Cryo-EM Refinement Protocols for Macromolecular Structures

All other image processing operations were performed in the XMIPP package.¹⁸ (link) Prior to refinement, all data sets were normalized using previously described procedures.⁵ (link) MAP refinements and projection matching refinements in XMIPP were performed with similar settings where possible. Although the implementation of the MAP approach readily handles anisotropic CTF models, all refinements were performed with isotropic CTFs (without envelope functions) for the sake of comparison with XMIPP. All orientational searches, or integrations in the statistical approach, were performed over the full five dimensions, that is, three Euler angles and two translations. For both the thermosome and the GroEL refinements, the first 10 iterations were performed with an angular sampling of 7.5°, and subsequent iterations were performed with an angular sampling interval of 3.75°. Thermosome refinements were stopped after 15 iterations, and GroEL refinements, after 20. Translational searches were limited to ± 10 pixels in both directions in the first 10 iterations and to ± 6 pixels in the subsequent iterations. Although it is common practice in XMIPP to reduce computational costs by breaking up the orientational search into separate rotational and translational searches and to limit rotational searches to local searches around previously determined orientations, this was not done in the refinements presented here for the sake of comparison with the MAP approach. Refinements with angular sampling intervals as fine as 1° where such tricks were employed did not result in better reconstructions (results not shown).
The true resolution of the GroEL reconstructions was assessed by FSC with a published crystal structure (Protein Data Bank ID: 1XCK). This structure contains 14 unique monomers in its asymmetric unit. Each of these monomers was fitted separately into the reconstructions using UCSF Chimera,⁴¹ (link) and for each monomer, the equatorial, intermediate, and apical domains were allowed to move independently as rigid bodies. The resulting coordinates were converted to an electron density map that was symmetrized according to D7 symmetry. Optimization of the relative magnification between this map and the cryo-EM reconstructions revealed that the effective pixel size of the cryo-EM images was 2.19 Å, differing by 3% from the nominal value, and this value was used to generate all plots in Fig. 3.
Ribosome refinements were performed for 25 iterations with an angular sampling of 7.5° and translational searches of ± 10 pixels. To generate K = 4 unsupervised initial starting models from a single  80-Å low-pass filtered initial ribosome structure, during the first iteration, we divided the data set into four random subsets in a way similar to that described before.²¹ (link)