The Transform Class in SPARX and EMAN2

Optimal 3D angular sampling with applications to cryo-EM problems

The goal of cryo-EM experiments in the biological sciences is to determine the atomic structure of a molecule and deduce insights into its functions and mechanisms. Despite improvements in instrumentation for data collection and new software algorithms, in most cases, individual atoms are not resolved. Model building of proteins, nucleic acids, or molecules in general, is feasible from the experimentally determined density maps at resolutions up to the range of 3-4 Angstroms. For lower-resolution maps or parts of maps, fitting smaller structures obtained by modelling or experimental techniques with higher resolution is a way to resolve the issue. In practice, we have an atomic structure, generate its density map at a given resolution, and translate/rotate the map within a region of interest in the experimental map, computing a measure-of-fit score with the corresponding areas of the experimental map. This procedure is computationally intensive since we work in 6D space. An optimal ordered list of rotations will reduce the angular error and help to find the best-fitting positions faster for a coarse global search or a local refinement. It can be used for adaptive approaches to stop fitting algorithms earlier once the desired accuracy has been achieved. We demonstrate how the performance of some fitting algorithms can be improved by grouping sets of rotations. We present an approach to generate more efficient 3D angular sampling, and provide the computer code to generate lists of optimal orientations for single and grouped rotations and the lists themselves.

CryoVirusDB: A Labeled Cryo-EM Image Dataset for AI-Driven Virus Particle Picking

With the advancements in instrumentation, image processing algorithms, and computational capabilities, single-particle electron cryo-microscopy (cryo-EM) has achieved nearly atomic resolution in determining the 3D structures of viruses. The virus structures play a crucial role in studying their biological function and advancing the development of antiviral vaccines and treatments. Despite the effectiveness of artificial intelligence (AI) in general image processing, its development for identifying and extracting virus particles from cryo-EM micrographs (images) has been hindered by the lack of manually labelled high-quality datasets. To fill the gap, we introduce CryoVirusDB, a labeled dataset containing the coordinates of expert-picked virus particles in cryo-EM micrographs. CryoVirusDB comprises 9,941 micrographs of 9 different viruses along with the coordinates of 339,398 labeled virus particles. It can be used to train and test AI and machine learning (e.g., deep learning) methods to accurately identify virus particles in cryo-EM micrographs for building atomic 3D structural models for viruses.

CryoTransformer: A Transformer Model for Picking Protein Particles from Cryo-EM Micrographs

Cryo-electron microscopy (cryo-EM) is a powerful technique for determining the structures of large protein complexes. Picking single protein particles from cryo-EM micrographs (images) is a crucial step in reconstructing protein structures from them. However, the widely used template-based particle picking process requires some manual particle picking and is labor-intensive and time-consuming. Though machine learning and artificial intelligence (AI) can potentially automate particle picking, the current AI methods pick particles with low precision or low recall. The erroneously picked particles can severely reduce the quality of reconstructed protein structures, especially for the micrographs with low signal-to-noise (SNR) ratios. To address these shortcomings, we devised CryoTransformer based on transformers, residual networks, and image processing techniques to accurately pick protein particles from cryo-EM micrographs. CryoTransformer was trained and tested on the largest labelled cryo-EM protein particle dataset - CryoPPP. It outperforms the current state-of-the-art machine learning methods of particle picking in terms of the resolution of 3D density maps reconstructed from the picked particles as well as F1-score and is poised to facilitate the automation of the cryo-EM protein particle picking.

A large expert-curated cryo-EM image dataset for machine learning protein particle picking

Cryo-electron microscopy (cryo-EM) is a powerful technique for determining the structures of biological macromolecular complexes. Picking single-protein particles from cryo-EM micrographs is a crucial step in reconstructing protein structures. However, the widely used template-based particle picking process is labor-intensive and time-consuming. Though machine learning and artificial intelligence (AI) based particle picking can potentially automate the process, its development is hindered by lack of large, high-quality labelled training data. To address this bottleneck, we present CryoPPP, a large, diverse, expert-curated cryo-EM image dataset for protein particle picking and analysis. It consists of labelled cryo-EM micrographs (images) of 34 representative protein datasets selected from the Electron Microscopy Public Image Archive (EMPIAR). The dataset is 2.6 terabytes and includes 9,893 high-resolution micrographs with labelled protein particle coordinates. The labelling process was rigorously validated through 2D particle class validation and 3D density map validation with the gold standard. The dataset is expected to greatly facilitate the development of both AI and classical methods for automated cryo-EM protein particle picking.

CryoPPP: A Large Expert-Labelled Cryo-EM Image Dataset for Machine Learning Protein Particle Picking

Cryo-electron microscopy (cryo-EM) is currently the most powerful technique for determining the structures of large protein complexes and assemblies. Picking single-protein particles from cryo-EM micrographs (images) is a key step in reconstructing protein structures. However, the widely used template-based particle picking process is labor-intensive and time-consuming. Though the emerging machine learning-based particle picking can potentially automate the process, its development is severely hindered by lack of large, high-quality, manually labelled training data. Here, we present CryoPPP, a large, diverse, expert-curated cryo-EM image dataset for single protein particle picking and analysis to address this bottleneck. It consists of manually labelled cryo-EM micrographs of 32 non-redundant, representative protein datasets selected from the Electron Microscopy Public Image Archive (EMPIAR). It includes 9,089 diverse, high-resolution micrographs (∼300 cryo-EM images per EMPIAR dataset) in which the coordinates of protein particles were labelled by human experts. The protein particle labelling process was rigorously validated by both 2D particle class validation and 3D density map validation with the gold standard. The dataset is expected to greatly facilitate the development of machine learning and artificial intelligence methods for automated cryo-EM protein particle picking. The dataset and data processing scripts are available at https://github.com/BioinfoMachineLearning/cryoppp.

Estimation of Projection Parameter Distribution and Initial Model Generation in Single-Particle Analysis

This study focused on the problem of projection parameter search in 3D reconstruction using single-particle analysis. We treated the sampling distribution for the parameter search as a prior distribution and designed a probabilistic model for efficient parameter estimation. Using our method, we showed that it is possible to perform 3D reconstruction from synthetic and actual electron microscope images using an initial model, and to generate the initial model itself. We also examined whether the optimization function used in the stochastic gradient descent method can be applied with loose constraints to improve the convergence of initial model generation and confirmed the effect. In order to investigate the advantage of generating a smooth sampling distribution from the stochastic model, we compared the distribution of estimated projection directions with the conventional method of performing a global search using spherical gridding. As a result, our method, which is simple in both mathematical model and implementation, showed no algorithmic artifacts.

The CRL4DCAF1 cullin-RING ubiquitin ligase is activated following a switch in oligomerization state

The cullin‐4‐based RING‐type (CRL4) family of E3 ubiquitin ligases functions together with dedicated substrate receptors. Out of the ˜29 CRL4 substrate receptors reported, the DDB1‐ and CUL4‐associated factor 1 (DCAF1) is essential for cellular survival and growth, and its deregulation has been implicated in tumorigenesis. We carried out biochemical and structural studies to examine the structure and mechanism of the CRL4^DCAF1 ligase. In the 8.4 Å cryo‐EM map of CRL4^DCAF1, four CUL4‐RBX1‐DDB1‐DCAF1 protomers are organized into two dimeric sub‐assemblies. In this arrangement, the WD40 domain of DCAF1 mediates binding with the cullin C‐terminal domain (CTD) and the RBX1 subunit of a neighboring CRL4^DCAF1 protomer. This renders RBX1, the catalytic subunit of the ligase, inaccessible to the E2 ubiquitin‐conjugating enzymes. Upon CRL4^DCAF1 activation by neddylation, the interaction between the cullin CTD and the neighboring DCAF1 protomer is broken, and the complex assumes an active dimeric conformation. Accordingly, a tetramerization‐deficient CRL4^DCAF1 mutant has higher ubiquitin ligase activity compared to the wild‐type. This study identifies a novel mechanism by which unneddylated and substrate‐free CUL4 ligases can be maintained in an inactive state.

Deep learning-based mixed-dimensional Gaussian mixture model for characterizing variability in cryo-EM

Structural flexibility and/or dynamic interactions with other molecules is a critical aspect of protein function. CryoEM provides direct visualization of individual macromolecules sampling different conformational and compositional states. While numerous methods are available for computational classification of discrete states, characterization of continuous conformational changes or large numbers of discrete state without human supervision remains challenging. Here we present e2gmm, a machine learning algorithm to determine a conformational landscape for proteins or complexes using a 3-D Gaussian mixture model mapped onto 2-D particle images in known orientations. Using a deep neural network architecture, e2gmm can automatically resolve the structural heterogeneity within the protein complex and map particles onto a small latent space describing conformational and compositional changes. This system presents a more intuitive and flexible representation than other manifold methods currently in use. We demonstrate this method on both simulated data as well as three biological systems, to explore compositional and conformational changes at a range of scales. The software is distributed as part of EMAN2.

Unit quaternion description of spatial rotations in 3D electron cryo-microscopy

Electron cryo-microscopy (cryoEM) involves the estimation of spatial rotations, or saying orientations, of projection images or three-dimensional (3D) volumes. Euler angle system is widely used to describe spatial rotations in most cryoEM algorithms and software. In this review, we introduce unit quaternion as an alternate to Euler angles for describing spatial rotations, customize and develop corresponding tools for increasing demands of statistical analysis of spatial rotations in cryoEM. Some basic properties and definitions of quaternion are first recalled. Thereafter, distance and geodesic between rotations are introduced to aid comparisons and interpolations between rotations, which are prerequisites of statistics of rotations in 3D cryoEM. Furthermore, statistics of rotations are reviewed. Techniques potentially useful in cryoEM, such as calculations of the average rotation, generation of quasi-regular grids, sampling, inference with uniform distribution and angular central Gaussian (ACG) distribution, and estimation of rotation precision, are reviewed and developed. Finally, molecular symmetry presented in unit quaternion form is discussed. Unit quaternion system is shown as a convenient and comprehensive mathematical tool for cryoEM.

Arrangement of the Polymerase Complexes inside a Nine-Segmented dsRNA Virus

Members of the family Reoviridae package several copies of the viral polymerase complex into their capsid to carry out replication and transcription within viral particles. Classical single-particle reconstruction encounters difficulties resolving structures such as the intraparticle polymerase complex because refinement can converge to an incorrect map and because the map could depict a nonrepresentative subset of particles or an average of heterogeneous particles. Using the nine-segmented Fako virus, we tested hypotheses for the arrangement and number of polymerase complexes within the virion by measuring how well each hypothesis describes the set of cryoelectron microscopy images of individual viral particles. We find that the polymerase complex in Fako virus binds at ten possible sites despite having only nine genome segments. A single asymmetric configuration describes the arrangement of these complexes in both virions and genome-free capsids. Similarities between the arrangements of Reoviridae with 9, 10, and 11 segments indicate the generalizability of this architecture.

Imaging Three-Dimensional Elemental Inhomogeneity in Pt-Ni Nanoparticles Using Spectroscopic Single Particle Reconstruction

The properties of nanoparticles are known to critically depend on their local chemistry but characterizing three-dimensional (3D) elemental segregation at the nanometer scale is highly challenging. Scanning transmission electron microscope (STEM) tomographic imaging is one of the few techniques able to measure local chemistry for inorganic nanoparticles but conventional methodologies often fail due to the high electron dose imparted. Here, we demonstrate realization of a new spectroscopic single particle reconstruction approach built on a method developed by structural biologists. We apply this technique to the imaging of PtNi nanocatalysts and find new evidence of a complex inhomogeneous alloying with a Pt-rich core, a Ni-rich hollow octahedral intermediate shell and a Pt-rich rhombic dodecahedral skeleton framework with less Pt at ⟨100⟩ vertices. The ability to gain evidence of local surface enrichment that varies with the crystallographic orientation of facets and vertices is expected to provide significant insight toward the development of nanoparticles for sensing, medical imaging, and catalysis.

Massively parallel unsupervised single-particle cryo-EM data clustering via statistical manifold learning

Structural heterogeneity in single-particle cryo-electron microscopy (cryo-EM) data represents a major challenge for high-resolution structure determination. Unsupervised classification may serve as the first step in the assessment of structural heterogeneity. However, traditional algorithms for unsupervised classification, such as K-means clustering and maximum likelihood optimization, may classify images into wrong classes with decreasing signal-to-noise-ratio (SNR) in the image data, yet demand increased computational costs. Overcoming these limitations requires further development of clustering algorithms for high-performance cryo-EM data processing. Here we introduce an unsupervised single-particle clustering algorithm derived from a statistical manifold learning framework called generative topographic mapping (GTM). We show that unsupervised GTM clustering improves classification accuracy by about 40% in the absence of input references for data with lower SNRs. Applications to several experimental datasets suggest that our algorithm can detect subtle structural differences among classes via a hierarchical clustering strategy. After code optimization over a high-performance computing (HPC) environment, our software implementation was able to generate thousands of reference-free class averages within hours in a massively parallel fashion, which allows a significant improvement on ab initio 3D reconstruction and assists in the computational purification of homogeneous datasets for high-resolution visualization.

Single-particle electron microscopy structure of UDP-glucose:glycoprotein glucosyltransferase suggests a selectivity mechanism for misfolded proteins

The enzyme UDP-glucose:glycoprotein glucosyltransferase (UGGT) mediates quality control of glycoproteins in the endoplasmic reticulum by attaching glucose to N-linked glycan of misfolded proteins. As a sensor, UGGT ensures that misfolded proteins are recognized by the lectin chaperones and do not leave the secretory pathway. The structure of UGGT and the mechanism of its selectivity for misfolded proteins have been unknown for 25 years. Here, we used negative-stain electron microscopy and small-angle X-ray scattering to determine the structure of UGGT from Drosophila melanogaster at 18-Å resolution. Three-dimensional reconstructions revealed a cage-like structure with a large central cavity. Particle classification revealed flexibility that precluded determination of a high-resolution structure. Introduction of biotinylation sites into a fungal UGGT expressed in Escherichia coli allowed identification of the catalytic and first thioredoxin-like domains. We also used hydrogen-deuterium exchange mass spectrometry to map the binding site of an accessory protein, Sep15, to the first thioredoxin-like domain. The UGGT structural features identified suggest that the central cavity contains the catalytic site and is lined with hydrophobic surfaces. This enhances the binding of misfolded substrates with exposed hydrophobic residues and excludes folded proteins with hydrophilic surfaces. In conclusion, we have determined the UGGT structure, which enabled us to develop a plausible functional model of the mechanism for UGGT's selectivity for misfolded glycoproteins.

High resolution single particle refinement in EMAN2.1

EMAN2.1 is a complete image processing suite for quantitative analysis of grayscale images, with a primary focus on transmission electron microscopy, with complete workflows for performing high resolution single particle reconstruction, 2-D and 3-D heterogeneity analysis, random conical tilt reconstruction and subtomogram averaging, among other tasks. In this manuscript we provide the first detailed description of the high resolution single particle analysis pipeline and the philosophy behind its approach to the reconstruction problem. High resolution refinement is a fully automated process, and involves an advanced set of heuristics to select optimal algorithms for each specific refinement task. A gold standard FSC is produced automatically as part of refinement, providing a robust resolution estimate for the final map, and this is used to optimally filter the final CTF phase and amplitude corrected structure. Additional methods are in-place to reduce model bias during refinement, and to permit cross-validation using other computational methods.

Architecture and dynamics of the autophagic phosphatidylinositol 3-kinase complex

The class III phosphatidylinositol 3-kinase complex I (PI3KC3-C1) that functions in early autophagy consists of the lipid kinase VPS34, the scaffolding protein VPS15, the tumor suppressor BECN1, and the autophagy-specific subunit ATG14. The structure of the ATG14-containing PI3KC3-C1 was determined by single-particle EM, revealing a V-shaped architecture. All of the ordered domains of VPS34, VPS15, and BECN1 were mapped by MBP tagging. The dynamics of the complex were defined using hydrogen–deuterium exchange, revealing a novel 20-residue ordered region C-terminal to the VPS34 C2 domain. VPS15 organizes the complex and serves as a bridge between VPS34 and the ATG14:BECN1 subcomplex. Dynamic transitions occur in which the lipid kinase domain is ejected from the complex and VPS15 pivots at the base of the V. The N-terminus of BECN1, the target for signaling inputs, resides near the pivot point. These observations provide a framework for understanding the allosteric regulation of lipid kinase activity.

DOI:http://dx.doi.org/10.7554/eLife.05115.001

To survive starvation and other hard times, cells have developed a unique recycling strategy: they can scavenge the resources they need from within the cell itself. To do this, the cell forms a double-layered envelope around particular sections of the cell to seal them off from the rest. Then, the contents of the envelope are taken apart and the resulting raw materials are sent elsewhere in the cell where they can be used as required. This process is called autophagy.

In more complex organisms like humans, autophagy can have additional roles. One of the key proteins involved in autophagy—called BECN1—suppresses the growth of tumors, and the gene that makes BECN1 is missing in 40–70% of human breast, ovarian, and prostate cancers. Autophagy may also help to prevent Huntington's disease and other similar conditions by stopping disease-causing proteins or broken cell parts from building up inside brain cells.

The BECN1 protein does not work alone. Instead, it becomes part of a group, or ‘complex’, of several proteins that are required to form the envelope made during autophagy. However, the three-dimensional structure of the protein complex is unclear.

Baskaran et al. used electron microscopy and other techniques to investigate this structure and found that the complex forms a V shape with two arms, which is held together by its largest protein, VPS15. This protein also acts as a bridge between BECN1 and another protein that is a target for new cancer drugs, called VPS34.

Next, Baskaran et al. used a different set of techniques to determine how the complex moves. This revealed that many of the connections between proteins in the complex are flexible. However, one of the arms is inflexible and this limits the ability of the VPS34 protein to move. Understanding this structural constraint may help us to design drugs that are able to target the protein complex more efficiently.

DOI:http://dx.doi.org/10.7554/eLife.05115.002

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.

Structural mimicry in transcription regulation of human RNA polymerase II by the DNA helicase RECQL5

RECQL5 is a member of the highly conserved RecQ family of DNA helicases involved in DNA repair. RECQL5 interacts with RNA polymerase II (Pol II) and inhibits transcription of protein-encoding genes by an unknown mechanism. We show that RECQL5 contacts the Rpb1 jaw domain of Pol II at a site that overlaps with the binding site for the transcription elongation factor TFIIS. Our cryo-EM structure of elongating Pol II arrested in complex with RECQL5 shows that the RECQL5 helicase domain is positioned to sterically block elongation. The crystal structure of the RECQL5 KIX domain reveals similarities with TFIIS, and binding of RECQL5 to Pol II interferes with the ability of TFIIS to promote transcriptional read-through in vitro. Together, our findings reveal a dual mode of transcriptional repression by RECQL5 that includes structural mimicry of the Pol II-TFIIS interaction.

Molecular architecture of human polycomb repressive complex 2

Polycomb Repressive Complex 2 (PRC2) is essential for gene silencing, establishing transcriptional repression of specific genes by tri-methylating Lysine 27 of histone H3, a process mediated by cofactors such as AEBP2. In spite of its biological importance, little is known about PRC2 architecture and subunit organization. Here, we present the first three-dimensional electron microscopy structure of the human PRC2 complex bound to its cofactor AEBP2. Using a novel internal protein tagging-method, in combination with isotopic chemical cross-linking and mass spectrometry, we have localized all the PRC2 subunits and their functional domains and generated a detailed map of interactions. The position and stabilization effect of AEBP2 suggests an allosteric role of this cofactor in regulating gene silencing. Regions in PRC2 that interact with modified histone tails are localized near the methyltransferase site, suggesting a molecular mechanism for the chromatin-based regulation of PRC2 activity.DOI:http://dx.doi.org/10.7554/eLife.00005.001.

Iterative stable alignment and clustering of 2D transmission electron microscope images

Identification of homogeneous subsets of images in a macromolecular electron microscopy (EM) image data set is a critical step in single-particle analysis. The task is handled by iterative algorithms, whose performance is compromised by the compounded limitations of image alignment and K-means clustering. Here we describe an approach, iterative stable alignment and clustering (ISAC) that, relying on a new clustering method and on the concepts of stability and reproducibility, can extract validated, homogeneous subsets of images. ISAC requires only a small number of simple parameters and, with minimal human intervention, can eliminate bias from two-dimensional image clustering and maximize the quality of group averages that can be used for ab initio three-dimensional structural determination and analysis of macromolecular conformational variability. Repeated testing of the stability and reproducibility of a solution within ISAC eliminates heterogeneous or incorrect classes and introduces critical validation to the process of EM image clustering.

Identifying conformational states of macromolecules by eigen-analysis of resampled cryo-EM images

We present the codimensional principal component analysis (PCA), a novel and straightforward method for resolving sample heterogeneity within a set of cryo-EM 2D projection images of macromolecular assemblies. The method employs PCA of resampled 3D structures computed using subsets of 2D data obtained with a novel hypergeometric sampling scheme. PCA provides us with a small subset of dominating "eigenvolumes" of the system, whose reprojections are compared with experimental projection data to yield their factorial coordinates constructed in a common framework of the 3D space of the macromolecule. Codimensional PCA is unique in the dramatic reduction of dimensionality of the problem, which facilitates rapid determination of both the plausible number of conformers in the sample and their 3D structures. We applied the codimensional PCA to a complex data set of Thermus thermophilus 70S ribosome, and we identified four major conformational states and visualized high mobility of the stalk base region.

Image restoration in cryo-electron microscopy

Image restoration techniques are used to obtain, given experimental measurements, the best possible approximation of the original object within the limits imposed by instrumental conditions and noise level in the data. In molecular electron microscopy (EM), we are mainly interested in linear methods that preserve the respective relationships between mass densities within the restored map. Here, we describe the methodology of image restoration in structural EM, and more specifically, we will focus on the problem of the optimum recovery of Fourier amplitudes given electron microscope data collected under various defocus settings. We discuss in detail two classes of commonly used linear methods, the first of which consists of methods based on pseudoinverse restoration, and which is further subdivided into mean-square error, chi-square error, and constrained based restorations, where the methods in the latter two subclasses explicitly incorporates non-white distribution of noise in the data. The second class of methods is based on the Wiener filtration approach. We show that the Wiener filter-based methodology can be used to obtain a solution to the problem of amplitude correction (or "sharpening") of the EM map that makes it visually comparable to maps determined by X-ray crystallography, and thus amenable to comparative interpretation. Finally, we present a semiheuristic Wiener filter-based solution to the problem of image restoration given sets of heterogeneous solutions. We conclude the chapter with a discussion of image restoration protocols implemented in commonly used single particle software packages.

Cryo-EM image alignment based on nonuniform fast Fourier transform

In single particle analysis, two-dimensional (2-D) alignment is a fundamental step intended to put into register various particle projections of biological macromolecules collected at the electron microscope. The efficiency and quality of three-dimensional (3-D) structure reconstruction largely depends on the computational speed and alignment accuracy of this crucial step. In order to improve the performance of alignment, we introduce a new method that takes advantage of the highly accurate interpolation scheme based on the gridding method, a version of the nonuniform fast Fourier transform, and utilizes a multi-dimensional optimization algorithm for the refinement of the orientation parameters. Using simulated data, we demonstrate that by using less than half of the sample points and taking twice the runtime, our new 2-D alignment method achieves dramatically better alignment accuracy than that based on quadratic interpolation. We also apply our method to image to volume registration, the key step in the single particle EM structure refinement protocol. We find that in this case the accuracy of the method not only surpasses the accuracy of the commonly used real-space implementation, but results are achieved in much shorter time, making gridding-based alignment a perfect candidate for efficient structure determination in single particle analysis.