One number does not fit all: mapping local variations in resolution in cryo-EM reconstructions

Abstract

The resolution of density maps from single particle analysis is usually measured in terms of the highest spatial frequency to which consistent information has been obtained. This calculation represents an average over the entire reconstructed volume. In practice, however, substantial local variations in resolution may occur, either from intrinsic properties of the specimen or for technical reasons such as a non-isotropic distribution of viewing orientations. To address this issue, we propose the use of a space-frequency representation, the short-space Fourier transform, to assess the quality of a density map, voxel-by-voxel, i.e. by local resolution mapping. In this approach, the experimental volume is divided into small subvolumes and the resolution determined for each of them. It is illustrated in applications both to model data and to experimental density maps. Regions with lower-than-average resolution may be mobile components or ones with incomplete occupancy or result from multiple conformational states. To improve the interpretability of reconstructions, we propose an adaptive filtering approach that reconciles the resolution to which individual features are calculated with the results of the local resolution map.

Keywords: Cryo-electron microscopy; Image heterogeneity; Masking; Resolution; Short-space Fourier transform; Three-dimensional reconstruction.

Figure 1

1D example of localized Fourier Correlation. A tapering window is applied to both the signals, and the result is transformed in the Fourier domain. The correlation is calculated between the two transformed signals to estimate the resolution, which is assigned to the center point in the window. The procedure is then repeated by moving the window successively along the data, until all the data are analyzed.

Figure 2

Accuracy of the localized Fourier Shell Correlation. The relative error of the FSC is plotted against the kernel-to-resolution ratio for three cutoff thresholds: 0.143, 0.3, 0.5.

Figure 3

Simulated 70S ribosome map. Reconstructions are color-coded according to the localized resolution estimate, and all were low-pass filtered to 10 Å. The color bars give the resolution scale in Å. (a, b) Effect of masking out background noise on estimation accuracy. (a) unmasked (b) masked. (c–f) Sensitivity of local resolution to occupancy level. Reconstructions from datasets with different levels of occupancy of the 30S subunit. (c) Surface rendering and (e) gray scale section for reconstruction with 40% occupancy. (d) and (f) similarly, with 80% occupancy. Scale bar, 10 nm.

Figure 4

Effect of kernel size on localized FSC estimation. The average of the localized FSC resolution estimated on a subset of voxels in the reconstruction is plotted for several values of the box size used for the estimation. (a) RSV CA icosahedral particle; (b) HSV-1 C capsid; (c) Clathrin basket. The secondary x-axis is the kernel-to-resolution ratio. Cutoff threshold: 0.5.

Figure 5

Surface rendering of cryo-EM reconstructions, colored according to localized resolution. (a) HSV-1 C capsid. The map is filtered to 16 Å, and the global resolution calculated for the capsid shell is estimated at ~ 20 Å. Kernel size used to estimate the localized resolution: 140 Å (38 pixels). Scale bar, 20 nm. (b) Clathrin D6 basket. The map is filtered to 24 Å, and the global resolution is estimated at ~ 28 Å. Kernel size: 193 Å (35 pixels). Scale bar, 20 nm. (c) RSV CA icosahedral assembly. The map is filtered to 9 Å, and the global resolution is estimated around 10 Å. Kernel size: 71 Å (56 pixels). Scale bar, 5 nm.

Figure 6

Example of localized filtering. The reconstruction from the synthetic data set of 70S ribosome particles, where the 30S subunit is simulated to be present in only 40% of particles, is low-pass filtered at every voxel according to the local resolution estimate. This result may be compared with Figure 3C, in which the entire reconstruction is low-pass filtered to 10 Å. The reconstruction is colored according to the localized resolution used for filtering, using the same scheme as in Figure 3c.