Nature Methods: doi: /nmeth Supplementary Figure 1

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1 Supplementary Figure 1 Schematic demonstrating the preferred orientation sampling problem in single-particle cryo-em. Specimens sticking to the air-water interface or a substrate support of a cryo-em grid in a single preferred orientation always adopt random in-plane orientations. Tilting of the specimen stage therefore leads to (a) a precession of views around the axis of preferred orientation in a conical manner (precession indicated in green with grey arrows, axis of preferred orientation is indicated by a red arrow). (b) Projections of the object in (a) are displayed for 30 and 60 tilts (theta angle), both at a φ angle increment of 15. Whereas the 30 tilted projections resemble more the top views of the object, the 60 tilted projections resemble more the side views of the object. (c) In reciprocal space, each Fourier slice inserted into the reconstruction is perpendicular to the direction of its real-space projection image. Therefore, a large missing cone is formed from a reconstruction using 30 tilted images, and a much smaller missing cone is present from a reconstruction using 60 tilted images. No missing cone would be present for (hypothetically) 90 tilted images, although the X/Y plane would be characterized by 1D lines rather than a complete 2D slice. The practical implications of this diagram and anisotropic sampling are demonstrated in Supplementary Figure 2.

2 Supplementary Figure 2 3D reconstructions of a synthetic, absolutely preferred dataset of an HA trimer presumed to be tilted at various angles.

3 (a) Euler angle distribution profiles of the synthetic projections. (b) The resulting 3D reconstructions. The red arrow shows the direction of preferred orientation. The grey arrows show the angle at which the synthetic projection images were generated at the various tilt angles. A synthetic dataset of equally sampled HA trimer is also shown for comparison in the last row. (c) Slice through the 3D FSC volumes describing the 3D reconstructions along the X/Z plane. The 3D FSC was thresholded at 0.143, while sphericity was calculated by thresholding the 3D FSC at 0.5 and applying a Gaussian filter of 2 pixels. Due to C3 symmetry along the Z-axis of the reconstruction, only the X/Z slice of the 3D FSC is shown. Missing cones are apparent within the 30, and especially the 60 3D FSCs. (d) Plots of the global FSC after reconstruction (solid blue line), the spread of the directional resolutions defined by plus and minus one standard deviation from the mean of the directional resolutions (green area encompassed by green dotted lines) and the histogram of one hundred directional resolutions evenly sampled over the 3D FSC (yellow bars). Labels on the left Y-axis refer to global FSC curves, while labels on the right Y-axis refer to directional FSC histograms. The grey dotted line indicates when FSC =

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5 Supplementary Figure 3 HA trimer per-tilt analysis. HA trimer cryo-em data was collected (a) untilted, or at tilts of (b) 10, (c) 20, (d) 30, (e) 40, and (f) 50. Representative 2D class averages for each tilt angle are shown as insert. (g) The average frame-to-frame shift for each tilt angle is shown for both the first 15 frames and also for the entire range of 100 frames (insert). The exact cause of the slightly higher beam-induced movement within the 0 dataset is unclear and was not observed for the ribosome dataset (Supplementary Figure 6g).

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7 Supplementary Figure 4 Tilting improves resolution and directional isotropy in a direct comparison of HA trimer reconstructions without and with tilting. (a) Euler angle distribution of the particles. (b) 3D reconstruction superimposed onto a projection of the HA trimer crystal structure (pink). Loss of axial density at typical display thresholds is clearly evident within reconstructions from 0, 10, and 20 tilted images. (c) Close-up of a particular region within the reconstruction. Circled region indicates false positive density resulting from elongation of the reconstruction along the Z-axis, which progressively disappears within reconstructions from higher tilts characterized by improved directional resolution isotropy. (d) Slice through the 3D FSC describing (top, solid blue outline) half-map, resolution evaluating internal consistency and (bottom, dotted purple outline) map-to-model resolution evaluating external consistency, along with their corresponding sphericity values (e). 3D FSC sphericity values. The slight dip in 3D FSC sphericity at 10 is caused by greater improvements in directional resolution perpendicular to the preferred orientation axis that are not met with a concomitant increase in Z resolution. (f) Graph showing the global half-map resolution (solid blue), map-to-model resolution (dotted purple), and spread of directional resolution (refer to Supplementary Figure 2 for detailed graph description).

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9 Supplementary Figure 5 HA particle titration experiment. HA trimer reconstructions using subsets of particles from (a) untilted and (b) 40 tilted images. Random subsets of particles from the 130,000 total particles, in multiples of 13,000, were selected for each titration point and refined independently. The half map resolution (using threshold) and map-to-model resolution (using 0.5 threshold) against the structure of HA (PDB 3WHE) is shown for each titration point. The Euler angle distribution of the reconstructions at each titration point for the (c) dataset from 0 images and (d) 40 tilted images show that the apparent side views in the untilted reconstruction (green arrows) only appear when more particles are added to the reconstruction, indicating overfitting.

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11 Supplementary Figure 6 Per-tilt analysis of L17-depleted 50S ribosomal assembly intermediates (LSU bl17dep ). Cryo-EM data was collected (a) untilted and at tilts of (b) 10, (c) 20, (d) 30, (e) 40 and (f) 50. The average frame-to-frame shift for each tilt angle is shown for both the first 15 frames (g) and also for the entire range of 50 frames (insert). (h) The 4 super-classes of L17-depleted 50S ribosomal assembly intermediates are shown.

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13 Supplementary Figure 7 LSU bl17dep Class B. For each tilt angle, the figure shows (a) Euler angle distributions of the particles, (b,c,d) 3D FSC at orthogonal views, and (e) global half-map and map-to-model FSC plots with the spread of directional resolutions defined by the green area and 3D FSC values overlaid as histograms. Direction of preferred orientation is indicated by the red arrow.

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15 Supplementary Figure 8 LSU bl17dep Class C. For each tilt angle, the figure shows (a) Euler angle distributions of the particles, (b) an alpha helix density from ul29 protein, (c,d,e) 3D FSC at orthogonal views, and (f) global half-map and map-to-model FSC plots with the spread of directional resolutions defined by the green area and 3D FSC values overlaid as histograms. Direction of preferred orientation is indicated by the red arrow.

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17 Supplementary Figure 9 LSU bl17dep Class D. For each tilt angle, the figure shows (a) Euler angle distributions of the particles, (b) an alpha helix density from ul29 protein, (c,d,e) 3D FSC at orthogonal views, and (f) global half-map and map-to-model FSC plots with the spread of directional resolutions defined by the green area and 3D FSC values overlaid as histograms. Direction of preferred orientation is indicated by the red arrow.

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19 Supplementary Figure 10 LSU bl17dep Class E. For each tilt angle, the figure shows (a) Euler angle distributions of the particles, (b) an alpha helix density from ul29 protein, (c,d,e) 3D FSC at orthogonal views, and (f) global half-map and map-to-model FSC plots with the spread of directional resolutions defined by the green area and 3D FSC values overlaid as histograms. Direction of preferred orientation is indicated by the red arrow.

20 Supplementary Figure 11 Tilting improves resolution and angular isotropy for all four super-classes of L17-depleted 50S ribosomal intermediates. For the four super-classes, B-E, the changes in (a) resolution, (b) half-map 3D FSC sphericity, and (c) map-to-model 3D FSC sphericity are plotted with respect to the dataset from untilted images and as a function of tilt angle (see Supplementary Figures 7-10 for all raw data). Map densities of (d) beta sheets and (e) alpha helices from reconstructions at various tilts for class E are also shown to illustrate the effects of change in resolution and resolution anisotropy (the two are interrelated). Beta sheets are from ul22 and the alpha helices are from ul29. Side chain densities are marked by red asterisks, while beta sheet separation is indicated by a green arrow. The direction of preferred orientation is indicated by the red double-headed arrow. As expected, map isotropy steadily improves with increasing angular tilt, which also affects global resolution and can accordingly facilitate interpretation of structural features. For example, smearing of beta-strands (d) and alpha-helices (e) parallel to the direction of preferred orientation is ameliorated with tilts, which can be especially important at borderline resolutions for interpreting atomic models.

21 Supplementary Figure 12 Tilt angles up to 50 provide near-atomic resolution single-particle reconstructions. (a) 3D reconstruction from a preferred oriented LSU bl17dep ribosomal intermediate dataset, where particles were combined from all super-classes but only using data from 50 tilted images. The sample heterogeneity from combining different super-classes is reflected in the local resolution colored onto the reconstruction. Whereas the peripheral density changes, the homogeneous core components are much better resolved. (b) Global half-map 3D FSC and (c) map-to-model 3D FSC. The high tilt angle used for collection results in nearly spherical 3D FSCs, with sphericity of 0.98 and 0.92 respectively. (d) The ten best resolved ribosomal proteins have resolutions of between 4.2 Å and 4.8 Å. (e-g) Map density of (e) bl21, (f) bl20 and (g) ul29 show side chain density and separation of beta strands.

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23 Supplementary Figure 13 Workflow for collection of single particle data at tilts. Data can be collected at either one or multiple tilt angles. Other than the need to tilt the stage and perform per-particle CTF estimation, the other processing steps are similar to a conventional single particle cryo-em workflow. In order to analyze the degree of directional anisotropy, 3D FSC is performed at the end (isosurface shown) and its results are visualized in Chimera - when rotating the map, the map s color and associated directional FSC line component changes on the fly, enabling immediate assessment of resolution anisotropy.

24 Supplementary Note 1 Previous efforts to overcome preferred specimen orientation in single-particle cryo-em Given the plethora of samples affected to various extents by preferred specimen orientation, efforts have been made to solve this problem, with and without the implementation of tilts. Experimentally, one can collect the same field of view at multiple tilts and rely upon the differences in the goniometer tilt angle to define relative differences in orientations, as exemplified by the random conical 1, 2 or orthogonal tilt 3 reconstruction schemes in their explicit implementations. The drawback of these approaches is that multiple exposures of the same area generates beam-induced movement that cannot be explicitly accounted for by the absolute difference in relative tilt 4, which in principle limits the achievable resolution. Variations on tilted single-particle 5 or tomographic reconstruction methods 6 have also generally been limited to low resolutions. One recent tomographic reconstruction has reached near-atomic resolution, but required ~600k asymmetric units for the reconstruction and benefitted from isotropic orientation distribution during sub-tomogram selection on virus surfaces 7. The grids themselves can also be treated to induce additional orientations, for example by using a continuous layer of carbon as a substrate 8, coating with self-assembled monolayers 9, treating the carbon support in the presence of N-amylamine 10, or mechanically deforming the grid 11. Additives like poly-l-lysine 12 or detergents 13 can sometimes increase the range of orientations the molecules adopt. None of these techniques are generally applicable, and most have drawbacks, such as reduced particle contrast (e.g. poly-l-lysine or support films) or the requirement of significantly higher specimen concentrations (e.g. detergents). Computationally, 3D reconstruction procedures can partially compensate for and up-weight under-represented views 14, but they are not able to recover missing information if it is absent. A brute force approach is to simply collect more particles to obtain sufficient quantities of low abundance views 15.

25 Supplementary Note 2 Preferred specimen orientation leads to uneven coverage in reciprocal space Preferred particle orientation on a cryo-em grid arises from specimen interaction with the air-waterinterface 16, 17. In a typical single-particle cryo-em data collection in the absence of any tilts, the axis of preferred orientation is approximately parallel to the axis of the electron beam. Since individual particles adopt random in-plane orientations with respect to the electron beam, physically tilting the stage induces a precession of angular sampling around each preferred orientation axis, of which there may be several in any individual dataset. Thus, for each subset of preferred angular orientations, tilting the specimen stage fills reciprocal space with Fourier slices that are distributed in a conical fashion around the axis of preferred orientation (Supplementary Fig. 1).

26 Supplementary Note 3 Evaluation of directional resolution and density isotropy within synthetic single-particle data To demonstrate how different angular samplings affect the directional resolution of a 3D reconstruction, we used a synthetic dataset that simulates the effects of imaging under an electron microscope at defined orientations relative to the electron beam. The HA envelope trimer (PDB 3WHE) was selected as the biological sample for the synthetic dataset, as it exhibits a highly preferred orientation when vitrified on an EM grid (see also Supplementary Note 4). Four synthetic datasets were generated (Supplementary Fig. 2), with the specimen assumed to be preferentially oriented along its long axis and tilted at 30, 60, 90, or uniformly in all directions (Supplementary Fig. 2a-b). The density map improves monotonically with increasing tilt angle; notably, at 60 tilt angle, the map becomes visually very similar to the more isotropic reconstructions. The 3D FSC effectively incorporates a series of 1D directional FSC curves computed over distinct angles and compiled into a 3D volume, which then fully describes directional anisotropy. Throughout this manuscript, the 3D FSC is displayed as a slice through the volume at a nominal threshold (0.143 here), which provides a quantitative evaluation of resolution and helps to show the degree of deformation in the directions along the displayed plane. A simple calculation of 3D FSC sphericity (ranging from 0 to 1) approximates density isotropy (Supplemental Fig. 2c). For example, the dataset from 30 images is characterized by a dramatic loss of resolution in the Z direction, parallel to the electron beam, resulting in a pancake-shaped 3D FSC (sphericity 0.63). This effect is smaller, albeit still present for the reconstruction from 60 tilts (sphericity 0.84). A reconstruction from 90 tilts (sphericity 0.99) or from uniformly distributed projection orientations (sphericity 1.00) produces an isotropic 3D FSC. Distinct directional resolution values obtained at a nominal cutoff threshold can also be plotted as a histogram onto a conventional 2D FSC plot and compared with the global resolution (Supplemental Fig. 2d). As expected, improvements in directional resolution isotropy parallel improvements in global resolution. In sum, this analysis shows that, under ideal conditions, improvement in angular distribution and density isotropy results in: 1) a reconstruction with higher resolution features, 2) a 3D FSC that becomes more spherical, 3) reduced spread of directional resolutions, and 4) overall improvement in individual directional resolution components.

27 Supplementary Note 4 Rationale for selecting influenza hemagglutinin (HA) trimer as test sample To evaluate how tilts affect structure determination of samples exhibiting a highly preferred orientation, we utilized the soluble portion of the small, 150 kda influenza hemagglutinin (HA) trimer. The HA trimer was selected as a test sample for several reasons: 1) there are numerous highresolution crystal structures present in the public domain; 2) it is clinically relevant 18 ; 3) its molecular weight is low for cryo-em structure determination; 4) most importantly, it exhibits a single, highly preferred top orientation on vitrified cryo-em grids (Supplementary Fig. 3). The HA trimer therefore presents many challenges to conventional EM structure determination it has been solved at low resolution using electron tomography and negative stain, but thus far there has not been a highresolution single particle cryo-em reconstruction.

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