Structure of Dynamic, Taxol-Stabilized, and GMPPCP-Stabilized

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Structure of Dynamic, Taxol-Stabilized, and GMPPCP-Stabilized Microtubule Avi Ginsburg, Asaf Shemesh, Abigail Millgram, Raviv Dharan, Yael Levi-Kalisman, Israel Ringel, and Uri Raviv J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b01057 • Publication Date (Web): 18 Aug 2017 Downloaded from http://pubs.acs.org on August 22, 2017

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The Journal of Physical Chemistry

Structure of Dynamic, Taxol-Stabilized, and GMPPCP-Stabilized Microtubule

Avi Ginsburg,

†, ‡, ¶ , ⊥

Asaf Shemesh,

Levi-Kalisman,

k,¶

†,¶,⊥

Abigail Millgram,

Israel Ringel,

‡, §

†, ¶

Raviv Dharan,

and Uri Raviv

†, §

Yael

∗, †, ¶

†Institute

of Chemistry, The Hebrew University of Jerusalem, Jerusalem, 9190401, Israel

‡Institute

for Drug Research, School of Pharmacy, The Hebrew University of Jerusalem, 9112102, Jerusalem, Israel

¶Center

for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, Jerusalem, 9190401, Israel

§Azrieli kInstitute

College of Engineering, Jerusalem, 9103501, Israel

of Life Sciences, The Hebrew University of Jerusalem, Jerusalem, 9190401, Israel

⊥These

authors contributed equally to this work

E-mail: [email protected] Phone: +972 (2) 6586030. Fax: +972 (2) 5660425

Abstract Microtubule (MT) is made of αβ -tubulin heterodimers that dynamically assemble into a hollow nanotube composed of straight protolaments. MT dynamics is facilitated by hydrolysis of guanosine-5'-triphosphate (GTP) and can be inhibited by either anticancer agents like taxol or by the non-hydrolyzable GTP analogues like GMPPCP. Using high-resolution synchrotron X-ray scattering, we have measured and analyzed the scattering curves from solutions of dynamic MT (in other words, in the presence of excess GTP and free of dynamic-inhibiting agents) and examined the eect of two MT 1

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stabilizers: taxol and GMPPCP. Previously, we have analyzed the structure of dynamic MT by docking the atomic model of tubulin dimer onto a 3-start left handed helical lattice, derived from the PDB ID 3J6F. 3J6F corresponds to MT with 14 protolaments. In this paper, we took into account the possibility of having MT structures containing between 12 and 15 protolaments. MT with 12 protolaments were never observed. We determined the radii, the pitch, and the distribution of protolament number that best t the scattering data from dynamic MT or stabilized MT by taxol or GMPPCP. We found that the protolament number distribution shifted when the MT was stabilized. Taxol increased the mass fraction of MT with 13 protolaments and decreased the mass fraction of MT with 14 protolaments. GMPPCP reduced the mass fraction of MT with 15 protolaments and increased the mass fraction of MT with 14 protolaments. The pitch, however, remained unchanged regardless of whether the

MT was dynamic or stabilized. Higher tubulin concentrations increased the fraction of dynamic MT with 14 protolaments.

Introduction Microtubule (MT) is a protein polymer, made of

αβ -tubulin

heterodimers. Tubulin dimers

dynamically assemble into hollow nanotubes composed of straight protolaments. MT plays an important role in cell division, organelle transport, cell motion, cell shape, and cell stability. Tubulin and MT function requires dynamic assembly and disassembly. MT dynamics is facilitated by the GTPase activity of tubulin, which hydrolyzes guanosine-5'-triphosphate (GTP) into guanosine-5'-diphosphate (GDP) upon MT assembly. Tubulin binds GTP in two dierent sites, an exchangeable (E-site) and a nonexchangeable (N-site) one. whereas

α-tubulin

binds GTP that is buried at the inter-monomer interface (N-site),

β -tubulin binds GTP that is exposed on the surface of the monomer (E-site), and is

hydrolyzed into GDP upon MT polymerization. On MT, the GDP is nonexchangeable.

1

In

solution, however, GDP-tubulin, which is inactive, can be exchanged for GTP, where GTP

2


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binds 3-fold tighter than GDP to the E-site.

2

The hydrolysis of GTP on polymerized tubulin

is a rst order reaction with a rate constant of polymerization rate (that may be faster). Tubulin dimer, whose

β -tubulin

≈ 0.25 min−1

and is uncoupled to the MT

1

has GTP at the E-site (GTP-tubulin) can promote and

initiate straight protolament and MT assembly.

3,4

Tubulin dimer, whose

GDP (GDP-tubulin) is under conformational tension when in MT

3,5

β -tubulin

has

and can promote MT

disassembly. In its unbound relaxed-state, GDP tubulin dimer assumes a straight conformation, however, neighboring GDP-tubulin dimers assume an angle of promote the assembly of GDP-tubulin rings.

10° to 15° between them 6

and can

3,7

MT dynamics can be inhibited by anticancer agents like paclitaxel (taxol) or by the slowly hydrolyzable GTP analogue GMPCPP or the non-hydrolyzable GTP analogue GMPPCP. High-resolution cryo transmission electron microscopy (cryo-TEM) structures of dynamic MT (in other words, in the presence of excess GTP and free of MT stabilizers) and MT stabilized by taxol or GMPCPP, were published.

5,8

In these studies MT with

14

protol-

aments was analyzed, although the possibility of having GMPCPP stabilized MT with protolament was indicated.

5

It is also known that the distribution of MT protolament

number vary with experimental conditions. In our earlier publication,

13

17

916

high-resolution synchrotron X-ray scattering from solution

of dynamic MT was measured. We then computed the expected scattering curve in solution, based on cryo-TEM data, which describe an atomic model of MT with

14

protolaments.

5

In this paper, we measured again the scattering from dynamic MT, using dierent MT preparations and synchrotron facilities, and examined the eects of taxol and GMPPCP. In our earlier work,

17

we have analyzed the structure of dynamic MT in the presence of

excess (4 mM) GTP by docking the atomic model of tubulin dimer onto a helical lattice

18

3-start left handed

where the atomic dimer model, the pitch ( 12.195 nm), the radius to the

geometric center of the dimer atomic coordinates ( 11.94 nm), and dimer orientations were

3



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derived from the PDB ID 3J6F 3J6F corresponds to MT with

5

Page 4 of 30

(see the second section in the Supporting Information, SI).

14

protolaments.

Here, we extended our earlier analysis

and took into account the possibility of having MT structures containing between

15

12

and

protolaments. We determined the radii, the pitch, and the distribution of protolament

number that best t the scattering data from dynamic MT or from MT that was stabilized by taxol or GMPPCP.

Results and discussion MT coexists with tubulin dimers and other small tubulin assemblies.

To better analyze

solution X-ray scattering data from solutions of MT, we tried to separate between the contributions of MT and the other coexisting tubulin assemblies. The MT is much larger than the other small tubulin assemblies and therefore precipitated by centrifugation. The other smaller assemblies are likely to stay at the supernatant. Therefore, after measuring the MT solutions we centrifuged the solutions. We then measured the supernatant and subtracted its scattering curve from the scattering curve of the MT solution. To characterize the MT solution and its supernatant, Cryo TEM imaging (Figures 1 - 3 and Figures S1 - S6) of each of the MT solutions and its corresponding supernatant was performed under the conditions used in our solution X-ray scattering measurements (Figures 4 and S7). Dynamic MT solution was obtained by polymerizing

4 mM GTP as explained in the Experimental section.

0.2 mM

tubulin in the presence of

Cryo-TEM studies of dynamic MT are

shown in Figure 1. Both MT and small globular tubulin structures were observed (Figure 1A). To separate between the MT and the small globular structures, the MT solution was centrifuged and the supernatant was collected. Figure 1B shows a cryo-TEM image of the supernatant.

As can be seen, the MT was separated from the small globular assemblies,

which remained in the supernatant.

As a control, solution of the BRB80 buer was also

studied (Figure 1C). No features were observed in the buer solution. Tubulin dimers and

4


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small assemblies were also observed in a solution of tubulin at Taxol-stabilized MT was obtained by adding

0.2 mM

4 ◦C

(Figure 1D).

taxol to the dynamic MT solution

at the steady-state phase of the GTP-polymerization process.

Figure 2A shows an image

of taxol-stabilized MT solution, which contains MT and globular assemblies.

An image

of the supernatant is shown in Figure 2B. The image shows a lower amount of globular assemblies compared with the dynamic MT sample (Figure 1), owing to the lower critical tubulin concentration in the presence of Taxol. GMPPCP-stabilized MT was obtained by polymerizing tubulin when replacing the GTP for

4 mM

4 mM

GMPPCP. When the same centrifugation protocol was applied to the GMP-

PCP stabilized MT solution (Figure 3), the supernatant contained a signicant amount of globular tubulin assemblies a side to a low concentration of MT. Figures S1 - S6 show additional images of the three MT solutions and their corresponding supernatant. High-resolution synchrotron X-ray scattering from solutions of dynamic MT, GMPPCPstabilized MT, and taxol-stabilized MT were measured. The solutions were then centrifuged and the supernatant of each sample as well as its buer were measured. The images were azimuthally integrated and the resulting Figure 4.

1D

2D

scattering

scattering curves are shown in

The scattering curves of the three supernatant solutions were consistent with

the cryo-TEM images, showing very low signal when taxol was added and much stronger scattering in the presence of GMPPCP. By subtracting the supernatant signal from the MT solution signal, the contribution from the coexisting small globular tubulin assemblies was minimized. In the case of GMPPCP, however, we attribute the higher scattering intensity to low MT concentration that remained in the supernatant. The reason for this is likely to be associated with the slower assembly kinetic in the presence of GMPCPP,

19,20

as demonstrated in Figure S8, under our

experimental conditions. After centrifugation was applied, MT polymerization could have continued in the supernatant from free tubulin or smaller tubulin assemblies that did not precipitate.

5



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In the presence of taxol, the critical tubulin concentration, which can lead to MT assembly, is between

0

and

2 µM

(compared with ca.

30 µM

for dynamic GTP-tubulin).

21,22

Hence, the supernatant was very similar to the buer (Figure 4, green broken curve). The dynamic and GMPPCP-stabilized MT supernatants contained higher tubulin concentrations and larger mass fractions of small tubulin assemblies. As a result, their supernatant scattering curves had a much higher intensity (Figures 4 and S7). Figure 5 presents the supernatant-subtracted scattering intensity curves from dynamic MT and stabilized MT and the computed scattering curves based on atomic MT models. The data and models had features up to

q

between

5

and

7 nm−1 ,

shown at the inset of

Figure 5A. The red, blue, and green curves in Figure 5A are the best computed scattering curves based on a wighted least-square t to a linear combination of three atomic MT models containing

16

tubulin dimers along the long MT axis with dierent protolament number

(Eq. 7). In addition, the models took into account the following possibilities. Our cryo-TEM images show that there were small globular tubulin assemblies that coexisted with the MT structures. The globular assemblies remained in the supernatant but some may have also pelleted together with the MT structures. We have therefore considered the possibility of having dierent concentrations of coexisting small globular tubulin assemblies or tubulin dimers in the MT solutions and in their corresponding supernatant solutions. The contribution of the small globular tubulin assemblies was obtained by subtracting the buer scattering curve from its corresponding supernatant curve (Figure S7A). Small tubulin assemblies and tubulin dimers contributions were obtained from buer-subtracted scattering curve from cold tubulin solution (Figure S7B and Figure 1D). In addition, the relevant tubulin dimer atomic form-factor model (Figure S7B) was also taken into account. To account for dierent options of tubulin dimer and/or globular tubulin assemblies concentration dierences between the supernatant and MT solution, both positive and negative scale prefactors were allowed to multiply those scattering curves. The MT models, however, were only

6


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allowed to assume non-negative contributions. As the total concentration of tubulin was xed, taking into account the contribution of tubulin dimer and small globular tubulin assemblies revealed the correct contribution of MT structures to the data in Figure 5.

Figure 6 illustrates the computed atomic MT models

that eventually contributed to modeling the scattering curves in Figure 5. In the red curves in Figure 5, which were tted to the GTP, taxol, and GMPPCP data, the dimer atomic model and the

3-start

helical pitch,

P,

values (12.21,

12.48,

and

12.48 nm)

were derived from the cryo-TEM PDB IDs 3J6F, 3J6G, and 3J6E, respectively.

5

In both

the blue and the green curves the helical pitch remained the same as in the dynamic MT structure (12.21 nm). In the blue curves the dimer atomic model was computed from 3J6F. In the green curves, the dimer atomic models were taken from 3J6G (for the taxol data) or 3J6E (for the GMPPCP data). All the models were convolved (Eq. 6) with a Gaussian instrument resolution function with standard deviation,

σq ,

of

0.01 nm−1

(Eq. 5). The mass

fraction distributions as a function of MT protolament number are shown in Figure 5B, C, and D. The normalized mass fraction distributions that best tted the data (red curve for the GTP data, green curve for the taxol data, and blue curve for the GMPPCP data) are shown in Figure 5D. In Figure S9 the analysis of Figure 5 was repeated, however, upper limit of

0.02 nm−1

σq

was set to our estimated

(see Experimental section). The measurements in Figure 5 were

repeated at ESRF an Lund Synchrotrons and were analyzed in Figure S10. Figure 7A compares between the computed scattering curves containing multiple population MT models ( 13, 14, and

15 protolaments), which best tted the data in Figure 5 and

the corresponding single population MT model with

14

protolaments. Figure 7B shows a

similar comparison for the corresponding data and models of Figure S9. At high curves were very similar. At low

q

all the

q , however, the models that contained multiple populations

signicantly improved the t to the data. When

σq

was set to the upper limit of

0.02 nm−1 ,

the dierences were smaller. In the case of dynamic MT and GMPPCP-stabilized MT the

7


14


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protolament model had a more dominant contribution to the total scattering signal. This result is consistent with the fact that the supernatant curves were closer to the minima of the scattering curves of dynamic and GMPPCP MT solutions (Figure 4), suggesting that each solution was dominated by a narrower distribution of MT structures. Our data and analysis show that under the conditions of our experiments, the pitch remained at

12.21 nm regardless of whether the MT was stabilized (either by GMPPCP or by

taxol) or not (in the presence of excess GTP). Furthermore, the number of MT protolaments did not change the pitch. This result is in agreement with the published dynamic MT cryoTEM data but slightly dierent than the published cryo-TEM results for stabilized MT.

5

In

the published cryo-TEM data a slightly larger pitch was obtained for taxol or GMPPCPstabilized MT ( 12.48 nm). This dierence, however, is well below the cryo-TEM resolution limit, which was ca.

0.4 nm. 5

The solution X-ray scattering data were more sensitive to the

size of the pitch. This sensitivity can be realized from the arrows in Figures 5 and S9 that show the deviations of the data from the models with the pitch that was derived from cryoTEM data of taxol- or GMPPCP-stabilized MT.

5

The arrows are located next to the local

maxima of the Bessel function of the rst kind resulting from the helical form factor of the MT structure.

2326

The red curves next to the taxol and GMPPCP-stabilized MT scattering

data were computed with a pitch of

q ≈ 1.5 nm−1

and

q ≈ 3.5 nm−1

12.48 nm.

The oscillations of the red curve between

(see arrows in Figures 5 and S9) are shifted from the data.

The green and blue curves were computed with the pitch of the dynamic MT ( 12.21 nm) and they better t the oscillations of the scattering data. The high similarity between the green and blue curves suggests that the exact atomic model (PDB ID 3JGF in the blue curves and 3J6G or 3J6E in the green curves) had little eect on the computed signal within our

q -range. The main dierence between the

3

solution conditions is in the distribution of protol-

ament number. Taxol increased the mass fraction of MT with

13

protolaments compared

with GTP or GMPPCP. GMPPCP reduced the formation of MT with

8


15

protolaments

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and increased the fraction of MT with (Figure S9), the fraction of MT with

14 14

protolaments. When

σq

was at its upper limit

was larger also in the other solution conditions

(when GTP was added or when GTP and taxol were added, while xing the other solution conditions). We may speculate that the additives slightly changed the conformation of tubulin

5

and as a result the preferred curvature of the assembled MT and hence the mass

fraction distribution as a function of protolament number. Taxol had a larger eect than GMPPCP in promoting MT with

13

protolaments. This observation is consistent with the

fact that GMPPCP is a GTP analogue and taxol acts through a dierent binding site. It is of interest to compare between the scattering curves of the buer-subtracted supernatant solutions (Figure S7) and that of cold (unpolymerized) tubulin solution. The supernatant of both dynamic (excess GTP) and GMPPCP-stabilized MT most likely contained tubulin dimer molecules as well as other (small) tubulin assemblies. The supernatant solution of the taxol-stabilized MT had much lower concentrations of dimers and tubulin assemblies. It has been demonstrated that in the presence of taxol or GMPCPP, MT is shorter compared with dynamic MT.

20,27

The variation in the length of the MT is expected to aect

the scattering curves at much lower

q -range than in our experimental setup, hence this eect

was not observed in our data. The MT length is of interest because it has been shown that it aects the interaction between tau-coated MT assemblies (tau is an important neuronal MT associated protein).

Weak attractive interactions between tau-coated MT assemblies

were observed only when the MT was dynamic and hence long enough so that the number of interacting units was large enough to form attractive tau-coated MT bundles.

28,29

Finally, in the case of dynamic MT, we examined the eect of tubulin concentration. Figure 8 shows the scattering curves from dynamic MT solution containing

0.15 mM

tubulin that were polymerized and measured at

25 ◦C.

13

or

15

and

The data show that as

the tubulin concentration was increased, the mass fraction of MT with increased and the mass fractions of tubulin with

0.05, 0.1,

14

protolaments

protolaments decreased.

We

considered the possibility of keeping the same distribution but increasing the fraction of MT

9



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Page 10 of 30

on the expanse of tubulin dimer or globular tubulin assemblies, but this possibility could not explain the data.

Conclusions Using cryo-TEM imaging, high-resolution synchrotron solution X-ray scattering and stateof-the-art data analysis tools developed in our lab,

17

we showed that the helical pitch of

dynamic MT (in other words, taxol-free and with excess GTP), taxol-stabilized MT, and GMPPCP-stabilized MT were identical and did not change with MT protolament number. The mass fraction distribution as a function of MT protolament number, however, shifted by adding MT stabilizers. Whereas taxol increased the fraction of MT with and decreased the fraction of MT with of MT with

14

13 protolaments

protolaments, GMPPCP decreased the fraction

15 protolaments and increased the fraction of MT with 14 protolaments.

The

possibility of MT with 12 protolaments was examined and under our conditions had no contribution. Higher tubulin concentration enriched dynamic MT with

14

protolaments.

Our ndings suggest that there are three possible lateral angles between protolaments. The most stable angle corresponds to MT with

14

protolaments. MT with

13

or

15

protola-

ments correspond to less stable states (namely, with higher free energies). Taxol decreases the free energy gap between MT with

13

protolaments and MT with

GMPPCP increases the stability of MT with gap between

14

14

protolaments.

14 protolaments by increasing the free energy

protolaments and the other two stable states (MT with

13

or

15

protola-

ments). These energetic changes result from the association of the tubulin dimers with taxol or GMPPCP that are likely to lead to structural changes, which aect the preferred angle between neighboring protolaments.

10


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C

A

200 nm

200 nm

D

B

200 nm Figure 1:

Cryo-TEM images of dynamic MT solution,

polymerized tubulin. merized for ◦ at 36 C for

200 nm

35 min 90 min

at

A. Dynamic MT solution:

36 ◦C

in the presence of

supernatant,

a solution of

4 mM

0.2 mM

buer and un-

tubulin was poly-

GTP. An aliquot was extracted, kept

prior to cryo-TEM sample preparation (vitrication). B. Dynamic MT ◦ solution supernatant: after polymerization the solution was centrifuged at 20 800 g and 36 C ◦ for 30 min. Supernatant sample was extracted, and kept at 36 C for 60 min, until vitried ◦ ◦ and imaged. C. BRB80 buer solution at 4 C. D. 0.3 mM tubulin at 4 C in the presence of

4 mM

GTP.

11



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Page 12 of 30

A

200 nm

B

200 nm Figure 2: Cryo-TEM images of Taxol stabilized MT solution and supernatant. stabilized MT solution: a solution of in the presence of

4 mM

tubulin was polymerized for

A. Taxol

35 min

at

36 ◦C

0.2 mM

Taxol were then added and mixed using a truncated ◦ tip. The sample was incubated for additional 5 min. An aliquot was extracted, kept at 36 C for

70 min

GTP.

0.2 mM

prior to cryo-TEM sample preparation (vitrication).

B. Taxol stabilized MT

solution supernatant: after taxol stabilized MT polymerization the solution was centrifuged ◦ ◦ at 20 800 g and 36 C for 30 min. Supernatant sample was extracted, and kept at 36 C for

50 min,

until vitried and imaged.

12


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A

200 nm

B

200 nm Figure 3:

Cryo-TEM images of GMPPCP stabilized MT solution and supernatant.

GMPCPP stabilized MT solution: a solution of 0.2 mM tubulin was polymerized for ◦ ◦ at 36 C in the presence of 4 mM GMPPCP. An aliquot was extracted, kept at 36 C for

A.

35 min 80 min

prior to cryo-TEM sample preparation (vitrication). B. GMPCPP stabilized MT solution supernatant:

after GMPCPP stabilized MT polymerization the solution was centrifuged ◦ ◦ and 36 C for 30 min. Supernatant sample was extracted, and kept at 36 C for

20 800 g 60 min, until vitried and imaged.

at

Black arrows mark typical examples of ice contamination.

13



S u p G T P

In te n s ity [a .u .]

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Page 14 of 30

S u p

T a x o l

S u p G M P P C P

0 .1

7

1 q [n m

-1

]

Figure 4: X-ray scattering data from dynamic and stabilized microtubule (MT) solutions. Azimuthally integrated scattering intensities are plotted as a function of the magnitude

0.2 mM tubulin that was polymerized in the presence of 4 mM GTP (solid red curve) or 4 mM GMPPCP (solid blue curve). The solid green scattering curve is from 0.2 mM tubulin that was polymerized in the presence of 4 mM GTP, which was followed by an addition of 0.2 mM taxol. Samples were polymerized and ◦ ◦ measured at 36 C. The samples were then centrifuged at 20 800 g, at 36 C for 30 min and of the scattering vector,

q,

from solutions of

the supernatant (Sup) of each sample was measured (red, green, and blue broken curves). The scattering from the buer of each solution was also measured (broken black curves). Measurements were performed in Soleil synchrotron at SWING beamline.

14


Page 15 of 30

A .

B .1 M a s s F r a c tio n

G T P T a x o l G T P

3 J 6 G , 1 2 .4 8 n m 3 J 6 G , 1 2 .2 1 n m 3 J 6 F , 1 2 .2 1 n m

.0 0 .8

T a x o l

0 .6 0 .4 0 .2

In te n s ity [a .u .]

0 .0 .0

G M P P C P 4

M a s s F r a c tio n

C .1 6

3 J 6 E , 1 2 .4 8 n m 3 J 6 E , 1 2 .2 1 n m 3 J 6 F , 1 2 .2 1 n m

0 .8

G M P P C P

0 .6 0 .4 0 .2

T a x o l

D . 10 .. 00

G T P T a x o l G M P P C P

0 .8

M a s s F r a c tio n

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


G M P P C P 1

2

0 .6 0 .4 0 .2

3

0 .0

q [n m -1 ]

1 3

1 4

1 5

P r o to fila m e n t N u m b e r

Figure 5: Supernatant-subtracted solution X-ray scattering data and atomic models of dynamic and stabilized MT. A. Using the measured scattering data from Figure 4 we calculated the supernatant subtracted scattering intensity black curves from dynamic (GTP) MT (top), taxol-stabilized MT (middle) and GMPPCP-stabilized MT (bottom). The inset shows data (black) and models at the high

q -range.

The red, blue, and green curves are the computed

scattering curves based on a non-negative linear combination of dierent atomic MT models (Eq. 7) and a linear combination of the curves in Figure S7. All the models were convolved (Eq. 6) with an estimated Gaussian instrument resolution function with standard deviation, σq , of 0.01 nm−1 (Eq. 5). In each model, the dimers were arranged in a 3-start left-handed helical lattices with radii to the geometric center of the dimer atomic coordinates,

R,

of

11.05, 11.9, and 12.75 nm, corresponding to 13, 14, and 15 protolaments. 12 protolaments (R = 10.2 nm), cold tubulin solution, buer subtracted supernatant (Figure S7), and tubulin dimer form-factor were included in the models. Each protolament contained 16 tubulin dimers assembled head-to-tail. B., C., and D. are bar diagrams of the mass fraction of each MT model as a function of the MT protolament number. B. The models that were tted to the taxol-stabilized MT data. C. The models that were tted to the GMPPCP-stabilized MT data. Mass fraction uncertainties were 10% or less. The pitch, which the atomic tubulin dimer model was taken

5

P , and the PDB le from

are indicated in the legends of each plot.

The mass fractions were determined by tting a linear combination of ve models (MT with

12, 13, 14,

and

15

protolaments and tubulin dimer) and the measured curves of Figure S7

to the scattering data. D. The mass fraction distributions that best tted the data (the bars with diagonal patterns in B. and C.). For the dynamic MT (GTP) case, and the atomic tubulin dimer model was 3J6F. match the colors in the mass fraction plots.

5

P

was

12.21 nm

The colors of the computed curves in A.

15



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 6: Illustration of the computed atomic MT models with

15

(purple) protolaments.

16


Page 16 of 30

13 (brown), 14 (yellow),

and

Page 17 of 30

A .

B .

G T P

G T P

T a x o l

T a x o l

G T P In te n s ity [a .u .]

G T P In te n s ity [a .u .]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


G M P P C P 4

6

G M P P C P 4

T a x o l

6

T a x o l

G M P P C P

G M P P C P 1

2 q [n m

3 -1

1

]

2 q [n m

3 -1

]

Figure 7: Comparing single with multiple population atomic models of dynamic and stabilized MT. Scattering intensity curves (data and models) of dynamic and stabilized MT from Figure 5A (in A) and Figure S9B (in B). Black curves are the scattering data and those are the same in A and B. The inset shows data and models at the high

q -range.

The

red, blue, and green solid curves are the computed scattering curves from Figure 5A, (with σq = 0.01 nm−1 ), and Figure S9B (with σq = 0.02 nm−1 ), that best tted the data. These curves were based on a non-negative linear combination of MT models with

15

12, 13, 14,

and

protolaments, whose mass fractions are presented in Figure 5D and Figure S9D and the

curves of Figure S7. The broken pink curves are the corresponding best tted single MT models with

14 protolaments,

using the dimer PDB IDs: 3J6F for the GTP and GMPPCP

curves; and 3J6G for the taxol curves.

The pitch,

P,

was

curves (See also Figure S11).

17


12.21 nm

in all the computed


A . In te n s ity [a .u .]

1 5

1 0 5

0 .3

B .

M a s s fr a c tio n

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 30

0 .8 0 .7 0 .6 0 .5 0 .4 0 .3 0 .2 0 .1 0 .0

0 .6 0 .9 q [n m -1 ]

1 .2

1 5 1 0 5

1 3

1 4 1 5 P r o to fila m e n t N u m b e r

Figure 8: Solution X-ray scattering data from dynamic MT at dierent tubulin concentrations. of

A. Supernatant subtracted scattering intensities as a function of

5, 10,

and

15 mg/mL

tubulin as indicated (equivalent to

0.05, 0.1,

q

and

from solutions

0.15 mM)

that

were polymerized in the presence of 4 mM GTP (solid symbols). Samples were polymerized ◦ and measured at 25 C, at beamline P12, (Desy synchrotron, Hamburg). Solid curves are the computed scattering curves based on a non-negative linear combination of atomic MT models with

13, 14,

and

curves of Figure S7.

15

protolaments, whose mass fractions are presented in B and the

MT with

12

protolaments, cold tubulin solution, buer subtracted

supernatant (Figure S7), and tubulin dimer form-factor were included in the models but their mass fraction was negligible. The models were convolved with an estimated Gaussian −1 instrument resolution function with standard deviation, σq , of 0.01 nm .

18


Page 19 of 30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Experimental Tubulin purication Tubulin was puried from porcine brains by three polymerization/depolymerization cycles. The rst cycle was at low salt buer.

30,31

and the other two cycles were performed in a high-molarity

32

Solution X-ray scattering measurements Solution X-ray scattering measurements were performed with energy of beamline in Soleil Synchrotron (GIF-sur-YVETTE), of

1377 mm,

33

10 keV

at SWING

using a sample-to-detector distance

at the high-brilliance synchrotron P12 beamline of the EMBL located at the

PETRA III storage ring (DESY, Hamburg), using sample-to-detector distance of

3100 mm, 34

at ID02 beamline in ESRF (Grenoble), and the SAXS beamline in Lund MAX II synchrotron. Detailed experimental description of these setups was provided elsewhere.

3437

The intensity

frames were normalized to the intensity of the transmitted beam, radially averaged, and background-subtracted as explained below and in our earlier publication. Dynamic MT was obtain by incubating piperazinediethanesulfonic acid, with

4 mM

GTP, at

36 ◦C

for

0.2 mM

17

tubulin in BRB80 buer ( 80 mM 1,4-

1 mM MgCl2 , 1 mM EGTA, adjusted to pH = 6.9 with KOH)

30 min.

The solution that by then contained dynamic MT,

was measured in a ow-cell capillary. The MT solution was then centrifuged at

36 ◦C for 30 min and a MT pellet was obtained.

20 800 g,

at

The supernatant, which contained coexisting

small tubulin assemblies, was measured through the same spot in the ow-cell capillary. At each synchrotron, all subsequent solutions were measured through the same spot of the same capillary. The scattering curve of the supernatant was then subtracted from the scattered intensity of the MT sample. The buer signal was subtracted from the supernatant and the MT sample. In the GMPPCP-stabilized MT sample, this protocol was repeated but GTP was replaced

19



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 30

with GMPPCP. In the taxol-stabilized MT sample, the dynamic MT protocol was repeated and at the end of the MT polymerization

0.2 mM taxol was added, leading to a tubulin:taxol

molar ratio of 1:1 that is known to best stabilize MT.

15

Measurements were repeated

3 times,

using dierent tubulin preparations and synchrotron facilities.

Solution X-ray scattering data analysis Background subtracted solution X-ray scattering intensity curves were tted to models of MT. The models were based on tubulin dimer structures available in the protein data bank (PDB).

5

The locations and orientations of the tubulin subunits were determined by the

algorithms presented in the supporting information. We then used our in-house state-of-the-art analysis software solution X-ray scattering curve of each model.

D+ to compute the expected

17

The scattering amplitude as a function of the magnitude of the scattering vector, each atom

(q) =

4 X

aij

j=1

vol. IV

38

of

i was evaluated by the ve Gaussian approximation atomic form-factor expression:

fi0 aij , bij , ci

q,

q 2 i + ci . · exp −bj 4π

were taken from Table 2.2B in the International Tables for X-ray Crystallography and its corrections.

39

Given a scattering vector in reciprocal space,

~q,

and a list of the atoms of the protein

and their coordinates (as in PDB les), the scattering amplitude of the entire structure, containing

n

atoms, is given by:

23

Fmol (~q) =

n X

fi0 (q) · ei~q·~ri

i=1

where

r~i

is the location of the

ith

atom.

Solvent subtraction was done by subtracting dummy atoms localized at the center of each atom with a Gaussian electron density prole:

40

20


Page 21 of 30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(r) = ρ0 exp − (r/ris )2 ρsolvent i where

ρ0

water

is the mean electron density of the solvent ( ρ0

radius of atom

i in the PDB le. 40,41

absent, replaced by empirical radii. dummy atom is then given by:

= 333 e/nm3 )

Published experimental

42

ris

radii

40

and

ris

is the atomic

were used and, where

The scattering amplitude contribution of the Gaussian

17

3 Fisolvent (q) = ρ0 π 2 (ris )3 exp − (ris ·q/2)2 .

The dummy atom volume, however, should be adjusted to

Vis =

4π(ris )3 by using: 3

h i 2/3 Fisolvent (q) = ρ0 Vis exp −(Vis ) ·q2/4π ,

which is in agreement with

43

and has been shown to well t experimental data.

4345

When

the contribution of the solvent is calculated, the scattering amplitude from the molecule in the solvent is:

F (~q) =

n X 0 fi (q) − Fisolvent (q) · exp (i~q · ~ri ) i=1

We can now dock

N

identical copies of the calculated molecule (tubulin dimer in our

case) into any given self-assembled structural symmetry (in which each copy of the basic submit is rotated and translated). The resulting amplitude is then:

Fassembly (~q) =

N X

F

A−1 q j ~

~ · exp i~q · Rj ,

(1)

j=1

where

Aj

is the rotation matrix and

~j R

the translation vector of the

j th

instance of the

molecule in the symmetry. The rotation matrix was computed according to the Tait-Bryan around the

x, y, z

axes, respectively, using the rotation matrix:

21


46

rotation angles,

α, β, γ ,


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 30

A (α, β, γ) = 



cos β cos γ − cos β sin γ sin β     cos α sin γ + cos γ sin α sin β cos α cos γ − sin α sin β sin γ − cos β sin α .     sin α sin γ − cos α cos γ sin β cos γ sin α + cos α sin β sin γ cos α cos β The location,

Rj = (xj , yj , zi )

and orientation,

Aj (αj , βj , γj )

of the

j -th

subunit were as

follows:

αj = βj = 0, γj = j ·

2π Np

(2)

2P xj = R · cos(γj ), yj = R · sin(γj ), zj = zStart + j · 3Np where

R

is the radius to the geometric center of the tubulin dimer atomic coordinates,

is the helical pitch, shift of the

3-start

Np

is the number of MT protolaments, and

helical model, where

zStart =

P

k·P is the vertical 3

k ∈ {0, 1, 2}.

The amplitude was then multiplied by its complex conjugate and all orientations were numerically averaged in which the vectors

~q-space

by selecting random azimuthal,

~qi = q sin θqi cos φiq , q sin θqi sin φiq , q cos θqi

φiq ,

and polar,

θqi ,

angles, from

, were computed. Orientation

average is given by:

PNo INo (q) =

i=1

|Fassembly (~qi )|2 sin θqi PNo i i=1 sin θq

No π X |Fassembly (~qi )|2 sin θqi . = 2No i=1

To uniformly sample the polar and azimuthal angles in reciprocal space we used:

φiq = 2π · u θqi

−1

= cos

(3)

(2 · v − 1)

22


Page 23 of 30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


where

u

and

v

[0, 1]

were random variates in the

range.

47

The intensity was then given by:

No 1 X INo (q) = |F (~qi )|2 , N i=1

and was computed until the number of orientations,

No ,

(4)

was suciently large so that the

intensity converged. Computations were performed on a Windows computer with an Intel Core i5

3.2 GHz

CPU and NVIDIA Titan GPU, using the Hybrid method explained in our earlier publication.

17

Each curve was computed in about half a minute.

The modeled scattering intensity was then convolved with a Gaussian instrument resolution function:

1 R (q, σq , hqi) = p exp 2πσq2 around the mean

q

value,

hqi. σq

parameters aect the value of that was

0.4 × 0.1 mm.

0.01

0.02 nm−1 .

and

q − hqi 2σq2

σq .

q

value. Several

The dominating factor, however, is the size of the beam

The smeared intensity at the mean

I

(5)

is the standard deviation around the mean

Based on geometrical considerations

sm

Z

q

48

we estimated

to be between

value was computed by:

∞

R (q, σq , hqi) IN (q) dq.

(hqi) =

σq

(6)

0

The scattering intensity from a mixture of multiple uncorrelated populations (MT with dierent protolament numbers) was obtained by the weighted sum of their smeared intensities, where each weight is the corresponding population mass fraction:

I

sm

(hqi) =

P X

Si Iism (hqi).

i=1

23


23

(7)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

P

is the total number of dierent populations.

fraction and smeared intensity of the

ith

Si

and

Page 24 of 30

Iism

are the normalized mass

population, correspondingly.

Cryo-transmission electron microscopy measurements MT, supernatant and buer solutions were imaged using transmission electron microscopy at cryogenic temperatures (Cryo-TEM). A droplet of

3 µL was deposited on a 300 mesh copper

Lacey grid (Ted Pella Ltd.) and blotted using Vitrobot Mark IV (FEI Co.). Ultrathin lms, whose thickness varied between

20 and 200 nm, were formed because most of the solution was

removed by blotting. Specimens were vitried by rapid plunging into liquid ethane precooled with liquid nitrogen at controlled temperature and

100%

relative humidity, using Vitrobot

Mark IV (FEI Co.). The vitried samples were then transferred to a cryo-specimen holder (Gatan model 626; Gatan Inc.). The samples were imaged at

−177 ◦C,

Spirit Twin T-12 TEM (FEI Co.), operated at an acceleration voltage of mode. Images were recorded on a varied between

2

and

4K × 4K

using a Tecnai G

2

120 kV in a low-dose

FEI Eagle CCD camera in defocus value that

4 µm.

Acknowledgement We thank Daniel Harries for helpful discussions and SWING beamline, in Soleil synchrotron (J. Perez and his team), P12 beamline of the EMBL at DESY, Hamburg (D. Svergun and his team), ESRF ID02 beamline (T. Narayanan and his team) and the SAXS beamline at Lund MAXII Synchrotron (A. Labrador and her team), as the data presented in the paper were acquired there. This project was supported by Israel Science Foundation (656/17), the United States-Israel Binational Science Foundation (2016311), and by the Israel Ministry of Science. We thank the Safra, Wolfson, and Rudin Foundations for supporting our laboratory.

24


Page 25 of 30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Supporting Information Available Additional cryo-TEM images, nding the rotation angles of an object, scattering curves of supernatants, turbidity kinetic measurements, instrument resolution eect, and additional solution X-ray scattering data are presented in the supporting information.

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Graphical TOC Entry

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Page 30 of 30

Structure of Dynamic, Taxol-Stabilized, and GMPPCP-Stabilized

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