New simulated annealing approach considering helix bending applied to determine the 8.8Å structure of 15-protofilament microtubules.

Journal of Structural Biology 188 (2014) 165–176

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Journal of Structural Biology journal homepage: www.elsevier.com/locate/yjsbi

New simulated annealing approach considering helix bending applied to determine the 8.8 Å structure of 15-protofilament microtubules Toshihiko Ogura a, Hiroaki Yajima b,c, Ryo Nitta b,c,1, Nobutaka Hirokawa b,c, Chikara Sato a,⇑ a

Biomedical Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Central 2, Umezono, Tsukuba, Ibaraki 305-8568, Japan Department of Cell Biology and Anatomy, Graduate School of Medicine, The University of Tokyo, Hongo, Tokyo 113-0033, Japan c Department of Molecular Structure and Dynamics, Graduate School of Medicine, The University of Tokyo, Hongo, Tokyo 113-0033, Japan b

a r t i c l e

i n f o

Article history: Received 9 April 2014 Received in revised form 16 August 2014 Accepted 25 August 2014 Available online 1 September 2014 Keywords: a- and b-Tubulin Single particle analysis Helical reconstruction Image analysis Cryo-electron microscopy

a b s t r a c t The helix is an important motif in biological architectures. The helical structures of nanoscale proteins are principally determined by three-dimensional (3D) reconstruction from electron micrographs. However, bending or distortion of flexible helices and the low contrast of the images recorded by cryo-electron microscopy, prevent the analysis from reaching high resolution. We have developed a novel helical reconstruction method that overcomes these issues, and present the processing of microtubule images to demonstrate its application. Cropping long helical structures into small square pieces allows bending or distortion of the helices to be accounted for. The initial image-frames are automatically positioned assuming perfect helical symmetry. A simulated annealing (SA)-based algorithm is then used to adjust the framing. This is guided by the contrast of 2D averages, which serve as an accuracy index. After the initial 3D reconstruction, the position and orientation of each average image is iteratively adjusted to give the best match between the input average and the reprojection from the reconstruction. Finally, reconstructions from images recorded at different defocus values, are aligned and averaged to compensate the contrast transfer modulation and improve the resolution. The method successfully determined the structure of a 15-protofilament microtubule. The 8.8 Å resolution (7.8 Å using the 0.143 FSC criterion) attained allows differences between the a- and b- tubulins to be discerned in the absence of a molecular landmark such as microtubule-associated proteins, for the first time by electron microscopy. The SA-based method is applicable to other helical protein complexes and in general to helical structures. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction Helical architecture is an important motif in biological macroand micro-structures, including proteins, nucleotides and their complexes. Microtubules (MTs) and F-actin, respectively formed by tubulin and actin in the cytoplasm, are typical examples and are essential for a range of cellular functions. MTs play principal roles in the fundamental physiological processes involved in

Abbreviations: 2D, two dimensional; 3D, three dimensional; Cryo-EM, cryo electron microscopy; CTF, contrast transfer function; EM, electron microscopy; FBP, filtered backprojection; FSC, Fourier shell correlation; GMPCPP, guanylyl 5’-a, b-methylenediphosphonate; MT, microtubule; Pf, protofilament; SA, simulated annealing; SD, standard deviation; SIRT, simultaneous iterative reconstruction technique. ⇑ Corresponding author. Fax: +81 29 861 6478. E-mail address: [email protected] (C. Sato). 1 Present address: Center for Life Science Technologies, RIKEN, Yokohama, Kanagawa 230-0045, Japan. http://dx.doi.org/10.1016/j.jsb.2014.08.009 1047-8477/Ó 2014 Elsevier Inc. All rights reserved.

eukaryotic cilia- and flagella-movement, the maintenance of cell shape, cell division and intracellular motility (Hirokawa et al., 2009; Verhey and Gaertig, 2007). They are long polar cylindrical structures with a diameter of 25 nm, and are comprised of aand b- tubulin heterodimers. These tubulin dimers connect head to tail to form a polar protofilament (Pf), with b-tubulin facing towards the plus-end. Pfs with the same polarity assemble side by side to form the tubular lattice structure of the MT. The type of MT is determined by two factors, (1) the number of Pfs present and (2) the lateral angle between neighboring tubulin monomers in the lattice (Fig. 1). In vivo, most MTs have 13 Pfs, although the number is known to vary from 8 to 17 (Aamodt and Culotti, 1986; Pierson et al., 1978). In 13 Pf MTs the Pf axis is parallel to the MT axis, whereas in MTs with more or less Pfs the Pf axis follows a long helical screw (Chretien and Wade, 1991) forming what has been termed the MT superhelix. The periodicity of the superhelix gives a moiré pattern in the electron microscope (EM) (Chretien et al., 1996;

166

A

T. Ogura et al. / Journal of Structural Biology 188 (2014) 165–176

B

Cryo-EM image (1)

Mask

Single MT structure (6)

B factor correction

(7)

Bilateral filter

Fig.1. Schematic diagram of a 15-Pf MT. (A) a- and b- tubulin heterodimers connect head-to-tail to form polar Pfs. Pfs with the same polarity assemble side by side to form a MT. (B) 2-Start helical structure (4- start for monomers) of the 150 nm MT superhelix.

Langford, 1980). The pitch and handedness (right or left) of the superhelix depend on the number of Pfs and on the number of helix ‘‘starts’’. If the helix rises by one and a half dimers (three monomers) in one turn, it is called a 1.5-start helix (3-start for monomers), and there is a break in the helical symmetry called a seam-line, where a-tubulin subunits are laterally adjacent to btubulin subunits (Kikkawa et al., 1994; Mandelkow et al., 1986). If the helix rises by two dimers (four monomers) in one turn, it is called as a 2-start helix (4-start for monomers). In this case there is no seam-line and helical symmetry materializes. The absence of a seam-line greatly simplifies the image processing required to obtain the three-dimensional (3D) MT structure from cryo-electron microscopy (cryo-EM) images, as helical rules can be applied. 15or 16- Pf MTs often form a 2-start helix and several groups, including us, have utilized 15-Pf 2-start MTs to solve the structure of MTs decorated with associated proteins (Hirose et al., 2006; Kikkawa and Hirokawa, 2006). Structural information at or close to atomic resolution is required to fully understand the functional mechanism of protein complexes. Electron microscopy (EM) and subsequent 3D reconstruction has been successfully applied to achieve 4–5 Å structures for several helical assemblies, notably, tobacco mosaic virus (Clare and Orlova, 2010), the bacterial flagellar filament (Yonekura et al., 2003) and the acetyl choline receptor (Miyazawa et al., 2003). However, the analysis of disordered or twisted helices or helices that display flexibility-induced bending remains challenging, even though real-space helical reconstruction methods using single particle analysis techniques have been developed (Bluemke et al., 1988; Burgess et al., 2000; Egelman, 2000, 2007; Holmes et al., 2003; Li et al., 2002; Pomfret et al., 2007; Sachse et al., 2007; Sosa et al., 1997). In the case of MTs, the high similarity of the aand b-tubulin subunits makes the analysis even more difficult. In recent years, single particle-based 3D reconstruction strategies have been applied to cryo-EM images of MTs (Li et al., 2002). As it was difficult to distinguish between a- and b-tubulins at the low spatial resolution and low signal-to-noise ratio (SNR) of such initial images, their structural differences were neglected in the processing unless landmark proteins such as kinesins were present (Kikkawa and Hirokawa, 2006; Sui and Downing, 2010), even though the difference between a- and b-tubulins is fundamental for MT dynamics, which is controlled by the nucleotide state of

(2)

(3)

SA class averaging

SA 3D optimization

(5)

(4)

Z slice averaging

(8)

Cross correlation of 3D MTs

(9)

SIRT Final 3D structure

Averaging of all MTs

Fig.2. Schematic flow diagram of the SA-based helical reconstruction method. The 3D reconstruction procedure consists of nine image processing steps: (1) Manual masking. (2) Auto-framing and class averaging with SA auto-frame adjustment. (3) SA 3D optimization. (4) 3D reconstruction by SIRT. (5) Z-slice averaging. (6) B-factor correction. (7) Noise reduction by a fast 3D bilateral filter. (8) Calculation of a 3D cross-correlation map to align MTs. (9) MT alignment and averaging. The red boxes indicate the new processing approaches outlined in this paper.

b-tubulin (Burbank and Mitchison, 2006; Desai and Mitchison, 1997). Here, we describe a novel helical reconstruction method employing a modified version of the template-free, simulatedannealing (SA)-based single particle reconstruction algorithm to process cryo-EM images of MTs (Fig. 2). In the new method an SA algorithm is adopted to precisely position sampling frames on the filament according to the periodicity of the image and helix bending. The contrast of two-dimensional (2D) averages calculated during the annealing reflects the framing accuracy and guides convergence. The method automatically reconstructs the high-resolution, 3D MT structure from low-contrast cryo-EM images, and can be applied to any helical filament provided the symmetry parameters are known. The 8.8 Å resolution using the 0.5 FSC criterion (7.8 Å resolution using the 0.143 FSC criterion) achieved for MTs allowed a- and b-tubulins to be distinguished; the method described was only very briefly outlined when the structure was reported (Yajima et al., 2012). 2. Materials and methods 2.1. Protein preparation MTs were purified and polymerized as described (Yajima et al., 2012). For the guanylyl 5’-a, b-methylenediphosphonate (GMPCPP)-MTs used here, tubulin (3.0 lM) was incubated in a polymerization buffer (100 mM PIPES pH 6.8 adjusted by KOH, 1 mM EGTA, 1 mM MgCl2, 0.6 mM GMPCPP, 5% DMSO) at 4 °C for 30 min, and then clarified by centrifugation at 4 °C for 30 min at 100,000 g using a TLA-110 rotor in a TLX ultracentrifuge. The supernatant was polymerized at 37 °C for 120 min, and the MTs were collected by centrifugation through a 20% glycerol cushion at 27 °C for 10 min at 20,000 g using a TLA-45 rotor in a TLX ultracentrifuge. This cycle, which caused GMPCPP uptake into the MTs, was repeated three times to increase the occupancy of GMPCPP on the E-site. 2.2. Cryo-EM Standard cryo-EM methods were employed as described in our previous paper (Yajima et al., 2012). The specimens were observed

167


A

Original

B

Mask

C

Center

Fig.3. Calculation of the preliminary center of the MT. (A) An original 15-Pf MT image after high-pass filtering (81 81 pixels, cut-off frequency of 0.025) and compression (5) in the longitudinal direction. (B) MT after manual masking. (C) MT with the longitudinal center (white line) calculated from the mask marked.

Fig.4. Flowchart indicating the class averaging method with auto-frame adjustment using the SA algorithm. The process involves the following steps: set initial frames assuming ideal helix periodicity. Randomly select one of the frames, change its position and rotational angle. Calculate the contrast score to judge whether to accept the shift or not. Repeat for the specified number of iterations and cycles.

168


Frame Class 1

Frame Class 2

Frame Class 18

8.2 nm

147.6 nm

Frame No.1

Frame No.19

Frame No.2

Frame No.18 Frame No.20

Frame No.37

Average

Fig.5. Initial frames used for the auto-frame adjustment method. Frames aligned to the preliminary center of the MT are positioned at intervals corresponding to the known periodicity of a perfect 15-Pf MT superhelix (8.2 nm per tubulin dimer) and sorted into classes according to the different views they give of its structure. From the helical symmetry of a 15-protofilament MT this results in 18 classes. Images within a class are separated by the helical repeat distance, 147.6 nm (8.2 nm 18) and Class (n + 1) is each Class (n) frame shifted down by the length of a tubulin dimer. The images at the bottom are the class averages, i.e., averages of the MT segments selected by the intact frames in each class.

using a 200-kV field emission cryo-electron microscope (JEM2010F; JEOL). Images were recorded at 40,000-fold magnification on SO163 film (Eastman Kodak) with defocus values ranging from 1.3 to 2.8 lm. The 15-protofilament and 2-start helical MTs (15protofilament and 4-start for tubulin monomers) were identified by the Moiré pattern, and the optical diffraction pattern of the relative peaks near 1/40 Å and their polarity was determined. Selected micrographs were placed so that the MT filament was upright, and digitized at a pixel size of 2.5 Å at the specimen level using a Scitex Leafscan 45 scanner (Leaf systems).

2.3. Image processing details Image filtering: a high-pass filter (kernel size of 81 81 pixels; cut-off frequency 0.025), was applied to the original cryo-EM images. Images with pixel intensities within ±4 times the SD in each filtered image were converted to 8-bit. Initial image selection: square regions including MTs were manually selected from a series of filtered 8-bit cryo-EM images. Specific MTs were then extracted in rectangular boxes and aligned with their long axis vertical (Fig. 3). These images were compressed 5 times in the axial direction and used to determine the longitudinal center of the MT. All subsequent processing was carried out on the uncompressed, filtered 8-bit MT images. Auto-framing: the algorithm requires the helical parameters of the perfect filament: a total of 270, 8.2 nm-long a, b tubulin dimers

are distributed in 9 turns of the 2-start helix of 15-Pf MTs. Frames are positioned at intervals along the filament (Figs. 4 and 5), their shift to one another being defined by the height of one subunit (8.2 nm for MTs). The whole filament is sampled. The sequentially numbered frames are then sorted into classes (Fig. 5). The number of classes is defined by the number of turns in the helical repeat, i.e., the number of turns required for a subunit to be in the exactly the same spatial orientation (18 for 15-Pf MTs). Accordingly, sequential frames in a class are separated by the length of the helical repeat (147.6 nm for 15-Pf MTs). The frames used to sample the MTs were 60 60 nm (240 240 pixels) in size (Figs. 5 and 6). CTF correction: the CTF of the fully aligned class averages was corrected using Imagic V (Image Science, Berlin). The CTF parameters were based on the defocus values determined for each micrograph by CTFFIND3 (Mindell and Grigorieff, 2003). 2.4. Calculation of the contrast score The contrast score, Lc, of a class average consists of a local average score Ln and a global average score La (Figs. 5 and 6). To obtain the local average score, the class average, I (n), is summed with the two neighboring class averages, I (n–1) and I (n + 1), with weightings of 1/2 for the average image and 1/4 for its neighbors (Eq. (1)):

In ðnÞ ¼

1 1 1 IðnÞ þ Iðn 1Þ þ Iðn þ 1Þ; 2 4 4

ð1Þ


When the number (n + 1) is larger than the maximum class number, 18, (n + 1) is set to 1. Moreover, when (n–1) is smaller than 1, (n–1) is set to the maximum class number. The average intensity is calculated for every local average image, and subtracted from the local average image In(n) to yield In’(n). Every pixel intensity of In’(n) is squared and then summed using the Michaelis–Menten equation, whose parameter is set at a half-saturation constant of H, to yield the Ln (Eq. (2)):

Ln ¼ Pd

N X M XX n

x

y

I0nðx;yÞ ðnÞ2 0 Inðx;yÞ ðnÞ2 þ H2

Fn 1 X I0 ðnÞ: Fn n n

N X M XX

ð3Þ

n

x

y

I0aðx;yÞ ðnÞ2 0 Iaðx;yÞ ðnÞ2 þ H2

3. Results

ð2Þ

After subtracting the average intensity of the total average image, each pixel intensity is squared and further summed using the Michaelis–Menten equation Eq. (4), with the parameters used to calculate the local average score.

La ¼ Pd

R2007b and the Image-processing Toolbox (Math work Inc.) on a personal computer (Intel Core2 Duo: 3.2 GHz, 4G byte RAM) running Windows XP. The whole system was programmed using Matlab script M-files and C-MEX files.

3.1. Principle of the SA-based helical reconstruction method

:

In these calculations, the half-saturation constant H was set at 20 and the pixel density Pd was set at 128, i.e., the median value of 8-bit densities. The width N and height M of the frame were both 240 pixels. This equation was introduced to avoid the effects of very high or low pixel densities that were locally observed in the average. The Ln quantifies the contrast in closely related class averages, which indicates the alignment accuracy of each subunit. In practice, three classes including approximately 30 images were merged for this step to improve the signal-to-noise ratio enough to allow the evaluation of fine alignment changes. Differences between the three merged class averages were subtle. To obtain the global average score, the total average image is calculated from all class averages Eq. (3):

I0a ¼

169

:

ð4Þ

The global average score reflects the overall alignment accuracy of the tubular structure. The contrast score, Lc, is the sum of the local and global average scores Eq. (5).

Lc ¼ Ln þ La

ð5Þ

2.5. Traditional single particle reconstruction carried out for comparison Initially, 331 MT images, 158 158 pixels in size, were manually picked from 12 cryo-EM images. After background subtraction, the cropped images were aligned rotationally and translationally by the multi-reference alignment method (van Heel et al., 2000) and sorted into 24 classes by the modified growing neural gas network method (Ogura et al., 2003). The class averages were adopted as new references, and the alignment and classification cycle was repeated. After 20 cycles, a 3D volume was reconstructed from each class average by the filter-back-projection method or the simultaneous iterative reconstruction technique (SIRT) method (Penczek et al., 1992). The volumes were aligned in 3D by crosscorrelation, the positions being indicated by the maximum in the map, and averaged. The reprojections from the averaged volume were employed as references for multi-reference alignment and the following classification. The 3D reconstruction cycle was repeated 8 times. 2.6. Image analysis system All the calculations in the SA-based helical reconstruction algorithm and image processing were performed using Matlab version

The SA-based reconstruction method is summarized in Fig. 2 and will be presented using the processing of a 1.3 lm-long 15Pf MT as an example. First, the cryo-EM image of the MT is masked to preliminarily determine the central longitudinal axis (Fig. 2). Square unit images (60 nm 60 nm) are then automatically selected along the central axis of the filament according to the periodicity of a perfect 15-Pf MT helix and assigned default coordinates. Corresponding unit images are picked up along the length of the MT based on these coordinates, aligned and averaged. Each 2D average is then optimized by adjusting the center and in-plain rotation of its constituent images according to the bending of the helix. Local minimums are overcome using SA, employing the contrast of the resulting 2D averages as an accuracy index. Utilizing the helical parameters in this way changed what would have been an exhaustive unit search for similar units into a concentrated search in a reasonable area. The final 2D averages are used to reconstruct a preliminary 3D structure by the filtered backprojection (FPB) method, exploiting the helical symmetry to assign them to corresponding positions on the helix. This step is followed by further adjustment of their centering and in-plain rotation using the echo-correlated 3D reconstruction method and SA. The final 3D map of the MT is then calculated using the SIRT (Penczek et al., 1992). Afterwards, each micrograph is corrected for the B-factor, and the volume is optimized by vertical 3D averaging, exploiting the symmetry of the filament in this direction. Finally, the structures obtained for a series of MTs are averaged at corresponding positions determined using cross-correlation maps, to further increase the signal-to-noise ratio and attain the highest possible resolution. 3.2. Preliminary axis of the MT MTs were extracted from filtered cryo-EM images (see Section 2). To facilitate visualization, each image was then compressed five times in the axial direction by sequentially averaging five pixels Fig. 3(A). A mask matching the overall dimensions of the compressed filament was created manually Fig. 3(B) and used to preliminarily define the longitudinal center of the MT; this is indicated by a curved line Fig. 3(C). All subsequent steps were carried out on the uncompressed, original MT image. 3.3. Auto-framing and auto-adjustment using SA Once the longitudinal axis has been preliminarily determined, an auto-frame adjustment algorithm including SA (Fig. 4) automatically places axially-centered, square sampling frames along the uncompressed filament image at a periodicity defined by the helix, i.e., initially according to the parameters of a perfect helix. Frames that sample corresponding views along the length of the filament are then sorted into classes (see Section 2) and averaged (Fig. 5). The contrast score of each average is calculated (see Section 2). The contrast scores guide the optimization procedure carried out by the SA-class averaging algorithm. This algorithm refines the helical parameters by changing both the shift between frames and the number of classes to find the maximum contrast scores (Figs. 6 and 7; see below). A total of 270, 8.2 nm-long a, b tubulin

170


A

Auto-frame adjustment process Previous position

B

New position

Selection of a frame Judgment of the shift Comparison scores

Calculation score

Fig.6. Outline of the auto-frame adjustment method using SA. (A) The images in the initial frames are averaged, and the contrast score is calculated. A frame is then randomly selected, and shifted by a vector randomly extracted from a 2D normal distribution with r set to 5. The frame is then rotated (not shown) at an angle randomly extracted from a normal distribution with r set to 5. Next, the average image and new contrast score are calculated. The new contrast score is compared to the previous one to evaluate, by the SA method, whether to accept the shift or not. If the shift is rejected, the frame is moved back to its previous position. A frame is randomly selected, shifted, and judged until the number of accepts, Ite2, reaches Itemax2, or the number of rejects, Ite1, reaches Itemax1. (B) After the annealing, each frame has reached its optimum position following the bending of the helix, and the contrast of the class average is higher.

dimers are distributed in 9 turns of a perfect 2-start 15-Pf MT superhelix, which has a helical repeat of 147.6 nm (8.2 18 = 147.6). Accordingly, the search was made for frame shifts of 8.1–8.3 nm and 16–20 classes. The highest contrast scores were obtained with a shift of about 8.2 nm between frames and 18 different classes. The SA algorithm (Fig. 4) carries out the following operations (Ogura and Sato, 2004): First, one of the frames is selected and shifted randomly; the shift (Dx, Dy) from the original position is randomly extracted from a 2D normal distribution, whose SD parameter, r, is set at 3 (Fig. 6). Further, the frame is rotated by an angle (Dh) that is also randomly extracted from a normal distribution with a set to 6. Second, an average including the moved frame is obtained, and the new contrast score is calculated. This new score is compared with the previous one by the SA algorithm to evaluate whether to accept the shift or not. If rejected, the frame is moved back to the previous position. A frame is randomly selected, shifted, and judged until the number of accepts, Ite2, reaches Itemax2, or the number of rejects, Ite1, reaches Itemax1. Itemax1 and Itemax2 are set at 20 and 50 times the total number of frames positioned on the MT, respectively. This cycle is repeated a preset number of times Cmax depending on the image conditions,

e.g., the S/N ratio (Fig. 7). Cmax was 300–500 for the 15-Pf MTs examined. The 2D class averages obtained after various numbers of cycles are shown in Fig. 7(A), and the score and annealing temperature of the various annealing cycles are presented in Fig. 7(B). Starting from unclear class averages, MT features gradually emerge as the temperature decreases (Fig. 7(A), cycles 0–200). During the annealing process, the score increases sigmoidally as the cycles proceed; it increases gradually for approximately the first 150 cycles, then drastically rises for the next 100 cycles and finally levels off (Fig. 7(B); cycles 400–500). At the end of the annealing, clear class averages appear (Fig. 7(A), cycles 300–500). After annealing, the intervals between neighboring frames are measured to check whether the filament maintains the positional subunit relationships expected from the refined helical rule (Fig. 8). For a 15-Pf MT tube this is the case if the interval is close to 8.2 nm, the length of an a, b-tubulin dimer (see above). If the interval was different, the tubular structure was considered to be either a 15-Pf MT with a disordered lattice or a MT with a different Pf stoichiometry and/or a- and b-tubulin arrangement. Accordingly, a region where the frame interval was always close to 8.2 nm was selected for the 3D reconstruction. For the MT documented by

171


A

Cycle = 0

100

200

300

500

Class 1

Class 5

Class 10

18

0.12

16

0.10 0.08

14

0.06 12

0.04

10

0.02

Temperature

Score

B

0.00

8 100

200

300

400

500

Cycle Fig.7. Changes in class averages and the contrast score during annealing cycles. (A) Changes in the features of class averages during 500 annealing cycles. Initially, class averages exhibit blurred MT projections. As annealing proceeds, the features of the MT gradually appear, and finally the MT structure is clearly visible. (B) Changes in the contrast score and the temperature during annealing cycles. As the temperature decreases exponentially, the score increases sigmoidally.

Fig. 8, this was between frame number 10 and frame number 153. The contrast transfer function (CTF) of the class averages (see Section 2) obtained from the frames in this region was corrected. The corrected averages were employed for the next step.

MT polarity was determined using the optimized 2D averages and the 5-times compressed image created to facilitate visualization and masking (see above). The MT was set plus-end up in each class average.

3.4. Correction algorithm for rotational angle and horizontal shift

3.5. Optimization algorithm for 3D reconstruction

Occasionally, although aligned to one another, the frames used to calculate a 2D class average were off center or slightly skewed relative to the longitudinal MT axis, which meant that the class average was also not optimally positioned within its frame. The software employs an automatic fine alignment method to check for this and adjust the angle and position of the average (Supplementary Fig. S1). For angular adjustment, a class average obtained by the SA method is rotated from 10 to 10°, with a step size of 1 degree. After each rotation, the pixel intensities are changed to their absolute values, and the rotated image and its vertically flipped counterpart are averaged to give a score image. A score profile is then created by summing the intensities of the score-image pixels in the vertical direction. Finally, the total score is obtained by summing the squared pixel intensities of the score profile. The total score has its maximum value when the MT segment in the frame is vertical. A similar strategy is used for the transversal adjustment (Supplementary Fig. S2). In this case a class average is shifted horizontally between 10 and +10 pixels in one-pixel steps. After each shift, the pixel intensities are changed to their absolute values, and the shifted image and its horizontally flipped counterpart are averaged to give a score image. A score profile is then created and the total score calculated as detailed above. The total score has its maximum value when the center of the frame is on the vertical axis of the MT.

An initial 3D volume is calculated by the filtered backprojection (FBP) method by assigning the CTF-weighted 2D class averages to the specifically directed projections predicted by the periodicity of a perfect helix. For the 15-Pf MT, class average 1 was successively associated with 15 angles around the tube, corresponding to the 15 protofilaments (Fig. 9). One turn of a, b-tubulin protomers is slightly smaller than 360°, resulting in a superhelix with a helical repeat of 18 turns. The angular interval (hf) between adjacent class averages is calculated to be 23.82°, from the number of protomer turns in a 2-start helix, Sn, and the number of protofilaments per turn Pt Eq. (6),

hf ¼

360 2 : 1 Pt Pt Sn

ð6Þ

where Pt is 15, and Sn is 18, corresponding to the total number of classes. After one 360° turn, the Euler angle of the class average is shifted by –1.33° relative to the previous turn, i.e., 360°/(Pt Sn) (Fig. 9). In total, 270 average images (Pt Sn) are required for the reconstruction, each class average being used in 15 different angular orientations. To improve the 3D volume, the echo-correlated 3D reconstruction method (Ogura and Sato, 2006) is employed to optimize the centering and rotational angle of each class average. In this process, the 18 averages are assigned Euler angles as detailed above, and

172


A Frame Interval (nm)

3.6. Averaging of structural periodicity within a single MT Since, the 3D structure of a MT has similar slice repeats (crosssections) at equal intervals along the Z-axis, corresponding slice images can be averaged to increase the signal-to-noise ratio. The MT targeted here has 15 Pfs and two starts. The vertical interval between structurally corresponding slices, Rs, is calculated to be 1.1 nm by Eq. (7),

12

8

4 0

100

200

Frame number

B 8.2 nm Frame No.79

8.2 nm Frame No.80

8.2 nm Frame No.152

Frame No.81

4.1 nm Frame No.153

Frame No.154

Rs ¼

2 Lp : Pt

ð7Þ

where, Lp is the dimer length of 8.2 nm and Pt is 15. The rotational orientation of the slices will differ by the inverse of the rotation defined by Eq. (6), i.e., 23.82°. Accordingly, corresponding slices were extracted at 1.1 nm intervals from top to bottom along the Z-axis, rotated by 23.82° increments until aligned, and averaged. This averaging procedure ensured that the a- and b- tubulin heterodimer subunits that form the 2-start helix were treated separately, allowing structural differences to be detected. The slices encompassing the whole MT were then averaged, and a refined 3D structure was built (Fig. 11). When all of the tubulin dimers in the reconstruction had been averaged, a fast 3D bilateral filter created with Matlab (MathWorks Inc., USA) was applied to reduce noise without blurring (a Matlab function of bilateral3 written by Igor Solovey, 2011). The temperature factor (B-factor) was subsequently calculated to be 400 Å2 using the program EM B-factor and applied to compensate the amplitude attenuation at higher frequency (Fernandez et al., 2008). Finally, the structure was averaged over all 270 a, b-tubulin dimers. Afterwards, a second 3D bilateral filter (a MATLAB function of bilateral3 written by Igor Solovey) was applied to reduce the noise even further without blurring the 3D structure. 3.7. Averaging multiple MT 3D structures

Fig.8. MT regularity checked by frame interval after annealing. (A) Frame intervals after annealing. The flat region between frame numbers 7 and 153 can be used for the reconstruction, as the frame interval of 8.2 nm is comparable to the length of a tubulin dimer. (B) Intervals between frames 79, 80, and 81, and 152, 153, and 154. Frame numbers 79, 80, 81 are in the middle of the flat 8.2 nm region. The interval between images 153 and 154 is 4.1 nm, which is comparable to the length of a tubulin monomer.

each is accordingly posted at 15 different positions around the cylinder. These angles are fixed. A 3D volume is then reconstructed in the center using FBP. Starting with the centering (x, y) and in-plain rotation (h) of each class average, x, y and h are adjusted. One class average is selected at random, its centering and rotational angle in the image plane are changed. The shift (Dx, Dy) from the original position is randomly extracted from a 2D normal distribution, whose SD parameter, r, is set at 4 (Fig. 6). The frame is further rotated at an angle (Dh) that is also randomly extracted from a normal distribution with r set to 3. The 14 copies of the class average are automatically moved accordingly. A new 3D volume is then reconstructed (Fig. 10). This new volume is reprojected back in all class average directions, and a matching score (cross-correlation) between each projection and the class average is calculated (Ogura and Sato, 2006). These matching scores are summed to yield a total 3D score. Using this score as a 3D reconstruction accuracy index, the image shift is evaluated by the SA algorithm to determine whether it should be accepted or not (Fig. 10). This process is iterated to improve the 3D volume over a predetermined number of cycles (Ogura and Sato, 2006). By the end of the annealing, each class average has been shifted to the most appropriate position. Using these averages, the improved 3D volume is reconstructed by the SIRT method (Penczek et al., 1992).

The MT structure calculated from a single EM image is partially modulated by the CTF at the particular TEM imaging condition. To overcome this, many MT structures from micrographs recorded at different defocus values must be averaged, so that weak-signal frequency areas of the constituent MT structures are fully covered and the best possible structure is obtained. Multiple independently-reconstructed MT structures must be aligned rotationally and translationally before the required averaging step. The orientation and position of one MT structure is fixed, and the others are rotated around its axis by 1° increments for 360°, and shifted vertically by as much as 10 pixels in one-pixel increments Fig. 12(A) and (B). Cross-correlation with the fixed reference MT generates a cross-correlation map for each of the shifted MTs indicating the best alignment Fig. 12(C). When tubulin subunits match in 3D, the cross-correlation map has a knob-like peak. Since a and b tubulins are slightly different, the knobs display alternating high and low correlation maxima, indicating that a and b tubulins are in matched and unmatched positions in the heterodimers Fig. 12(C) and (D). The maximum correlation value is obtained when the a, b tubulin dimers match completely, i.e., the MTs are aligned. Finally, the MTs are aligned using the indicated rotation and shift parameters and averaged. The 3D auto-correlation map of the average structure obtained from five MTs indicates that there is a large structural difference between the a- and b-tubulin subunits (Supplementary Fig. S3 left). Moreover, the difference was still obvious in the auto-correlation map of the final reconstruction even when heavy 3D noise (minimum SNR, 10 dB) was added (Supplementary Fig. S3 right). The clear difference was further ascertained in the final optimization cycle of a MT reconstruction using the cross-correlation map between a 3D reference and one of the 12 reconstructions after the addition of


173

Fig.9. Initial 3D reconstruction of MT by filtered backprojection. (A) 3D volume, calculated by the filtered backprojection method using class averages corresponding to the specifically directed projections. Class average 1 is successively associated with 15 angles around the microtubule, corresponding to the 15 protofilaments. One turn of protomers is slightly less than 360°, resulting in a shift of 337.3°, one protomer less, after 18 turns. (B) The angular interval between each class average used for the reconstruction is calculated to be 23.82°, from the number of protomer turns in a superhelix and the number of protofilaments per turn. Each turn represents a 1.33° rotation.

heavy 3D noise (minimum SNR, 10 dB) (Supplementary Fig. S4). The resolution of the final average reconstruction obtained from the five MTs without added artificial noise, is better than 8.8 Å according to 0.5 criterion (7.8 Å according to the 0.143 criterion) of the Fourier shell correlation (FSC; Fig. 13).

and D). By contrast, the height of the auto-correlation peaks differs by 0.286 for our reconstruction (Supplementary Fig. S3C), which is much more.

4. Discussion 3.8. Method assessment To assess the advances brought by the presented procedure, we processed the MT images by a traditional single particle reconstruction method (Supplementary Figs. S5 and S6) and compared the results (Supplementary Fig. S6A and Fig. 13(A)). Although, the two 3D volumes are similar, the spatial resolution indicated by the FSC (0.143 criterion) is slightly lower for the traditional method, 8.4 Å compared to 7.8 Å for our method (Supplementary Fig. S6B and Fig. 13). Further, the a- and b-tubulin subunits of the reconstruction obtained by the traditional single particle method look very similar, and almost identical rotational auto-correlation peak heights are obtained (difference, 0.017; Supplementary Fig. S6C

The new reference-free reconstruction method based on an auto-frame adjustment strategy allowed a- and b-tubulins, which are known to be very similar (Gigant et al., 2000), to be completely resolved in a helical 15-Pf MT structure from cryo-EM data. Separate auto-framing of each MT based on the known periodicity of tubulin dimers in a perfect helix (8.2 nm), ensured that only MTs with the same stoichiometry and a- and b-tubulin arrangement were processed further. It also revealed lattice defects (Fig. 8) allowing bending to be accounted for and the most uniform MT segments to be selected. It is difficult to distinguish between a- and b-tubulins using earlier EM-based reconstruction methods, as the necessary signals are buried in the noise of the original low

174


1

18

2

Simulated annealing process FBP

Reprojection

1

1

18

18

2

2

Calculation of new score Selection of an image, changing its position

Judgment of the change

Fig.10. Outline of the simulated annealing 3D optimization method. The initial volume was improved by optimizing the centering (x, y) and in-plane rotation of the class averages using the echo-correlated 3D reconstruction method (Ogura and Sato, 2006). Starting from the primary centering and rotations (Fig. 9), one of the class averages is selected and its position (x, y) and rotational angle is changed at the 15 associated positions, corresponding to the 15 protofilaments. A new 3D volume is reconstructed by FBP (left). To evaluate the change, the volume is reprojected back in all class average directions. The cross-correlation between each reprojection and the class average is calculated, and the correlations are summed to yield the total 3D score, which serves as a 3D reconstruction accuracy index. The SA method evaluates whether or not to accept the change by comparing this score with the previous score. This process is iterated for the predetermined number of cycles. By the end of the annealing, each class average has been shifted to the appropriate position, improving the 3D structure.

Rotation 0o

1.1 nm

1.1 nm

-23.82o

-786.1o

Store

Average

Fig.11. 3D averaging method utilizing the Z-direction periodicity of a single MT structure. Similar slices appear at 1.1 nm intervals along the Z-axis. Each of the extracted images is rotated by 23.82° increments and averaged. Averaging is performed for the whole MT, and a refined 3D structure is built using these averages.

contrast micrographs (Li et al., 2002; Sui and Downing, 2010). This is illustrated by the MT reconstruction that we generated using a traditional single particle reconstruction method (Supplementary Figs. S5 and S6). Although the resulting 3D volume is similar to our structure, the spatial resolution is worse (compare Supplementary Fig. S6 and Fig. 13). Further, the a- and b-tubulin subunits building it are very similar, as documented by the almost identical rotational auto-correlation peak heights (Supplementary Fig. S6C and D), which is not the case for our reconstruction (Supplementary Fig. S3C).

Fig.12. Averaging multiple MT structures aligned using 3D cross-correlation map. (A) Reference MT structure; its orientation and position are fixed. (B) Target 3D structure to be aligned. (C) Cross-correlation map between the reference MT and the shifted/rotated target MT. The horizontal and vertical axes are rotation (degrees) and shift (pixels), respectively. The map shows many small knobs, which indicate positions where tubulin subunits of the target and reference match. The best rotational correlation (the maximum value in the horizontal direction) was between 248° and 270° depending on the shift (orange box). (D) Vertical line profile passing through the maximum values found in the horizontal direction from 248° to 270°. The profile is similar to a sine curve, but the heights of its peaks are alternately high and low, indicating matched and unmatched positions for a, btubulin dimers.


A

α β

Fourier shell correlation

B

1

0.5

175

by this new method might be longer than for other helical reconstruction methods. For the MT shown, the calculation of 60 cycles with 18 classes was finished in one day using a typical PC. The SA algorithm and its projection task can be effectively parallelized using a multi-core computer to shorten calculation time. Further, the method is promising for automation because the masking step is the only fully manual process. Our next goal is to develop a multi-process algorithm to automate the whole calculation and reduce the processing time to one hour. Most of the MTs in cells are comprised of 13-Pfs. As described in the introduction, 13-Pf MTs have a seam-line where different types of tubulins become neighbors. They are thus not strictly helical. The absence of a helical rule means that it is not possible to simply rotate the 3D volume by 27.7° (360°/13) to position an average subunit projection in equivalent positions along each Pf of the MT. This complicates the construction of an initial model and also makes echo-correlated 3D optimization and 3D averaging within the MT structure less straightforward. Further, as the seam-line of 13-Pf MTs is parallel to the longitudinal axis, all of the images cropped from a single MT will be classified in the same class and generate one 2D average. Together, these facts mean that images of several differently oriented MTs are required. After the autoframing and the averaging steps have been completed for every MT imaged, the 2D averages can be classified, assigned Euler angles and used to reconstruct a 3D volume, assuming asymmetry. Fortunately, adjustment of the Euler angles is restricted by the rotational direction around the longitudinal axis, simplifying the calculation. The modifications required to make the SA procedure outlined here applicable to 13-Pf MTs and to automate the processing are ongoing.

5. Conclusion

0.143 0

1/20

1/10

1/6.6

1/5

Resolution 1/Å Fig.13. Resolution of the average 3D MT structure. (A) Surface representation of the final average structure obtained by merging five different MT reconstructions. (B) The resolution of the 3D map was estimated using the FSC function. The 3D resolution calculated for the whole map was 8.8 Å using the 0.5 criterion (7.8 Å resolution using the 0.143 criterion).

Other single particle averaging techniques (Bluemke et al., 1988; Burgess et al., 2000; Egelman, 2000, 2007; Holmes et al., 2003; Li et al., 2002; Pomfret et al., 2007; Sachse et al., 2007; Sosa et al., 1997) aim to overcome helix perturbations occurring when flexible structures such as MTs are bent before or while they are frozen for cryo-EM. Nevertheless, the best resolution obtained to date for MTs is only about 10 Å. The SA-annealing method outlined here, adjusts the required filament framing to successfully follow bending. During the following annealing steps and Z-direction 3D averaging, the positional relationship between the a- and b-tubulin subunits is maintained in every class average, enabling the reconstruction of a 3D structure clearly revealing the a- and b-tubulin subunits. In this new method, a slow temperature decrease per cycle enhances convergence of the data to an accurate 3D reconstruction, which is similar to the crystallization of molecules in nature. As many annealing cycles have to be carried out in a limited period of time, this part of the processing is CPU-intensive. Furthermore, 3D-echo correlated calculation, including FBP and reconstruction, is itself CPU-intensive. Consequently, the calculation time required

Our results demonstrate that the reference-free, SA-based helical reconstruction method is a powerful tool for the reconstruction of 15-Pf MTs; a resolution of 8.8 Å using the 0.5 FSC criterion (7.8 Å resolution using the 0.143 FSC criterion) was obtained from the cryo-EM images allowing differences between a- and b-tubulins to be distinguished (Fig. 13; Yajima et al., 2012). The method can be applied to other helical protein complexes, and to helical structures in general, no matter whether they are tubes or rod-like. The prerequisite is knowledge of the helical rule describing their symmetry. If unknown, this can be determined from the Fourier transform of the 2D projections or by other single particle-based methods (Ramey et al., 2009; Wang and Nogales, 2005). Program parameters are easily set and the alignment and averaging steps improve the resolution obtained from cryo-EM images of flexible filaments. The procedure is expected to be automated and to be widely applied to noisy projections of elastic helices. Acknowledgments This work was supported by KAKENHI Grant-in-Aid for Scientific Research (B) and Grant-in-Aid for Exploratory Research from the Japan Society for the Promotion of Science, Grants from the Ministry of Education, Culture, Sports, Science, and Technology and CREST to T. Ogura and C. Sato and Grants to N. Hirokawa from the Ministry of Education, Culture, Sports, Science, and Technology of Japan, a Grant-in-Aid for Specially Promoted Research.

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jsb.2014.08.009.

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