DeepRes: a new deep-learning- and aspect-based local resolution method for electron-microscopy maps

A method (DeepRes) is presented to estimate a new local quality measure for 3D cryoEM maps that adopts the form of a ‘local resolution’ type of information. DeepRes is fully automatic and parameter-free and avoids the issues of most current methods, such as their insensitivity to enhancements owing to B-factor sharpening, among others.


S1.1. Fourier Shell Correlation (FSC)
The FSC is currently the most widely used algorithm to determine the resolution of CryoEM maps (Saxton & Baumeister, 1982, Saxton, 1978, Harauz & van Heel, 1986. To measure the FSC curve, two independently determined 3D volumes are required. This algorithm defines the resolution as the maximum frequency at which the correlation between both is above a given threshold. Based on this principle, but with a moving window of a previously fixed size, BlocRes (Cardone et al., 2013) was proposed to determine the local resolution of cryoEM maps. However, as described by Unser and colleague s (Unser et al., 2005) and Sorzano and colleagues (Sorzano et al., 2017); the FSC is invariant to isotropic filters, therefore being invariant to a transformation of the type B-factor correction (Rosenthal & Henderson, 2003). Despite this, it is known that CryoEM maps significantly benefit of a post-processing step (sharpening) that allows increase signal at medium/high resolution, and qualitatively improve map quality. One of the most widely used methods for sharpening is just the correction for a negative B-factor, and most of the maps deposited in EMDB are the result of this processing step. Although the quality of the map is significantly improved with postprocessing, the FSC and all its derived measured are insensitive to the change produced (unless other changes are introduced at the same time such as, for instance, at the masking level). The insensitivity of the FSC to an isotropic filter (as B-factor correction) is shown below.
Consider two independent reconstructed density maps f1 and f2, being F1 and F2 the Fourier transform of f1 and f2 respectively, the FSC is normally defined as where is the three-dimensional frequency vector, R its module and (R , ∆R)the shell of those frequencies such that ≤ ‖ ‖ < + ∆ .
Consider H(R) as an isotropic filter that acts on the volumes f1 and f2 (HF1 and HF2), then the FSC is defined as Note that as H(R) is an isotropic filter, then H( ) = H(R) ∈ ℝ and FSC(R, ∆R) = FSC (R, ∆R), being the FSC curve insensitive to the filter application (in this case B-factor correction).
Supplementary Figure 1A shows the aforementioned. The crystal structure of ϕ29 pRNA proheadbinding domain (PDB: ID-3R4F) (Ding et al., 2011) was converted into a density volume with sampling rate of 0.5 Å/pixel, low-pass filtered at 4 Å. Then, two maps were created by adding Gaussian noise with zero mean and 0.08 SD. These two maps were considered to calculate the FSC curve (red profile in Supplementary Figure S1). Subsequently, a B-factor correction was applied to these two maps, applying a B-factor of -60, and the new FSC (gray profile in Supplementary Figure 1) was determined. As shown in the figure, the FSC curve does not change with the correction.

S1.2. Methods based on signal-to-noise ratio
Other local methods define the resolution as the maximum detectable frequency above the noise power. In this principle, although using different algorithms, MonoRes (Vilas et al., 2018) and Resmap (Kucukelbir et al., 2014) are based. These methods also have limitations to detect the quality changes produced by applying a B-factor correction. When an isotropic filter (as B-factor correction) is applied, all spectral components at a given radial frequency are modified proportionally and therefore, the signal-to-noise ratio does not change.
In Supplementary Figure 1B we exemplify this fact for the particular case of MonoRes. In this test, the simulated map (low-pass filtered at 4 Å) from the structure of ϕ29 pRNA prohead-binding domain previously introduced in the main section was used. As shown in the figure, the resolution map estimated by MonoRes is similar to the estimated resolution map when a correction with a B-factor of -60 is used.

S2. Limitation of methods based on the signal-to-noise ratio for maps affected by noise suppression
The need to determine the variance of the noise to estimate the local resolution is the main limitation of methods like MonoRes or ResMap. Not only because differentiating between noise and signal can be a challenge, but also because in some cases the processing methods apply techniques of noise suppression and signal enhancement, as in the case of algorithms such as HighRes (Sorzano et al., 2018) or LocalDeblur (Ramirez-Aportela et al., 2018). In these cases the application of methods based on SNR could cause an overestimation of resolution.
Supplementary Figure 1C   added noise with mean 0 and 0.08 SD (above) and for the same map after applying a B-factor of -60