Arch[END_REF] described the interaction between tubulin CR(430-441) and Câ(422-434) and two tau repeat domains R1 and R3, indicating that tubulin peptides induced structural changes in the tau R3 domain. Contrary to these results on small peptides, our CD analysis with entire tau and tubulin dimers has shown no significant folding upon binding as evidenced by CD of the tubulintau ring solutions (Figures 3 and5). Moreover, our results are in agreement with another binding study performed on R3 and a different small â tubulin peptide (434-445), which revealed a lack of secondary structural modification upon interaction [START_REF] Hoffmann | Oxidized and phosphorylated synthetic peptides corresponding to the second and third tubulin-binding repeats of the tau protein reveal structural features of paired helical filament assembly[END_REF]. We can thus conclude that recombinant tau does not need to gain a specific R-helical structure to bind to tubulin C-terminal. This is consistent with the very recent results of Santarella et al., who showed that tau retains most of its disordered structure when bound to tubulin-microtubules [START_REF] Santarella | Surface-decoration of microtubules by human tau[END_REF]. Furthermore, we showed that the H11 and H12 belonging to CR and Câ, which are suspected to bind specifically to tau, are sufficient for tau binding to the C-terminal peptides, and their helical folding does not seem necessary. This also could imply a role of the unstructured C-terminal tails in the binding via charge-charge interactions. Indeed, it has been shown previously that the Cterminal tails could also play a important role in MAP binding [START_REF] Mejillano | Assembly properties of tubulin after carboxyl group modification[END_REF] and its regulation [START_REF] Boucher | Polyglutamylation of tubulin as a progressive regulator of in vitro interactions between the microtubule-associated protein tau and tubulin[END_REF].

Finally, we showed that, contrary to taxol, tau is able to compensate for the absence of magnesium. A parallel can be drawn between tau and Mg 2+ , which gives us new clues toward understanding the tau molecular mechanism of action. Magnesium is known to be an absolute requirement for tubulin assembly in vitro [START_REF] Lee | In vitro reconstitution of calf brain microtubules: Effects of solution variables[END_REF]. It stabilizes both the R-â association in the tubulin heterodimer [START_REF] Menendez | Control of the structural stability of the tubulin dimer by one high affinity bound magnesium ion at nucleotide N-site[END_REF] and the â-R association between heterodimers [START_REF] Vulevic | Thermodynamic and structural analysis of microtubule assembly: The role of GTP hydrolysis[END_REF]. Tubulin dimer has several low-affinity and two high-affinity binding sites for Mg 2+ . The first high-affinity magnesium ion is coordinated with the GTP bound to the N site of the R subunit at the R-R dimerization interface [START_REF] Lowe | Refined structure of alpha beta-tubulin at 3.5 A resolution[END_REF] and is necessary for the structural integrity of the tubulin dimer [START_REF] Menendez | Control of the structural stability of the tubulin dimer by one high affinity bound magnesium ion at nucleotide N-site[END_REF]. The second one was proposed to be coordinated with the hydrolyzable GTP bound to the â subunit at the â-R-protofilament-forming interface in the E site. In our case, in PGT buffer, which did not contain any added Mg 2+ , tau was able to induce tubulin self-association, whereas taxol, a well-known Mg 2+ -dependent microtubule inducer [START_REF] Howard | Linkages between the effects of taxol, colchicine, and GTP on tubulin polymerization[END_REF], was unable to induce tubulin assembly. We thus measured the concentration of Mg 2+ in our samples to evaluate the proportion of residual Mg 2+ in tubulin. We detected 24 íM Mg 2+ for 22 íM tubulin, i.e., roughly 1 Mg 2+ per tubulin dimer, corresponding probably to the high-affinity Mg 2+ of the N site. When this Mg 2+ , necessary for the structure of tubulin dimer, was removed from the N site by the addition of 1 mM EDTA, the tauinduced tubulin self-association did not occur (data not shown). This indicates that tau does not substitute for the Mg 2+ located in the N site. Instead, tau probably substitutes for either the Mg 2+ of the E site or a low-affinity binding site. In conclusion, tau substitutes for magnesium and, by means of a completely different mechanism consisting of binding to the C-terminal domains of tubulin monomers, stabilizes the longitudinal protofilament-forming interactions among tubulin molecules. This induces tubulin self-association into rings at 20 C or microtubules at 37 C.

This tau-tubulin interaction study was conducted in minimal conditions as a model system that does not take into consideration the numerous post-translational modifications that tau may undergo in the cell, such as phosphorylation. Nevertheless, it was the prerequisite step to understand the molecular basis of the tau-stabilizing effect on microtubule cytoskeleton. Now, we will be able to study the effect of post-translational tau modifications or mutations and the effect of molecular crowding on this system.

²

  Part of this work was supported by the ARC Grant 7264, the Ligue Contre le Cancer (2000-2001), Gefluc Marseille-Provence, MCyT Bio 2002-03665 Grant, and PAI Picasso Grant 07074PH.

FIGURE 1 :

 1 FIGURE 1: Effect of tau on tubulin assembly. Tubulin (5 íM) was incubated at 37 C in PEMGT buffer. At the time indicated by the first arrow, tau (5 íM) was added to the sample (line 1), whereas buffer was added to the control (line 2). At the time indicated by the second arrow, samples were cooled to 9 C. (Inset) Electron micrographs of tau-induced microtubules at the plateau. The bar represents 200 nm.

FIGURE 2 :

 2 FIGURE 2: Tau characterization by AUC. (A) Sedimentation equilibrium analysis of tau at 20 C.The symbols show the experimental radial distribution of tau at sedimentation equilibrium at 1.5 mg mL -1 (4), 3 mg mL -1 (0), and 4.5 mg mL -1 (O). The solid lines represent the best fit curves of global analysis of multiple sedimentation equilibrium data with the single, ideal species model. Of nine fitted data sets (the three protein concentrations indicated above at three speeds: 10 000, 12 000, and 16 000 rpm) only three (the ones at 16 000 rpm) are shown. The r m is the radial distance at the meniscus, with the residuals representing the variation between the experimental data and those generated by the fit with single species. (B) Continuous sedimentation coefficient distribution C(s) of tau at 1.9 mg mL -1 at 20 C. Inset shows the dependence of the apparent sedimentation coefficient at 20 C in water.

FIGURE 3 :

 3 FIGURE 3: Sedimentation velocity of tau-tubulin interaction at 20 C. (A) Apparent sedimentation coefficient g(s*) distribution computed from the time derivative of the concentration profile by the method of Stafford (see the Experimental Procedures). The concentration of tau is 7.5 íM, and the concentration of tubulin is 15 íM. This distribution was analyzed by DCDT+ software, with three Gaussian curves representing three sedimentation boundaries respectively in the plane line, dotted line, and dashed line. Open circles represent experimental values. The long dashed line represents the best fit curve. The inset shows the same analysis for tubulin alone (15 íM). (B) shows the percentage of three peaks area described above by DCDT+, with 6 S (b), 35 S (1) and 45 S (9) boundaries in the function of the tau/tubulin molar ratio for various concentration of tubulin: 15 íM (s); 10 íM (âââ), and 5 íM(---). The inset shows the variation of the apparent sedimentation coefficient in the function of the tau/tubulin ratio with tubulin 15 íM. This coefficient was obtained by analysis of the S* distribution described above. Tau by itself does not contribute to the signal. Note that for 5 íM tubulin there is no 45 S boundary.

FIGURE 4 :

 4 FIGURE 4: Electron micrographs of tau-induced tubulin oligomers at 20 C. Ring structures at 20 C for a tau/tubulin ratio of 1.2. In (A), the grid is covered with circular structures with single wall rings (white arrow) and possibly partial rings or spirals (black arrow), whereas in (B), thicker wall rings that might correspond to double rings are observed. The standard bar represents in both cases 200 nm.

FIGURE 5 :

 5 FIGURE 5: Spectrometric study of tau-tubulin interaction at 20 C (A) Far-UV spectra of 10 íM tau (1), 10 íM tubulin (2), and 10 and 10 íM tau-tubulin mixture (3). (4) Linear combination of the separate spectra of tau and tubulin (4 ) 1 + 2). The difference between (3) and (4) is drawn in[START_REF] Panda | Differential regulation of microtubule dynamics by threeand four-repeat tau: Implications for the onset of neurodegenerative disease[END_REF]. Spectra were recorded in a 0.1 mm cuvette. The inset represents 2 íM tau spectra without TFE (1) or with 40% TFE (2). Spectra were recorded with a 1 mm cuvette with 2 íM tau. (B) Fluorescence spectra of 15 íM tau (1), 15 íM tubulin (2), and 15 and 15 íM tau-tubulin mixture (3). (4) Linear combination of the separate spectra of tau and tubulin (4 ) 1 + 2). The excitation wavelength is 275 nm. The inset represents an enlarged view of the peak area of (3) and (4). To clarify the inset, tubulin spectrum (2) was omitted.

FIGURE 6 :

 6 FIGURE 6: Tau-tubulin interaction at 37 C. (A) Compared effect of tau and taxol on 6 íM tubulin in PGT buffer with 10 -4 M GTP. Line 1 shows 2 cycles of assembly-disassembly upon addition of 5 íM tau (addition marked by the first arrow). Line 2 shows no assembly upon addition of equimolar taxol (addition marked by the first arrow). (B and C) Electron micrographs of tau-induced tubulin oligomers. (B) At 37 C, we observe standard microtubules, whereas (C) at 25 C, we see microtubules, which start to depolymerize, with protofilaments pealing outward at the microtubule ends. The bar represents 200 nm.FIGURE 7: Tubulin assembly in the presence of tau in nonassembly conditions at 37 C. (A) Effect of various concentrations of tau (1, 0 íM; 2, 3 íM; 3, 5 íM; 4, 7.5 íM; 5, 10 íM; and 6, 20 íM) on 10 íM tubulin in PGT buffer with 10 -4 M GTP. Assembly was started by tau addition (first arrow), and disassembly was induced by switching the temperature to 9 C. (B and C) Electron micrographs of tau-induced bundles at 37 C, with the standard bar representing respectively 2 ím and 200 nm. (D) SDS-PAGE analysis of the interaction. Tubulin is constant (5 íM), and tau increased from 1 to 10 íM. Samples were centrifuged at 50 000 rpm (see the Experimental Procedures), and the supernatant (S) and pellet (P) were analyzed side by side to determine tau and tubulin concentrations in both fractions relative to itself. The upper band is tau, and the lower band is tubulin.

FIGURE 7 :

 7 FIGURE 6: Tau-tubulin interaction at 37 C. (A) Compared effect of tau and taxol on 6 íM tubulin in PGT buffer with 10 -4 M GTP. Line 1 shows 2 cycles of assembly-disassembly upon addition of 5 íM tau (addition marked by the first arrow). Line 2 shows no assembly upon addition of equimolar taxol (addition marked by the first arrow). (B and C) Electron micrographs of tau-induced tubulin oligomers. (B) At 37 C, we observe standard microtubules, whereas (C) at 25 C, we see microtubules, which start to depolymerize, with protofilaments pealing outward at the microtubule ends. The bar represents 200 nm.FIGURE 7: Tubulin assembly in the presence of tau in nonassembly conditions at 37 C. (A) Effect of various concentrations of tau (1, 0 íM; 2, 3 íM; 3, 5 íM; 4, 7.5 íM; 5, 10 íM; and 6, 20 íM) on 10 íM tubulin in PGT buffer with 10 -4 M GTP. Assembly was started by tau addition (first arrow), and disassembly was induced by switching the temperature to 9 C. (B and C) Electron micrographs of tau-induced bundles at 37 C, with the standard bar representing respectively 2 ím and 200 nm. (D) SDS-PAGE analysis of the interaction. Tubulin is constant (5 íM), and tau increased from 1 to 10 íM. Samples were centrifuged at 50 000 rpm (see the Experimental Procedures), and the supernatant (S) and pellet (P) were analyzed side by side to determine tau and tubulin concentrations in both fractions relative to itself. The upper band is tau, and the lower band is tubulin.

Table 1 :

 1 Hydrodynamic Parameters of Human Tau 40

	MM (Da)
	S20,w a (S)
	f/f0 b
	Rs c (Å)

a S20,w is the corrected sedimentation coefficient at 20 C in water for infinite dilution. b f and f0 are the frictional coefficients. c Rs is the Stokes radius. d D20,w is the corrected diffusion coefficient.

ACKNOWLEDGMENT

We are very grateful to Dr. M. Goedert (MRC, Cambridge, U.K.) for htau40 plasmid, M. Lo Âpez (Santiago, Chile) for peptide purification, and P. Lopez Navajas and Dr. G. Rivas (CIB, Madrid, Spain) for the divalent cation measurements, as well as Pr. J. M. Verdier (EPHE, Montpellier, France) and Svetlana Gorokhova (Rockefeller University, New York) for helpful discussion.


Nicolas Dugué

Jean-Charles Lamirel

Pascal Cuxac
email: pascal.cuxac@inist.fr

Diachronic'Explorer : keep track of your clusters !

We introduce Diachronic'Explorer, a toolbox to produce and visualize diachronic results, which is based on a new complete theoretic framework for diachrony that we detail. This toolbox, which is dedicated to run diachronic algorithms from clustering results, allows also to explore complex diachronic results at all the granularity levels through a web application.

I. INTRODUCTION

The ISTEX project compiles and provides access to scientific publications to French research. ISTEX-R project aims to highlight evolution of research topics using the ISTEX database. To that aim, we designed a new theoretical framework to track scientific fields changes and similarities across time : appearing and disappearing topics, splitting and merging topics. This framework is based on diachronic analysis, which aims to compare data or results from two distinct periods. Furthermore, this framework was implemented as a toolbox called Diachronic'Explorer that integrates all diachronic analysis steps and provides efficient visualizations.

In the context of our framework, we basically consider tp time periods, containing documents split into separate sets according to these time periods and described by a set of features F (words or expressions) : D = ∪ 0≤i≤tp D i . For each time period, clustering algorithms detect cluster sets such as

CS = ∪ 0≤i≤tp C i . Each set of clusters C i = {c 1 , • • • , c ni } is constituted of n i = |C i | clusters describing data D i .
Clusters gather similar documents and thus represent topics. Consequently, to monitor topic changes, our framework aims to track cluster changes and similarities across time periods.

The first step of our new framework consists in labeling clusters of every cluster sets. These labels will then be used to track cluster changes and similarities. Our labeling step consists in extracting prevalent features sets S cj for each cluster c j ∈ C i of all the cluster sets C i ∈ CS using a feature selection method. We implement the feature maximization method proposed by Lamirel et al. [START_REF] Lamirel | Optimizing text classification through efficient feature selection based on quality metric[END_REF] that has proven to be efficient for both supervised and unsupervised learning. The second step processes diachronic analysis between time periods using cluster labels. Basically, using S cj , the prevalent features sets of each cluster, we apply a diachronic algorithm based on MVDA, an unsupervised Bayesian process operating between views (here periods) for diachronic mining [START_REF] Lamirel | A new approach for automatizing the analysis of research topics dynamics: application to optoelectronics research[END_REF].

II. FEATURE SELECTION FOR CLUSTER LABELING

The first step of our framework consists in labeling clusters using a feature selection method. The one we implement is non-parametric, only weakly influenced by feature scaling, and it allows to label clusters with ordered weighted features [START_REF] Lamirel | Optimizing text classification through efficient feature selection based on quality metric[END_REF]. We apply it independently to each period. Thus, for each cluster set C i , 0 ≤ i ≤ tp, two ratios are processed over each cluster c j ∈ C i , 0 ≤ j ≤ n i to give a weight to features of F for the cluster considered. On the first hand, Feature Predominance (Equation 1) aims to evaluate if a feature f ∈ F allows to discriminate c j from other clusters of C i . On the other hand, Feature Recall (Equation 2) aims to evaluate whether f allows to faithfully describe data in c j .

F P cj (f ) = W f cj W c (1) F R cj (f ) = W f cj W f Di (2)
with W f cj = d∈cj W f d the weighted sum of f across cluster c j , W f Di = d∈Di W f d the weighted sum of f across the data of the time period considered, W cj = f ∈F W f cj the weighted sum of all features across cluster c j . The Feature F-Measure F F cj (f ) is the harmonic mean of these two values.

The Feature F-Measure is thus used to select features that are discriminant and representative for each cluster c j using Equation 3.

Sc j = f ∈ F |F Fc j (f ) > F FC i (f ), F Fc j (f ) > F FD i (3)
with F F (f ) the mean F-Measure value of f across clusters of C i where f is non-null, and F F Di the mean F-Measure across all features and all data of the considered period.

Figure 1 shows how features selected for a cluster with Diachronic'Explorer are used as labels to describe the cluster in the visualization module.

III. DIACHRONY WITH MVDA

Once the representative labels of each cluster extracted, our second step consists in applying MVDA diachronic analysis between each time periods pairs. MVDA was firstly experimented as a fully unsupervised approach by Lamirel [START_REF] Lamirel | A new approach for automatizing the analysis of research topics dynamics: application to optoelectronics research[END_REF], Exploring matchs between two sets of clusters using Diachronic'Explorer. The matching kernel of Classe8 and Classe3 is displayed in the yellow box while the match strength between these clusters is represented with the thickness of the link between them.

but here, we use cluster labels instead of indexer keywords. This process is theoretically based on Bayesian reasoning [START_REF] Lamirel | A new approach for automatizing the analysis of research topics dynamics: application to optoelectronics research[END_REF] whose operating mode can be summarized as this in our context : the diachronic analysis is processed by computing matching probabilities between clusters of distinct sets (thus time periods) using the selected labels they share or not. The matching probability of a cluster s from a set C src and a cluster t from a set C tgt is computed as shown in Equation 4.

P (t|s) = f ∈Ss∩St F F t (f ) f ∈St F F t (f ) (4)
The matching probability between t and s is processed symmetrically. Finally, an asymmetric match from s to t is detected if the matching probability P (t|s) is greater than the average matching probability of s with the clusters of C tgt . A symmetric match exists if both asymmetric match from s to t, and from t to s are detected. In such a case, the set of features describing this match is called the matching kernel (Figure 2). These different kind of match detected by Diachronic'Explorer allow us to track and describe changes and similarities between cluster sets of distinct periods.

IV. EXPERIMENTAL RESULTS AND VISUALIZATIONS

Experiments and visualizations shown in this papers were conducted on a corpus constituted of bibliographic data from the ISTEX project [START_REF] Dugué | Feature selection and complex networks methods for an analysis of collaboration evolution in science: an application to the ISTEX digital library[END_REF]. The ISTEX database is queried to extract papers related to research in medical care between years 1996 and 2010. This results in a dataset of 9779 papers. Because the goal is to observe evolution of this field across time, a community detection algorithm [START_REF] Pons | Computing Communities in Large Networks Using Random Walks[END_REF] exploiting the relationship between documents indexes and the publication years is used to extract meta-periods. Obtained meta-periods are 1996-2000, 2000-2005, 2006-2010 [START_REF] Cuxac | Analysis of evolutions and interactions between science fields: the cooperation between feature selection and graph representation[END_REF]. GNG clustering [START_REF] Fritzke | A growing neural gas network learns topologies[END_REF] is launched several times on the data of each meta-period to extract an optimal number of clusters with the help of adhoc quality indexes [START_REF] Lamirel | A new approach for automatizing the analysis of research topics dynamics: application to optoelectronics research[END_REF]. Then, using Diachronic'Explorer 1 , we Fig. 3. Exploring cluster labels of a cluster set using Diachronic'Explorer. Each column/color describes a period where rectangles stands for labels clusters. Grey flows between the colored rectangles represent different kind of matchs (asymmetric/symmetric) and their strength.

produce and then visually explore the diachronic results with powerful dynamic visualizations using advanced Javascript 2 . Visualization tool of Diachronic'Explorer makes possible to navigate easily from one granularity level to another : cluster and their labels (Figure 1), match between two periods (Figure 2), overall dataset evolution (Figure 3).

V. CONCLUSION

Integrating a new framework using powerful labeling method and unsupervised Bayesian reasoning among clusters sets, Diachronic'Explorer allows to produce diachronic results and provides a web application to visualize these results, navigating easily from one granularity level to another.

Fig. 1 .

 1 Fig. 1. Cluster labels extracted and visualized with Diachronic'Explorer.

Fig. 2 .

 2 Fig. 2.

Acknowledgments. ISTEX receives assistance from the French state managed by the National Research Agency under the program Future Investments bearing the reference ANR-10-IDEX-0004-12.