Control of the Structural Stability of the Tubulin Dimer by One High Affinity Bound Magnesium Ion at Nucleotide N-site*

Tubulin liganded with GTP at the N-site in the α-subunit and with GDP at the E-site in the β-subunit (GDP-tubulin) reversibly binds one high affinity Mg2+ cation (K b = 1.1 × 107 m −1), whereas tubulin liganded with GTP at both subunits (GTP-tubulin) binds one more high affinity Mg2+. The two cation binding loci are identified as nucleotide sites N and E, respectively. Mg2+ at the N-site controls the stability and structure of the αβ-tubulin dimer. Mg2+ dissociation is followed by the slow release of bound nucleotide and functional inactivation. Mg2+ bound to the N-site significantly increases the thermal stability of the GDP-tubulin dimer (by 10 °C and ∼50 kcal mol−1 of experimental enthalpy change). However, the thermal stability of Mg2+-liganded GDP- and GTP-tubulin is the same. Mg2+ binding to the N-site is linked to the αβ-dimer formation. The binding of Mg2+ to the α-subunit communicates a marked enhancement of fluorescence to a colchicine analogue bound to the β-subunit. Colchicine, in turn, thermally stabilizes Mg2+-depleted tubulin. The tubulin properties described would be simply explained if the N-site and the colchicine site are at the α-β dimerization interface. It follows that the E-site would be at the β-end of the tubulin dimer, consistent with the known functional role of the E nucleotide γ-phosphate and coordinated cation controlling microtubule stability.

Tubulins are GTP-binding proteins that play central roles in eukaryotic cell division and organization. The ␣␤-tubulin dimers reversibly assemble to form the microtubules. The closest relatives of tubulins are the predicted homologous bacterial cell division FtsZ proteins (1). The GTP bound to the ␤-subunit is exchangeable in the dimer (E-site 1 ; Ref. 2), and is hydrolyzed to GDP and P i as a result of microtubule formation. The nucleotide ␥-phosphate and a coordinated Mg 2ϩ ion control the assembly activity of tubulin and microtubule stability (3)(4)(5)(6). Tubulin with GDP in the ␤-subunit (GDP-tubulin) is unable to assemble into microtubules except by ligand binding to the paclitaxel site (7). GDP-tubulin is in an inactive conformation (8,9) which favors curved assembly into double rings corresponding to pairs of curved protofilament segments (10,11), and the curling of exposed protofilaments at microtubule ends (12,13). In contrast to ␤-tubulin, the molecule of GTP bound to the ␣-subunit is considered non-exchangeable (N-site; Ref. 2), stays essentially bound during the entire life of the protein suggesting that it may be a structural cofactor of tubulin (14), and is coordinated to a slowly dissociating divalent cation (4).
Magnesium ions have a well established influence on tubulin-nucleotide interactions (3,4,15,16) and on tubulin selfassociation (17,18), including microtubule assembly (19). Equilibration in Mg 2ϩ -free buffers results in a partial release of the GTP bound, followed by an irreversible loss of activity (4,20). Previous studies of divalent cation binding (3,4,17,21,22) indicated that tubulin has two classes of Mg 2ϩ binding sites, one of high affinity (with an association binding constant, K 1,Mg , in the order of 10 6 M Ϫ1 ) and the other of low affinity (K 2,Mg , 10 2 to 10 3 M Ϫ1 ). The stoichiometry of the first class of sites depends on the nucleotide bound to the E-site; GTPtubulin has two tightly bound Mg 2ϩ (at the N-and E-sites), whereas GDP-tubulin has a single high affinity Mg 2ϩ (N-site; the E-site becomes low affinity (see Ref. 3)). This has been confirmed by studying the binding of Mg 2ϩ to tubulin having GTP, GDP, or no nucleotide at the exchangeable site of the ␤-subunit and one Mg 2ϩ ion already bound (23). The low affinity Mg 2ϩ binding sites are involved in tubulin polymerization (19) and in the equilibrium association of the ␣␤-dimer (8). In contrast, neither the high affinity binding of Mg 2ϩ to the N-site nor its intriguing role are well understood (3,4,23,24).
The present study aims to understand the specific roles of the respective Mg 2ϩ ions coordinated with the GTP bound to Eand N-sites in tubulin stability, structure and function. Toward these purposes, the isotherm of binding of Mg 2ϩ to the N-site has been measured, and the different effects of the high affinity cations bound to GDP-and GTP-tubulin have been compared employing DSC, CD, fluorescence, and sedimentation equilibrium methods. It will be shown that the functional microtubule-stabilizing cation and ␥-phosphate at the E-site impart negligible stabilization to the ␣␤-tubulin dimer, whereas the non-functional cation bound to the N-site, at the ␣-subunit, is essential for tubulin stability, and communicates with the colchicine site at the ␤-subunit.

EXPERIMENTAL PROCEDURES
Preparation of calf brain tubulin, without (GDP-tubulin) or with (GTP-tubulin) a ␥-phosphate at the E-site was performed as described in Ref. 7, with minor modifications. GDP-tubulin was finally equilibrated in PEDTA buffer with 1 mM GDP by chromatography in Sephadex G-25 columns (10 or 25 ϫ 0.9 cm). To prepare GTP-tubulin, 1 mM GTP and Mg 2ϩ were added to GDP-tubulin. In the experiments at the lower free Mg 2ϩ concentration, the EDTA concentration in the buffer was 2 mM. Nucleotides and Mg 2ϩ quantification by high performance * This work was supported by Direccion General de Ensetranse Superior Grants PB93-0114 (to M. M.), PB95-0120 (to G. R.), and PB95-0116 (to J. M. A.). The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Binding of Mg 2ϩ to Tubulin-The binding of Mg 2ϩ was measured as follows. Aliquots of 200 l of tubulin (15 M) with a known total Mg 2ϩ concentration were incubated at 10°C for 30 min and centrifuged at 100,000 rpm for 1 h in a TLA-100 rotor, using a TLX-120 ultracentrifuge (Beckman Instruments Inc.). After centrifugation, the lower half of the tubes, which contain tubulin in equilibrium with free Mg 2ϩ , and the upper half, with cation and essentially no protein, were carefully withdrawn, and the total Mg 2ϩ concentration was determined in both halves. Mg 2ϩ bound to tubulin was quantified by the difference in the cation concentration between the lower and the upper parts of the centrifuge tube. Free Mg 2ϩ was calculated from the total Mg 2ϩ concentration in the upper half, by solving the multiple equilibria, which take into account the cation binding to phosphate, nucleotide, and EDTA. The stability constants for Mg 2ϩ complexes at pH 7.0 employed were as follows: phosphate, 68 M Ϫ1 (26,27); GDP, 607 M Ϫ1 (3); GTP, 2830 M Ϫ1 (3); and EDTA, 2.5 ϫ 10 5 M Ϫ1 (28). These values are within 5% variation with respect to other constants reported in the literature (26, 29 -32). This, together with the calculated errors in the measurement of the total amount of Mg 2ϩ , resulted in an estimated uncertainty of 10 -15% for the lower calculated free Mg 2ϩ concentrations, and less than 10% for the higher concentrations. Note that, in the buffer solution employed, the small free Mg 2ϩ concentration approximates the mean ionic activity of MgCl 2 within experimental error.
A model of ligand binding assuming multiple classes of independent binding sites for Mg 2ϩ (33) in the tubulin molecule was fitted to the experimental data, using a non-linear least squares procedure, based on the modified Nelder-Mead simplex algorithm (34).
Time Course of Tubulin Inactivation-The effect of Mg 2ϩ on the kinetics of tubulin inactivation at constant temperature was followed by monitoring two independent properties: (i) the loss of the assembly capacity of tubulin (20 M) with paclitaxel, monitored turbidimetrically (7) and (ii) the loss of colchicine binding sites, measured from the fluorescence of the MTC-tubulin complex (see below). Before measurement, samples were supplemented to final total Mg 2ϩ concentrations of 7 and 5 mM in the assembly and MTC binding buffers, respectively. Control experiments were run in parallel at 7 mM Mg 2ϩ in the initial equilibration buffer.
Circular Dichroism-The far-UV CD spectra of tubulin (1-5 M, equilibrated in PEDTA with 1 mM nucleotide and a known amount of Mg 2ϩ ) were acquired in a JASCO J720 dichrograph equipped with a temperature regulated cell holder (1,35), with a 0.1-cm cell at 20 Ϯ 1°C. Thermal denaturation was monitored following the variation in ellipticity at 220 nm, using a temperature scan rate of 0.5°C⅐min Ϫ1 . Changes in secondary structure were estimated by deconvolution of the CD spectra using Yang (36), LIMCOMB, and CCA (37,38) methods.
Fluorescence of the MTC-Tubulin Complex-The effect of Mg 2ϩ on the fluorescence spectrum of the colchicine analog MTC (50 M total concentration) bound to tubulin (5 M) was measured essentially as described (39), using a Shimadzu RF-540 spectrofluorimeter (Kyoto, Japan; ex ϭ 350 nm, em ϭ 423 nm). The fluorescence cell (5 ϫ 10 mm) was mounted on a holder thermostated with a water bath at 20°C. The free and bound ligand were measured with the same high speed centrifugation method described for Mg 2ϩ binding, except that MTC was measured spectrophotometrically (⑀ 343 ϭ (1.76 Ϯ 0.01) ϫ 10 4 M Ϫ1 cm Ϫ1 ) (39).
Analytical Ultracentrifugation-The measurements were performed at 10°C with a Beckman Optima XL-A analytical ultracentrifuge equipped with absorbance optics, using an An60Ti rotor and either 12-mm double sector or six-channel centerpieces. Tubulin samples (loading concentrations between 0.5 and 15 M) were equilibrated in PEDTA, 20 M nucleotide, with the desired amount of Mg 2ϩ . Short column (40 -50 l) sedimentation equilibrium was performed either at low speed (30 min at 30,000 rpm, followed by 2-3 h at 15,000 rpm) or as described (40): 1 h at 32,000 rpm, followed by 1-2 h at 26,000 rpm, which permitted attainment of equilibrium. Absorbance scans were taken at the appropriate wavelength (230, 275, or 290 nm). In all cases, base-line offsets were determined subsequently by high speed sedimentation. Whole-cell apparent weight-average molecular masses (M w,a c ) were obtained using the programs XLAEQ and EQASSOC (supplied by Beckman; see Ref. 41). The partial specific volume was 0.736 cm 3 /g (42), which was corrected for temperature (43).
To determine the equilibrium constant for tubulin dimerization (K 2 ), two different methodologies were employed. (i) Equilibrium association models were globally fitted to multiple sedimentation equilibrium data using either the MicroCal-Origin version of NONLIN (44) or the pro-grams MULTEQ1B and MULTEQ3B based on the conservation of signal algorithm (41). A value of 1.16 ml mg Ϫ1 cm Ϫ1 was used for the extinction coefficient of tubulin at 275 nm in phosphate buffer (45), and the subunit relative molecular mass was taken as 55,000 (46). (ii) The dependence of the apparent weight-average molecular mass (M w,a ) on protein concentration was calculated from the local slopes of transformed data (lnC versus r 2 ) at defined radial distance intervals, using the program MWPLOTZ (kindly supplied by A. Minton, National Institutes of Health, Bethesda, MD). In this study, the M w,a values were calculated by superimposing data obtained from different loading protein concentrations and averaging over a concentration interval of Ϯ0.1 log units. Models for self-association (47,48) were fitted to the M w,a versus concentration data using a non-linear least-squares method (34).
Sedimentation velocity experiments were performed at 42,000 and 60,000 rpm. Sedimentation coefficients were calculated from the rate of the movement of (i) the solute boundary (with XLAVEL, Beckman) or (ii) the second moment of the boundary (with VELGAMMA, Beckman), and (iii) from the distribution of the apparent sedimentation coefficients, g(s*), using the DCDT program (49,50). The sedimentation coefficients were corrected to standard conditions (51) to get the corresponding s 20,w values.
Differential Scanning Calorimetry-The heat capacity measurements were performed in a MicroCal MC2 differential scanning calorimeter, as described previously (52). Tubulin samples (15 M) for DSC were equilibrated in PEDTA buffer with 1 mM GDP (or GTP) and the desired Mg 2ϩ concentration. The scanning rate was 0.5°C min Ϫ1 , unless otherwise stated. The reversibility of thermal transitions was checked by reheating the samples after the first scan. The influence of scanning conditions on the profiles of the calorimetric transitions of tubulin was checked by running samples at several rates. The kinetic analysis of the DSC curves was carried out as described (53,54).

RESULTS AND DISCUSSION
The thermal stability of GDP-and GTP-tubulin measured by DSC was found to be similar at free Mg 2ϩ concentrations above 1 M. However, it was dramatically reduced at the low activity of Mg 2ϩ ions of the EDTA containing buffer employed for nucleotide exchange (7). This prompted an in-depth examination of the system by means of the following complementary biochemical and DSC experiments.
Binding of Mg 2ϩ to GDP-and GTP-tubulin-The binding isotherms of Mg 2ϩ to GDP-and GTP-tubulin in PEDTA buffer at 10°C were directly determined by high speed sedimentation of the protein (Fig. 1). The experimental data for GDP-tubulin can be described assuming two classes of independent binding sites in the ␣␤-tubulin dimer: one Mg 2ϩ high affinity site (n 1,Mg , plus several low affinity sites (n 2,Mg ϭ 48, K 2,Mg ϭ 106 M Ϫ1 ; the latter values were taken from Frigon and Timasheff (17) and constrained in the fitting procedure). Measurements of samples incubated for an extra 1-2-h period at the lower ligand concentrations were essentially identical, indicating equilibrium. High affinity Mg 2ϩ binding to tubulin is reversible, since supplementing cation-depleted tubulin (equilibrated in 40 Ϯ 5 nM free Mg 2ϩ ) to 360 Ϯ 20 nM free Mg 2ϩ increased binding from 0.4 Ϯ 0.1 to 0.75 Ϯ 0.1 Mg 2ϩ per tubulin heterodimer, which is within the experimental error of the reference isotherm ( Fig. 1).
GTP-tubulin has one more Mg 2ϩ binding site ( Fig. 1, empty symbols) than GDP-tubulin, with an apparent affinity in the order of 10 5 M Ϫ1 . The analysis of its Mg 2ϩ binding isotherm is complicated by the presence of GDP, which has a much higher affinity than GTP for the tubulin E-site at low Mg 2ϩ concentration (3,4). Therefore, as the cation concentration decreases, GDP progressively exchanges into the GTPtubulin samples. GTP-tubulin in 63 M free Mg 2ϩ had a measured nucleotide content (0.1 GDP and 1.7 GTP per tubulin molecule), corresponding to a 90% of GTP-tubulin, and its stoichiometry of binding of Mg 2ϩ is one more cation than that of GDP-tubulin. On the other hand, at 3.2 M free Mg 2ϩ the binding stoichiometry is slightly higher than 1, but the nucleotide content (0.7 GDP and 1.2 GTP per tubulin molecule) indicates that only 25% of the protein is GTP-tubulin. The results are compatible with the partial Mg 2ϩ binding data of Mejillano and Himes (23) in a different buffer.
These high affinity Mg 2ϩ binding sites of tubulin, one in GDP-tubulin and two in GTP-tubulin, have been previously identified as the cation-binding loci at the N and E GTPbinding sites in ␣and ␤-tubulin, respectively (3,4,24). However, binding isotherm of the highest affinity Mg 2ϩ to the N-site had not been measured; nor had cation-depleted tubulin been studied.
Effect of Mg 2ϩ Depletion on Nucleotide Release from Tubulin-Equilibration of tubulin in Mg 2ϩ free buffers results in a decrease in bound nucleotide, supposedly coming from either nucleotide dissociation from the E-site or from the irreversible protein denaturation which occurs for prolonged incubation times (4,20). To know the role of the Mg 2ϩ cation bound to the N-site of GDP-tubulin in nucleotide binding, and to identify the sites from which nucleotide may come off by cation removal, the GDP and GTP bound to tubulin were determined as a function of the free Mg 2ϩ and incubation time (see Table I for a summary). Tubulin samples with the high affinity Mg 2ϩ site saturated contain close to one GTP and one GDP per ␣␤-dimer. However, samples partially depleted from the high affinity cation have their nucleotide content reduced to 0.6 -0.7 GTP and 0.9 GDP per heterodimer at the conclusion of sample preparation (an equivalent time of 0.5 h). Upon prolonged incubation at 20°C, the GTP (and GDP) stoichiometry de-creased more slowly, to values approaching the Mg 2ϩ /tubulin stoichiometry of the samples (Table I). These results indicate that dissociation of Mg 2ϩ from the N-site (␣-subunit), which is quite reversible at short periods of time as shown above, results in dissociation of GTP (and GDP), supposedly coming from the N-site (and the E-site, respectively). This reveals the instability of the cation-depleted tubulin. The results suggest the possibility that the nucleotide binding capacity and, hence, the functionality of the ␤-subunit in the ␣␤-dimer is controlled by the cation ligation state of the ␣-subunit, and will be further addressed later.
GDP-tubulin equilibrated at 55 nM free Mg 2ϩ and re-equilibrated in 6 mM MgCl 2 and 1 mM GTP polymerized in 3.4 M glycerol-containing buffer with a critical concentration (15 M) 1.7 times higher than that of a GTP-tubulin control directly equilibrated in 6 mM MgCl 2 (9 M). The slope of the plot of plateau turbidity versus total protein concentration was about 1.3 times lower than that of the control (data not shown). Since GDP-tubulin is unable to assemble in Mg 2ϩ -glycerol buffer (7), this implies that around 70 Ϯ 10% of the Mg 2ϩ -depleted protein has been able to back-exchange GTP and reassemble. This result also suggests that nucleotide dissociation during the time of cation depletion of tubulin results in an irreversible conformational change, preventing the subsequent binding of nucleotide to a fraction of ␣and ␤-subunits.
The Kinetics of Tubulin Inactivation Depends on Mg 2ϩ Activity-The role of Mg 2ϩ bound to the N-site on tubulin inactivation at 20°C was investigated monitoring the time courses for the decay of paclitaxol-induced assembly, and for the binding of the colchicine analogue MTC to GDP-tubulin, at different free Mg 2ϩ concentrations. GDP-tubulin equilibrated in 60 nM free Mg 2ϩ initially retains more than 80% of the corresponding activity at higher cation concentrations. However, its inactivation is more rapid (half-life, t1 ⁄2 ϭ 5 h; Fig. 2) than at 300 nM free Mg 2ϩ (t1 ⁄2 ϭ 7 h; data not shown), and much faster than at 100 M free Mg 2ϩ (estimated t1 ⁄2 ϳ 47 h; Fig. 2), compatible with previous measurements of tubulin aging (20,55). For practical purposes, the kinetics after the initial decay can be apparently described by first order reactions, whose rate constants, k,  decrease with the Mg 2ϩ concentration (4.0 -5.5 ϫ 10 Ϫ5 s Ϫ1 at 60 nM, 2.5-3.0 ϫ 10 Ϫ5 s Ϫ1 at 300 nM, and 3.8 -4.6 ϫ 10 Ϫ6 s Ϫ1 at 100 M free Mg 2ϩ ). 2 As a control for sedimentation equilibrium measurements, the decay of MTC binding by tubulin was also measured at 10°C in 65 nM free Mg 2ϩ , giving an apparent first order constant of 0.9 ϫ 10 Ϫ5 s Ϫ1 (t1 ⁄2 ϭ 21 h; data not shown).
High Affinity Mg 2ϩ Binding Enhances the Fluorescence of MTC Bound to the Colchicine Site of Tubulin-The addition of Mg 2ϩ to the complex of the colchicine analogue MTC with tubulin, previously equilibrated at 50 -60 nM free Mg 2ϩ , leads in a few seconds to a large increase in the fluorescence of the ligand (Fig. 3). The variation is equivalent to the change in fluorescence observed upon MTC binding to GDP-tubulin with its Mg 2ϩ high affinity site previously saturated with the cation. Control experiments indicated that Mg 2ϩ affects neither the negligible fluorescence of unbound MTC nor the intrinsic (tryptophan) fluorescence of tubulin. Furthermore, Mg 2ϩ -induced increase in the fluorescence of the MTC-tubulin complex cannot be explained in terms of variation in the extent of MTC binding to tubulin, since it was found to be independent of the free Mg 2ϩ concentration (0.7 Ϯ 0.1 MTC/tubulin heterodimer). The apparent association constant of Mg 2ϩ to GDP-tubulin estimated from the MTC fluorescence change (Fig. 3) was 9 ϫ 10 6 M Ϫ1 , essentially coincident with the association constant of the high affinity Mg 2ϩ (Fig. 1). Mg 2ϩ binding also increased the fluorescence of colchicine bound to tubulin, but only when the cation was bound prior to the addition of colchicine (data not shown). This different Mg 2ϩ effect with MTC and colchicine might indicate that the slow dissociation rate of the latter prevents the ligation of Mg 2ϩ to the N-site.
The simplest interpretation of these results is that the microenvironment of tubulin-bound MTC is sensitive to the high affinity bound Mg 2ϩ ion, which actually induces the fluorescence of this colchicine site probe. Furthermore, the results also reveal communication between tubulin subunits, since the binding of the cation to N-site in ␣-tubulin modifies the properties of the colchicine site, whose locus is at the ␤-subunit, possibly near the ␣␤-subunit interface (56).
Modification of tubulin secondary structure upon removal of the high affinity bound Mg 2ϩ was checked by CD spectroscopy. Equilibration of the protein in 65 nM free Mg 2ϩ leads to a small reduction in the absolute magnitude of the dichroic signal at 210 -220 nm (Fig. 4). The effect is independent of having GDP or GTP in the buffer, suggesting that the observed change is in part induced by Mg 2ϩ coordination at the N-site. The analysis of this small change in the CD spectrum of tubulin indicated very small differences in the estimated secondary structure content. The CD change can be partially reversed by increasing the free Mg 2ϩ concentration up to 1 mM (data not shown). Preliminary CD kinetic experiments of Mg 2ϩ dissociation from tubulin and their subsequent reassociation, indicated that dissociation is slow (on the order of minutes), whereas reassociation is comparatively fast (on the order of seconds).
Role of Mg 2ϩ in ␣␤-Tubulin Association-Cations bound with high affinity to oligomeric proteins frequently have structural roles, and their removal is linked to a marked weakening of protein-protein association equilibria (two examples are the platelet integrin ␣ IIb ␤ 3 (57) and the complement C1 subcomponent (48)). For this reason, the influence of Mg 2ϩ (low and high affinity binding sites) on the dimerization equilibrium of tubulin was analyzed by analytical ultracentrifugation. GDP-tubulin equilibrated in 50 -60 nM Mg 2ϩ , at an initial protein concentration of 15 M, has the same sedimentation coefficient (s 20,w ϭ 5.8 Ϯ 0.2 S) and relative molecular mass (109,000 Ϯ 8,000; Fig. 5) as the intact ␣␤-tubulin dimer. However, the tubulin dimer dissociation is patent at lower concentrations, as was analyzed by sedimentation equilibrium at 10°C. Fig. 6 shows the variation in the average molecular mass of tubulin as a function of total tubulin and free Mg 2ϩ concentrations. The results indicate that removal of Mg 2ϩ from its high affinity site increases dissociation of the tubulin dimer. This behavior reflects the linkage of Mg 2ϩ binding and tubulin self-association equilibria. Lowering the free Mg 2ϩ concentration reduced by an order of magnitude the apparent equilibrium dimerization con- 2 The first order fit does not account for the initial decay at 60 nM Mg 2ϩ . The data are also compatible with a two-phase inactivation model (data not shown). This gives a fast phase (t1 ⁄2 ϭ 1.5 h) that practically starts from fully active cation-depleted tubulin at time zero (simultaneous with the initial nucleotide release, Table I) and a slow phase (t1 ⁄2 ϭ 15 h) that might consist of the inactivation of the remaining fraction of cation-containing tubulin. stant of ␣␤-tubulin (K 2 ), from ϳ10 7 M Ϫ1 at ϳ100 M free cation, to 4 ϫ 10 6 M Ϫ1 at 1-2 M cation, and to 1.6 ϫ 10 6 M Ϫ1 at 50 nM free cation (see Table II and Fig. 6).
The simplest interpretation of these results is that both the high affinity binding of one Mg 2ϩ ion to the N-site and the binding of lower affinity cations stabilize the tubulin heterodimer. The data are compatible with the results obtained in the 10 Ϫ3 to 10 Ϫ4 M free Mg 2ϩ concentration range by Shearwin et al. (8), who suggested the involvement of two weakly bound Mg 2ϩ ions in the association of the GDP-tubulin heterodimer. A linked equilibria analysis of our data supports the notion that both low and high affinity Mg 2ϩ enhance tubulin dimerization. As shown under "Appendix," the combined sedimentation equilibria data may be reasonably accounted for by a Mg 2ϩ -dependent dimerization model, which is compatible with both the experimental dependence of K 2 on the cation concentration (Table II) and the Mg 2ϩ -binding isotherm at high protein concentration (Fig. 1). According to this model, only one of the isolated subunits of GDP-tubulin bears a high affinity Mg 2ϩ binding site, with an intrinsic binding constant of 2 ϫ 10 6 M Ϫ1 , whereas the heterodimer has two independent Mg 2ϩ binding sites, with binding constants 1 ϫ 10 7 M Ϫ1 and 6 ϫ 10 4 M Ϫ1 , respectively. The estimated value for the intrinsic dimerization constant of tubulin in the absence of Mg 2ϩ is K 2 0 ϭ 10 6 M Ϫ1 . The limited dissociation range of tubulin at the lowest protein concentration that could be measured in the analytical ultracentrifuge, as well as the need for avoiding the possible influence of tubulin denaturation processes at longer equilibrium times, preclude a more complete quantitative analysis in terms of linked functions (58,59).

Roles of Mg 2ϩ and Nucleotide in the Thermal Stability of
Tubulin-The influence of Mg 2ϩ on the thermal stability of tubulin was analyzed by differential scanning calorimetry.  Table II. For illustrative purposes, the M r of ␣and ␤-tubulin (55,000), as well as the value for the heterodimer (2 ϫ 55,000) are indicated by the dashed and dotted lines, respectively. Inset, sedimentation equilibrium gradients of tubulin (loading protein concentrations: 1, 2.5, and 5 M; 26,000 rpm and 10°C) at 60 nM free magnesium. The solid lines represent the best-fit function (see Table II). tubulin stabilization by Mg 2ϩ , which nearly reaches a plateau above 1 M free Mg 2ϩ (Fig. 7B). The results strongly suggest that the cation responsible for the substantial tubulin stabilization observed is the Mg 2ϩ ion coordinated with the nucleotide N-site, since (i) the stabilization essentially coincides with the binding of this high affinity cation, (ii) the additional cation bound by GTP-tubulin has insignificant effect on the thermal stability of the protein, and (iii) the affinity of Mg 2ϩ for the E-site in GDP-tubulin is known to be about 10 3 times lower than in GTP-tubulin (3,4). Table III summarizes the parameters measured for the thermal denaturation of tubulin. The reversal of tubulin destabilization induced by Mg 2ϩ depletion was checked by preparing protein samples equilibrated at different cation concentrations and then adding Mg 2ϩ up to saturation (Table IV). The destabilization induced by the cation dissociation was 95% reversible in tubulin samples initially equilibrated in 180 nM free Mg 2ϩ and immediately supplemented with 280 M free Mg 2ϩ (⌬H d ϭ 176 kcal mol Ϫ1 , T m ϭ 56.1°C; Fig. 8, curve b). However, when Mg 2ϩ was added after 2 h of incubation at 20°C in the equilibration buffer, the shape of the calorimetric profile was indistinguishable from that obtained upon saturation with the cation immediately after protein elution, but the enthalpy change dropped to about 75% of the initial value (⌬H d ϭ 139 kcal⅐mol Ϫ1 ; T ϭ 56.1°C; curve c in Fig. 8).The drop in ⌬H d observed after 2 h at 20°C correlates with the value expected from the kinetics of tubulin inactivation under same conditions (Fig. 2). Reconstitution of tubulin samples initially prepared in 40 nM free Mg 2ϩ ( Mg ϭ 0.4, GTP ϭ 0.65) results in heat capacity denaturation curves with the same T m value as in the control experiments but with a lower enthalpy change (142 kcal⅐mol Ϫ1 ; curve e, Fig. 8). The percentage of reversibility obtained by saturation with Mg 2ϩ immediately after preequilibration in Mg 2ϩ -depleted buffers, correlates well with the initial GTP/tubulin stoichiometry of the samples. These results indicate that Mg 2ϩ -or nucleotide-depleted tubulin slowly evolves in an irreversible way toward a state that does not undergo a temperature induced cooperative transition, and that GTP bound to the N-site of tubulin might determine the reversibility of Mg 2ϩ dissociation. Addition of colchicine stabilized the cation-depleted tubulin, similarly to addition of Mg 2ϩ , whereas the reversible binding of the colchicine analogue MTC had a much weaker effect (Table V).
Kinetic Control of the Thermal Denaturation of Tubulin by High Affinity Mg 2ϩ Binding: Mechanism of Thermal Denaturation-Reheating of tubulin samples cooled after the first thermal scan showed that thermal denaturation of tubulin is irreversible under all the conditions tested. The thermograms depend on the scan rate (see Fig. 9, A and B) and the analysis of DSC curves showed that, on saturation of the high affinity Mg 2ϩ binding site, the variation in the excess heat capacity with temperature follows the behavior predicted by the twostate kinetic model (53,54). Fig. 9C shows the temperature dependence of the apparent denaturation rate constant at different free Mg 2ϩ concentrations, calculated according to this model. This result means that only Mg 2ϩ liganded (N-site) and denatured tubulin are significantly populated within the dena-  turation temperature range. A good correlation was found between the kinetic constants of inactivation calculated from the rate of CD change at 55°C ( 220 , free [Mg 2ϩ ] ϭ 180 nM) or from DSC data at the same temperature and cation concentration (3 ϫ 10 Ϫ3 s Ϫ1 and 3.5 ϫ 10 Ϫ3 s Ϫ1 , respectively). However, the kinetic constants extrapolated from the DSC data to 20°C are several orders of magnitude smaller than those measured from tubulin inactivation at this temperature, suggesting a different origin for the two processes in the lower temperature range.
At the lowest free Mg 2ϩ concentrations (40 -100 nM), the denaturation process becomes complex as indicated by the presence of a shoulder or small peak in the low temperature side (Figs. 7-9). This is also evident in the loss of secondary structure, monitored by CD at 220 nm (Fig. 10).The enthalpy change associated with the low temperature shoulder can be roughly estimated to be ϳ30 Ϯ 5 kcal⅐mol Ϫ1 . The CD spectra of thermally denatured tubulin has residual ␤ sheet secondary structure (60). The apparent biphasic denaturation of tubulin at subsaturating levels of Mg 2ϩ could be generated by different processes such as kinetic stabilization of unfolding intermediates, uncoupling of ␣and ␤-subunit denaturation, or association of the denatured state. In addition, given the slow dissociation of the nucleotide from tubulin and the presence of GTP at substoichiometric ratios under these conditions (61)(62)(63), the low and high temperature peaks could also derive from the unligated and nucleotide-bound tubulin, respectively.
Sedimentation velocity measurements have shown that the association state of thermally denatured tubulin depends on the Mg 2ϩ concentration. Incubation of GDP-tubulin equilibrated in 50 nM free Mg 2ϩ at 40°C for 30 min induces a partial aggregation of tubulin, giving a bimodal sedimentation velocity profile, in which approximately half of the protein sediments as the tubulin dimer (s 20,w ϭ 5.7 S) and the other half as a 12 S oligomer (see dotted line in the inset of Fig. 5). Furthermore, 30-min incubation at 60°C results in a higher percentage (ϳ70%) of tubulin aggregation (13-14 S). However, when the same treatment was performed on GDP-tubulin with the high affinity site occupied by Mg 2ϩ , aggregation was not evident (s 20,w ϭ 5.9 S). These results suggest that tubulin aggregation might be involved in the generation of the biphasic denaturation curves. Nevertheless, contributions from other processes (see above) cannot be ruled out. A possible minimal scheme to account for thermal denaturation of tubulin at the Mg 2ϩ concentration range explored is as follows.
are the GTP and Mg 2ϩ binding constants to N-site, k 3 is the denaturation rate constant of tubulin⅐GTP⅐Mg, and k 1 and k 2 are the limiting rate constants for denaturation of N-site unliganded and GTP-bound tubulin, respectively; I i are irreversibly denatured state(s) of tubulin (I 1 and I 2 are 12-14 S aggregated species, and I 3 is 5.9 S denatured tubulin) and X i indicates the possibility of intermediate steps during denaturation. CONCLUSION The results reported in this study provide new insights into tubulin structure and function. This is schematically summarized in Fig. 11. The nucleotide ␥-phosphate and the coordinated Mg 2ϩ ion at the E-site (␤) of tubulin, which regulate the tubulin assembly function and microtubule stability, have practically undetectable effects on the stability and on most of the solution properties of the ␣␤-tubulin dimer. However, one  high affinity Mg 2ϩ ion, bound to a site identified as the nonfunctional nucleotide N-site (␣), has profound kinetic and thermal stabilizing effects, and induces the association of the ␣␤dimer. The ␣and ␤-subunits seem to communicate with each other; the binding of Mg 2ϩ to the N-site in the ␣-subunit induces the fluorescence of a probe bound to the colchicine site in the ␤-subunit, and colchicine binding thermally stabilizes Mg 2ϩ -depleted tubulin. These properties are most simply explained by proposing that both the colchicine site (␤) (56) and the N-site Mg 2ϩ (␣) (this study) are located at the ␣␤ dimerization interface. It follows from subunit homology that the functional E-site (in ␤) should be at the longitudinal dimerdimer interface leading to protofilament formation (64), consistent with the activation of tubulin GTPase in linear oligomers (65).
All tubulins probably evolved from a common nucleotidebinding ancestor. The GTP and Mg 2ϩ binding functionalities were made essential for the maintenance of the protein stability in ␣-tubulin, whereas ␤-tubulin acquired the capability to FIG. 11. Model scheme proposed to explain and summarize the results of this work. The nucleotide and Mg 2ϩ bound to the E-site, which are known to regulate the tubulin assembly function, have insignificant effects on the stability of tubulin. The high affinity Mg 2ϩ ion bound at the nucleotide N-site controls the stability of the ␣␤-tubulin dimer. The simplest explanation for the observed effect of the Mg 2ϩ binding at the N-site on the fluorescence of a probe bound to the colchicine site (COL) is close communication, i.e. both sites being near the ␣-␤ dimerization interface. It follows that nucleotide-Mg 2ϩ E-site should be at the interface of association of the dimer with the next dimer along one protofilament of the microtubule. The dashed arrow from the colchicine site to E-site indicates the allosteric communication, which activates the GTPase activity in the ␣␤-dimer upon colchicine binding, although the sites are more than 2.4 nm apart (for this and other distances, see Ref. 66). The shape of the tubulin dimer corresponds to a contour view from the outside of a low resolution microtubule model deduced from x-ray solution scattering (67). hydrolyze bound GTP upon activation by proper contact with other tubulin molecules, which is the basic mechanism controlling microtubule stability. The sites of binding of the antimitotic drugs colchicine, vinblastine, and paclitaxel, for which endogenous ligands are unknown, are also primarily located in ␤-tubulin. It is presently unclear how a dimer was selected to assemble microtubules. ligand stoichiometry of the subunits and the heterodimer was constrained, the fitting parameters being K 2 0 and the different K ji (see Table VI). These models were compatible with the sedimentation equilibrium gradients. The goodness of the fit was assessed by comparison of: (i) the calculated K 2 versus [Mg 2ϩ ] curves with the experimental data (Fig. 12A) and (ii) the theoretical with the experimental binding isotherms (Fig.  12B). The best fit to the experimental values was obtained with a single binding site in one of the isolated subunits (K 11 ϭ 2 ϫ 10 6 M Ϫ1 ), two independent sites in the tubulin heterodimer (K 21 ϭ 1 ϫ 10 7 M Ϫ1 , K 22 ϭ 6 ϫ 10 4 M Ϫ1 ), and a dimerization constant in the absence of Mg 2ϩ , K 2 0 , of ϳ10 6 M Ϫ1 . Note that the deviation observed above 0.1 mM free Mg 2ϩ in the binding isotherm should probably arise from the existence of several low affinity binding sites.