The procedures outlined above were evaluated using simulated as well as experimental data. First, a simulated density map, or phantom, was used to assess the accuracy and speed of the projection and back-projection operations. For this purpose, a set of atomic coordinates of the 70S ribosome (PDB-IDs 2J00 and 2J01 ) (Selmer et al., 2006 (link)) was converted to a density map of voxels, with a voxel size of 2.8 Å, using the xmipp_convert_pdb2vol program (Sorzano et al., 2004 (link)). This map was projected in 5000 different orientations that were taken from a previously reported cryo-EM study on 70S ribosomes (Scheres et al., 2007a (link)). The resulting projections were then back-projected in their perfect orientations to generate a reconstructed density map, and the accuracy of this projection/reconstruction cycle was assessed by FSC-curves between this reconstruction and the original phantom.
Second, general refinement behaviour and computational costs of the MAP optimization approach were tested using an experimental cryo-EM data set of 5168 GroEL particles that is distributed as part of a workshop on the EMAN2 software package (Tang et al., 2007 (link)). Using standard procedures in XMIPP, see (Scheres, 2010 ) for details, all particles were normalized, 115 particles were discarded after initial sorting, and the remaining 5053 particles were windowed to images of 128 × 128 pixels, with a pixel size of 2.12 Å. Refinements with these data were performed in symmetry group D7; a soft spherical mask with a diameter of 205 Å was applied to the reconstructions at every iteration; and the starting model was obtained from a 50 Å low-pass filtered GroEL map from a previous study (Scheres, 2012 (link)). Reconstruction quality was assessed by FSC calculations between the reconstructed maps and a symmetrized GroEL crystal structure (PDB-ID1XCK ) (Bartolucci et al., 2005 (link)) that was also used to assess GroEL reconstructions in a previous study (Scheres, 2012 (link)). All estimated values in these refinements were multiplied by a constant . As explained in more detail in Scheres (2012) (link), values of T in the range of 2–4 typically yield better maps than those obtained with the original algorithm.
Additional tests to assess alignment accuracies were performed using simulated data that were designed to be similar to the experimental GroEL data. The symmetrized GroEL crystal structure was converted to a density map, to which a B-factor of 350 Å2 and an arbitrary scale factor were applied to yield a phantom with a similar power spectrum as the reconstruction obtained from the experimental data. This phantom was then projected into 5053 orientations, which comprised small random perturbations of the optimal orientations as determined for the experimental particles. For each simulated particle, identical CTF parameters were used as estimated for the experimental particles, and independent Gaussian noise was added in the Fourier domain using the same power spectra as estimated for the experimental data. FSC curves with the original phantom were used to assess the quality of reconstructions from these images, while the known orientations of all particles allowed the calculation of histograms of orientational error distributions.
Finally, to further illustrate its general applicability, RELION was applied to three additional cryo-EM data sets: 50,330 β-galactosidase particles that were described by Scheres et al. (2012) (link); 5403 hepatitis B capsids that were selected from re-scanned micrographs that were previously described by Boettcher et al. (1997) (link); and 3700 recoated rotavirus particle (RP7) that were described by Chen et al. (2009) (link). Crystal structures for these complexes are available: PDB-ID3I3E for β-galactosidase (Dugdale et al., 2010 (link)); PDB-ID 1QGT for hepatitis B capsid (Wynne et al., 1999 (link)); and PDB-ID 1QHD for the rotavirus VP6 protein (Mathieu et al., 2001 (link)). FSC calculations of the reconstructed maps vs. these crystal structures were used to assess the quality of the refinement results.
All calculations described in this paper were performed on Dell M610 computing nodes of eight 2.4 GHz Xeon E5530 cores and 16 Gb of RAM each. Projection and back-projection operations with the phantom were performed using a single core, while all other calculations used the hybrid parallelization scheme to launch eight threads on each of seven nodes, i.e. using 56 cores in parallel.
Second, general refinement behaviour and computational costs of the MAP optimization approach were tested using an experimental cryo-EM data set of 5168 GroEL particles that is distributed as part of a workshop on the EMAN2 software package (Tang et al., 2007 (link)). Using standard procedures in XMIPP, see (Scheres, 2010 ) for details, all particles were normalized, 115 particles were discarded after initial sorting, and the remaining 5053 particles were windowed to images of 128 × 128 pixels, with a pixel size of 2.12 Å. Refinements with these data were performed in symmetry group D7; a soft spherical mask with a diameter of 205 Å was applied to the reconstructions at every iteration; and the starting model was obtained from a 50 Å low-pass filtered GroEL map from a previous study (Scheres, 2012 (link)). Reconstruction quality was assessed by FSC calculations between the reconstructed maps and a symmetrized GroEL crystal structure (PDB-ID
Additional tests to assess alignment accuracies were performed using simulated data that were designed to be similar to the experimental GroEL data. The symmetrized GroEL crystal structure was converted to a density map, to which a B-factor of 350 Å2 and an arbitrary scale factor were applied to yield a phantom with a similar power spectrum as the reconstruction obtained from the experimental data. This phantom was then projected into 5053 orientations, which comprised small random perturbations of the optimal orientations as determined for the experimental particles. For each simulated particle, identical CTF parameters were used as estimated for the experimental particles, and independent Gaussian noise was added in the Fourier domain using the same power spectra as estimated for the experimental data. FSC curves with the original phantom were used to assess the quality of reconstructions from these images, while the known orientations of all particles allowed the calculation of histograms of orientational error distributions.
Finally, to further illustrate its general applicability, RELION was applied to three additional cryo-EM data sets: 50,330 β-galactosidase particles that were described by Scheres et al. (2012) (link); 5403 hepatitis B capsids that were selected from re-scanned micrographs that were previously described by Boettcher et al. (1997) (link); and 3700 recoated rotavirus particle (RP7) that were described by Chen et al. (2009) (link). Crystal structures for these complexes are available: PDB-ID
All calculations described in this paper were performed on Dell M610 computing nodes of eight 2.4 GHz Xeon E5530 cores and 16 Gb of RAM each. Projection and back-projection operations with the phantom were performed using a single core, while all other calculations used the hybrid parallelization scheme to launch eight threads on each of seven nodes, i.e. using 56 cores in parallel.
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