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.

Introduction

In single particle analysis (SPA) reconstructions of cryo-electron micrographs, the final density map represents the end product of a complex sequence of processing steps, which include filtering, alignment and orientation determination, deconvolution to correct for contrast transfer effects, and reconstruction. Its quality reflects the accuracy of the algorithms employed for these steps, as well as the quality and number of input particles. To interpret the map, it is important to know the resolution to which reliable structural details extend. This is commonly done by using Fourier space techniques applied to the transform of the reconstruction. Several methods for assessing resolution have been proposed (Liao and Frank, 2010). Chronologically, they include differential phase residual (Frank et al., 1981), Q-factor (Kessel et al., 1985), Fourier shell phase residual (van Heel, 1987), Fourier shell correlation (FSC) (Harauz and van Heel, 1986), Spectral signal-to-noise ratio 3D (SSNR3D) (Penczek, 2002, Unser et al., 2005), and R measure (Sousa and Grigorieff, 2007).

In SPA it is assumed that the sample is homogeneous, so that all the images can be treated as projections of the same particle. However, in practice, some complexes are quite heterogeneous: for example, they may have components that are intrinsically flexible (Ishikawa et al., 2004, Leschziner and Nogales, 2007) or present at less than full occupancy (Belnap et al., 2003). In other cases, the complexes may exist in different conformations in solution. Specimen heterogeneity translates into reconstructions in which distinct regions show different levels of detail, and they need to be interpreted accordingly. Some approaches to this issue have been already been made. In studies of spherical viruses, resolution has been calculated as a function of radius (Harris et al., 2006, Huiskonen et al., 2004). More generally, substructures of interest can be selected from the map by masking out everything else, thus restricting the resolution estimation to the remaining sub-volume (Gao et al., 2004, Marles-Wright et al., 2008, Menetret et al., 2007). Here, we study the extent to which this approach can be localized. Based on the results of this analysis, we propose an adaptation of the approach for the integral analysis of resolution in a voxel-wise manner. Within the framework of our localization formalism, resolution is specified in terms of the familiar Fourier shell correlation coefficient (Harauz and van Heel, 1986), but it can be readily extended to other criteria. The approach is illustrated in terms of some applications to both synthetic and experimental data. We also present the implementation of two tools for performing the analysis. Finally, we propose an adaptive filtering approach, which is based on the results of the localized resolution analysis, to improve interpretability of maps that are affected by marked inhomogeneities in resolution.