Date Published: June 01, 2018
Publisher: International Union of Crystallography
Author(s): Thomas C. Terwilliger, Oleg V. Sobolev, Pavel V. Afonine, Paul D. Adams.
A procedure for optimizing the sharpening of a map based on maximizing the level of detail and connectivity of the map has been developed and applied to 361 pairs of deposited cryo-EM maps and associated models.
Current methods for single-particle reconstruction of cryo-EM maps are capable of yielding maps with resolutions that are often better than 4.5 Å and are sometimes as high as 2 Å or better (see Kühlbrandt, 2014 ▸; Baldwin et al., 2018 ▸). The level of noise in the images used in reconstruction and in the resulting maps is highly resolution-dependent. For this reason, it is standard practice to represent a map as a Fourier series, estimate the signal and noise in the reconstruction as a function of resolution, and use this information to weight the Fourier terms as a function of resolution to maximize the interpretability of the final sharpened (or blurred) map (Rosenthal & Henderson, 2003 ▸). As the various errors in reconstruction are difficult to estimate accurately, other approaches for resolution-dependent weighting have also been considered. For example, feature-enhanced maps (FEMs; Afonine et al., 2015 ▸) and the model-building software Coot (Emsley et al., 2010 ▸) use maximization of the kurtosis of a map to choose an overall sharpening Bsharpen (an exponential factor applied to Fourier terms; see DeLaBarre & Brunger, 2006 ▸; Wlodawer et al., 2008 ▸). Nicholls et al. (2012 ▸) developed procedures for optimizing anisotropic versions of displacement factors based on considering sharpening as an inverse deblurring problem. Joseph et al. (2016 ▸) used the method of Rosenthal and Henderson for map sharpening during the refinement of macromolecular structures. Burnley et al. (2017 ▸) have recently noted that the challenge of optimizing map sharpening is an open one, with the comment that Presently, the optimum sharpening coefficient (where ‘optimum’ means maximizing the interpretable density features) cannot be analytically determined either locally or globally, although attempts are ongoing.Model-based approaches have been used for this purpose, however. Falke et al. (2005 ▸) used the resolution-dependence of a model-based map in a sharpening procedure, and recently Jakobi et al. (2017 ▸) applied such a sharpening procedure locally to optimize the contrast and interpretability of density maps. Sharpening is also commonly applied in X-ray crystal structure analysis. DeLaBarre & Brunger (2006 ▸) suggested strongly sharpening low-resolution maps; their procedure leads to an overall B value Biso (isotropic Wilson B factor; here iso stands for isotropic; closely related to B factors or atomic displacement factors; see DeLaBarre & Brunger, 2006 ▸; Wlodawer et al., 2008 ▸) of about zero. The PHENIX (Adams et al., 2010 ▸) tools AutoSol (Terwilliger et al., 2009 ▸) and AutoBuild (Terwilliger et al., 2009 ▸) use map sharpening routinely in automated map interpretation and sharpen maps to an overall B value numerically given by ten times the resolution in Å units (e.g.Biso = 40 Å2 at a resolution of 4 Å; Terwilliger et al., 2008 ▸). Liu & Xiong (2014 ▸) applied sharpening to nearly 2000 X-ray maps and found that the map–model correlation could generally be improved through map sharpening.
Our major observation is that it is possible to automatically identify optimized sharpening parameters for cryo-EM maps by simultaneously maximizing the level of detail in the maps and the connectivity of the maps. The adjusted surface area of a map reflects these factors and does not require a model or any other prior interpretation of a map, and maximizing it leads to improved maps. A secondary observation is that a useful metric of cryo-EM map quality is the correlation between the map and a model-based map in which the atomic B values all have values of zero. Applying our automatic map-sharpening procedure to 361 cryo-EM maps with resolutions from 1.8 to 4.5 Å and evaluating the resulting maps using this metric, we find that our procedure can improve deposited maps, that it is an improvement over both kurtosis-based and half-map sharpening procedures, and that it is about equal overall to model-based map sharpening, all as implemented in our tools.