Date Published: June 01, 2018
Publisher: International Union of Crystallography
Author(s): Robert A. Nicholls, Michal Tykac, Oleg Kovalevskiy, Garib N. Murshudov.
REFMAC5 and related tools for the refinement of atomic models into cryo-EM reconstructions in CCP-EM are reviewed. An upper bound on the correlation between observed and calculated Fourier coefficients is identified, and the practical utility of map blurring/sharpening is discussed. The Divide and Conquer pipeline for refining large complexes in parallel, and ProSHADE for the identification of symmetries in a given map or coordinate set, are presented.
Macromolecular X-ray crystallography (MX), nuclear magnetic resonance (NMR) and cryo-electron microscopy (cryo-EM) are the three main experimental techniques that are used to elucidate macromolecular structures in order to answer biological questions. At present, the majority of the structural models deposited in the Protein Data Bank (PDB; Berman et al., 2002 ▸) have been derived using MX (>120 000 models), an order of magnitude more than the second most commonly used technique, NMR (>12 000 ensembles). Although the current proportion of models derived using cryo-EM is comparatively small (>2000), it is becoming the tool of choice owing to the so-called ‘resolution revolution’ caused by rapid advances in instrumentation and software (Faruqi & McMullan, 2011 ▸; Lyumkis et al., 2013 ▸; Kühlbrandt, 2014 ▸; Scheres, 2014 ▸).
It is well known that for the purpose of map calculation the phases of structure factors are more important than their amplitudes. To analyse this statement, we can consider the correlation between the current and ‘ideal’ maps. Specifically, since correlations calculated in real and reciprocal space are equivalent, we consider the Fourier shell correlation (FSC) calculated over all structure factors,where a subscript C denotes the current map and a subscript t denotes the ‘true’ (or ‘ideal’) map, and ρ represents map density with corresponding structure factors F with amplitudes |F| and phases φ. If we consider structure factors in a narrow resolution range then we can express the FSC in terms of the normalized amplitudes |E|. Then, under the assumptions that the reciprocal-space points are sufficiently dense and that the distribution of Fourier coefficients in shells reflects the ‘true’ distribution, we can express the FSC as the expected value of the weighted cosine of phase differences,
In practice, we are not able to directly calculate the FSC between the current and ‘ideal’ maps. However, we are able to calculate the correlation between the observed and calculated coefficients: cor(Fo, Fc). Furthermore, if half-data sets are available then we are also able to calculate the FSC between the two half-data sets: FSC1/2. Therefore, we are able to consider the relationship between FSC1/2 and cor(Fo, Fc).
In cryo-EM, variability of the reconstructed molecule owing to heterogeneity of the sample and computational inaccuracies during the reconstruction causes blurring of the signal in the map. Map sharpening has been used to counter over-blurred maps, resulting in features in the map being revealed (Brunger et al., 2009 ▸; Nicholls et al., 2012 ▸), noting that other approaches towards map modification have been employed with a similar objective both in the context of MX (Afonine et al., 2015 ▸) and cryo-EM (Jakobi et al., 2017 ▸; Terwilliger et al., 2018 ▸). Conversely, if the map has been over-sharpened then blurring may be required. Reconstruction programs perform post-processing in order to deblur or sharpen the resultant map. However, even if the noise variance is constant within the reconstructed map, owing to the varying mobility of the molecule over space it can be expected that the signal-to-noise ratio will also vary over space. The deblurring parameter should depend on the signal-to-noise ratio, so a single parameter value may not be sufficient for all parts of the map. Consequently, different parts of the map may require different levels of sharpening/blurring for optimal interpretation, and thus may still need additional sharpening or blurring in order to achieve optimal results.
One important similarity between MX and cryo-EM is that the data derived using both techniques come from scattering experiments. In both cases there is typically high-resolution information loss. Sufficient quality lower resolution information is typically obtained (for example regarding the overall shape and position of macromolecular domains) but the quality of the data degrades as the resolution increases, inhibiting the observation of finer structural details. Thus, for both techniques it is necessary to somehow account for the loss of high-resolution information that could not be observed sufficiently well during the experiment.
Many protein structures are known to have rotational symmetry, with over 38% of the entries in the PDB having some form of rotational symmetry assigned. The symmetry information is frequently used in structure solution as well as to decrease the storage requirements by storing only the asymmetric portion of the structure and all symmetry operators required to generate the full structure. While the symmetry is usually known when the structure is being solved, there is a lack of a simple tool for rotational symmetry detection in either electron-density maps or atomic models.
In this contribution, we describe several tools available from CCP-EM (Wood et al., 2015 ▸) and CCP4 (Winn et al., 2011 ▸). We anticipate that the Divide and Conquer algorithm will become useful in facilitating the refinement of large molecules with potentially multiple maps corresponding to multiple focused reconstructions. We emphasize the importance of selecting appropriate levels of map blurring/sharpening, which may be facilitated by considering the behaviour of the average map amplitude at different resolutions, and the utility of simultaneously viewing multiple blurred/sharpened maps. These tools are available from within the CCP-EM interface (Burnley et al., 2017 ▸).