Single-particle reconstruction statistics: a diagnostic tool in solving biomolecular structures by cryo-EM

Cryo-EM structure and B-factor refinement with ensemble representation

Cryo-EM experiments produce images of macromolecular assemblies that are combined to produce three-dimensional density maps. Typically, atomic models of the constituent molecules are fitted into these maps, followed by a density-guided refinement. We introduce TEMPy-ReFF, a method for atomic structure refinement in cryo-EM density maps. Our method represents atomic positions as components of a Gaussian mixture model, utilising their variances as B-factors, which are used to derive an ensemble description. Extensively tested on a substantial dataset of 229 cryo-EM maps from EMDB ranging in resolution from 2.1-4.9 Å with corresponding PDB and CERES atomic models, our results demonstrate that TEMPy-ReFF ensembles provide a superior representation of cryo-EM maps. On a single-model basis, it performs similarly to the CERES re-refinement protocol, although there are cases where it provides a better fit to the map. Furthermore, our method enables the creation of composite maps free of boundary artefacts. TEMPy-ReFF is useful for better interpretation of flexible structures, such as those involving RNA, DNA or ligands.

The Ewald sphere/focus gradient does not limit the resolution of cryoEM reconstructions

In our quest to solve biomolecular structures to higher resolutions in cryoEM, care must be taken to deal with all aspects of image formation in the electron microscope. One of these is the Ewald sphere/focus gradient that derives from the scattering geometry in the microscope and its implications for recovering high resolution and handedness information. While several methods to deal with it has been proposed and implemented, there are still questions as to the correct approach. At the high acceleration voltages used for cryoEM, the traditional projection approximation that ignores the Ewald sphere breaks down around 2-3 Å and with large particles. This is likely not crucial for most biologically interesting molecules, but is required to understand detail about catalytic events, molecular orbitals, orientation of bound water molecules, etc. Through simulation I show that integration along the Ewald spheres in frequency space during reconstruction, the "simple insertion method" is adequate to reach resolutions to the Nyquist frequency. Both theory and simulations indicate that the handedness information encoded in such phases is irretrievably lost in the formation of real space images. The conclusion is that correct reconstruction along the Ewald spheres avoids the limitations of the projection approximation.

The progressive spectral signal-to-noise ratio of cryo-electron micrograph movies as a tool to assess quality and radiation damage

BACKGROUND AND OBJECTIVE

The quality of a cryoEM reconstruction is fundamentally a function of the signal-to-noise ratio (SNR) of the original micrographs. The SNR embodies multiple aspects of image formation, including microscope details and alignment, specimen composition and thickness, how it is recorded, and how the specimen degrades during imaging. With the advent of direct electron detectors and the recording of a series of images for each micrograph (a movie), we have an opportunity to count every electron and derive fully quantitative results. After alignment of the movie frames of a micrograph, we can calculate the SNR, or its spatial frequency equivalent, the spectral SNR (SSNR). This SSNR reflects residual movement between frames and the progressive effect of radiation damage. The goal is to develop a quantitative analysis of the SSNR and radiation damage to assess and improve the quality of micrographs.

METHODS

Several test cases were selected from the EMPIAR database and ten micrograph movies downloaded for each case. The movie frames were aligned as rigid bodies to compensate for stage and support movement. The SSNR for subsets of frames was then calculated to assess the effect of residual movement. The progressive SSNR (PSSNR) was subsequently calculated to determine the decrease in signal accumulation as a result of radiation damage.

RESULTS

In all cases the alignment of the movie frames compensated for global movement to the extent that the effect on the SSNR is negligible. The subset SSNR can be used as a tool to further confirm the extent of residual movement. The progressive SSNR indicates an increase in value up to an asymptote, consistent with the theory for radiation damage. Fitting these curves gives the inherent SNR before exposure, and the critical dose, which decreases with spatial frequency with an exponential parameter roughly between one and two.

CONCLUSIONS

The implementation of the PSSNR for movie frames provides a tool for assessing micrograph quality and progression of radiation damage. The estimation of the critical dose further quantifies radiation damage and may shed some light on the mechanisms of damage. These are likely both a function of the specimen composition and the imaging parameters used.

High resolution electron tomography and segmentation-by-modeling interpretation in Bsoft

Bsoft offers many tools for the processing of tomographic tilt series and the interpretation of tomograms. Since I introduced tomography into Bsoft almost two decades ago, the field has advanced significantly, requiring refinement of old algorithms and development of new ones. The current direct detectors allow us to collect data more efficiently and with better quality, progressing towards automation. The goal is then to also automate alignment of tilt series and reconstruction. I added an estimation of the specimen thickness as well as fiducialless alignment, to augment the existing fiducial-based alignment. High-resolution work requires correction for the contrast transfer function, in tomography complicated by the tilted specimen. For this, I developed a method to generate a power spectrum using the whole micrograph, compensating for tilting. This is followed by routine determination of the contrast transfer function, and correction for it during reconstruction. The next steps involve interpretation of the tomogram, either by subtomogram averaging where possible, or by segmentation and modeling otherwise. Such interpretation actually constitutes the main time-consuming part of tomography and is less amenable to automation compared to the initial reconstruction.

Throughput and resolution with a next-generation direct electron detector

Direct electron detectors (DEDs) have revolutionized cryo-electron microscopy (cryo-EM) by facilitating the correction of beam-induced motion and radiation damage, and also by providing high-resolution image capture. A new-generation DED, the DE64, has been developed by Direct Electron that has good performance in both integrating and counting modes. The camera has been characterized in both modes in terms of image quality, throughput and resolution of cryo-EM reconstructions. The modulation transfer function, noise power spectrum and detective quantum efficiency (DQE) were determined for both modes, as well as the number of images per unit time. Although the DQE for counting mode was superior to that for integrating mode, the data-collection throughput for this mode was more than ten times slower. Since throughput and resolution are related in single-particle cryo-EM, data for apoferritin were collected and reconstructed using integrating mode, integrating mode in conjunction with a Volta phase plate (VPP) and counting mode. Only the counting-mode data resulted in a better than 3 Å resolution reconstruction with similar numbers of particles, and this increased performance could not be compensated for by the increased throughput of integrating mode or by the increased low-frequency contrast of integrating mode with the VPP. These data show that the superior image quality provided by counting mode is more important for high-resolution cryo-EM reconstructions than the superior throughput of integrating mode.

Non-uniformity of projection distributions attenuates resolution in Cryo-EM

Virtually all single-particle cryo-EM experiments currently suffer from specimen adherence to the air-water interface, leading to a non-uniform distribution in the set of projection views. Whereas it is well accepted that uniform projection distributions can lead to high-resolution reconstructions, non-uniform (anisotropic) distributions can negatively affect map quality, elongate structural features, and in some cases, prohibit interpretation altogether. Although some consequences of non-uniform sampling have been described qualitatively, we know little about how sampling quantitatively affects resolution in cryo-EM. Here, we show how inhomogeneity in any projection distribution scheme attenuates the global Fourier Shell Correlation (FSC) in relation to the number of particles and a single geometrical parameter, which we term the sampling compensation factor (SCF). The reciprocal of the SCF is defined as the average over Fourier shells of the reciprocal of the per-particle sampling and normalized to unity for uniform distributions. The SCF therefore ranges from one to zero, with values close to the latter implying large regions of poorly sampled or completely missing data in Fourier space. Using two synthetic test cases, influenza hemagglutinin and human apoferritin, we demonstrate how any amount of sampling inhomogeneity always attenuates the FSC compared to a uniform distribution. We advocate quantitative evaluation of the SCF criterion to approximate the effect of non-uniform sampling on resolution within experimental single-particle cryo-EM reconstructions.

Acta Crystallographica Section F - another home for cryo-electron microscopy contributions

Two of the Acta Cryst. F editors introduce a number of articles on cryo-electron microscopy.