Gilbert et al. 10.1073/pnas.0505062102. |
Fig. 4. Cryo-EM of SHBsAg particles as used in the reconstructions reported in the main paper.
Fig. 5. Class averages for SHBsAg particles as used in the reconstructions reported in the main paper. (Upper) A variety of sizes and morphologies are apparent. (Lower) Rotationally averaged representative class averages for two different sizes of particle, as used in initial fractionation of the data set.
Fig. 6. Self-rotation functions of tetrahedrally averaged reconstructions of small- and large-particle forms for SHBsAg and of HBV core antigen (HBcAg) viewed in each case for the sections k = 72°, 90°, 120°, and 180°, for fivefold, fourfold, threefold, and twofold symmetry, respectively.
Fig. 7. Reprojections of maps of the small- and large-particle forms of SHBsAg, covering the asymmetric unit of the octahedral reconstructions.
Fig. 8. (a) Plot of particle cross-correlation coefficient (CC) for each data image against either the large reconstruction (x axis) or the small reconstruction (y axis). Data points for those particles that were assigned to the large particle subset are red, and data points for those particles assigned to the small particle subset are blue. (b) Plot of particle rank by cross-correlation coefficient against either the large reconstruction (x axis) or the small reconstruction (y axis). Data points are colored as in a.
Fig. 9. (a) Octahedral assembly of dimers of bacteriorhodopsin fitted into the asymmetric unit of the small SHBsAg reconstruction, as used in scaling of Fourier amplitudes for the final reconstructions. (b) As a for the large reconstruction.
Fig. 10. The upper plot shows the determination of the hand of the Escherichia coli ribosome by using a –15° tilt, with the phase residual minimum arising in the correct position, at –15° in the horizontal axis. The lower plots show hand determination of the small- and large-mHBsAg particle maps. On the Left, the small map plot is shown in the hand in which it was originally reconstructed, which shows a peak at +15° and, therefore, that the hand was incorrect. The hand of the maps was inverted and the hand determination was repeated (Right), confirming that the correct hand has been determined.
Supporting Text
For most of the image processing, the images were binned to a pixel size of 4.38 Å to ease computational load, but the final reconstruction cycle used images with pixels of 2.738 Å. A raw image of mHBsAg particles in shown in Fig. 4.
Classification of cryo-EM projection images of mSHBsAg by multivariate statistical analysis by using the image-processing program imagic (1) produced image classes and thereby class averages that were clearly of differing size and could be roughly separated by eye into a larger and a smaller subset of images, with the smaller subset predominating (Fig. 5 Upper). To separate particles of different size from each other we cross-correlated individual projection images that had been filtered to low resolution and rotationally averaged in spider (2) with representative rotational averages of a small and a large form of the particle (Fig. 5 Lower). We then selected only those images for the small and large subsets that correlated highly with one or other of the reference rotational averages. The total data set of mHBsAg particles was 1,793 projection images, obtained at 26 different defocuses and corrected for their contrast transfer functions. From these, the 764 particles best correlating to the small rotational average were used in seeking a first reconstruction of the small mHBsAg particle, and the 318 best correlating to the large rotational average were used in the same way for the large particle form.
The embl suite of icosahedral image processing programs (3) was used to make an icosahedral reconstruction of both large and small forms of the HBsAg particle. The reconstructions obtained were "featured" but lacked, in particular, any orientation that gave an ovoid appearance as previously observed (4) and as seen in some class averages (Fig. 4 and ref. 5). Furthermore, although two- and threefold axes have been observed in HBsAg particles previously, fivefold axes have not (4). The formation of two discrete populations of particle by the same molecule indicates self-assembly by equivalent or quasiequivalent interactions, implying that the mSHBsAg particles have the symmetry of one of the five Platonic solids (6, 7). We, therefore, used the lowest Platonic symmetry, tetrahedral symmetry, to align particles and calculate reconstructions, and searched for signals from higher symmetry in the resulting maps. We first calculated a reconstruction for both small and large forms by using imagic (1) with orthogonal 2-2-2 symmetry imposed. We then used frealign (8) to perform cycles of reconstruction with 3-2 symmetry imposed. As a control, images of the icosahedral HB core were reconstructed in the same way. The 3-2 averaged map was further averaged up to full 4-3-2 and full 5-3-2 symmetry (for the 5-3-2 symmetry in both possible settings of the twofold axes), monitored by calculation of correlation coefficients and R factors, by using gap (9, 10). Additionally, self-rotation functions (11) were calculated to locate symmetry axes present in the map and so diagnose 5-3-2 or 4-3-2 symmetry from the presence or absence of fivefolds, the number and position of threefolds, etc. Self-rotation functions were computed in cns (12) and were displayed by using gropat (R. M. Esnouf, personal communication). The result was that although the HB core particle averaged with the best self-correlation and R factor as an icosahedron such that the correct twofold-axis setting could be distinguished [octahedral cross-correlation coefficient (CC) 0.30, R factor 80%; icosahedral CC 0.64, R factor 56%], the HB sAg particles averaged best as octahedra (small data set, octahedral CC 0.89, R factor 42%; icosahedral CC 0.59, R factor 67%; large data set, octahedral CC 0.89, R factor 37%; icosahedral CC 0.65, R factor 62%). Furthermore, whereas the core particle self-rotation function indicated the correct symmetry axes for 5-3-2 symmetry in the object, the mSHBsAg particle gave the correct axes for 4-3-2 symmetry (Fig. 6). Finally, the subaveraged (tetrahedral, 3-2) map showed the same morphology as an octahedrally averaged map. We, therefore, concluded that the HBsAg particle in both small and large forms is octahedral. To ensure that the small and large particle structures resulted from ensembles of projection images with the correct projection angles, we averaged the two reconstructions together and repeated the alignment procedure. The small-particle subpopulation yielded a map similar to that previously determined for the small particle, and the large-particle subpopulation likewise, presumably because the symmetry assists in determination of particle orientations to a significant extent. We, therefore, concluded that the two reconstructions were genuine and do not arise from erroneously assigned projection angles.
We then began the structure determination again, using octahedral symmetry in frealign (8) for the original small and large data subsets. The reconstructions were refined iteratively, monitored by the Fourier shell correlation (FSC) of the last cycle’s map. When the FSC was free of oscillations and >0.5 at the resolution to which the structure had then been calculated, the resolution was raised. Additionally, B-factor-defined weighting of individual images was used. When no further advance in resolution could be made (at 15 Å for the small particle form, at 17 Å for the large) the small and large particle size subsets were reselected by using cross-correlation of rotational averages, with rotational averages of computed reprojections covering the asymmetric unit of each current small and large map. The 945 images best correlating to the small reference were then taken as a new small-particle data set, and the 721 images best correlating to the large reference, as a new large one. The resolution was relaxed to 25 Å and the iterative refinement of the two reconstructions, using the new data sets, recommenced. The inclusion of more images than before in both small and large classes together with the refinement of particle selection produced an increase in the resolution to which the structures could be refined of 13.5 Å and 14 Å, respectively. This same procedure was repeated once more, using images with a pixel sampling of 2.738 Å. Each projection image was assigned to either the class of small particles (911 images) or the class of large particles (882 images). In this final round of reconstruction, the resolution was refined to 12.5 Å in both cases. Finally, the particles were reconstructed in spider (2), yielding maps with resolutions of 12.0 Å each. Reprojections of those maps within the limits of the asymmetric unit are shown in Fig. 7, and a graphical analysis of the data set is shown in Fig. 8.
Fig. 9 shows representations of the atomic model built for each particle size by using bacteriorhodopsin for the purpose of the scaling of the Fourier amplitudes of each map. This exercise serves to put the amplitude distribution on an appropriate scale and so to counteract the effects of the amplitude component of the Contrast Transfer Function (13).
The hand of the structure was determined by using the method of Rosenthal and Henderson (14). Pairs of cryomicrographs were captured with a –15° rotation (anticlockwise when viewing the sample holder down its axis and toward the microscope column). Particles from the scans had to be separated into those that are projections of small mSHBsAg particles and those that represent large ones. This fractionation was done by using the same approach outlined above for the data set proper and resulted in the designation of 18 particles as small and 24 particles as large. The hand determination showed that both reconstructions had the same, incorrect hand. The correctness of hand was with respect to the previously determined handedness of the Escherichia coli ribosome, which has a known hand (Fig. 10). The hand of the reconstructions was then flipped (in gap; ref. 9) and the hand determination was repeated (Fig. 10 shows one result each from before and after hand calculation). Demonstrating the absolute hand of a reconstruction in this way in addition validates the reconstruction.
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