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

Margarita MenéndezDagger , Germán Rivas§, J. Fernando Díaz§, and José M. Andreu§

From the Dagger  Instituto de Química Física and § Centro de Investigaciones Biológicas, Consejo Superior de Investigaciones Científicas, 28006 Madrid, Spain

    ABSTRACT
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Abstract
Introduction
Procedures
Results & Discussion
Conclusion
References

Tubulin liganded with GTP at the N-site in the alpha -subunit and with GDP at the E-site in the beta -subunit (GDP-tubulin) reversibly binds one high affinity Mg2+ cation (Kb = 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 alpha beta -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 alpha beta -dimer formation. The binding of Mg2+ to the alpha -subunit communicates a marked enhancement of fluorescence to a colchicine analogue bound to the beta -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 alpha -beta dimerization interface. It follows that the E-site would be at the beta -end of the tubulin dimer, consistent with the known functional role of the E nucleotide gamma -phosphate and coordinated cation controlling microtubule stability.

    INTRODUCTION
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Abstract
Introduction
Procedures
Results & Discussion
Conclusion
References

Tubulins are GTP-binding proteins that play central roles in eukaryotic cell division and organization. The alpha beta -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 beta -subunit is exchangeable in the dimer (E-site1; Ref. 2), and is hydrolyzed to GDP and Pi as a result of microtubule formation. The nucleotide gamma -phosphate and a coordinated Mg2+ ion control the assembly activity of tubulin and microtubule stability (3-6). Tubulin with GDP in the beta -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 beta -tubulin, the molecule of GTP bound to the alpha -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 self-association (17, 18), including microtubule assembly (19). Equilibration in Mg2+-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 Mg2+ binding sites, one of high affinity (with an association binding constant, K1,Mg, in the order of 106 M-1) and the other of low affinity (K2,Mg, 102 to 103 M-1). The stoichiometry of the first class of sites depends on the nucleotide bound to the E-site; GTP-tubulin has two tightly bound Mg2+ (at the N- and E-sites), whereas GDP-tubulin has a single high affinity Mg2+ (N-site; the E-site becomes low affinity (see Ref. 3)). This has been confirmed by studying the binding of Mg2+ to tubulin having GTP, GDP, or no nucleotide at the exchangeable site of the beta -subunit and one Mg2+ ion already bound (23). The low affinity Mg2+ binding sites are involved in tubulin polymerization (19) and in the equilibrium association of the alpha beta -dimer (8). In contrast, neither the high affinity binding of Mg2+ 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 Mg2+ ions coordinated with the GTP bound to E- and N-sites in tubulin stability, structure and function. Toward these purposes, the isotherm of binding of Mg2+ 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 gamma -phosphate at the E-site impart negligible stabilization to the alpha beta -tubulin dimer, whereas the non-functional cation bound to the N-site, at the alpha -subunit, is essential for tubulin stability, and communicates with the colchicine site at the beta -subunit.

    EXPERIMENTAL PROCEDURES
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Abstract
Introduction
Procedures
Results & Discussion
Conclusion
References

Preparation of calf brain tubulin, without (GDP-tubulin) or with (GTP-tubulin) a gamma -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 × 0.9 cm). To prepare GTP-tubulin, 1 mM GTP and Mg2+ were added to GDP-tubulin. In the experiments at the lower free Mg2+ concentration, the EDTA concentration in the buffer was 2 mM. Nucleotides and Mg2+ quantification by high performance liquid chromatography and atomic absorption spectrometry, respectively, and microtubule assembly were performed as described (7, 25), unless otherwise indicated. Fresh MilliQ grade water was employed to prepare all the solutions, as well as plasticware containers; any glassware material was rinsed with PEDTA buffer before use.

Binding of Mg2+ to Tubulin-- The binding of Mg2+ was measured as follows. Aliquots of 200 µl of tubulin (15 µM) with a known total Mg2+ 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 Mg2+, and the upper half, with cation and essentially no protein, were carefully withdrawn, and the total Mg2+ concentration was determined in both halves. Mg2+ bound to tubulin was quantified by the difference in the cation concentration between the lower and the upper parts of the centrifuge tube. Free Mg2+ was calculated from the total Mg2+ 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 Mg2+ complexes at pH 7.0 employed were as follows: phosphate, 68 M-1 (26, 27); GDP, 607 M-1 (3); GTP, 2830 M-1 (3); and EDTA, 2.5 × 105 M-1 (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 Mg2+, resulted in an estimated uncertainty of 10-15% for the lower calculated free Mg2+ concentrations, and less than 10% for the higher concentrations. Note that, in the buffer solution employed, the small free Mg2+ concentration approximates the mean ionic activity of MgCl2 within experimental error.

A model of ligand binding assuming multiple classes of independent binding sites for Mg2+ (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 Mg2+ 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 µM) 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 Mg2+ concentrations of 7 and 5 mM in the assembly and MTC binding buffers, respectively. Control experiments were run in parallel at 7 mM Mg2+ in the initial equilibration buffer.

Circular Dichroism-- The far-UV CD spectra of tubulin (1-5 µM, equilibrated in PEDTA with 1 mM nucleotide and a known amount of Mg2+) were acquired in a JASCO J720 dichrograph equipped with a temperature regulated cell holder (1, 35), with a 0.1-cm cell at 20 ± 1 °C. Thermal denaturation was monitored following the variation in ellipticity at 220 nm, using a temperature scan rate of 0.5 °C·min-1. 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 Mg2+ on the fluorescence spectrum of the colchicine analog MTC (50 µM total concentration) bound to tubulin (5 µM) was measured essentially as described (39), using a Shimadzu RF-540 spectrofluorimeter (Kyoto, Japan; lambda ex = 350 nm, lambda em = 423 nm). The fluorescence cell (5 × 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 Mg2+ binding, except that MTC was measured spectrophotometrically (epsilon 343 = (1.76 ± 0.01) × 104 M-1 cm-1) (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 µM) were equilibrated in PEDTA, 20 µM nucleotide, with the desired amount of Mg2+. Short column (40-50 µl) 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 (Mw,ac) were obtained using the programs XLAEQ and EQASSOC (supplied by Beckman; see Ref. 41). The partial specific volume was 0.736 cm3/g (42), which was corrected for temperature (43).

To determine the equilibrium constant for tubulin dimerization (K2), 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 programs MULTEQ1B and MULTEQ3B based on the conservation of signal algorithm (41). A value of 1.16 ml mg-1 cm-1 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 (Mw,a) on protein concentration was calculated from the local slopes of transformed data (lnC versus r2) at defined radial distance intervals, using the program MWPLOTZ (kindly supplied by A. Minton, National Institutes of Health, Bethesda, MD). In this study, the Mw,a values were calculated by superimposing data obtained from different loading protein concentrations and averaging over a concentration interval of ±0.1 log units. Models for self-association (47, 48) were fitted to the Mw,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 s20,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 µM) for DSC were equilibrated in PEDTA buffer with 1 mM GDP (or GTP) and the desired Mg2+ concentration. The scanning rate was 0.5 °C min-1, 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
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Abstract
Introduction
Procedures
Results & Discussion
Conclusion
References

The thermal stability of GDP- and GTP-tubulin measured by DSC was found to be similar at free Mg2+ concentrations above 1 µM. However, it was dramatically reduced at the low activity of Mg2+ 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 Mg2+ to GDP- and GTP-tubulin-- The binding isotherms of Mg2+ 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 alpha beta -tubulin dimer: one Mg2+ high affinity site (n1,Mg = 1.1 ± 0.2; K1,Mg = (1.1 ± 0.3) × 107 M-1), plus several low affinity sites (n2,Mg = 48, K2,Mg = 106 M-1; 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 Mg2+ binding to tubulin is reversible, since supplementing cation-depleted tubulin (equilibrated in 40 ± 5 nM free Mg2+) to 360 ± 20 nM free Mg 2+ increased binding from 0.4 ± 0.1 to 0.75 ± 0.1 Mg2+ per tubulin heterodimer, which is within the experimental error of the reference isotherm (Fig. 1).


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Fig. 1.   Binding of Mg2+ to GDP-tubulin (solid circles) and GTP-tubulin (open circles). Solid line, binding isotherm calculated assuming a simple binding model (n1,Mg = 1.1 ± 0.2, K1,Mg = (1.1 ± 0.3) × 107 M-1 plus the low affinity sites n2,Mg = 48, K2,Mg = 106 M-1 described by Frigon and Timasheff (17); see the text for details). Dashed line, Mg2+ binding values obtained by adding one to the GDP-tubulin isotherm (solid line) in the interval indicated.

GTP-tubulin has one more Mg2+ binding site (Fig. 1, empty symbols) than GDP-tubulin, with an apparent affinity in the order of 105 M-1. The analysis of its Mg2+ binding isotherm is complicated by the presence of GDP, which has a much higher affinity than GTP for the tubulin E-site at low Mg2+concentration (3, 4). Therefore, as the cation concentration decreases, GDP progressively exchanges into the GTP-tubulin samples. GTP-tubulin in 63 µM free Mg2+ 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 Mg2+ is one more cation than that of GDP-tubulin. On the other hand, at 3.2 µM free Mg2+ 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 Mg2+ binding data of Mejillano and Himes (23) in a different buffer.

These high affinity Mg2+ 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 GTP-binding sites in alpha - and beta -tubulin, respectively (3, 4, 24). However, binding isotherm of the highest affinity Mg2+ to the N-site had not been measured; nor had cation-depleted tubulin been studied.

Effect of Mg2+ Depletion on Nucleotide Release from Tubulin-- Equilibration of tubulin in Mg2+ 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 Mg2+ 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 Mg2+ and incubation time (see Table I for a summary). Tubulin samples with the high affinity Mg2+ site saturated contain close to one GTP and one GDP per alpha beta -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 decreased more slowly, to values approaching the Mg2+/tubulin stoichiometry of the samples (Table I). These results indicate that dissociation of Mg2+ from the N-site (alpha -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 beta -subunit in the alpha beta -dimer is controlled by the cation ligation state of the alpha -subunit, and will be further addressed later.

                              
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Table I
Effect of Mg2+ on nucleotide content of tubulin

GDP-tubulin equilibrated at 55 nM free Mg2+ and re-equilibrated in 6 mM MgCl2 and 1 mM GTP polymerized in 3.4 M glycerol-containing buffer with a critical concentration (15 µM) 1.7 times higher than that of a GTP-tubulin control directly equilibrated in 6 mM MgCl2 (9 µM). 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 Mg2+-glycerol buffer (7), this implies that around 70 ± 10% of the Mg2+-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 alpha - and beta -subunits.

The Kinetics of Tubulin Inactivation Depends on Mg2+ Activity-- The role of Mg2+ 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 Mg2+ concentrations. GDP-tubulin equilibrated in 60 nM free Mg2+ initially retains more than 80% of the corresponding activity at higher cation concentrations. However, its inactivation is more rapid (half-life, t1/2 = 5 h; Fig. 2) than at 300 nM free Mg2+ (t1/2 = 7 h; data not shown), and much faster than at 100 µM free Mg2+ (estimated t1/2 ~ 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 Mg2+ concentration (4.0-5.5 × 10-5 s-1 at 60 nM, 2.5-3.0 × 10-5 s-1 at 300 nM, and 3.8-4.6 × 10 -6 s -1 at 100 µM free Mg2+).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 Mg2+, giving an apparent first order constant of 0.9 × 10-5 s-1 (t1/2 = 21 h; data not shown).


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Fig. 2.   Kinetics of GDP-tubulin inactivation at 20 °C, followed by either fluorescence of the MTC-tubulin complex (circles) or Taxol®-induced microtubule assembly (triangles). Closed symbols correspond to samples equilibrated at ~0.1 mM free Mg2+, whereas data in open symbols were taken at 60 nM free Mg2+. The lines correspond to first order kinetic rate constants of 4.6 × 10-6 s-1 (closed circles), 3.8 × 10-6 s-1 (closed triangles), and 4 × 10-5 s-1 (open circles).

High Affinity Mg2+ Binding Enhances the Fluorescence of MTC Bound to the Colchicine Site of Tubulin-- The addition of Mg2+ to the complex of the colchicine analogue MTC with tubulin, previously equilibrated at 50-60 nM free Mg2+, 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 Mg2+ high affinity site previously saturated with the cation. Control experiments indicated that Mg2+ affects neither the negligible fluorescence of unbound MTC nor the intrinsic (tryptophan) fluorescence of tubulin. Furthermore, Mg2+-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 Mg2+ concentration (0.7 ± 0.1 MTC/tubulin heterodimer). The apparent association constant of Mg2+ to GDP-tubulin estimated from the MTC fluorescence change (Fig. 3) was 9 × 106 M-1, essentially coincident with the association constant of the high affinity Mg2+ (Fig. 1). Mg2+ 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 Mg2+ effect with MTC and colchicine might indicate that the slow dissociation rate of the latter prevents the ligation of Mg2+ to the N-site.


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Fig. 3.   Effect of Mg2+on the fluorescence intensity of the tubulin-MTC complex (5 µM) at 20 °C. The line is a fluorescence titration curve calculated for cation-binding to a single site (Fmax = 71, Fmin = 8, Kb = 9 × 106 M-1). Inset, fluorescence spectra of the complex at 8 µM (solid line) and 65 nM (dotted line) free Mg2.


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Fig. 4.   Effect of Mg2+ on the far-UV CD spectrum of GDP-tubulin (5 µM). Each spectrum represents an average of four scans. Free Mg2+ concentrations are 1 mM (solid line), 3 µM (dotted line), and 65 nM (dashed line).

The simplest interpretation of these results is that the microenvironment of tubulin-bound MTC is sensitive to the high affinity bound Mg2+ 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 alpha -tubulin modifies the properties of the colchicine site, whose locus is at the beta -subunit, possibly near the alpha beta -subunit interface (56).

Modification of tubulin secondary structure upon removal of the high affinity bound Mg2+ was checked by CD spectroscopy. Equilibration of the protein in 65 nM free Mg2+ 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 Mg2+ 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 Mg2+ concentration up to 1 mM (data not shown). Preliminary CD kinetic experiments of Mg2+ 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 Mg2+ in alpha beta -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 alpha IIbbeta 3 (57) and the complement C1 subcomponent (48)). For this reason, the influence of Mg2+ (low and high affinity binding sites) on the dimerization equilibrium of tubulin was analyzed by analytical ultracentrifugation. GDP-tubulin equilibrated in 50-60 nM Mg2+, at an initial protein concentration of 15 µM, has the same sedimentation coefficient (s20,w = 5.8 ± 0.2 S) and relative molecular mass (109,000 ± 8,000; Fig. 5) as the intact alpha beta -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 Mg2+ concentrations. The results indicate that removal of Mg2+ from its high affinity site increases dissociation of the tubulin dimer. This behavior reflects the linkage of Mg2+ binding and tubulin self-association equilibria. Lowering the free Mg2+ concentration reduced by an order of magnitude the apparent equilibrium dimerization constant of alpha beta -tubulin (K2), from ~107 M-1 at ~100 µM free cation, to 4 × 106 M-1 at 1-2 µM cation, and to 1.6 × 106 M-1 at 50 nM free cation (see Table II and Fig. 6).


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Fig. 5.   Analytical ultracentrifugation of GDP-tubulin at 50-60 nM free Mg2+ (10 °C). Sedimentation equilibrium profile of tubulin under the conditions used in DSC experiments (15 µM loading protein concentration). Inset, sedimentation velocity distribution of tubulin samples. The solid line corresponds to the same tubulin showed in the main figure. The dashed and dotted lines are GDP-tubulin after 30 min at 40 °C and 60 °C, respectively.


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Fig. 6.   Influence of Mg2+on the GDP-tubulin dimerization equilibrium. Dependence of the apparent weight-average molecular mass of GDP-tubulin on free Mg2+ and protein concentration. Cation concentrations: 50 µM (closed circles), 1.6 µM (open circles), 60 nM (solid triangles). The solid lines were calculated for a monomer-dimer equilibrium model using the equilibrium constants given in Table II. For illustrative purposes, the Mr of alpha - and beta -tubulin (55,000), as well as the value for the heterodimer (2 × 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 µM; 26,000 rpm and 10 °C) at 60 nM free magnesium. The solid lines represent the best-fit function (see Table II).

                              
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Table II
Effect of Mg2+ on the dimerization equilibrium of alpha beta -tubulin

The simplest interpretation of these results is that both the high affinity binding of one Mg2+ 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 10-3 to 10-4 M free Mg2+ concentration range by Shearwin et al. (8), who suggested the involvement of two weakly bound Mg2+ 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 Mg2+ enhance tubulin dimerization. As shown under "," the combined sedimentation equilibria data may be reasonably accounted for by a Mg2+-dependent dimerization model, which is compatible with both the experimental dependence of K2 on the cation concentration (Table II) and the Mg2+-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 Mg2+ binding site, with an intrinsic binding constant of 2 × 106 M-1, whereas the heterodimer has two independent Mg2+ binding sites, with binding constants 1 × 107 M-1 and 6 × 104 M-1, respectively. The estimated value for the intrinsic dimerization constant of tubulin in the absence of Mg2+ is K20 = 106 M-1. 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 Mg2+ and Nucleotide in the Thermal Stability of Tubulin-- The influence of Mg2+ on the thermal stability of tubulin was analyzed by differential scanning calorimetry. Fig. 7A compares representative DSC profiles of GDP-tubulin in PEDTA buffer at increasing free Mg2+ concentrations. The experimental curves show that tubulin is strongly stabilized against thermally induced denaturation through interaction with the cation in the 10 nM to ~1 µM range of free ligand concentration. Above 1 µM free Mg2+, the heat capacity curve presents a single asymmetric peak with an enthalpy change of 180 ± 10 kcal mol-1 and a Tm of 55 °C, whereas at the lower cation concentrations (25-40 nM free Mg2+) the denaturation enthalpy change decreases to 130 ± 25 kcal mol-1, and the endotherm tends to become separated into two peaks (Figs. 7A and 9B), the main one with a Tm of 46 °C at 25 nM free Mg2+. The origin of the two peaks will be analyzed later.


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Fig. 7.   Panel A, thermal denaturation curves of GDP-tubulin (15 µM) at increasing concentrations of Mg2+. The experiments were done at a scan rate of 0.5 K·min-1. Free Mg2+ concentrations (from top to bottom): 280 µM, 4 µM, 920 nM, 500 nM, 182 nM, and 50 nM. Panel B, dependence of denaturation Tm values of GDP-tubulin (15 µM) on the free Mg2+ concentration (solid circles); open circles correspond to GTP-tubulin.

Substitution of GDP by GTP at the E-site does not modify tubulin stabilization by Mg2+, which nearly reaches a plateau above 1 µM free Mg2+ (Fig. 7B). The results strongly suggest that the cation responsible for the substantial tubulin stabilization observed is the Mg2+ 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 Mg2+ for the E-site in GDP-tubulin is known to be about 103 times lower than in GTP-tubulin (3, 4). Table III summarizes the parameters measured for the thermal denaturation of tubulin.

                              
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Table III
Thermal denaturation data of GDP- and GTP-tubulin at different free Mg2+ concentrations and scanning rates

The reversal of tubulin destabilization induced by Mg2+ depletion was checked by preparing protein samples equilibrated at different cation concentrations and then adding Mg2+ up to saturation (Table IV). The destabilization induced by the cation dissociation was 95% reversible in tubulin samples initially equilibrated in 180 nM free Mg2+ and immediately supplemented with 280 µM free Mg2+ (Delta Hd = 176 kcal mol-1, Tm = 56.1 °C; Fig. 8, curve b). However, when Mg2+ 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 (Delta Hd = 139 kcal·mol-1; T = 56.1 °C; curve c in Fig. 8).The drop in Delta Hd 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 Mg2+ (nu Mg = 0.4, nu GTP = 0.65) results in heat capacity denaturation curves with the same Tm value as in the control experiments but with a lower enthalpy change (142 kcal·mol-1; curve e, Fig. 8). The percentage of reversibility obtained by saturation with Mg2+ immediately after preequilibration in Mg2+-depleted buffers, correlates well with the initial GTP/tubulin stoichiometry of the samples. These results indicate that Mg2+- 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 Mg2+ dissociation. Addition of colchicine stabilized the cation-depleted tubulin, similarly to addition of Mg2+, whereas the reversible binding of the colchicine analogue MTC had a much weaker effect (Table V).

                              
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Table IV
Reversibility of thermal destabilization induced by Mg2+ removal from GDP-tubulin


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Fig. 8.   Reversibility of the Mg2+ stabilizing effect on thermal denaturation of GDP-tubulin (15 µM). Curve a, endotherm of tubulin equilibrated at 180 µM free Mg2+; curve b, the same as a but supplemented with Mg2+ (280 µM final free concentration) immediately after column elution; curve c, the same as a but supplemented with Mg2+ after incubation for 2 h at 20 °C (scan rate 30 °C·h-1); curve d, endotherm of GDP-tubulin equilibrated at 45 nM free Mg2+; curve e, the same as d, but supplemented up to 470 µM free Mg2+ immediately after elution from the preparative column (scan rate 45 °C·h-1).

                              
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Table V
Influence of MTC and colchicine on GDP-tubulin stability

Kinetic Control of the Thermal Denaturation of Tubulin by High Affinity Mg2+ 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 Mg2+ binding site, the variation in the excess heat capacity with temperature follows the behavior predicted by the two-state kinetic model (53, 54). Fig. 9C shows the temperature dependence of the apparent denaturation rate constant at different free Mg2+concentrations, calculated according to this model. This result means that only Mg2+ liganded (N-site) and denatured tubulin are significantly populated within the denaturation temperature range. A good correlation was found between the kinetic constants of inactivation calculated from the rate of CD change at 55 °C (theta 220, free [Mg2+] = 180 nM) or from DSC data at the same temperature and cation concentration (3 × 10-3 s-1 and 3.5 × 10-3 s-1, 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.


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Fig. 9.   Panels A and B, DSC traces of GDP-tubulin (15 µM) at different scanning rates and free Mg2+ concentrations. Panel A, 280 µM free Mg2+ (30 and 20 °C·h-1; top to bottom). Panel B, 40 nM free Mg2+ (60, 45, and 30 °C·h-1; from top to bottom). Panel C, Arrhenius plot of the kinetic rate constant, kapp, derived from calorimetric data assuming the two-state kinetic model, at different free Mg2+ concentrations: 280 µM (diamonds), 927 nM (circles), 500 nM (triangles), and 182 nM (squares).

At the lowest free Mg2+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 ~30 ± 5 kcal·mol-1. The CD spectra of thermally denatured tubulin has residual beta sheet secondary structure (60). The apparent biphasic denaturation of tubulin at subsaturating levels of Mg2+ could be generated by different processes such as kinetic stabilization of unfolding intermediates, uncoupling of alpha - and beta -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 (61-63), the low and high temperature peaks could also derive from the unligated and nucleotide-bound tubulin, respectively.


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Fig. 10.   Dependence of the excess enthalpy function (Hexcess) and the CD signal at 220 nm (theta 220) of tubulin with temperature (65 nM free Mg2+). The solid line shows the excess enthalpy values of the corresponding DSC curve. The symbols show the experimental CD data. Tubulin concentration was 15 µM and the temperature scan rate 0.5 °C min-1.

Sedimentation velocity measurements have shown that the association state of thermally denatured tubulin depends on the Mg2+ concentration. Incubation of GDP-tubulin equilibrated in 50 nM free Mg2+ 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 (s20,w = 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 (~70%) of tubulin aggregation (13-14 S). However, when the same treatment was performed on GDP-tubulin with the high affinity site occupied by Mg2+, aggregation was not evident (s20,w = 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 Mg2+ concentration range explored is as follows.
<AR><R><C></C><C>K<SUP>&agr;</SUP><SUB><UP>GTP</UP></SUB></C><C></C><C>K<SUP>&agr;</SUP><SUB><UP>Mg</UP></SUB></C></R><R><C><UP>TB</UP>+<UP>GTP</UP>+<UP>Mg</UP><SUP>2<UP>+</UP></SUP></C><C>⇄</C><C><UP>TB</UP> · <UP>GTP</UP>+<UP>Mg</UP><SUP>2<UP>+</UP></SUP></C><C>⇄</C><C><UP>TB</UP> · <UP>GTP</UP> · <UP>Mg</UP><SUP>2<UP>+</UP></SUP></C></R><R><C>           ↑↓</C><C></C><C>          ↑↓</C></R><R><C>            X<SUB>1</SUB></C><C></C><C>           X<SUB>2</SUB></C><C></C><C>            ↓k<SUB>3</SUB></C></R><R><C>           ↓k<SUB>1</SUB></C><C></C><C>          ↓k<SUB>2</SUB></C></R><R><C>            I<SUB>1</SUB> </C><C></C><C>      I<SUB>2</SUB>+<UP>GTP</UP></C><C></C><C>I<SUB>3</SUB>+<UP>GTP</UP>+<UP>Mg</UP><SUP>2<UP>+</UP></SUP></C></R></AR>
<UP><SC>Scheme</SC> 1</UP>
KGTPalpha and KMgalpha are the GTP and Mg2+ binding constants to N-site, k3 is the denaturation rate constant of tubulin·GTP·Mg, and k1 and k2 are the limiting rate constants for denaturation of N-site unliganded and GTP-bound tubulin, respectively; Ii are irreversibly denatured state(s) of tubulin (I1 and I2 are 12-14 S aggregated species, and I3 is 5.9 S denatured tubulin) and Xi indicates the possibility of intermediate steps during denaturation.

    CONCLUSION
Top
Abstract
Introduction
Procedures
Results & Discussion
Conclusion
References

The results reported in this study provide new insights into tubulin structure and function. This is schematically summarized in Fig. 11. The nucleotide gamma -phosphate and the coordinated Mg2+ ion at the E-site (beta ) 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 alpha beta -tubulin dimer. However, one high affinity Mg2+ ion, bound to a site identified as the non-functional nucleotide N-site (alpha ), has profound kinetic and thermal stabilizing effects, and induces the association of the alpha beta -dimer. The alpha - and beta -subunits seem to communicate with each other; the binding of Mg2+ to the N-site in the alpha -subunit induces the fluorescence of a probe bound to the colchicine site in the beta -subunit, and colchicine binding thermally stabilizes Mg2+-depleted tubulin. These properties are most simply explained by proposing that both the colchicine site (beta ) (56) and the N-site Mg2+ (alpha ) (this study) are located at the alpha beta dimerization interface. It follows from subunit homology that the functional E-site (in beta ) should be at the longitudinal dimer-dimer interface leading to protofilament formation (64), consistent with the activation of tubulin GTPase in linear oligomers (65).


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Fig. 11.   Model scheme proposed to explain and summarize the results of this work. The nucleotide and Mg2+ 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 Mg2+ ion bound at the nucleotide N-site controls the stability of the alpha beta -tubulin dimer. The simplest explanation for the observed effect of the Mg2+ 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 alpha -beta dimerization interface. It follows that nucleotide-Mg2+ 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 alpha beta -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).

All tubulins probably evolved from a common nucleotide-binding ancestor. The GTP and Mg2+ binding functionalities were made essential for the maintenance of the protein stability in alpha -tubulin, whereas beta -tubulin acquired the capability to 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 beta -tubulin. It is presently unclear how a dimer was selected to assemble microtubules.

    ACKNOWLEDGEMENT

We thank Victoria Lopez Moyano for able technical assistance.

    FOOTNOTES

* 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. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

To whom correspondence should be addressed: Centro de Investigaciones Biológicas, Consejo Superior de Investigaciones Científicas, Velázquez 144, 28006 Madrid, Spain. Fax: 34-1-2627518; E-mail: cibjm07{at}cc.csic.es.

1 The abbreviations and trivial names used are: E-site, exchangeable nucleotide binding site of tubulin; N-site, non-exchangeable nucleotide binding site of tubulin; DSC, differential scanning calorimetry; CD, circular dichroism; MTC, 2-methoxy-5-(2,3,4-trimethoxyphenyl)-2,4,6-cycloheptatrien-1-one; PEDTA, 10 mM phosphate buffer containing 1 mM EDTA, pH 7.0; paclitaxel, 4,10-diacetoxy-2alpha -(benzoyloxy)-5beta ,20epoxy-1,7beta -dihydroxy-9-oxotax-11-en-13alpha -y1(2R,3S)-3-[(phenylcarbonyl)-amino]-2-hydroxy-3-phenylpropionate.

2 The first order fit does not account for the initial decay at 60 nM Mg2+. The data are also compatible with a two-phase inactivation model (data not shown). This gives a fast phase (t1/2 = 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 = 15 h) that might consist of the inactivation of the remaining fraction of cation-containing tubulin.

    APPENDIX

Tubulin exists as an equilibrium mixture of monomers (alpha - and beta - subunits) and dimers (alpha beta -heterodimer), with molecular weights Malpha , Mbeta , and Malpha beta , respectively (Malpha  = Mbeta ). The equilibrium dimerization constant, K2, is shown in Equation 1 below.
&agr;+&bgr; <LIM><OP><ARROW>⇄</ARROW></OP><UL>K<SUB>2</SUB></UL></LIM>  &agr;&bgr;      K<SUB>2</SUB>=c<SUB>&agr;&bgr;</SUB>/(c<SUB>&agr;</SUB> · c<SUB>&bgr;</SUB>)
calpha , cbeta , and calpha beta represent the concentrations of the different forms in dilute solution, expressed in molar units.

The total concentration of tubulin, ctot, and the weight-average molecular weight are given by Equations 2 and 3, respectively:
c<SUB><UP>tot</UP></SUB>=c<SUB>&agr;</SUB>+c<SUB>&bgr;</SUB>+2c<SUB>&agr;&bgr;</SUB> (Eq. 1)
M<SUB>w,a</SUB>=<LIM><OP>∑</OP></LIM>(c<SUB>j</SUB> · M<SUB>wj</SUB><SUP>2</SUP>)/<LIM><OP>∑</OP></LIM>(c<SUB>j</SUB> · M<SUB>wj</SUB>) (Eq. 2)
j represents any tubulin species (alpha , beta , or alpha beta ).

A simple general model of Mg2+ binding to tubulin assumes multiple classes of independent binding sites in any of the tubulin species. The Mg2+ binding isotherms for the alpha - and beta -subunits and the alpha beta -heterodimer are given in Equations 4-6.
&ngr;<SUB>&agr;</SUB>=<LIM><OP>∑</OP></LIM> n<SUB>&agr;i</SUB> · <UP>K</UP><SUB>&agr;i</SUB> · [<UP>Mg</UP><SUP>2<UP>+</UP></SUP>]/(1+K<SUB>&agr;i</SUB> · [<UP>Mg</UP><SUP>2<UP>+</UP></SUP>]) (Eq. 3)
&ngr;<SUB>&bgr;</SUB>=<LIM><OP>∑</OP></LIM> n<SUB>&bgr;i</SUB> · <UP>K</UP><SUB>&bgr;i</SUB> · [<UP>Mg</UP><SUP>2<UP>+</UP></SUP>]/(1+K<SUB>&bgr;i</SUB> · [<UP>Mg</UP><SUP>2<UP>+</UP></SUP>]) (Eq. 4)
&ngr;<SUB>&agr;&bgr;</SUB>=<LIM><OP>∑</OP></LIM> n<SUB>&agr;&bgr;i</SUB> · <UP>K</UP><SUB>&agr;&bgr;i</SUB> · [<UP>Mg</UP><SUP>2<UP>+</UP></SUP>]/(1+K<SUB>&agr;&bgr;i</SUB> · [<UP>Mg</UP><SUP>2<UP>+</UP></SUP>]) (Eq. 5)
nu alpha , nu beta , and nu alpha beta are the number of moles of Mg2+ bound per mole of isolated alpha - and beta -subunits and tubulin heterodimer, respectively; nji and Kji are the number of sites and the intrinsic association constant for the class i of binding sites in the isolated monomers or heterodimer (j = alpha , beta , or alpha beta ). The global binding isotherm is given in Equation 7.
&ngr;<SUB><UP>tot</UP></SUB>=[c<SUB>&agr;</SUB> · &ngr;<SUB>1&agr;</SUB>+c<SUB>&bgr;</SUB> · &ngr;<SUB>1&bgr;</SUB>+c<SUB>&agr;&bgr;</SUB> · &ngr;<SUB>2&agr;&bgr;</SUB>]/c<SUB><UP>tot</UP></SUB> (Eq. 6)
The apparent dimerization constant K2 at a given ligand concentration, [Mg2+], may be expressed, in terms of linked equilibria theory (48, 58), by Equation 8.
<UP>log</UP>K<SUB>2</SUB>=<UP>log</UP>K<SUP>0</SUP><SUB>2</SUB>+<LIM><OP>∑</OP></LIM>n<SUB>&agr;&bgr;i</SUB> · <UP>log</UP>(1+K<SUB>&agr;&bgr;i</SUB> · [<UP>Mg</UP><SUP>2<UP>+</UP></SUP>]) (Eq. 7)
−<FENCE><LIM><OP>∑</OP></LIM>n<SUB>&agr;i</SUB> · <UP>log</UP><FENCE>1+K<SUB>&agr;i</SUB> · [<UP>Mg</UP><SUP>2<UP>+</UP></SUP>]+<LIM><OP>∑</OP></LIM>n<SUB>&bgr;i</SUB> · <UP>log</UP>(1+K<SUB>&bgr;i</SUB> · [<UP>Mg</UP><SUP>2<UP>+</UP></SUP>])</FENCE></FENCE>
From this, Equation 9 can be derived.
d(<UP>log</UP> K<SUB>2</SUB>)/d(<UP>log</UP>[<UP>Mg</UP><SUP>2<UP>+</UP></SUP>])=&ngr;<SUB>&agr;&bgr;</SUB>−(&ngr;<SUB>&bgr;</SUB>+&ngr;<SUB>&agr;</SUB>) (Eq. 8)
To obtain the number of binding sites and the equilibrium binding constants for each subunit and the heterodimer, the value of Mw as a function of tubulin and Mg2+ concentration were determined in the following way. The equilibrium constant, K2, was calculated from Equation 8, given the values of K20, [Mg2+], and ctot, together with the values of nji and Kji for the different species. The values of calpha and cbeta were determined by solving Equations 1 and 2. Finally, Equation 3 was used to calculate Mw. The global binding isotherm was then obtained from Equation 7.

Using this analytical procedure, different models were fitted to the combined Mw,a versus concentration data (derived from nine sedimentation equilibrium gradients, at three initial concentrations of tubulin and Mg2+; see Fig. 6). In all of them, the ligand stoichiometry of the subunits and the heterodimer was constrained, the fitting parameters being K20 and the different Kji (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 K2 versus [Mg2+] 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 (K11 = 2 × 106 M-1), two independent sites in the tubulin heterodimer (K21 = 1 × 107 M-1, K22 = 6 × 104 M-1), and a dimerization constant in the absence of Mg2+, K20, of ~106 M-1. Note that the deviation observed above 0.1 mM free Mg2+ in the binding isotherm should probably arise from the existence of several low affinity binding sites.

                              
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Table VI
Models of Mg2+-linked dimerization applied to the combined sedimentation equilibrium data
Data from Fig. 6 are shown.


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Fig. 12.   Linkage between Mg2+ binding and tubulin dimerization. Panel A, dependence of the tubulin dimerization constant on free Mg2+ concentration. Symbols correspond to dimerization constants determined from sedimentation equilibrium data in the present work (solid circles; Table II), compared with those obtained by Shearwin and Timasheff (open circles; Ref. 56). The solid line corresponds to the theoretical values calculated from Equation 7, using the parameters of the best model described in the text (see model 3 in Table VI). The dashed line corresponds to the data and model of Shearwin and Timasheff (see Equation 7 in Ref. 56). The dotted lines show the calculated functions from models 1 (curve a) and 5 (curve b) (see Table VI). Panel B, number of Mg2+ ions bound per tubulin as a function of free Mg2+ concentration. Solid squares are the experimental data (see Fig. 1). Lines, binding isotherms calculated for the linkage models and parameters described in the text; solid line, model 3 (best fit); dotted lines, models 1 (curve a) and 5 (curve b) (see Table VI).

    REFERENCES
Top
Abstract
Introduction
Procedures
Results & Discussion
Conclusion
References
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