Sjors H.W. Scheres

RELION: implementation of a Bayesian approach to cryo-EM structure determination.

RELION, for REgularized LIkelihood OptimizatioN, is an open-source computer program for the refinement of macromolecular structures by single-particle analysis of electron cryo-microscopy (cryo-EM) data. Whereas alternative approaches often rely on user expertise for the tuning of parameters, RELION uses a Bayesian approach to infer parameters of a statistical model from the data. This paper describes developments that reduce the computational costs of the underlying maximum a posteriori (MAP) algorithm, as well as statistical considerations that yield new insights into the accuracy with which the relative orientations of individual particles may be determined. A so-called gold-standard Fourier shell correlation (FSC) procedure to prevent overfitting is also described. The resulting implementation yields high-quality reconstructions and reliable resolution estimates with minimal user intervention and at acceptable computational costs.

Prevention of overfitting in cryo-EM structure determination

In the field of single-particle analysis of electron cryo-microscopy (cryo-EM) data, a growing concern that some resolution claims might not be substantiated by the data has been one of the instigators of community-wide efforts to develop new validation tools1. A known issue with commonly used cryo-EM structure determination procedures is their liability to overfit the data. Most procedures counter overfitting by low-pass filtering, but the effective frequencies for these filters are often based on suboptimal Fourier Shell Correlation2 (FSC) procedures. In the suboptimal procedure, FSC curves are calculated between reconstructions from two halves of the data, while a single model is used to determine the relative orientations of all particles. It is well known that bias towards noise in the single model may inflate the resulting resolution estimates. To illustrate this, we applied the suboptimal procedure to a simulated cryo-EM data set of 20,212 GroEL particles. Whereas the reported resolution was 4.6 A, the true resolution of the map was only 7.8 A. Also the presence of expected density features in the map does not necessarily provide sufficient evidence for a resolution claim: we could make convincingly looking figures of apparent side-chain density that in reality corresponded to overfitted noise (Supplementary Figure 1). Consequently, overfitting may remain undetected and interpretation of cryo-EM maps may be subject to errors. The dangers of overfitting have been recognized, and refinement procedures with resolution-dependent weighting schemes to reduce overfitting have been proposed3,4. However, two known solutions to prevent it are not in common use. By refining two models independently (one for each half of the data), so-called gold-standard1 FSC curves may be calculated that are free from spurious correlations. Alternatively, the data used for the orientation determination may be limited to a user-specified frequency, so that model bias beyond that frequency may be avoided. However, the argument that withholding part of the data from the refinement would substantially deteriorate the orientations and thereby the quality of the structure has prevented the wide-spread use of either of these solutions. In what follows, we prove this thesis to be false. Analysis of simulated data with realistic signal-to-noise ratios (SNRs) indicates that the accuracy of the orientation determination is not affected by the exclusion of high-frequency terms, nor by the use of a model that is reconstructed from only half of the particles (Supplementary Figure 2). These simulations illustrate that only the low-medium frequency terms in the individual particles contain sufficiently high SNRs to contribute significantly to the orientation determination, which is in good agreement with experimental evidence that cryo-EM particles may be aligned accurately using only low-frequency data5. Because in most cryo-EM studies the low-medium frequencies of reconstructions from half of the particles are not expected to be significantly worse than those of reconstructions from all particles, we hypothesize that overfitting may be prevented without a notable loss of resolution using either frequency-limited refinement or refinement based on gold-standard FSCs. Since the former involves a decision by the user, i.e. choosing the frequency at which to limit the refinement, we favour gold-standard FSCs and implemented a procedure to independently refine two models as a script on top of the conventional projection matching protocol in the XMIPP package6 (Supplementary Figure 3 & Supplementary Software). We tested our hypothesis using three cryo-EM data sets: 5,053 GroEL particles that are distributed by the National Center for Macromolecular Imaging; an in-house collected data set of 50,330 β-galactosidase particles (Supplementary Methods); and 5,403 hepatitis B capsid particles from a previously published study7. High-resolution crystal structures are available for all three data sets, and these were used to assess the “true” resolution obtained using refinements based on either gold-standard or conventional FSC procedures (Figure 1). For all three cases, the conventional procedure reported apparently better FSC curves than the gold-standard procedure, but in no case did the gold-standard procedure actually result in a lower resolution map compared to the crystal structure. On the contrary, for the β-galactosidase data the gold-standard procedure yielded a structure that correlated up to higher frequencies with the crystal structure than the conventional procedure, which suffered from severe overfitting and gave rise to strong artefacts in the map. We also note that, in the absence of overfitting, the frequency at which the gold-standard FSC drops below 0.143 is a good indicator of the true resolution of the map (Supplementary Table 1), which is as expected from theory8. Finally, in the limit of very small data sets, division of the data into two halves might affect resolution. However, calculations with subsets of the GroEL particles suggest that this only becomes an issue for data sets that are much smaller than those typically used in cryo-EM reconstructions (Supplementary Figure 4). Figure 1 The prevention of overfitting The principal conclusion is therefore that overfitting of noise using suboptimal FSCs causes worse orientations and leads to a worse structure. In contrast, the use of gold-standard FSCs provides a realistic estimate of the true signal, which ultimately leads to a better map. The procedures proposed here are straightforward to implement in existing programs, and their application will eradicate the hazards of overfitting from cryo-EM structure determination procedures.

Disentangling conformational states of macromolecules in 3D-EM through likelihood optimization

Although three-dimensional electron microscopy (3D-EM) permits structural characterization of macromolecular assemblies in distinct functional states, the inability to classify projections from structurally heterogeneous samples has severely limited its application. We present a maximum likelihood–based classification method that does not depend on prior knowledge about the structural variability, and demonstrate its effectiveness for two macromolecular assemblies with different types of conformational variability: the Escherichia coli ribosome and Simian virus 40 (SV40) large T-antigen.

A Bayesian View on Cryo-EM Structure Determination

Three-dimensional (3D) structure determination by single-particle analysis of cryo-electron microscopy (cryo-EM) images requires many parameters to be determined from extremely noisy data. This makes the method prone to overfitting, that is, when structures describe noise rather than signal, in particular near their resolution limit where noise levels are highest. Cryo-EM structures are typically filtered using ad hoc procedures to prevent overfitting, but the tuning of arbitrary parameters may lead to subjectivity in the results. I describe a Bayesian interpretation of cryo-EM structure determination, where smoothness in the reconstructed density is imposed through a Gaussian prior in the Fourier domain. The statistical framework dictates how data and prior knowledge should be combined, so that the optimal 3D linear filter is obtained without the need for arbitrariness and objective resolution estimates may be obtained. Application to experimental data indicates that the statistical approach yields more reliable structures than existing methods and is capable of detecting smaller classes in data sets that contain multiple different structures.

Image processing for electron microscopy single-particle analysis using XMIPP

We describe a collection of standardized image processing protocols for electron microscopy single-particle analysis using the XMIPP software package. These protocols allow performing the entire processing workflow starting from digitized micrographs up to the final refinement and evaluation of 3D models. A particular emphasis has been placed on the treatment of structurally heterogeneous data through maximum-likelihood refinements and self-organizing maps as well as the generation of initial 3D models for such data sets through random conical tilt reconstruction methods. All protocols presented have been implemented as stand-alone, executable python scripts, for which a dedicated graphical user interface has been developed. Thereby, they may provide novice users with a convenient tool to quickly obtain useful results with minimum efforts in learning about the details of this comprehensive package. Examples of applications are presented for a negative stain random conical tilt data set on the hexameric helicase G40P and for a structurally heterogeneous data set on 70S Escherichia coli ribosomes embedded in vitrified ice.

High-resolution noise substitution to measure overfitting and validate resolution in 3D structure determination by single particle electron cryomicroscopy

Three-dimensional (3D) structure determination by single particle electron cryomicroscopy (cryoEM) involves the calculation of an initial 3D model, followed by extensive iterative improvement of the orientation determination of the individual particle images and the resulting 3D map. Because there is much more noise than signal at high resolution in the images, this creates the possibility of noise reinforcement in the 3D map, which can give a false impression of the resolution attained. The balance between signal and noise in the final map at its limiting resolution depends on the image processing procedure and is not easily predicted. There is a growing awareness in the cryoEM community of how to avoid such over-fitting and over-estimation of resolution. Equally, there has been a reluctance to use the two principal methods of avoidance because they give lower resolution estimates, which some people believe are too pessimistic. Here we describe a simple test that is compatible with any image processing protocol. The test allows measurement of the amount of signal and the amount of noise from overfitting that is present in the final 3D map. We have applied the method to two different sets of cryoEM images of the enzyme beta-galactosidase using several image processing packages. Our procedure involves substituting the Fourier components of the initial particle image stack beyond a chosen resolution by either the Fourier components from an adjacent area of background, or by simple randomisation of the phases of the particle structure factors. This substituted noise thus has the same spectral power distribution as the original data. Comparison of the Fourier Shell Correlation (FSC) plots from the 3D map obtained using the experimental data with that from the same data with high-resolution noise (HR-noise) substituted allows an unambiguous measurement of the amount of overfitting and an accompanying resolution assessment. A simple formula can be used to calculate an unbiased FSC from the two curves, even when a substantial amount of overfitting is present. The approach is software independent. The user is therefore completely free to use any established method or novel combination of methods, provided the HR-noise test is carried out in parallel. Applying this procedure to cryoEM images of beta-galactosidase shows how overfitting varies greatly depending on the procedure, but in the best case shows no overfitting and a resolution of ~6 Å. (382 words)

Accelerated cryo-EM structure determination with parallelisation using GPUs in relion-2

By reaching near-atomic resolution for a wide range of specimens, single-particle cryo-EM structure determination is transforming structural biology. However, the necessary calculations come at large computational costs, which has introduced a bottleneck that is currently limiting throughput and the development of new methods. Here, we present an implementation of the RELION image processing software that uses graphics processors (GPUs) to address the most computationally intensive steps of its cryo-EM structure determination workflow. Both image classification and high-resolution refinement have been accelerated more than an order-of-magnitude, and template-based particle selection has been accelerated well over two orders-of-magnitude on desktop hardware. Memory requirements on GPUs have been reduced to fit widely available hardware, and we show that the use of single precision arithmetic does not adversely affect results. This enables high-resolution cryo-EM structure determination in a matter of days on a single workstation. DOI: http://dx.doi.org/10.7554/eLife.18722.001

Ribosome structures to near-atomic resolution from thirty thousand cryo-EM particles

Although electron cryo-microscopy (cryo-EM) single-particle analysis has become an important tool for structural biology of large and flexible macro-molecular assemblies, the technique has not yet reached its full potential. Besides fundamental limits imposed by radiation damage, poor detectors and beam-induced sample movement have been shown to degrade attainable resolutions. A new generation of direct electron detectors may ameliorate both effects. Apart from exhibiting improved signal-to-noise performance, these cameras are also fast enough to follow particle movements during electron irradiation. Here, we assess the potentials of this technology for cryo-EM structure determination. Using a newly developed statistical movie processing approach to compensate for beam-induced movement, we show that ribosome reconstructions with unprecedented resolutions may be calculated from almost two orders of magnitude fewer particles than used previously. Therefore, this methodology may expand the scope of high-resolution cryo-EM to a broad range of biological specimens. DOI: http://dx.doi.org/10.7554/eLife.00461.001

How cryo-EM is revolutionizing structural biology

For many years, structure determination of biological macromolecules by cryo-electron microscopy (cryo-EM) was limited to large complexes or low-resolution models. With recent advances in electron detection and image processing, the resolution by cryo-EM is now beginning to rival X-ray crystallography. A new generation of electron detectors record images with unprecedented quality, while new image-processing tools correct for sample movements and classify images according to different structural states. Combined, these advances yield density maps with sufficient detail to deduce the atomic structure for a range of specimens. Here, we review the recent advances and illustrate the exciting new opportunities that they offer to structural biology research.

An atomic structure of human γ-secretase

Dysfunction of the intramembrane protease γ-secretase is thought to cause Alzheimer’s disease, with most mutations derived from Alzheimer’s disease mapping to the catalytic subunit presenilin 1 (PS1). Here we report an atomic structure of human γ-secretase at 3.4 Å resolution, determined by single-particle cryo-electron microscopy. Mutations derived from Alzheimer’s disease affect residues at two hotspots in PS1, each located at the centre of a distinct four transmembrane segment (TM) bundle. TM2 and, to a lesser extent, TM6 exhibit considerable flexibility, yielding a plastic active site and adaptable surrounding elements. The active site of PS1 is accessible from the convex side of the TM horseshoe, suggesting considerable conformational changes in nicastrin extracellular domain after substrate recruitment. Component protein APH-1 serves as a scaffold, anchoring the lone transmembrane helix from nicastrin and supporting the flexible conformation of PS1. Ordered phospholipids stabilize the complex inside the membrane. Our structure serves as a molecular basis for mechanistic understanding of γ-secretase function.