Noise bias in the refinement of structures derived from single particles

Baited reconstruction with 2D template matching for high-resolution structure determination in vitro and in vivo without template bias

Previously we showed that 2D template matching (2DTM) can be used to localize macromolecular complexes in images recorded by cryogenic electron microscopy (cryo-EM) with high precision, even in the presence of noise and cellular background (Lucas et al., 2021; Lucas et al., 2022). Here, we show that once localized, these particles may be averaged together to generate high-resolution 3D reconstructions. However, regions included in the template may suffer from template bias, leading to inflated resolution estimates and making the interpretation of high-resolution features unreliable. We evaluate conditions that minimize template bias while retaining the benefits of high-precision localization, and we show that molecular features not present in the template can be reconstructed at high resolution from targets found by 2DTM, extending prior work at low-resolution. Moreover, we present a quantitative metric for template bias to aid the interpretation of 3D reconstructions calculated with particles localized using high-resolution templates and fine angular sampling.

A strategy combining denoising and cryo-EM single particle analysis

In cryogenic electron microscopy (cryo-EM) single particle analysis (SPA), high-resolution three-dimensional structures of biological macromolecules are determined by iteratively aligning and averaging a large number of two-dimensional projections of molecules. Since the correlation measures are sensitive to the signal-to-noise ratio, various parameter estimation steps in SPA will be disturbed by the high-intensity noise in cryo-EM. However, denoising algorithms tend to damage high frequencies and suppress mid- and high-frequency contrast of micrographs, which exactly the precise parameter estimation relies on, therefore, limiting their application in SPA. In this study, we suggest combining a cryo-EM image processing pipeline with denoising and maximizing the signal's contribution in various parameter estimation steps. To solve the inherent flaws of denoising algorithms, we design an algorithm named MScale to correct the amplitude distortion caused by denoising and propose a new orientation determination strategy to compensate for the high-frequency loss. In the experiments on several real datasets, the denoised particles are successfully applied in the class assignment estimation and orientation determination tasks, ultimately enhancing the quality of biomacromolecule reconstruction. The case study on classification indicates that our strategy not only improves the resolution of difficult classes (up to 5 Å) but also resolves an additional class. In the case study on orientation determination, our strategy improves the resolution of the final reconstructed density map by 0.34 Å compared with conventional strategy. The code is available at https://github.com/zhanghui186/Mscale.

On bias, variance, overfitting, gold standard and consensus in single-particle analysis by cryo-electron microscopy

Cryo-electron microscopy (cryoEM) has become a well established technique to elucidate the 3D structures of biological macromolecules. Projection images from thousands of macromolecules that are assumed to be structurally identical are combined into a single 3D map representing the Coulomb potential of the macromolecule under study. This article discusses possible caveats along the image-processing path and how to avoid them to obtain a reliable 3D structure. Some of these problems are very well known in the community. These may be referred to as sample-related (such as specimen denaturation at interfaces or non-uniform projection geometry leading to underrepresented projection directions). The rest are related to the algorithms used. While some have been discussed in depth in the literature, such as the use of an incorrect initial volume, others have received much less attention. However, they are fundamental in any data-analysis approach. Chiefly among them, instabilities in estimating many of the key parameters that are required for a correct 3D reconstruction that occur all along the processing workflow are referred to, which may significantly affect the reliability of the whole process. In the field, the term overfitting has been coined to refer to some particular kinds of artifacts. It is argued that overfitting is a statistical bias in key parameter-estimation steps in the 3D reconstruction process, including intrinsic algorithmic bias. It is also shown that common tools (Fourier shell correlation) and strategies (gold standard) that are normally used to detect or prevent overfitting do not fully protect against it. Alternatively, it is proposed that detecting the bias that leads to overfitting is much easier when addressed at the level of parameter estimation, rather than detecting it once the particle images have been combined into a 3D map. Comparing the results from multiple algorithms (or at least, independent executions of the same algorithm) can detect parameter bias. These multiple executions could then be averaged to give a lower variance estimate of the underlying parameters.

Identification of incorrectly oriented particles in cryo-EM single particle analysis

The quality of a 3D map produced by the single-particle analysis method is highly dependent on an accurate assignment of orientations to the many experimental images. However, the problem's complexity implies the presence of several local minima in the optimized goal functions. Consequently, validation methods to confirm the angular assignment are very useful to yield higher-resolution 3D maps. In this work, we present a graph-signal-processing-based methodology that analyzes the correlation landscape as a function of the orientation, an approach allowing the estimation of the assigned orientations' reliability. Using this method, we may identify low-reliability images that probably incorrectly contribute to the final 3D reconstruction.

Locating macromolecular assemblies in cells by 2D template matching with cisTEM

For a more complete understanding of molecular mechanisms, it is important to study macromolecules and their assemblies in the broader context of the cell. This context can be visualized at nanometer resolution in three dimensions (3D) using electron cryo-tomography, which requires tilt series to be recorded and computationally aligned, currently limiting throughput. Additionally, the high-resolution signal preserved in the raw tomograms is currently limited by a number of technical difficulties, leading to an increased false-positive detection rate when using 3D template matching to find molecular complexes in tomograms. We have recently described a 2D template matching approach that addresses these issues by including high-resolution signal preserved in single-tilt images. A current limitation of this approach is the high computational cost that limits throughput. We describe here a GPU-accelerated implementation of 2D template matching in the image processing software cisTEM that allows for easy scaling and improves the accessibility of this approach. We apply 2D template matching to identify ribosomes in images of frozen-hydrated Mycoplasma pneumoniae cells with high precision and sensitivity, demonstrating that this is a versatile tool for in situ visual proteomics and in situ structure determination. We benchmark the results with 3D template matching of tomograms acquired on identical sample locations and identify strengths and weaknesses of both techniques, which offer complementary information about target localization and identity.

Mitigating local over-fitting during single particle reconstruction with SIDESPLITTER

Single particle analysis has become a key structural biology technique. Experimental images are extremely noisy, and during iterative refinement it is possible to stably incorporate noise into the reconstruction. Such "over-fitting" can lead to misinterpretation of the structure and flawed biological results. Several strategies are routinely used to prevent over-fitting, the most common being independent refinement of two sides of a split dataset. In this study, we show that over-fitting remains an issue within regions of low local signal-to-noise, despite independent refinement of half datasets. We propose a modification of the refinement process through the application of a local signal-to-noise filter: SIDESPLITTER. We show that our approach can reduce over-fitting for both idealised and experimental data while maintaining independence between the two sides of a split refinement. SIDESPLITTER refinement leads to improved density, and can also lead to improvement of the final resolution in extreme cases where datasets are prone to severe over-fitting, such as small membrane proteins.

Retrieving high-resolution information from disordered 2D crystals by single-particle cryo-EM

Electron crystallography can reveal the structure of membrane proteins within 2D crystals under close-to-native conditions. High-resolution structural information can only be reached if crystals are perfectly flat and highly ordered. In practice, such crystals are difficult to obtain. Available image unbending algorithms correct for disorder, but only perform well on images of non-tilted, flat crystals, while out-of-plane distortions are not addressed. Here, we present an approach that employs single-particle refinement procedures to locally unbend crystals in 3D. With this method, density maps of the MloK1 potassium channel with a resolution of 4 Å were obtained from images of 2D crystals that do not diffract beyond 10 Å. Furthermore, 3D classification allowed multiple structures to be resolved, revealing a series of MloK1 conformations within a single 2D crystal. This conformational heterogeneity explains the poor diffraction observed and is related to channel function. The approach is implemented in the FOCUS package.

emClarity: software for high-resolution cryo-electron tomography and subtomogram averaging

Macromolecular complexes are intrinsically flexible and often challenging to purify for structure determination by single-particle cryo-electron microscopy (cryo-EM). Such complexes can be studied by cryo-electron tomography (cryo-ET) combined with subtomogram alignment and classification, which in exceptional cases achieves subnanometer resolution, yielding insight into structure-function relationships. However, it remains challenging to apply this approach to specimens that exhibit conformational or compositional heterogeneity or are present in low abundance. To address this, we developed emClarity ( https://github.com/bHimes/emClarity/wiki ), a GPU-accelerated image-processing package featuring an iterative tomographic tilt-series refinement algorithm that uses subtomograms as fiducial markers and a 3D-sampling-function-compensated, multi-scale principal component analysis classification method. We demonstrate that our approach offers substantial improvement in the resolution of maps and in the separation of different functional states of macromolecular complexes compared with current state-of-the-art software.

Rapid near-atomic resolution single-particle 3D reconstruction with SIMPLE

Cryogenic electron microscopy (cryo-EM) and single-particle analysis enables determination of near-atomic resolution structures of biological molecules. However, large computational requirements limit throughput and rapid testing of new image processing tools. We developed PRIME, an algorithm part of the SIMPLE software suite, for determination of the relative 3D orientations of single-particle projection images. PRIME has primarily found use for generation of an initial ab initio 3D reconstruction. Here we show that the strategy behind PRIME, iterative estimation of per-particle orientation distributions with stochastic hill climbing, provides a competitive approach to near-atomic resolution single-particle 3D reconstruction. A number of mathematical techniques for accelerating the convergence rate are introduced, leading to a speedup of nearly two orders of magnitude. We benchmarked our developments on numerous publicly available data sets and conclude that near-atomic resolution ab initio 3D reconstructions can be obtained with SIMPLE in a matter of hours, using standard over-the-counter CPU workstations.

An Investigation of Atomic Structures Derived from X-ray Crystallography and Cryo-Electron Microscopy Using Distal Blocks of Side-Chains

Cryo-electron microscopy (cryo-EM) is a structure determination method for large molecular complexes. As more and more atomic structures are determined using this technique, it is becoming possible to perform statistical characterization of side-chain conformations. Two data sets were involved to characterize block lengths for each of the 18 types of amino acids. One set contains 9131 structures resolved using X-ray crystallography from density maps with better than or equal to 1.5 Å resolutions, and the other contains 237 protein structures derived from cryo-EM density maps with 2–4 Å resolutions. The results show that the normalized probability density function of block lengths is similar between the X-ray data set and the cryo-EM data set for most of the residue types, but differences were observed for ARG, GLU, ILE, LYS, PHE, TRP, and TYR for which conformations with certain shorter block lengths are more likely to be observed in the cryo-EM set with 2–4 Å resolutions.

cisTEM, user-friendly software for single-particle image processing

We have developed new open-source software called cisTEM (computational imaging system for transmission electron microscopy) for the processing of data for high-resolution electron cryo-microscopy and single-particle averaging. cisTEM features a graphical user interface that is used to submit jobs, monitor their progress, and display results. It implements a full processing pipeline including movie processing, image defocus determination, automatic particle picking, 2D classification, ab-initio 3D map generation from random parameters, 3D classification, and high-resolution refinement and reconstruction. Some of these steps implement newly-developed algorithms; others were adapted from previously published algorithms. The software is optimized to enable processing of typical datasets (2000 micrographs, 200 k – 300 k particles) on a high-end, CPU-based workstation in half a day or less, comparable to GPU-accelerated processing. Jobs can also be scheduled on large computer clusters using flexible run profiles that can be adapted for most computing environments. cisTEM is available for download from cistem.org.

Single-particle cryo-EM using alignment by classification (ABC): the structure of Lumbricus terrestris haemoglobin

Single-particle cryogenic electron microscopy (cryo-EM) can now yield near-atomic resolution structures of biological complexes. However, the reference-based alignment algorithms commonly used in cryo-EM suffer from reference bias, limiting their applicability (also known as the 'Einstein from random noise' problem). Low-dose cryo-EM therefore requires robust and objective approaches to reveal the structural information contained in the extremely noisy data, especially when dealing with small structures. A reference-free pipeline is presented for obtaining near-atomic resolution three-dimensional reconstructions from heterogeneous ('four-dimensional') cryo-EM data sets. The methodologies integrated in this pipeline include a posteriori camera correction, movie-based full-data-set contrast transfer function determination, movie-alignment algorithms, (Fourier-space) multivariate statistical data compression and unsupervised classification, 'random-startup' three-dimensional reconstructions, four-dimensional structural refinements and Fourier shell correlation criteria for evaluating anisotropic resolution. The procedures exclusively use information emerging from the data set itself, without external 'starting models'. Euler-angle assignments are performed by angular reconstitution rather than by the inherently slower projection-matching approaches. The comprehensive 'ABC-4D' pipeline is based on the two-dimensional reference-free 'alignment by classification' (ABC) approach, where similar images in similar orientations are grouped by unsupervised classification. Some fundamental differences between X-ray crystallography versus single-particle cryo-EM data collection and data processing are discussed. The structure of the giant haemoglobin from Lumbricus terrestris at a global resolution of ∼3.8 Å is presented as an example of the use of the ABC-4D procedure.

Ultrastructural Analysis of Self-Associated RyR2s

In heart, type-2 ryanodine receptor (RyR2) forms discrete supramolecular clusters in the sarcoplasmic reticulum known as calcium release units (CRUs), which are responsible for most of the Ca(2+) released for muscle contraction. To learn about the substructure of the CRU, we sought to determine whether RyR2s have the ability to self-associate in the absence of other factors and if so, whether they do it in a specific manner. Purified RyR2 was negatively stained and imaged on the transmission electron microscope, and RyR2 particles closely associated were further analyzed using bias-free multivariate statistical analysis and classification. The resulting two-dimensional averages show that RyR2s can interact in two rigid, reproducible configurations: "adjoining", with two RyR2s alongside each other, and "oblique", with two partially overlapped RyR2s forming an angle of 12°. The two configurations are nearly identical under two extreme physiological Ca(2+) concentrations. Pseudo-atomic models for these two interactions indicate that the adjoining interaction involves contacts between the P1, SPRY1 and the helical domains. The oblique interaction is mediated by extensive contacts between the SPRY1 domains (domains 9) and P1 domains (domains 10) of both RyR2s and not through domain 6 as previously thought; in addition its asymmetric interface imposes steric constrains that inhibit the growth of RyR2 as a checkerboard, which is the configuration usually assumed, and generates new configurations, i.e., "branched" and "interlocked". This first, to our knowledge, structural detailed analysis of the inter-RyR2 interactions helps to understand important morphological and functional aspects of the CRU in the context of cardiac EC coupling.

Robust image alignment for cryogenic transmission electron microscopy

Cryo-electron microscopy recently experienced great improvements in structure resolution due to direct electron detectors with improved contrast and fast read-out leading to single electron counting. High frames rates enabled dose fractionation, where a long exposure is broken into a movie, permitting specimen drift to be registered and corrected. The typical approach for image registration, with high shot noise and low contrast, is multi-reference (MR) cross-correlation. Here we present the software package Zorro, which provides robust drift correction for dose fractionation by use of an intensity-normalized cross-correlation and logistic noise model to weight each cross-correlation in the MR model and filter each cross-correlation optimally. Frames are reliably registered by Zorro with low dose and defocus. Methods to evaluate performance are presented, by use of independently-evaluated even- and odd-frame stacks by trajectory comparison and Fourier ring correlation. Alignment of tiled sub-frames is also introduced, and demonstrated on an example dataset. Zorro source code is available at github.com/CINA/zorro.

A guide to the 3D structure of the ryanodine receptor type 1 by cryoEM

Signal transduction by the ryanodine receptor (RyR) is essential in many excitable cells including all striated contractile cells and some types of neurons. While its transmembrane domain is a classic tetrameric, six-transmembrane cation channel, the cytoplasmic domain is uniquely large and complex, hosting a multiplicity of specialized domains. The overall outline and substructure readily recognizable by electron microscopy make RyR a geometrically well-behaved specimen. Hence, for the last two decades, the 3D structural study of the RyR has tracked closely the technological advances in electron microscopy, cryo-electron microscopy (cryoEM), and computerized 3D reconstruction. This review summarizes the progress in the structural determination of RyR by cryoEM and, bearing in mind the leap in resolution provided by the recent implementation of direct electron detection, analyzes the first near-atomic structures of RyR. These reveal a complex orchestration of domains controlling the channel's function, and help to understand how this could break down as a consequence of disease-causing mutations.

Single particle electron cryomicroscopy: trends, issues and future perspective

There has been enormous progress during the last few years in the determination of three-dimensional biological structures by single particle electron cryomicroscopy (cryoEM), allowing maps to be obtained with higher resolution and from fewer images than required previously. This is due principally to the introduction of a new type of direct electron detector that has 2- to 3-fold higher detective quantum efficiency than available previously, and to the improvement of the computational algorithms for image processing. In spite of the great strides that have been made, quantitative analysis shows that there are still significant gains to be made provided that the problems associated with image degradation can be solved, possibly by minimising beam-induced specimen movement and charge build up during imaging. If this can be achieved, it should be possible to obtain near atomic resolution structures of smaller single particles, using fewer images and resolving more conformational states than at present, thus realising the full potential of the method. The recent popularity of cryoEM for molecular structure determination also highlights the need for lower cost microscopes, so we encourage development of an inexpensive, 100 keV electron cryomicroscope with a high-brightness field emission gun to make the method accessible to individual groups or institutions that cannot afford the investment and running costs of a state-of-the-art 300 keV installation. A key requisite for successful high-resolution structure determination by cryoEM includes interpretation of images and optimising the biochemistry and grid preparation to obtain nicely distributed macromolecules of interest. We thus include in this review a gallery of cryoEM micrographs that shows illustrative examples of single particle images of large and small macromolecular complexes.

Single-Particle Refinement and Variability Analysis in EMAN2.1

CryoEM single-particle reconstruction has been growing rapidly over the last 3 years largely due to the development of direct electron detectors, which have provided data with dramatic improvements in image quality. It is now possible in many cases to produce near-atomic resolution structures, and yet 2/3 of published structures remain at substantially lower resolutions. One important cause for this is compositional and conformational heterogeneity, which is both a resolution-limiting factor and presenting a unique opportunity to better relate structure to function. This manuscript discusses the canonical methods for high-resolution refinement in EMAN2.12, and then considers the wide range of available methods within this package for resolving structural variability, targeting both improved resolution and additional knowledge about particle dynamics.

Frealign: An Exploratory Tool for Single-Particle Cryo-EM

Frealign is a software tool designed to process electron microscope images of single molecules and complexes to obtain reconstructions at the highest possible resolution. It provides a number of refinement parameters and options that allow users to tune their refinement to achieve specific goals, such as masking to classify selected regions within a particle, control over the refinement of specific alignment parameters to accommodate various data collection schemes, refinement of pseudosymmetric particles, and generation of initial maps. This chapter provides a general overview of Frealign functions and a more detailed guide to using Frealign in typical scenarios.

Robust w-Estimators for Cryo-EM Class Means

A critical step in cryogenic electron microscopy (cryo-EM) image analysis is to calculate the average of all images aligned to a projection direction. This average, called the class mean, improves the signal-to-noise ratio in single-particle reconstruction. The averaging step is often compromised because of the outlier images of ice, contaminants, and particle fragments. Outlier detection and rejection in the majority of current cryo-EM methods are done using cross-correlation with a manually determined threshold. Empirical assessment shows that the performance of these methods is very sensitive to the threshold. This paper proposes an alternative: a w-estimator of the average image, which is robust to outliers and which does not use a threshold. Various properties of the estimator, such as consistency and influence function are investigated. An extension of the estimator to images with different contrast transfer functions is also provided. Experiments with simulated and real cryo-EM images show that the proposed estimator performs quite well in the presence of outliers.

Single-particle cryoEM analysis at near-atomic resolution from several thousand asymmetric subunits

A single-particle cryoEM reconstruction of the large ribosomal subunit from Saccharomyces cerevisiae was obtained from a dataset of ∼75,000 particles. The gold-standard and frequency-limited approaches to single-particle refinement were each independently used to determine orientation parameters for the final reconstruction. Both approaches showed similar resolution curves and nominal resolution values for the 60S dataset, estimated at 2.9 Å. The amount of over-fitting present during frequency-limited refinement was quantitatively analyzed using the high-resolution phase-randomization test, and the results showed no apparent over-fitting. The number of asymmetric subunits required to reach specific resolutions was subsequently analyzed by refining subsets of the data in an ab initio manner. With our data collection and processing strategies, sub-nanometer resolution was obtained with ∼200 asymmetric subunits (or, equivalently for the ribosomal subunit, particles). Resolutions of 5.6 Å, 4.5 Å, and 3.8 Å were reached with ∼1000, ∼1600, and ∼5000 asymmetric subunits, respectively. At these resolutions, one would expect to detect alpha-helical pitch, separation of beta-strands, and separation of Cα atoms, respectively. Using this map, together with strategies for ab initio model building and model refinement, we built a region of the ribosomal protein eL6, which was missing in previous models of the yeast ribosome. The relevance for more routine high-resolution structure determination is discussed.

A primer to single-particle cryo-electron microscopy

Cryo-electron microscopy (cryo-EM) of single-particle specimens is used to determine the structure of proteins and macromolecular complexes without the need for crystals. Recent advances in detector technology and software algorithms now allow images of unprecedented quality to be recorded and structures to be determined at near-atomic resolution. However, compared with X-ray crystallography, cryo-EM is a young technique with distinct challenges. This primer explains the different steps and considerations involved in structure determination by single-particle cryo-EM to provide an overview for scientists wishing to understand more about this technique and the interpretation of data obtained with it, as well as a starting guide for new practitioners.

Validation methods for low-resolution fitting of atomic structures to electron microscopy data

Fitting of atomic-resolution structures into reconstructions from electron cryo-microscopy is routinely used to understand the structure and function of macromolecular machines. Despite the fact that a plethora of fitting methods has been developed over recent years, standard protocols for quality assessment and validation of these fits have not been established. Here, we present the general concepts underlying current validation ideas as they relate to fitting of atomic-resolution models into electron cryo-microscopy reconstructions, with an emphasis on reconstructions with resolutions below the sub-nanometer range.

Transmission electron microscopy and the molecular structure of icosahedral viruses

The field of structural virology developed in parallel with methodological advances in X-ray crystallography and cryo-electron microscopy. At the end of the 1970s, crystallography yielded the first high resolution structure of an icosahedral virus, the T=3 tomato bushy stunt virus at 2.9Å. It took longer to reach near-atomic resolution in three-dimensional virus maps derived from electron microscopy data, but this was finally achieved, with the solution of complex icosahedral capsids such as the T=25 human adenovirus at ∼3.5Å. Both techniques now work hand-in-hand to determine those aspects of virus assembly and biology that remain unclear. This review examines the trajectory followed by EM imaging techniques in showing the molecular structure of icosahedral viruses, from the first two-dimensional negative staining images of capsids to the latest sophisticated techniques that provide high resolution three-dimensional data, or snapshots of the conformational changes necessary to complete the infectious cycle.

Cryogenic electron microscopy and single-particle analysis

About 20 years ago, the first three-dimensional (3D) reconstructions at subnanometer (<10-Å) resolution of an icosahedral virus assembly were obtained by cryogenic electron microscopy (cryo-EM) and single-particle analysis. Since then, thousands of structures have been determined to resolutions ranging from 30 Å to near atomic (<4 Å). Almost overnight, the recent development of direct electron detectors and the attendant improvement in analysis software have advanced the technology considerably. Near-atomic-resolution reconstructions can now be obtained, not only for megadalton macromolecular complexes or highly symmetrical assemblies but also for proteins of only a few hundred kilodaltons. We discuss the developments that led to this breakthrough in high-resolution structure determination by cryo-EM and point to challenges that lie ahead.

Do's and don'ts of cryo-electron microscopy: a primer on sample preparation and high quality data collection for macromolecular 3D reconstruction

Cryo-electron microscopy (cryoEM) entails flash-freezing a thin layer of sample on a support, and then visualizing the sample in its frozen hydrated state by transmission electron microscopy (TEM). This can be achieved with very low quantity of protein and in the buffer of choice, without the use of any stain, which is very useful to determine structure-function correlations of macromolecules. When combined with single-particle image processing, the technique has found widespread usefulness for 3D structural determination of purified macromolecules.

The protocol presented here explains how to perform cryoEM and examines the causes of most commonly encountered problems for rational troubleshooting; following all these steps should lead to acquisition of high quality cryoEM images. The technique requires access to the electron microscope instrument and to a vitrification device. Knowledge of the 3D reconstruction concepts and software is also needed for computerized image processing. Importantly, high quality results depend on finding the right purification conditions leading to a uniform population of structurally intact macromolecules.

The ability of cryoEM to visualize macromolecules combined with the versatility of single particle image processing has proven very successful for structural determination of large proteins and macromolecular machines in their near-native state, identification of their multiple components by 3D difference mapping, and creation of pseudo-atomic structures by docking of x-ray structures. The relentless development of cryoEM instrumentation and image processing techniques for the last 30 years has resulted in the possibility to generate de novo 3D reconstructions at atomic resolution level.

Single-particle cryo-EM of the ryanodine receptor channel in an aqueous environment

Ryanodine receptors (RyRs) are tetrameric ligand-gated Ca2+ release channels that are responsible for the increase of cytosolic Ca2+ concentration leading to muscle contraction. Our current understanding of RyR channel gating and regulation is greatly limited due to the lack of a high-resolution structure of the channel protein. The enormous size and unwieldy shape of Ca2+ release channels make X-ray or NMR methods difficult to apply for high-resolution structural analysis of the full-length functional channel. Single-particle electron cryo-microscopy (cryo-EM) is one of the only effective techniques for the study of such a large integral membrane protein and its molecular interactions. Despite recent developments in cryo-EM technologies and break-through single-particle cryo-EM studies of ion channels, cryospecimen preparation, particularly the presence of detergent in the buffer, remains the main impediment to obtaining atomic-resolution structures of ion channels and a multitude of other integral membrane protein complexes. In this review we will discuss properties of several detergents that have been successfully utilized in cryo-EM studies of ion channels and the emergence of the detergent alternative amphipol to stabilize ion channels for structure-function characterization. Future structural studies of challenging specimen like ion channels are likely to be facilitated by cryo-EM amenable detergents or alternative surfactants.

Robust evaluation of 3D electron cryomicroscopy data using tilt-pairs

Determining the structure of a protein complex using electron microscopy requires the calculation of a 3D density map from 2D images of single particles. Since the individual images are taken at low electron dose to avoid radiation damage, they are noisy and difficult to align with each other. This can result in incorrect maps, making validation essential. Pairs of electron micrographs taken at known angles to each other (tilt-pairs) can be used to measure the accuracy of assigned projection orientations and verify the soundness of calculated maps. Here we establish a statistical framework for evaluating images and density maps using tilt-pairs. The directional distribution of such angular data is modelled using a Fisher distribution on the unit sphere. This provides a simple, quantitative and easily comparable metric, the concentration parameter κ, for evaluating the quality of datasets and density maps that is independent of the data collection and analysis methods. A large κ is indicative of good agreement between the particle images and the 3D density map. For structure validation, we recommend κ>10 and a p-value <0.01. The statistical framework herein allows one to objectively answer the question: Is a reconstructed density map correct within a particular confidence interval?

Finding the right fit: chiseling structures out of cryo-electron microscopy maps

Cryo-electron microscopy is a central tool for studying the architecture of macromolecular complexes at subnanometer resolution. Interpretation of an electron microscopy map requires its computational integration with data about the structure's components from all available sources, notably atomic models. Selecting a protocol for EM density-guided integrative structural modeling depends on the resolution and quality of the EM map as well as the available complimentary datasets. Here, we review rigid, flexible, and de novo integrative fitting into EM maps and provide guidelines and considerations for the design of modeling experiments. Finally, we discuss efforts towards establishing unified criteria for map and model assessment and validation.

Frealix: model-based refinement of helical filament structures from electron micrographs

The structures of many helical protein filaments can be derived from electron micrographs of their suspensions in thin films of vitrified aqueous solutions. The most successful and generally-applicable approach treats short segments of these filaments as independent "single particles", yielding near-atomic resolution for rigid and well-ordered filaments. The single-particle approach can also accommodate filament deformations, yielding sub-nanometer resolution for more flexible filaments. However, in the case of thin and flexible filaments, such as some amyloid-β (Aβ) fibrils, the single-particle approach may fail because helical segments can be curved or otherwise distorted and their alignment can be inaccurate due to low contrast in the micrographs. We developed new software called Frealix that allows the use of arbitrarily short filament segments during alignment to approximate even high curvatures. All segments in a filament are aligned simultaneously with constraints that ensure that they connect to each other in space to form a continuous helical structure. In this paper, we describe the algorithm and benchmark it against datasets of Aβ(1-40) fibrils and tobacco mosaic virus (TMV), both analyzed in earlier work. In the case of TMV, our algorithm achieves similar results to single-particle analysis. In the case of Aβ(1-40) fibrils, we match the previously-obtained resolution but we are also able to obtain reliable alignments and ∼8-Å reconstructions from curved filaments. Our algorithm also offers a detailed characterization of filament deformations in three dimensions and enables a critical evaluation of the worm-like chain model for biological filaments.

Single particle analysis integrated with microscopy: a high-throughput approach for reconstructing icosahedral particles

In cryo-electron microscopy and single particle analysis, data acquisition and image processing are generally carried out in sequential steps and computation of a three-dimensional reconstruction only begins once all the micrographs have been acquired. We are developing an integrated system for processing images of icosahedral particles during microscopy to provide reconstructed density maps in real-time at the highest possible resolution. The system is designed as a combination of pipelines to run in parallel on a computer cluster and analyzes micrographs as they are acquired, handling automatically all the processing steps from defocus estimation and particle picking to origin/orientation determination. An ab initio model is determined independently from the first micrographs collected, and new models are generated as more particles become available. As a proof of concept, we simulated data acquisition sessions using three sets of micrographs of good to excellent quality that were previously recorded from different icosahedral viruses. Results show that the processing of single micrographs can keep pace with an acquisition rate of about two images per minute. The reconstructed density map improves steadily during the image acquisition phase and its quality at the end of data collection is only moderately inferior to that obtained by expert users who processed semi-automatically all the micrographs after the acquisition. The current prototype demonstrates the advantages of integrating three-dimensional image processing with microscopy, which include an ability to monitor acquisition in terms of the final structure and to predict how much data and microscope resources are needed to achieve a desired resolution.

Web server for tilt-pair validation of single particle maps from electron cryomicroscopy

Three-dimensional structures of biological assemblies may be calculated from images of single particles obtained by electron cryomicroscopy. A key step is the correct determination of the orientation of the particle in individual image projections. A useful tool for validation of the quality of a 3D map and its consistency with images is tilt-pair analysis. In a successful tilt-pair test, the relative angle between orientations assigned to each image of a tilt-pair agrees with the known relative rotation angle of the microscope specimen holder during the experiment. To make the procedure easy to apply to the increasing number of single particle maps, we have developed software and a web server for tilt-pair analysis. The tilt-pair analysis program reports the overall agreement of the assigned orientations with the known tilt angle and axis of the experiment and the distribution of tilt transformations for individual particles recorded in a single image field. We illustrate application of the validation tool to several single particle specimens and describe how to interpret the scores.

Single particle cryo-electron microscopy and 3-D reconstruction of viruses

With fast progresses in instrumentation, image processing algorithms, and computational resources, single particle electron cryo-microscopy (cryo-EM) 3-D reconstruction of icosahedral viruses has now reached near-atomic resolutions (3-4 Å). With comparable resolutions and more predictable outcomes, cryo-EM is now considered a preferred method over X-ray crystallography for determination of atomic structure of icosahedral viruses. At near-atomic resolutions, all-atom models or backbone models can be reliably built that allow residue level understanding of viral assembly and conformational changes among different stages of viral life cycle. With the developments of asymmetric reconstruction, it is now possible to visualize the complete structure of a complex virus with not only its icosahedral shell but also its multiple non-icosahedral structural features. In this chapter, we will describe single particle cryo-EM experimental and computational procedures for both near-atomic resolution reconstruction of icosahedral viruses and asymmetric reconstruction of viruses with both icosahedral and non-icosahedral structure components. Procedures for rigorous validation of the reconstructions and resolution evaluations using truly independent de novo initial models and refinements are also introduced.

ResLog plots as an empirical metric of the quality of cryo-EM reconstructions

Compared to the field of X-ray crystallography, the field of single particle three-dimensional electron microscopy has few reliable metrics for assessing the quality of 3D reconstructions. New metrics are needed that can determine whether a given 3D reconstruction accurately reflects the structure of the particles from which it was derived or instead depicts a plausible though incorrect structure due to coarse misalignment of particles. Here an empirical procedure is presented for differentiating between a reconstruction with well-aligned particles and a reconstruction with grossly misclassified particles. For a given dataset, 3D reconstructions are computed from subsets of particles with decreasing numbers of particles contributing to the reconstruction. A plot of inverse resolution vs. the logarithm of the number of particles (a "ResLog" plot) provides metrics for the reliability of the reconstruction and the overall quality of the dataset and processing. Specifically, the y-intercept of a regression line provides a measure of the relative accuracy of the particle alignment and classification, and the slope is an indicator of the overall data quality including the imaging conditions and processing steps. ResLog plots can also be used to optimize conditions for data collection and reconstruction parameters. Although resolution estimates can vary by method of calculation, ResLog-derived parameters are consistent whether calculated by Fourier shell correlation or Fourier neighbor correlation, or a new coordinate-based metric that serves as a yardstick for structures where atomic coordinates are available. ResLog plots could become part of a standard set of parameters to be included in 3D reconstruction reports.

Cryo-EM structure of a fully glycosylated soluble cleaved HIV-1 envelope trimer

The HIV-1 envelope glycoprotein (Env) trimer contains the receptor binding sites and membrane fusion machinery that introduce the viral genome into the host cell. As the only target for broadly neutralizing antibodies (bnAbs), Env is a focus for rational vaccine design. We present a cryo-electron microscopy reconstruction and structural model of a cleaved, soluble Env trimer (termed BG505 SOSIP.664 gp140) in complex with a CD4 binding site (CD4bs) bnAb, PGV04, at 5.8 angstrom resolution. The structure reveals the spatial arrangement of Env components, including the V1/V2, V3, HR1, and HR2 domains, as well as shielding glycans. The structure also provides insights into trimer assembly, gp120-gp41 interactions, and the CD4bs epitope cluster for bnAbs, which covers a more extensive area and defines a more complex site of vulnerability than previously described.

SPRING - an image processing package for single-particle based helical reconstruction from electron cryomicrographs

Helical reconstruction from electron cryomicrographs has become a routine technique for macromolecular structure determination of helical assemblies since the first days of Fourier-based three-dimensional image reconstruction. In the past decade, the single-particle technique has had an important impact on the advancement of helical reconstruction. Here, we present the software package SPRING that combines Fourier based symmetry analysis and real-space helical processing into a single workflow. One of the most time-consuming steps in helical reconstruction is the determination of the initial symmetry parameters. First, we propose a class-based helical reconstruction approach that enables the simultaneous exploration and evaluation of many symmetry combinations at low resolution. Second, multiple symmetry solutions can be further assessed and refined by single-particle based helical reconstruction using the correlation of simulated and experimental power spectra. Finally, the 3D structure can be determined to high resolution. In order to validate the procedure, we use the reference specimen Tobacco Mosaic Virus (TMV). After refinement of the helical symmetry, a total of 50,000 asymmetric units from two micrographs are sufficient to reconstruct a subnanometer 3D structure of TMV at 6.4Å resolution. Furthermore, we introduce the individual programs of the software and discuss enhancements of the helical reconstruction workflow. Thanks to its user-friendly interface and documentation, SPRING can be utilized by the novice as well as the expert user. In addition to the study of well-ordered helical structures, the development of a streamlined workflow for single-particle based helical reconstruction opens new possibilities to analyze specimens that are heterogeneous in symmetries.

Allosteric regulation of DNA cleavage and sequence-specificity through run-on oligomerization

SgrAI is a sequence specific DNA endonuclease that functions through an unusual enzymatic mechanism that is allosterically activated 200- to 500-fold by effector DNA, with a concomitant expansion of its DNA sequence specificity. Using single-particle transmission electron microscopy to reconstruct distinct populations of SgrAI oligomers, we show that in the presence of allosteric, activating DNA, the enzyme forms regular, repeating helical structures characterized by the addition of DNA-binding dimeric SgrAI subunits in a run-on manner. We also present the structure of oligomeric SgrAI at 8.6 Å resolution, demonstrating the conformational state of SgrAI in its activated form. Activated and oligomeric SgrAI displays key protein-protein interactions near the helix axis between its N termini, as well as allosteric protein-DNA interactions that are required for enzymatic activation. The hybrid approach reveals an unusual mechanism of enzyme activation that explains SgrAI's oligomerization and allosteric behavior.

Maximizing the potential of electron cryomicroscopy data collected using direct detectors

Single-particle electron cryomicroscopy is undergoing a technical revolution due to the recent developments of direct detectors. These new recording devices detect electrons directly (i.e. without conversion into light) and feature significantly improved detective quantum efficiencies and readout rates as compared to photographic films or CCDs. We evaluated here the potential of one such detector (Gatan K2 Summit) to enable the achievement of near-atomic resolution reconstructions of biological specimens when coupled to a widely used, mid-range transmission electron microscope (FEI TF20 Twin). Compensating for beam-induced motion and stage drift provided a 4.4Å resolution map of Sulfolobus turreted icosahedral virus (STIV), which we used as a test particle in this study. Several motion correction and dose fractionation procedures were explored and we describe their influence on the resolution of the final reconstruction. We also compared the quality of this data to that collected with a FEI Titan Krios microscope equipped with a Falcon I direct detector, which provides a benchmark for data collected using a high-end electron microscope.

Likelihood-based classification of cryo-EM images using FREALIGN

We describe an implementation of maximum likelihood classification for single particle electron cryo-microscopy that is based on the FREALIGN software. Particle alignment parameters are determined by maximizing a joint likelihood that can include hierarchical priors, while classification is performed by expectation maximization of a marginal likelihood. We test the FREALIGN implementation using a simulated dataset containing computer-generated projection images of three different 70S ribosome structures, as well as a publicly available dataset of 70S ribosomes. The results show that the mixed strategy of the new FREALIGN algorithm yields performance on par with other maximum likelihood implementations, while remaining computationally efficient.

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)

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A new method to validate 3D cryoEM maps of biological structures is described.

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High-resolution noise substitution is a tool to measure the amount of overfitting of noise in single particle cryoEM.

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A reliable, unbiased resolution estimation can be obtained even when some overfitting is present.

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Structure of beta-galactosidase at ~6 Å resolution is determined by cryoEM.

Validation of cryo-EM structure of IP₃R1 channel

About a decade ago, three electron cryomicroscopy (cryo-EM) single-particle reconstructions of IP3R1 were reported at low resolution. It was disturbing that these structures bore little similarity to one another, even at the level of quaternary structure. Recently, we published an improved structure of IP3R1 at ∼1 nm resolution. However, this structure did not bear any resemblance to any of the three previously published structures, leading to the question of why the structure should be considered more reliable than the original three. Here, we apply several methods, including class-average/map comparisons, tilt-pair validation, and use of multiple refinement software packages, to give strong evidence for the reliability of our recent structure. The map resolution and feature resolvability are assessed with the gold standard criterion. This approach is generally applicable to assessing the validity of cryo-EM maps of other molecular machines.

Protein secondary structure determination by constrained single-particle cryo-electron tomography

Cryo-electron microscopy (cryo-EM) is a powerful technique for 3D structure determination of protein complexes by averaging information from individual molecular images. The resolutions that can be achieved with single-particle cryo-EM are frequently limited by inaccuracies in assigning molecular orientations based solely on 2D projection images. Tomographic data collection schemes, however, provide powerful constraints that can be used to more accurately determine molecular orientations necessary for 3D reconstruction. Here, we propose "constrained single-particle tomography" as a general strategy for 3D structure determination in cryo-EM. A key component of our approach is the effective use of images recorded in tilt series to extract high-resolution information and correct for the contrast transfer function. By incorporating geometric constraints into the refinement to improve orientational accuracy of images, we reduce model bias and overrefinement artifacts and demonstrate that protein structures can be determined at resolutions of ∼8 Å starting from low-dose tomographic tilt series.