Effect of Tubulin Self-Association on GTP Hydrolysis and Nucleotide Exchange Reactions
Tubulin nucleation, microtubule (MT) assembly, stability, and dynamics depend on GTP hydrolysis and nucleotide exchange reactions. We investigated how the selfassociation of isolated tubulin dimers affects the rate of GTP hydrolysis and the equilibrium of nucleotide exchange. We used HPLC to determine the concentrations of GDP and GTP and thereby the GTPase activity of SEC-eluted tubulin dimers in assembly buffer solution, free of glycerol and tubulin aggregates. When GTP hydrolysis was negligible, the nucleotide exchange mechanism was studied using HPLC for determining the concentrations of tubulin-free and tubulin-bound GTP and GDP and by SAXS and cryo-TEM. We observed no GTP hydrolysis below the critical conditions for MT assembly, despite the assembly of tubulin 1D curved oligomers and single rings, showing that their assembly did not involve GTP hydrolysis under our conditions. Under conditions enabling spontaneous slow MT assembly, a slow pseudo-first-order GTP hydrolysis kinetics was detected, limited by the rate of MT assembly. Nucleotide exchange depended on the total tubulin concentration and the molar ratio between tubulin-free GDP and GTP. We used a thermodynamic model of isodesmic tubulin self-association, terminated by the formation of tubulin single-rings to calculate, at each tubulin concentration, the distributions of single rings, 1D oligomers, and free dimers, and thereby the molar fractions of dimers with exposed and buried nucleotide exchangeable sites (E-sites). Our analysis shows that the GDP to GTP exchange reaction equilibrium constant was an order-of-magnitude larger for tubulin dimers with exposed E-sites than for assembled dimers with buried E-sites.
INTRODUCTION<!>MATERIALS AND METHODS<!>Tubulin Purification<!>Incubation Protocol<!>Heat-Cool Cycles<!>SEC Protocol<!>Buffer Exchange<!>Nucleotide Extraction by Protein Precipitation<!>HPLC Analysis<!>GTP to GDP Molar Ratio<!>Simultaneous Measurements in the Buffer and on Tubulin<!>Solution X-ray Scattering<!>Cryo-Transmission Electron Microscopy<!>Protocol Validation and Control Measurements<!>Purchased Nucleotides Purity<!>Nucleotide Composition of Different Tubulin Preparation Protocols<!>GTP Hydrolysis Was Negligible in the Absence of Tubulin<!>GTP Hydrolysis Was Not Involved in the Formation of Tubulin 1D Oligomers and Single Rings<!>GTP Hydrolysis Above the Critical Conditions for MT Assembly<!>Analyzing the Exchange Reaction Excluding the Contribution of Tubulin Self-Association<!>Association<!>Free Nucleotides<!>CONCLUSIONS<!>ACCESSION CODES
<p>Microtubules (MTs) are dynamic biopolymers, self-assembled from αβ-tubulin heterodimer subunits. MTs are essential components of several cellular architectures including the cytoskeleton and the mitotic spindle. 1,2 MT dynamics, allowing assembly and disassembly of these structures, depends on a plethora of parameters including, post-translational modifications, 3 ionic composition and strength, [4][5][6] temperature, 5 additives and drugs, 5 and MTassociated proteins (MAPs). 7,8 Two nucleotides are attached to each tubulin dimer, one at a non-exchangeable site (N-site), located on the α subunit at the interface between the subunits, and one at an exchangeable site (E-site), located on the β subunit. 9,10 The N-site nucleotide is predominantly guanosine triphosphate (GTP), whereas, at the E-site, the nucleotide can be either guanosine diphosphate (GDP) or GTP. In curved assemblies of GDP-tubulin, the E-site nucleotide is not directly exposed to the solvent (Figure 1). 11 MTs nucleate and elongate mainly from tubulin dimers with GTP at their E-site, (GTPtubulin). [16][17][18] GTP hydrolysis to GDP-tubulin at the tubulin E-site, occurs during MT assembly following either tubulin nucleation (leading to the creation of a new MT) or MT elongation. 8,[19][20][21][22][23][24] The kinetics of GTP hydrolysis is critical for MT stability and dynamics. 1,8,18 The hydrolysis is tightly associated with structural changes in the MT lattice, leading to more compact dimers, and weakening the lateral interaction between dimer subunits. 1,22,[24][25][26][27][28][29][30][31] Recently, it was suggested that GTP hydrolysis increases the longitudinal lattice tension, contributing to a more confined and correlated GDP-tubulin dynamics, thereby entropically destabilizing the MT lattice. [32][33][34] Hydrolysis interferes with tubulin nucleation and MT assembly 17,18,29,[35][36][37] and may affect the affinity of MAPs to the MT lattice. 22 The molar ratio between GTP-and GDP-tubulin is constantly changing during the hydrolysis reaction.</p><p>GTP-hydrolysis occurs at the interface between the GTP-tubulin cap and the GDP-tubulin MT core, 23 and may be slower than the rate of subunit addition. 19,38 The delay is associated with structural rearrangements of the tubulin on the MT lattice, required for GTP  The interface between α-and β-tubulin in a curved 1D GDP-tubulin assembly, leading to tubulin single ring symmetry. 12 The atomic tubulin model is based on PDB ID 5JQG. 11 Missing residues were added and refined using Modeller, 13 as explained. 14 The cartoon was created by PyMOL. 15 β-and α-tubulin are colored in red and green, respectively. The GDP molecule, occupying the E-site on the β-tubulin, is represented by cyan spheres, whereas the GTP molecule occupying the N-site on the α-tubulin, is represented by orange spheres. The first tubulin dimer in the assembly, for which the β monomer is shown (red), is in a Buried conformation.</p><p>In addition to GTP hydrolysis, a tubulin-bound nucleotide can be modified by the following exchange reaction with a tubulin-free nucleotide GDP−tubulin + GTP −− −− GTP−tubulin + GDP</p><p>where K eq is the equilibrium constant of the exchange reaction. GTP-tubulin can facilitate MT assembly, hence nucleotide exchange is a fundamental process in MT dynamics. 18 The extent of exchange varies with solution conditions such as nucleotide composition and concentration. 39 When Mg 2+ is added, it can form complexes with the nucleotides, the tubulin or both, and several reversible equilibrium reactions can take place. 40 The molar ratio between GTP-and GDP-tubulin controls the nucleation of tubulin and the stability of preassembled MTs. 16 Knowing its value is therefore crucial for analyzing tubulin nucleation and assembly reactions. 41 In this paper, we examined how the self-association of isolated tubulin dimers affects the rate of GTP hydrolysis and the thermodynamics of nucleotide exchange. We determined the GTPase activity of size exclusion chromatography (SEC) eluted tubulin dimers in assembly buffer solutions free of glycerol 42 and tubulin aggregates. These conditions have been used only in a few earlier studies 14,43 but were essential for excluding the effect of tubulin aggregation on the hydrolysis and exchange reactions. In addition, the rate of MT assembly is significantly slower when using SEC-eluted tubulin dimes in glycerol-free assembly buffer. 14 We measured the rates of GTP hydrolysis in the absence and presence of SEC-eluted tubulin dimers, at 4 and 36 • C. In the absence of tubulin, marginal GTP hydrolysis was observed at 36 • C. In the presence of SEC-eluted tubulin dimers, no GTP hydrolysis was observed below the critical conditions for MT assembly, even though tubulin 1D curved oligomers and single rings assembled, 12,14 suggesting that GTP hydrolysis was not involved in their formation. Slow GTP hydrolysis was observed under conditions enabling spontaneous slow MT assembly 14 and the hydrolysis was fitted to a pseudo-first-order kinetics, limited by the rate of MT assembly.</p><p>By simultaneously measuring the tubulin-free and the tubulin-bound nucleotide composition, we investigated the mechanism of GDP to GTP exchange reaction on tubulin. We examined conditions under which GTP hydrolysis was negligible, using different tubulin concentrations and GDP to GTP molar ratios. We found that the nucleotide exchange reaction mechanism should take into account the self-association of tubulin, leading to the formation of tubulin dimers with exposed and buried E-sites. 44,45 The extent of GDP to GTP exchange reaction was an order of magnitude greater for dimers with exposed E-sites than dimers with buried E-sites. Our data also suggest that the association of Mg 2+ ions with the tubulin dimers was primarily via their association with the free nucleotides.</p><!><p>Materials were purchased from Sigma-Aldrich Co. Israel. The precision of our temperature measurements was ±1 • C.</p><!><p>αβ-Tubulin dimer was purified from porcine brains, using a modified version of the highmolarity buffer purification method, 46 described 12 and used in our earlier publications. 6,[47][48][49] The tubulin assembly buffer was BRB80 (80 mM 1,4-piperazineediethanesulfonic acid (PIPES),</p><p>at pH 6.9 (KOH) and typically contained 0.4 ± 0.1 mM adenosine triphosphate (ATP), 0.5 ± 0.1 mM GTP, and 0.4 ± 0.1 mM GDP. After the purification, aliquots of 36 ± 2 mg/mL tubulin were flash-frozen in liquid nitrogen and stored at −80 • C. Before used, tubulin solutions were thawed on ice.</p><!><p>Tubulin samples for steady-state experiments, at different GDP to GTP molar ratios, obtained by either nucleotide addition or the Buffer Exchange protocol, were incubated for about 2 h at the experimental temperature. The samples were then analyzed by the Nucleotide Extraction by Protein Precipitation protocol.</p><!><p>GDP-tubulin was also obtained through hydrolysis of GTP by applying seven heat-cool cycles to the tubulin solutions, as explained. 12 A heat-cool cycle included a 35 min incubation at</p><!><p>500 µL of ice-cold 36±2 mg/mL tubulin solution was injected into a Superdex TM 200 Increase 10/300 GL size-exclusion chromatography (SEC) column at 6 • C. The running buffer was BRB80, supplemented with 1 mM GTP, at a flow rate of 0.5 mL/min. The 1 mL fraction with the highest eluted tubulin concentration (between 5 and 6 mg/mL) was collected and used for the experiments. This tubulin was free of residual glycerol. We have recently published a detailed SAXS analysis of the entire SEC elution profile, using an in-line SEC-SAXS setup. 43 We showed that the fraction of the highest tubulin concentration contained mostly dimers in coexistence with 1D curved oligomers (mainly tetramers and hexamers).</p><!><p>We exchanged the buffer of the tubulin solution using a microcentrifuge column (Micro Bio-Spin TM P-6 Gel column, Bio-Rad) and a 5810 R Eppendorf centrifuge, at 4 • C. This SEC column adsorbs from the applied solution 99% (under our conditions) of the compounds whose molecular weight is under 6 kD 1 .</p><p>Each new column was reconditioned to BRB80 by adding 500 µL BRB80, spinning down at 1000 g for 1 min. This process was repeated four times, followed by a final spin at 1000 g for 3 min to remove any excess buffer.</p><p>Between 20 and 50 µL tubulin solution was then added to the column and spun at 1000 g for 4 min. The eluted tubulin solution maintained its initial volume whereas 99% of the free (unbound) nucleotides were removed 2 . The buffer of the eluted tubulin solution was then exchanged again (using a reconditioned column), attaining an overall free nucleotide dilution factor of 10 4 .</p><!><p>Tubulin-bound nucleotides were extracted by denaturing and precipitating the protein, using a modified version of a published protocol. 50 Samples were placed on ice to quench GTP hydrolysis. Ice-cold 70% w/w aqueous perchloric acid (HClO 4 ) solution was then added at a final concentration of 0.5 M. A byproduct of the HClO 4 addition was salt sedimentation, also observed in tubulin-free control samples. When tubulin was present, the HClO 4 immediately denatured the protein 3 . For complete precipitation, the samples were incubated on ice for 10 min. The precipitants (denatured tubulin and salt) were then removed by centrifugation at 4 • C for 10 min at 14, 000 g. The top 60% of the initial total solution volume was buffered by adding an ice-cold solution of 1 M K 2 HPO 4 and 0.5 M acetic acid, whose volume was 10% of the initial solution volume. The perchloric acid was then neutralized by adding a similar volume of ice-cold 3 M KOH solution. These additions led to additional salt sedimentation. 1 The small compounds are retained in the beads of the column, made of polyacrylamide gel (Bio-Gel P-6).</p><p>2 At this stage, no more than 0.5% of the nucleotides dissociated from the tubulin dimer into the buffer (based on the values of K 1 -K 4 , see below). 3 The HClO 4 led to tubulin aggregation on the tip of the pipette used for adding the acid and prevented mixing of the solution by pipetting up and down. In the absence of protein, we verified that the fact that we did not mix the solutions did not change the results.</p><p>The samples were then stored at −20 • C.</p><!><p>Reverse-phase ion-pair high performance liquid chromatography (HPLC) analysis was performed at 25 • C using a Waters Alliance e2695 Separation Module (Waters Corporation, Milford, USA), equipped with a 2489 UV-Vis detector that recorded the absorbance at 260 nm.</p><p>Following a published protocol, 50 the HPLC column was Supelcosil TM LC-18-DB, which was 25 cm long, had an internal diameter of 4.6 mm, and packed with 5 µm particles. The HPLC mobile phase contained 0.2 M K 2 HPO 4 , 0.1 M acetic acid, and 4 mM tetrabutylammonium phosphate, at pH 6.7. At this pH, all the measured nucleotide species were charged (GTP, GDP, guanosine monophosphate (GMP), and ATP had a negative charge of 4, 3, 2 and 4 e, respectively). 51 The mobile phase was filtered using Millex-GV syringe filter (Polyvinylidene fluoride (PVDF) membrane, 33 mm in diameter, and pore size of 0.22 µm). A flow-rate of 1 mL/min was used, unless otherwise is indicated. The column was equilibrated by flowing at least 40 mL of the filtered mobile phase.</p><p>Before HPLC analysis, frozen samples were thawed and centrifuged at 4 • C for 10 min at 20, 800 g. The top 60% or less of the initial volume was diluted with the HPLC elution buffer to reach between 10 and 60 µM total nucleotide concentration. This range was selected to ensure good separation between the peaks at the HPLC elution profile, avoid saturation of the UV-Vis detector, and be sensitive to the nucleotide content in our lowest tubulin concentration (1 mg/mL).</p><p>A typical purified tubulin concentration of 36 mg/mL (0.31 mM, using a tubulin dimer molar mass of 116 kDa) had a bound nucleotide concentration of 0.62 mM (assuming that two nucleotides were bound to each dimer). Addition of 0.5 M HClO 4 , 1 M K 2 HPO 4 , 0.5 M acetic acid, and 3 M KOH diluted the nucleotide concentration to 0.45 mM. To be within the optimal HPLC working conditions, the sample was ten-fold diluted by the HPLC mobile phase to 45 µM, before it was injected into the HPLC.</p><p>Each HPLC experiment included calibration samples of mixed GTP, GDP, and GMP, dissolved in the HPLC mobile phase, filtered using PVDF membrane syringe filters, 13 mm in diameter and pore size of 0.2 µm (mdi Membrane Technologies, Inc.). Figure 2 shows the elution profiles of a mixture of GTP, GDP, GMP, ATP, and guanosine (Gu). This mixture included the compounds of the calibration sample. The ATP elution peak appeared at 14.5 ± 0.1 mL (or 14.5 ± 0.1 min, as the flow rate was 1 mL/min) and was disregarded in our analyses (Figure 2). The column dead volume was 3.6 ± 0.1 mL (regardless of the injected sample).</p><p>When more than 9 samples were measured sequentially, the HPLC tubing and pumps were wet-primed, using 40 mL water, followed by 20 mL of the HPLC mobile phase (using a flow rate of 4 mL/min). The column was then equilibrated by flowing 15 mL of the mobile phase at a flow rate of 1 mL/min. A calibration sample was then measured.</p><p>The HPLC peak area measurements were extremely precise, as can be seen by the error bars of Figure S1. Nevertheless, temperature variations of up to 5 • C between successive measurements could shift the position of the eluted peaks by 0.3 mL or less (Figure S3). An equilibration time of 25 min, could shift the position of the peaks by 5 mL or less (Figure S4). Prior to each set of measurements, the column was equilibrated with at least 40 mL of the filtered mobile phase at a flow rate of 1 mL/min (i.e an equilibration time of 40 min).</p><!><p>To determine the total (tubulin-bound and unbound) GTP to GDP molar ratio (in either tubulin or tubulin-free solutions), the Nucleotide Extraction by Protein Precipitation protocol was applied, followed by HPLC Analysis.</p><p>The GTP to GDP molar ratio was determined by numerical integration of the GDP-and GTP-peak areas (A GDP and A GTP ) in the elution chromatograms (absorbance at 260 nm as  a function of elution volume). As the extinction coefficients of GDP and GTP are similar at 260 nm, 12 the GTP to GDP molar ratio,</p><p>was measured before applying the Nucleotide Extraction by Protein Precipitation protocol, by UV-vis, as described. 12 As the hydrolysis was slow, the measurements were more sensitive to the accumulation of GDP, given by</p><!><p>To isolate the tubulin-bound nucleotides from the free nucleotides, we applied the Buffer Exchange protocol into BRB80. The tubulin-bound GTP to GDP Molar Ratio was then determined and the GTP and GDP mole fractions at the E-site were calculated, assuming the nucleotide at the N-site was always GTP.</p><p>To determine the GTP to GDP molar ratio in the buffer, we collected the first 500 µL of BRB80, from the first Buffer Exchange (out of two), applied to the tubulin sample. Based on UV-Vis measurements, about 60% of the free (unbound) nucleotides were eluted into the buffer. Depending on the volume of the loaded tubulin sample, the nucleotide concentration in the eluted buffer was 20-to 40-fold diluted. We then took an aliquot of 100 µL (out of the 500 µL) and determined its GTP to GDP Molar Ratio.</p><!><p>Synchrotron small-angle X-ray scattering (SAXS) experiments were performed as explained 6 at ID02 beamline at ESRF (Grenoble) 52 or P12 EMBL beamline in PETRA III at DESY (Hamburg). 53</p><!><p>Transmission electron microscopy at cryogenic temperatures (cryo-TEM) was used to image our samples, using a Tecnai G2 Spirit Twin T-12 TEM (FEI Co.), operated at 120 kV in a low-dose mode, as explained. 6 Images were recorded on a 4 K × 4 K FEI Eagle CCD camera in defocus value that varied between 2 and 4 µm.</p><!><p>Tubulin Activity Following Heat-Cool Cycles</p><p>Cryo-TEM and solution SAXS measurements verified that our tubulin retained its activity and was able to form MTs to a similar extent before and after seven heat-cool cycles (Figure 3). This result is in agreement with an earlier report. 54</p><!><p>The molar ratio between GTP, GDP, and GMP nucleotides was determined in the purchased GTP, GDP, and GMP powders (Figure S5). The powders were dissolved in the HPLC mobile phase, filtered through PVDF membrane syringe filters, and injected into the HPLC.</p><p>As was previously noted, 39,50 impurity traces of GTP, GDP, and GMP, are shown in Figures S1 and S5, and summarized in Table 1.   at −20 • C as well as the initial nucleotide concentration did not change the GTP to GDP molar ratio (Figure S1).</p><!><p>The molar ratio of tubulin-bound GTP to tubulin-bound GDP (and the corresponding molar ratio at the tubulin E-site) was measured for several GTP-and GDP-tubulin preparation protocols (Table 2). The result after incubation with 10 mM GTP was similar to previously published data, 55 in which the GTP-tubulin complex was isolated by chromatography after incubation in 0.5 mM GTP. The GTP in the earlier experiments, 55 however, was 99% pure, unlike our GTP that was only 96% pure (Table 1).</p><p>Seven heat-cool cycles resulted in tubulin-bound GTP to GDP molar ratio similar to tubulin that was incubated in a BRB80 buffer, supplemented with 10 mM GDP. We attribute the residual (6%) tubulin-bound GTP in the sample, incubated in 10 mM GDP (Table 2), to the 0.5 ± 0.1 mM GTP in the purified tubulin sample, and to the GTP/GDP tubulin exchange reaction (Reaction 1). GDP was not added to the samples to which seven heat-cool cycles were applied. The tubulin-bound GTP (after the purification), was hydrolyzed in each cycle when the samples were incubated at 36 • C, during which spontaneous tubulin nucleation and MT assembly took place. The nucleation and assembly rates, however, decreased as the number of cycles proceeded because the GTP to GDP molar ratio of both tubulin-bound and tubulin-free nucleotides decreased (Table 2). 21 As a result, during the last cycle or two, when the GTP to GDP molar ratio was low, the rates of nucleation and assembly were slower than the 35 min incubation period at 36 • C.</p><!><p>We examined the rate of GTP hydrolysis, GTP</p><p>where k h is the hydrolysis rate constant. In the absence of tubulin, no hydrolysis was detected in the MT assembly buffer, unless the temperature was raised to 36 • C (Figure 4). At 36 • C, the hydrolysis reaction was fitted to a pseudo-first-order kinetics with a k h of 7.5 ± 0.3 × 10 −8 s −1 . This implies that hydrolysis of tubulin-free GTP (i.e., GTP that is not bound to tubulin) was extremely slow and can be neglected in tubulin assembly kinetics experiments.</p><!><p>Tubulin, eluted from SEC in glycerol-free assembly buffer, did not hydrolyze GTP under conditions that did not allow spontaneous tubulin nucleation and MT assembly (Figure 5). Under these conditions, our earlier cryo-TEM and SAXS measurements revealed that tubulin dimers coexist with dimers that self-associate head-to-tail into 1D curved oligomers, terminated by the formation of tubulin single rings, and the solutions are free of larger tubulin aggregates. 12,14,43 Our hydrolysis data therefore suggest that GTP hydrolysis was not involved in the formation of 1D oligomers and single rings. I n c u b a t i o n t i m e ( h )</p><p>Figure 4: GTP hydrolysis kinetics in the absence of tubulin. Solutions of 4 mM GTP in BRB80 were incubated at different temperatures, as indicated. The GTP to GDP molar ratio was measured as a function of time. The logarithm of the ratio between the GTP concentration at any time t ([GTP] t ) and the initial GTP concentration, ([GTP] 0 ), is plotted as a function of the incubation time (at time zero, the solution contained 0.2 mM GDP impurity, based on Table 1). Assuming a pseudo-first-order hydrolysis kinetics at 36 • C (solid red diamonds), the slope of the broken red line corresponds to a rate constant, k h , of 7.5 ± 0.3 × 10 −8 s −1 . The horizontal broken black line is a guide for the eye, indicating the initial state of the solutions (Table S3).</p><p>glycerol-supplemented assembly buffer, under conditions that did not allow spontaneous MT assembly. 21 The hydrolysis was associated with the formation of tubulin oligomers. Whereas glycerol does not alter the MT lattice structure, 56 the MT assembly rate, and consequently GTP hydrolysis rate, increase dramatically in the presence of glycerol. 57,58 This increase was previously attributed to the preferential hydration of tubulin in the presence of glycerol, which is excluded from the dimer. When glycerol is added, the standard chemical potentials of a free tubulin-dimer and a tubulin-dimer inside the MT lattice are both higher than the corresponding standard chemical potentials in the equivalent glycerol-free assembly buffer. In the presence of glycerol, however, the difference between the chemical potentials of the dimer in the free and the polymer states is larger. The greater stabilization of the MT polymer was attributed to the smaller excluded volume of glycerol in the assembled state. 59,60 It was also reported that tubulin aggregates are present in significant amounts in highmolarity glycerol assembly buffers. The GTP hydrolysis rate-constant in the presence of the aggregates is similar to that in the presence of MT. 57 It is therefore likely that in the presence of glycerol, under conditions that do not allow spontaneous MT assembly, tubulin aggregates, rather than tubulin oligomers, were involved in the hydrolysis of GTP. 21</p><!><p>Above the critical conditions for MT assembly, glycerol increases the rate of MT assembly and slows disassembly. 57 Hence, to examine the GTPase activity of tubulin dimers in assembly buffer solution, free of glycerol and tubulin aggregates, we analyzed the hydrolysis of GTP using tubulin that was eluted from SEC. We showed that SEC eluted cold (∼ 10 • C) tubulin contains only dimers and a small fraction of short 1D oligomers (tetramers and hexamers). 14,43 Larger tubulin assemblies, which were eluted at lower volumes 14,43 and could facilitate GTP hydrolysis, 21 were also excluded from our experiments.</p><p>Unlike an earlier study, performed in the presence of glycerol, 21 glycerol-free SEC eluted T i m e ( m i n ) was plotted as a function of the incubation time and an effective pseudo-first-order hydrolysis rate constant of k eff = 1.27±0.02×10 −6 s −1 was fitted to the data (broken line). The horizontal solid black line is a guide for the eye, indicating the initial state of each solution, before the temperature change (Table S4). tubulin did not hydrolyze GTP below the critical conditions for MT assembly (Figure 5). GTP hydrolysis was detected only at conditions that permitted spontaneous non-templated MT assembly (Figure 5). Under typical assembly conditions, after a few minutes of assembly, MT assembles and exhibits a complex dynamic instability behavior. 1,34,42,[61][62][63][64] However, in our glycerol-free SEC eluted tubulin concentrations, time-resolved SAXS data with subsecond temporal resolution and cryo-TEM images revealed that MT assembly was very slow and took about an 1 h). 14 Under those conditions, a pseudo-first-order kinetics: 57</p><p>with an effective GTP hydrolysis rate-constant, k eff , of 1.27±0.02×10 −6 s −1 , could adequately fit our data (Figure 5).</p><p>[GTP] t is the total GTP concentration (both tubulin-free and tubulinbound) at time t and [GTP] 0 is the initial total GTP concentration.</p><p>The slow rate of GTP hydrolysis is consistent with the slow rate of MT assembly. 14 GTP hydrolysis occurs mainly on the MT lattice; hence the hydrolysis was limited by the rate of MT assembly. 14,19 To accurately determine the mass fraction of SEC eluted tubulin that assembled into MT, we analyzed SAXS and cryo-TEM data after ∼ 1 h of assembly, as explained. 49 Unlike typical 350 nm adsorption measurements, 57 in this analysis, the scattering signal was decomposed, and the MT contribution was clearly distinguished from the contributions of tubulin dimers and other tubulin assemblies (Figure 6). The analysis revealed that after ∼ 1 h incubation at 36 • C, under our conditions, less than ∼ 30% (i.e. ∼ 20 µM)</p><p>of the SEC eluted tubulin self-assembled into MT and small intermediates.</p><p>After 1 h incubation at 36 • C, about 30 µM GTP was hydrolyzed (Figure 5). The amount of tubulin in the MT polymer state was lower than the total GTP hydrolysis owing to MT disassembly and reassembly, associated with MT dynamic instability. 62 k eff was fitted to data taken over a period of about 10 h, during which 160 µM GTP was hydrolyzed (about three times the total tubulin concentration). We measured for such a long time because under our  Azimuthally integrated background-subtracted solution SAXS curve in absolute intensity units from (A.) 6 mg • mL −1 SEC eluted cold (∼ 5 • C) tubulin solution, supplemented with 4 mM GTP, following ∼ 1 h incubation at 36 • C (open square symbols). The solid green curve is a linear combination of the measured SAXS curve from the same SEC eluted cold tubulin solution prior to the temperature change (B.), the measured SAXS curve from 36 mg • mL −1 tubulin (not eluted from SEC), supplemented with 4 mM GTP, after ∼ 1 h incubation at 36 • C (C.), and the computed solution SAXS curve (using X+ program 65 ) from a model of uniform spheres with a radius of 15 ± 3 nm (D.). The last curve is approximating the contribution of intermediate structures on the assembly path from dimer to microtubule. The insets show the cryo-TEM images of the corresponding states. Scale bars equal 100 nm. The best fit in A. was obtained when the molar fraction of the SEC eluted cold tubulin was 0.713. SAXS measurements were performed at ID02 beamline, at ESRF (Grenoble). 52 21 conditions the rate of hydrolysis was slow, reflecting the overall integrated rate of assembly and dynamic instability.</p><p>In the presence of SEC eluted tubulin (Figure 5), the effective hydrolysis rate was about 20-fold faster than in the absence of tubulin (Figure 4). In the presence of glycerol and with tubulin that was not eluted from SEC, the hydrolysis rate was much faster (4 × 10 −3 s −1 ). 19 In the absence of free nucleotides, nucleotide exchange reaction does not occur. Under those conditions, the GTP hydrolysis rates on a polymerized GTP-tubulin subunit, during the prenucleation phase (containing tubulin oligomers), interacting with a GTP-bound (homologous) or a GDP-bound tubulin (heterologous) neighbor were reported to be 3.8 × 10 −4 s −1 and 1.3 × 10 −3 s −1 , respectively. 21 It has been previously shown that the rate of GTP hydrolysis per MT is maximal (∼ 40 s −1 ) during MT elongation (when the tubulin concentration is well above the critical tubulin concentration for MT elongation, ∼ 1 mg/mL). 38 This measurement was done by adding preassembled MT seeds to tubulin solutions at increasing concentrations. 38 At higher tubulin concentrations, the MT cap is about an order of magnitude larger than when the tubulin concentration is close to the critical concentration (where the cap is about ten dimers). 38,66,67 Low Mg 2+ concentrations and/or high GDP concentration decrease MT assembly and consequently the rate of GTP hydrolysis. 25,68,69 Tubulin-Bound Nucleotide Exchange Reaction</p><p>Apart from GTP hydrolysis, the composition of tubulin-bound nucleotides can be varied by an exchange reaction between tubulin-bound and tubulin-free nucleotides. To investigate only the exchange reaction, we used conditions at which GTP hydrolysis was negligible.</p><p>Tubulin samples were buffer exchanged to BRB80, containing either 4 mM GTP, 2 mM GTP and 2 mM GDP, or 4 mM GDP, and incubated on ice for ∼ 2 h. We then simultaneously measured the tubulin-bound GTP to GDP molar ratio and the tubulin-free GDP to GTP molar ratio, [GDP/GTP] 0 (Figure 7, open circle symbols). The tubulin-free nucleotides could be either bound to Mg 2+ ions or Mg 2+ -free. In a separate set of experiments, the tubulin solutions were eluted from SEC in BRB80, supplemented with 1 mM GTP. Nucleotides were then added to attain the final nucleotide composition. The measured mole fraction of GDPtubulin out of the total tubulin concentration, X GDP−tubulin , was plotted as a function of</p><p>[GDP/GTP] 0 (Figure 7, solid squares, and Figure S7).</p><!><p>Initially, the data were fitted to the following set of coupled equilibrium reactions (Figure S7), suggested in an earlier study.</p><p>where 'tub' corresponds to tubulin whose E-site is nucleotide-free. tub -GTP and tub -GDP correspond to tubulin whose E-site is bound only to GTP or GDP, respectively. As the nucleotides may complex with Mg 2+ ions, the tub -GTP/GDP complexes could further bind a Mg 2+ ion, leading to tub -GDP/GTP -Mg 2+ complexes. We ignored the additional Mg 2+</p><p>binding sites on the tubulin dimer (mainly at the carboxyl-terminal of both monomers 40 ), owing to their relatively weak binding constants ( ≈ 100 M −1 ). 40,45 K 2 , K 5 , K 6 , and K 9 were taken from earlier measurements. 40,70 K 7 and K 8 were computed from the other equilibrium constants</p><p>K 3 and K 4 were kept within the error range of the earlier study (performed at 0 • C in 100 mM PIPES buffer at pH 6.9). 40 Hence, practically, only K 1 was fitted to the data.</p><p>In Figure S7, the measured X GDP−tubulin as a function of [GDP/GTP] 0 , was fitted (using Equation S31) to reactions 3-11, excluding the contribution of tubulin self-association, assuming all of the tubulin dimers similarly reacted with the nucleotides and Mg 2+ ions. The fit was obtained by solving Equation Sets S29 and S30, using the algorithm described in Excluding the Difference Between Tubulin Dimers With Exposed and Buried E-Sites section of the Supporting Information (SI). The best fitted equilibrium constants are provided in Table 3. The fit to the data was weakly sensitive to the value of K 1 .</p><p>Analyzing the Exchange Reaction Including the Contribution of Tubulin Self-</p><!><p>In Figure S7, the fitted curves captured the general trend of the data set but missed the effect of tubulin concentration, observed even under excess GTP or excess GDP. At a fixed</p><p>[GDP/GTP] 0 , the measured X GDP−tubulin increased with tubulin concentration, most likely, owing to the enhanced oligomerization of tubulin. 14,43 Below the critical MT assembly conditions, GTP-and GDP-tubulin rapidly assemble into small 1D assemblies, described by a thermodynamic model of isodesmic tubulin self-association, terminated by the formation of tubulin single-rings. 21,43 Time-resolved SAXS data with msec temporal resolution reveal that when changing the tubulin concentration or the nucleotide composition, equilibrium is attained within few seconds. 14 Nevertheless, assembly and disassembly dynamics below the SAXS detection limit, cannot be excluded. The observed increase in the mole fraction of tubulin, buried in small assemblies, when increasing the total tubulin concentration and</p><p>[GDP/GTP] 0 , is therefore consistent with the stronger self-association standard free-energy of GDP-tubulin compared with GTP-tubulin. 12,14,21 In GDP-rich tubulin assemblies (1D curved oligomers and rings), the E-site is somewhat covered by the neighboring α-tubulin (green monomer and cyan GDP molecule in Figure 1), hence the rate of nucleotide exchange is limited by the rate of oligomer dissociation. 18 In the presence of MT-associated proteins (MAPs), tubulin dimers, incorporated into rings, were previously shown to prohibit nucleotide exchange reactions. 20 A similar block, most likely, occurred (to a lesser extent) also without MAPs and affected the degree of nucleotide exchange. 18 Furthermore, simulations revealed that GTP-tubulin dimers are more flexible than GDP-tubulin dimers. Both dimers, however, were shown to assume a similar average curvature (or angle between monomers). 71 Besides, GTP-tubulin dimers were previously shown to retain their ability to exchange nucleotides while incorporated in a MT lattice. 19 Taken together, these results suggest that tubulin oligomerization may affect nucleotide exchange reaction. We, therefore, propose the following mechanism, illustrated in Figure 8. The E-site of the tubulin dimer can be either exposed to the solution or buried in the interdimer interface (Figure 1) within a tubulin assembly (an assembly of size n has n − 1 buried E-sites and one exposed E-site). We postulate that a nucleotide bound at an exposed E-site may be exchanged more readily than a nucleotide bound at a buried E-site. We should therefore include (in addition to Reactions 3-11, relevant for dimers with exposed E-site), the following set of exchange reactions (relevant for dimers with buried E-site):</p><p>To reduce the number of free parameters from 15 (Table 3) to 5, we did not change the values of K 2 , K 5 , K 6 , and K 9 ; K 3 and K 4 were kept within the error range of the earlier fit (and the earlier study); 40 K 7 and K 8 were calculated according to Equation 12; and K 14 and K 15 were computed from the other equilibrium constants, according to:</p><p>In addition, the ratio between the total tubulin concentration with exposed ( tub tot Exposed )</p><p>and buried E-sites ( tub tot Buried ) was determined by applying an isodesmic model of tubulin self-association into single rings and 1D curved oligomers, adopted from earlier publications (summarized in Thermodynamic Model of Tubulin Self-Association into Single Rings and Curved 1D Oligomers section in the SI). 12,14,21,[43][44][45] We have also assumed that the standard Helmholtz dimer-dimer association free energy per longitudinal contact, ∆F • c , and for closing a curved oligomer into a ring, ∆F • RC , vary with [GDP/GTP] 0 (as shown in Figure S6 and explained in section Standard Helmholtz Association Free Energies in the SI). Furthermore, we assumed that 10 % of the tubulin dimers formed stable rings when prepared according to the Buffer Exchange protocol. 12,14,43 In Figure 7, X GDP−tubulin is plotted as a function of [GDP/GTP] 0 and the data were fitted (using Equation S45) to reactions 3-11 and 13-18, by solving Equation Sets S43 and S44, which take into account the difference between tubulin dimers with exposed and buried E-sites (Including the Difference Between Tubulin Dimers with Exposed and Buried E-sites section in the SI). The resulting equilibrium constants are presented in Table 3, based on which the mole fractions of all the species in each of the solutions were computed and plotted as a function of [GDP/GTP] 0 (Figures S8 -S20). Based on the data in Figures 7, S12, and S13, we computed the equilibrium constants of the GDP to GTP exchange reaction on buried</p><p>and exposed</p><p>tubulin dimers at 1 and 36 mg • mL −1 as a function of [GDP/GTP] 0 (Figure 9). The analysis reveals that K B eq and K Ex eq were essentially independent of tubulin concentration but K Ex eq is an order of magnitude greater than K B eq . When computing K eq based on the total GTP-and GDP-tubulin concentrations, we find a strong dependence on tubulin concentration, suggesting that the simple reaction mechanism in Equation 1 is insufficient. The separation to K Ex eq and K B eq is sufficient to diminish the relevant (exposed or buried) tubulin concentration dependence. The equilibrium constants, however, are still weakly dependent on [GDP/GTP] 0 , suggesting that our proposed detailed exchange reaction mechanism is yet incomplete.</p><p>Figure 10 illustrates the computed equilibrium state of a 6 mg/mL tubulin solution with</p><p>[GDP/GTP] 0 = 1, where the model in Figure 7 fits the data well. The suggested reaction mechanism, however, misses the data at high [GDP/GTP] 0 values at low tubulin concentrations, indicating that the proposed mechanism is incomplete.</p><p>Mg 2+ Ions Associated with Tubulin Primarily Via Their Initial Association With</p><!><p>The values of K 5 and K 6 indicate that in the absence of tubulin, Mg 2+ ions bind more readily to GTP than to GDP. When 4 mM GTP are mixed with 1 mM Mg 2+ , about 22% of the GTP complex with Mg 2+ whereas when 4 mM GDP are mixed with 1 mM Mg 2+ , the affinity to Mg 2+ is weaker and only 17% of the GDP complex with Mg 2+ (based on Reactions 7 and 8).</p><p>Figure S16 shows that in the presence of tubulin and in excess GTP, between 80% and 90% of the Mg 2+ ions bind tubulin-free GTP. Most of the remaining Mg 2+ ions are free, and only at high tubulin concentration, about 7% of the Mg 2+ ions bind GTP-tubulin dimers whose E-site is buried in assemblies. In excess GDP, no more than 65% of the Mg 2+ ions bind tubulin-free GDP and most of the remaining Mg 2+ ions remain free. Only at high tubulin concentration, about 4% of the Mg 2+ ions bind GDP-tubulin dimers whose E-site is buried in assemblies. When [GDP/GTP] 0 = 1, the mole fraction of GTP • Mg 2+ is about 3 times larger than the mole fraction of GDP • Mg 2+ . In other words, the stronger affinity of Mg 2+ to GTP is preserved also in the presence of tubulin.</p><p>Figure S11 shows that when excluding the contribution of tubulin self-association, the affinity of Mg 2+ ions to GTP-tubulin is much stronger than its affinity to GDP-tubulin.</p><p>When including the contribution of tubulin self-association, however, the Mg 2+ affinity became weaker, yet still stronger to GTP-tubulin.</p><p>When including the contribution of tubulin self-association, we distinguished between tubulin dimers with buried and exposed E-sites. Figure S13 shows that under excess GTP, about 25% of the GTP-tubulin dimers with buried E-sites (Tub Buried -GTP) bind Mg 2+</p><p>ions. Under excess GDP, no more than 15% of the GDP-tubulin dimers with buried Esites (Tub Buried -GDP) bind Mg 2+ ions. When [GDP/GTP] 0 = 1, the mole fraction of Tub Buried -GTP•Mg 2+ is about 3 times larger than the mole fraction of Tub Buried -GDP•Mg 2+ .</p><p>Figure S12 shows a similar trend for tubulin dimers with exposed E-sites. Taken together, these results show that the binding of Mg 2+ ions to the tubulin-bound nucleotides is weakly affected by the presence of tubulin. In other words, the association of Mg 2+ ions with tubulin is mainly a result of their association with the tubulin-free nucleotides.</p><p>reaction of EGTA with Mg 2+ can be neglected. Using the published equilibrium constant (K 9 = 3.2 M −1 ), 70 in the absence of tubulin and nucleotides, if 1 mM EGTA is mixed with 1 mM Mg 2+ (as in our buffer), the EGTA will chelate only 0.3 % of the Mg 2+ ions. Figure S16 shows that the binding of EGTA to Mg 2+ remains negligible also in the presence of tubulin and nucleotides. In addition, Figures S8 -S14 show that under the conditions of our experiments the mole fraction of nucleotide-free tubulin dimers (tub) is negligible.</p><p>Table 3: The equilibrium constants that best fitted the HPLC data. K 2 ,K 5 , K 6 , and K 9 were adopted from earlier publications.</p><!><p>Our results show that GTP hydrolysis in MT assembly buffer was negligible in the absence of tubulin. We examined the GTPase activity of isolated tubulin dimers in assembly buffer solution, free of glycerol and tubulin aggregates, using SEC eluted dimers. Below the critical conditions for MT assembly, in the presence of excess GTP, GTP hydrolysis was not involved in the formation of tubulin 1D oligomers and single rings. Above the critical conditions for MT assembly, the GTP hydrolysis reaction was fitted to a pseudo-first-order kinetics with an effective rate constant of 1.27 ± 0.02 × 10 −6 s −1 , limited by the rate of tubulin assembly.</p><p>The assembly rate was slower than the rate of GTP hydrolysis in the presence of tubulin that was not eluted from SEC.</p><p>Below the critical conditions for MT assembly, ice-cold tubulin dimers self-associated and a fraction of their nucleotide exchangeable sites (E-site) was buried. The GDP to GTP exchange reaction equilibrium constant was an order of magnitude larger on tubulin dimers with exposed E-sites than on dimers with buried E-sites. Finally, we showed that the association of Mg 2+ ions with tubulin was primarily achieved via their earlier association with the tubulin-free nucleotides. Understanding GTP hydrolysis and nucleotide-exchange reactions is critical for analyzing tubulin self-association, nucleation, and MT assembly dynamics. 14 S30), as a function of the molar ratio between tubulin-free GDP to tubulin-free GTP ([GDP/GTP] 0 , taking into account the nucleotide composition presented in Table 1 ). The tubulin-free nucleotides may be either bound or unbound to Mg 2+ ions (Equations S40 and S41). The reactions were performed at different added nucleotide compositions and total (ice-cold) tubulin concentrations. 1 (green), 6 (red), and 36 mg/mL (black, open circle symbols) tubulin samples underwent Buffer Exchange for BRB80, supplemented with a total nucleotide concentration of 4 mM. In another set of experiments, ice cold tubulin solutions were eluted by SEC in BRB80, supplemented with 1 mM GTP, as described in SEC Protocol. The eluted fraction with the highest tubulin concentration was then diluted with the running buffer to 1 (green), 2 (blue), and 6 mg/mL (red, solid squares), to which nucleotides were added to their final concentrations. The best fitted modeled mole fraction of GDP-tubulin (Equation S45) was computed based on Reactions 3-18, by solving Equation Sets S43 and S44, using the equilibrium constants which accounted for the difference between tubulin with exposed and buried E-sites (Table 3). The best fitted models are presented by curves in the colors of the corresponding data, where SEC elution and buffer exchanged models are presented as solid and broken curves, respectively. The measured HPLC data are provided in Tables S1 and  S2. [ G D P / G T P ] 0 K B e q K e q K E x e q / K B e q</p><!><p>Figure 9: GDP to GTP exchange reaction equilibrium constants for 1 (solid curves) and 36 mg • mL −1 (broken curves) tubulin, as a function of [GDP/GTP] 0 . The equilibrium constants for buried, K B eq , and exposed K Ex eq , dimers were computed using Equations 20 and 21 and the data in Figures S12, S13, S17, and S19). The total equilibrium constant, K eq , was computed using the data in Figure 7 and Equation 1. The ratio between the exposed and buried equilibrium constants is also plotted. , where the model in Figure 7 fits the data well. The box shows the legends of the various participating species. Note that the proportion of GTP, GDP, Mg 2+ , and EGTA molecules, with respect to tubulin subunits, is 100-fold smaller than their actual number in the solution. The cartoon was created using PyMOL. 15</p>