De novo backbone trace of GroEL from single particle electron cryomicroscopy

Predictive modeling and cryo-EM: A synergistic approach to modeling macromolecular structure

Over the last 15 years, structural biology has seen unprecedented development and improvement in two areas: electron cryo-microscopy (cryo-EM) and predictive modeling. Once relegated to low resolutions, single-particle cryo-EM is now capable of achieving near-atomic resolutions of a wide variety of macromolecular complexes. Ushered in by AlphaFold, machine learning has powered the current generation of predictive modeling tools, which can accurately and reliably predict models for proteins and some complexes directly from the sequence alone. Although they offer new opportunities individually, there is an inherent synergy between these techniques, allowing for the construction of large, complex macromolecular models. Here, we give a brief overview of these approaches in addition to illustrating works that combine these techniques for model building. These examples provide insight into model building, assessment, and limitations when integrating predictive modeling with cryo-EM density maps. Together, these approaches offer the potential to greatly accelerate the generation of macromolecular structural insights, particularly when coupled with experimental data.

Unsupervised Cryo-EM Images Denoising and Clustering Based on Deep Convolutional Autoencoder and K-Means+

Cryo-electron microscopy (cryo-EM) is a widely used structural determination technique. Because of the extremely low signal-to-noise ratio (SNR) of images captured by cryo-EM, clustering single-particle cryo-EM images with high accuracy is challenging. To address this, we proposed an iterative denoising and clustering method based on a deep convolutional variational autoencoder and K-means++. The proposed method contains two modules: a denoising ResNet variational autoencoder (DRVAE), and Balance size K-means++ (BSK-means++). First, the DRVAE is trained in a fully unsupervised manner to initialize the neural network and obtain preliminary denoised images. Second, BSK-means++ is built for clustering denoised images, and images closer to class centers are divided into reliable samples. Third, the training of DRVAE is continued, while the class-average images are used as pseudo supervision of reliable samples to reserve more detailed information of denoised images. Finally, the second and third steps mentioned above can be performed jointly and iteratively until convergence occurs. The experimental results showed that the proposed method can generate reliable class average images and achieve better clustering accuracy and normalized mutual information than current methods. This study confirmed that DRVAE with BSK-means++ could achieve a good denoise performance on single-particle cryo-EM images, which can help researchers obtain information such as symmetry and heterogeneity of the target particles. In addition, the proposed method avoids the extreme imbalance of class size, which improves the reliability of the clustering result.

Reconstruction of 3D density from solution scattering

Ab initio modeling methods have proven to be powerful means of interpreting solution scattering data. In the absence of atomic models, or complementary to them, ab initio modeling approaches can be used for generating low-resolution particle envelopes using only solution scattering profiles. Recently, a new ab initio reconstruction algorithm has been introduced to the scientific community, called DENSS. DENSS is unique among ab initio modeling algorithms in that it solves the inverse scattering problem, i.e., the 1D scattering intensities are directly used to determine the 3D particle density. The reconstruction of particle density has several advantages over conventional uniform density modeling approaches, including the ability to reconstruct a much wider range of particle types and the ability to visualize low-resolution density fluctuations inside the particle envelope. In this chapter we will discuss the theory behind this new approach, how to use DENSS, and how to interpret the results. Several examples with experimental and simulated data will be provided.

Cryo-EM Analyses Permit Visualization of Structural Polymorphism of Biological Macromolecules

The functions of biological macromolecules are often associated with conformational malleability of the structures. This phenomenon of chemically identical molecules with different structures is coined structural polymorphism. Conventionally, structural polymorphism is observed directly by structural determination at the density map level from X-ray crystal diffraction. Although crystallography approach can report the conformation of a macromolecule with the position of each atom accurately defined in it, the exploration of structural polymorphism and interpreting biological function in terms of crystal structures is largely constrained by the crystal packing. An alternative approach to studying the macromolecule of interest in solution is thus desirable. With the advancement of instrumentation and computational methods for image analysis and reconstruction, cryo-electron microscope (cryo-EM) has been transformed to be able to produce “in solution” structures of macromolecules routinely with resolutions comparable to crystallography but without the need of crystals. Since the sample preparation of single-particle cryo-EM allows for all forms co-existing in solution to be simultaneously frozen, the image data contain rich information as to structural polymorphism. The ensemble of structure information can be subsequently disentangled through three-dimensional (3D) classification analyses. In this review, we highlight important examples of protein structural polymorphism in relation to allostery, subunit cooperativity and function plasticity recently revealed by cryo-EM analyses, and review recent developments in 3D classification algorithms including neural network/deep learning approaches that would enable cryo-EM analyese in this regard. Finally, we brief the frontier of cryo-EM structure determination of RNA molecules where resolving the structural polymorphism is at dawn.

Study of GroEL Conformational Mobility by Cryo-Electron Microscopy and Molecular Dynamics

Abstract

Bacterial chaperonin GroEL is a complex ring-shaped protein oligomer that promotes the folding of other proteins by encapsulating them in the cavity. There is very little structural information about the disordered C-terminal fragment of the GroEL subunits, which is involved in the folding of the substrate protein. A 3D reconstruction of the GroEL apo-form was obtained by cryo-electron microscopy (cryo-EM) with a resolution of 3.02 Å and supplemented by molecular dynamics (MD) calculations. The results of cryo-EM and MD are in good agreement and demonstrate a diverse mobility of the protein subunit domains. The MD results predict the dynamics and the network of intramolecular contacts of the C-terminal sections of the protein. These results are of great importance for the subsequent study of the mechanism of protein folding in the GroEL cavity.

Evolution of standardization and dissemination of cryo-EM structures and data jointly by the community, PDB, and EMDB

Cryogenic electron microscopy (cryo-EM) methods began to be used in the mid-1970s to study thin and periodic arrays of proteins. Following a half-century of development in cryo-specimen preparation, instrumentation, data collection, data processing, and modeling software, cryo-EM has become a routine method for solving structures from large biological assemblies to small biomolecules at near to true atomic resolution. This review explores the critical roles played by the Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in partnership with the community to develop the necessary infrastructure to archive cryo-EM maps and associated models. Public access to cryo-EM structure data has in turn facilitated better understanding of structure–function relationships and advancement of image processing and modeling tool development. The partnership between the global cryo-EM community and PDB and EMDB leadership has synergistically shaped the standards for metadata, one-stop deposition of maps and models, and validation metrics to assess the quality of cryo-EM structures. The advent of cryo-electron tomography (cryo-ET) for in situ molecular cell structures at a broad resolution range and their correlations with other imaging data introduce new data archival challenges in terms of data size and complexity in the years to come.

Auto3DCryoMap: an automated particle alignment approach for 3D cryo-EM density map reconstruction

BACKGROUND

Cryo-EM data generated by electron tomography (ET) contains images for individual protein particles in different orientations and tilted angles. Individual cryo-EM particles can be aligned to reconstruct a 3D density map of a protein structure. However, low contrast and high noise in particle images make it challenging to build 3D density maps at intermediate to high resolution (1-3 Å). To overcome this problem, we propose a fully automated cryo-EM 3D density map reconstruction approach based on deep learning particle picking.

RESULTS

A perfect 2D particle mask is fully automatically generated for every single particle. Then, it uses a computer vision image alignment algorithm (image registration) to fully automatically align the particle masks. It calculates the difference of the particle image orientation angles to align the original particle image. Finally, it reconstructs a localized 3D density map between every two single-particle images that have the largest number of corresponding features. The localized 3D density maps are then averaged to reconstruct a final 3D density map. The constructed 3D density map results illustrate the potential to determine the structures of the molecules using a few samples of good particles. Also, using the localized particle samples (with no background) to generate the localized 3D density maps can improve the process of the resolution evaluation in experimental maps of cryo-EM. Tested on two widely used datasets, Auto3DCryoMap is able to reconstruct good 3D density maps using only a few thousand protein particle images, which is much smaller than hundreds of thousands of particles required by the existing methods.

CONCLUSIONS

We design a fully automated approach for cryo-EM 3D density maps reconstruction (Auto3DCryoMap). Instead of increasing the signal-to-noise ratio by using 2D class averaging, our approach uses 2D particle masks to produce locally aligned particle images. Auto3DCryoMap is able to accurately align structural particle shapes. Also, it is able to construct a decent 3D density map from only a few thousand aligned particle images while the existing tools require hundreds of thousands of particle images. Finally, by using the pre-processed particle images, Auto3DCryoMap reconstructs a better 3D density map than using the original particle images.

A comparative study of single-particle cryo-EM with liquid-nitrogen and liquid-helium cooling

Radiation damage is the most fundamental limitation for achieving high resolution in electron cryo-microscopy (cryo-EM) of biological samples. The effects of radiation damage are reduced by liquid-helium cooling, although the use of liquid helium is more challenging than that of liquid nitrogen. To date, the benefits of liquid-nitrogen and liquid-helium cooling for single-particle cryo-EM have not been compared quantitatively. With recent technical and computational advances in cryo-EM image recording and processing, such a comparison now seems timely. This study aims to evaluate the relative merits of liquid-helium cooling in present-day single-particle analysis, taking advantage of direct electron detectors. Two data sets for recombinant mouse heavy-chain apoferritin cooled with liquid-nitrogen or liquid-helium to 85 or 17 K were collected, processed and compared. No improvement in terms of resolution or Coulomb potential map quality was found for liquid-helium cooling. Interestingly, beam-induced motion was found to be significantly higher with liquid-helium cooling, especially within the most valuable first few frames of an exposure, thus counteracting any potential benefit of better cryoprotection that liquid-helium cooling may offer for single-particle cryo-EM.

Assessment of detailed conformations suggests strategies for improving cryoEM models: Helix at lower resolution, ensembles, pre-refinement fixups, and validation at multi-residue length scale

We find that the overall quite good methods used in the CryoEM Model Challenge could still benefit greatly from several strategies for improving local conformations. Our assessments primarily use validation criteria from the MolProbity web service. Those criteria include MolProbity's all-atom contact analysis, updated versions of standard conformational validations for protein and RNA, plus two recent additions: first, flags for cis-nonPro and twisted peptides, and second, the CaBLAM system for diagnosing secondary structure, validating Cα backbone, and validating adjacent peptide CO orientations in the context of the Cα trace. In general, automated ab initio building of starting models is quite good at backbone connectivity but often fails at local conformation or sequence register, especially at poorer than 3.5 Å resolution. However, we show that even if criteria (such as Ramachandran or rotamer) are explicitly restrained to improve refinement behavior and overall validation scores, automated optimization of a deposited structure seldom corrects specific misfittings that start in the wrong local minimum, but just hides them. Therefore, local problems should be identified, and as many as possible corrected, before starting refinement. Secondary structures are confusing at 3-4 Å but can be better recognized at 6-8 Å. In future model challenges, specific steps being tested (such as segmentation) and the required documentation (such as PDB code of starting model) should each be explicitly defined, so competing methods on a given task can be meaningfully compared. Individual local examples are presented here, to understand what local mistakes and corrections look like in 3D, how they probably arise, and what possible improvements to methodology might help avoid them. At these resolutions, both structural biologists and end-users need meaningful estimates of local uncertainty, perhaps through explicit ensembles. Fitting problems can best be diagnosed by validation that spans multiple residues; CaBLAM is such a multi-residue tool, and its effectiveness is demonstrated.

Atomic-Level Description of Protein Folding inside the GroEL Cavity

Chaperonins (ubiquitous facilitators of protein folding) sequester misfolded proteins within an internal cavity, thus preventing protein aggregation during the process of refolding. GroEL, a tetradecameric bacterial chaperonin, is one of the most studied chaperonins, but the role of the internal cavity in the refolding process is still unclear. It has been suggested that rather than simply isolating proteins while they refold, the GroEL cavity actively promotes protein folding. A detailed characterization of the folding dynamics and thermodynamics of protein substrates encapsulated within the cavity, however, has been difficult to obtain by experimental means, due to the system's complexity and the many steps in the folding cycle. Here, we examine the influence of the GroEL cavity on protein folding based on the results of unbiased, atomistic molecular dynamics simulations. We first verified that the computational setup, which uses a recently developed state-of-the-art force field that more accurately reproduces the aggregation propensity of unfolded states, could recapitulate the essential structural dynamics of GroEL. In these simulations, the GroEL tetradecamer was highly dynamic, transitioning among states corresponding to most of the structures that have been observed experimentally. We then simulated a small, unfolded protein both in the GroEL cavity and in bulk solution and compared the protein's folding process within these two environments. Inside the GroEL cavity, the unfolded protein interacted strongly with the disordered residues in GroEL's C-terminal tails. These interactions stabilized the protein's unfolded states relative to its compact states and increased the roughness of its folding free-energy surface, resulting in slower folding compared to the rate in solution. For larger proteins, which are more typical GroEL substrates, we speculate that these interactions may allow substrates to more quickly escape kinetic traps associated with compact, misfolded states, thereby actively promoting folding.

Trapping an octahedral Ag6 kernel in a seven-fold symmetric Ag56 nanowheel

High-nuclearity silver clusters are appealing synthetic targets for their remarkable structures, but most are isolated serendipitously. We report here six giant silver-thiolate clusters mediated by solvents, which not only dictate the formation of an octahedral Ag₆⁴⁺ kernel, but also influence the in situ-generated Mo-based anion templates. The typical sevenfold symmetric silver nanowheels show a hierarchical cluster-in-cluster structure that comprises an outermost Ag₅₆ shell and an inner Ag₆⁴⁺ kernel in the centre with seven MoO₄^2- anion templates around it. Electrospray ionization mass spectrometry analyses reveal the underlying rule for the formation of such unique silver nanowheels. This work establishes a solvent-intervention approach to construct high-nuclearity silver clusters in which both the formation of octahedral Ag₆⁴⁺ kernel and in situ generation of various Mo-based anion templates can be simultaneously controlled.

Validating Resolution Revolution

Recent advances in instrumentation and image-processing software have resulted in a resolution revolution in cryo-electron microscopy (cryo-EM) and a surge in the popularity of this technique. However, despite technical progress and hundreds of structures determined so far, development of standards assessing the agreement between the cryo-EM map and the respective model has fallen behind. Here we establish a validation procedure evaluating this agreement and applied it to a set of 565 cryo-EM structures. Analysis of the results revealed that three-quarters of the validated structures exhibit moderate or low agreement between the map and the corresponding model, mostly due to limited structural features possessed by these maps. Model re-refinement significantly improved the agreement for only one-fifth of the structures, reaffirming the necessity to re-evaluate map resolution. The presented procedure provides an approach to re-estimate the resolution of cryo-EM map areas interpreted by the model.

Subunit conformational variation within individual GroEL oligomers resolved by Cryo-EM

Single-particle electron cryo-microscopy (cryo-EM) is an emerging tool for resolving structures of conformationally heterogeneous particles; however, each structure is derived from an average of many particles with presumed identical conformations. We used a 3.5-Å cryo-EM reconstruction with imposed D7 symmetry to further analyze structural heterogeneity among chemically identical subunits in each GroEL oligomer. Focused classification of the 14 subunits in each oligomer revealed three dominant classes of subunit conformations. Each class resembled a distinct GroEL crystal structure in the Protein Data Bank. The conformational differences stem from the orientations of the apical domain. We mapped each conformation class to its subunit locations within each GroEL oligomer in our dataset. The spatial distributions of each conformation class differed among oligomers, and most oligomers contained 10-12 subunits of the three dominant conformation classes. Adjacent subunits were found to more likely assume the same conformation class, suggesting correlation among subunits in the oligomer. This study demonstrates the utility of cryo-EM in revealing structure dynamics within a single protein oligomer.

Electron Cryomicroscopy of Viruses at Near-Atomic Resolutions

Recently, dozens of virus structures have been solved to resolutions between 2.5 and 5.0 Å by means of electron cryomicroscopy. With these structures we are now firmly within the "atomic age" of electron cryomicroscopy, as these studies can reveal atomic details of protein and nucleic acid topology and interactions between specific residues. This improvement in resolution has been the result of direct electron detectors and image processing advances. Although enforcing symmetry facilitates reaching near-atomic resolution with fewer particle images, it unfortunately obscures some biologically interesting components of a virus. New approaches on relaxing symmetry and exploring structure dynamics and heterogeneity of viral assemblies have revealed important insights into genome packaging, virion assembly, cell entry, and other stages of the viral life cycle. In the future, novel methods will be required to reveal yet-unknown structural conformations of viruses, relevant to their biological activities. Ultimately, these results hold the promise of answering many unresolved questions linking structural diversity of viruses to their biological functions.

Selective Capture of Histidine-tagged Proteins from Cell Lysates Using TEM grids Modified with NTA-Graphene Oxide

We report the fabrication of transmission electron microscopy (TEM) grids bearing graphene oxide (GO) sheets that have been modified with N^α, N^α-dicarboxymethyllysine (NTA) and deactivating agents to block non-selective binding between GO-NTA sheets and non-target proteins. The resulting GO-NTA-coated grids with these improved antifouling properties were then used to isolate His₆-T7 bacteriophage and His₆-GroEL directly from cell lysates. To demonstrate the utility and simplified workflow enabled by these grids, we performed cryo-electron microscopy (cryo-EM) of His₆-GroEL obtained from clarified E. coli lysates. Single particle analysis produced a 3D map with a gold standard resolution of 8.1 Å. We infer from these findings that TEM grids modified with GO-NTA are a useful tool that reduces background and improves both the speed and simplicity of biological sample preparation for high-resolution structure elucidation by cryo-EM.

Use of evolutionary information in the fitting of atomic level protein models in low resolution cryo-EM map of a protein assembly improves the accuracy of the fitting

Protein-protein interface residues, especially those at the core of the interface, exhibit higher conservation than residues in solvent exposed regions. Here, we explore the ability of this differential conservation to evaluate fittings of atomic models in low-resolution cryo-EM maps and select models from the ensemble of solutions that are often proposed by different model fitting techniques. As a prelude, using a non-redundant and high-resolution structural dataset involving 125 permanent and 95 transient complexes, we confirm that core interface residues are conserved significantly better than nearby non-interface residues and this result is used in the cryo-EM map analysis. From the analysis of inter-component interfaces in a set of fitted models associated with low-resolution cryo-EM maps of ribosomes, chaperones and proteasomes we note that a few poorly conserved residues occur at interfaces. Interestingly a few conserved residues are not in the interface, though they are close to the interface. These observations raise the potential requirement of refitting the models in the cryo-EM maps. We show that sampling an ensemble of models and selection of models with high residue conservation at the interface and in good agreement with the density helps in improving the accuracy of the fit. This study indicates that evolutionary information can serve as an additional input to improve and validate fitting of atomic models in cryo-EM density maps.

De Novo modeling in cryo-EM density maps with Pathwalking

As electron cryo-microscopy (cryo-EM) can now frequently achieve near atomic resolution, accurate interpretation of these density maps in terms of atomistic detail has become paramount in deciphering macromolecular structure and function. However, there are few software tools for modeling protein structure from cryo-EM density maps in this resolution range. Here, we present an extension of our original Pathwalking protocol, which can automatically trace a protein backbone directly from a near-atomic resolution (3-6Å) density map. The original Pathwalking approach utilized a Traveling Salesman Problem solver for backbone tracing, but manual adjustment was still required during modeling. In the new version, human intervention is minimized and we provide a more robust approach for backbone modeling. This includes iterative secondary structure identification, termini detection and the ability to model multiple subunits without prior segmentation. Overall, the new Pathwalking procedure provides a more complete and robust tool for annotating protein structure function in near-atomic resolution density maps.

Unraveling low-resolution structural data of large biomolecules by constructing atomic models with experiment-targeted parallel cascade selection simulations

Various low-resolution experimental techniques have gained more and more popularity in obtaining structural information of large biomolecules. In order to interpret the low-resolution structural data properly, one may need to construct an atomic model of the biomolecule by fitting the data using computer simulations. Here we develop, to our knowledge, a new computational tool for such integrative modeling by taking the advantage of an efficient sampling technique called parallel cascade selection (PaCS) simulation. For given low-resolution structural data, this PaCS-Fit method converts it into a scoring function. After an initial simulation starting from a known structure of the biomolecule, the scoring function is used to pick conformations for next cycle of multiple independent simulations. By this iterative screening-after-sampling strategy, the biomolecule may be driven towards a conformation that fits well with the low-resolution data. Our method has been validated using three proteins with small-angle X-ray scattering data and two proteins with electron microscopy data. In all benchmark tests, high-quality atomic models, with generally 1-3 Å from the target structures, are obtained. Since our tool does not need to add any biasing potential in the simulations to deform the structure, any type of low-resolution data can be implemented conveniently.

Hollow Cone Electron Imaging for Single Particle 3D Reconstruction of Proteins

The main bottlenecks for high-resolution biological imaging in electron microscopy are radiation sensitivity and low contrast. The phase contrast at low spatial frequencies can be enhanced by using a large defocus but this strongly reduces the resolution. Recently, phase plates have been developed to enhance the contrast at small defocus but electrical charging remains a problem. Single particle cryo-electron microscopy is mostly used to minimize the radiation damage and to enhance the resolution of the 3D reconstructions but it requires averaging images of a massive number of individual particles. Here we present a new route to achieve the same goals by hollow cone dark field imaging using thermal diffuse scattered electrons giving about a 4 times contrast increase as compared to bright field imaging. We demonstrate the 3D reconstruction of a stained GroEL particle can yield about 13.5 Å resolution but using a strongly reduced number of images.

2.9 Å Resolution Cryo-EM 3D Reconstruction of Close-Packed Virus Particles

Single-particle cryoelectron microscopy typically discards close-packed particle images as unusable data. Here, we report an image processing strategy and case study of obtaining near-atomic resolution 3D reconstructions from close-packed particles. Multiple independent de novo initial models were constructed to determine and cross-validate the particle parameters. The particles with consistent views were further refined including not only Euler angles and center positions but also defocus, astigmatism, beam tilt, and overall and anisotropic magnification. We demonstrated this strategy with a 2.9 Å resolution reconstruction of a 1.67 MDa virus-like particle of a circovirus, PCV2, recorded on 86 photographic films. The map resolution was further validated with a phase-randomization test and local resolution assessment, and the atomic model was validated with MolProbity and EMRinger. Close-packed virus particles were thus shown not only to be useful for high-resolution 3D reconstructions but also to allow data collection at significantly improved throughput for near-atomic resolution reconstructions.

Single-particle cryo-electron microscopy of macromolecular complexes

Recent technological breakthroughs in image acquisition have enabled single-particle cryo-electron microscopy (cryo-EM) to achieve near-atomic resolution structural information for biological complexes. The improvements in image quality coupled with powerful computational methods for sorting distinct particle populations now also allow the determination of compositional and conformational ensembles, thereby providing key insights into macromolecular function. However, the inherent instability and dynamic nature of biological assemblies remain a tremendous challenge that often requires tailored approaches for successful implementation of the methodology. Here, we briefly describe the fundamentals of single-particle cryo-EM with an emphasis on covering the breadth of techniques and approaches, including low- and high-resolution methods, aiming to illustrate specific steps that are crucial for obtaining structural information by this method.

Two promising future developments of cryo-EM: capturing short-lived states and mapping a continuum of states of a macromolecule

The capabilities and application range of cryogenic electron microscopy (cryo-EM) method have expanded vastly in the last two years, thanks to the advances provided by direct detection devices and computational classification tools. We take this review as an opportunity to sketch out promising developments of cryo-EM in two important directions: (i) imaging of short-lived states (10-1000 ms) of biological molecules by using time-resolved cryo-EM, particularly the mixing-spraying method and (ii) recovering an entire continuum of coexisting states from the same sample by employing a computational technique called manifold embedding. It is tempting to think of combining these two methods, to elucidate the way the states of a molecular machine such as the ribosome branch and unfold. This idea awaits further developments of both methods, particularly by increasing the data yield of the time-resolved cryo-EM method and by developing the manifold embedding technique into a user-friendly workbench.

Single particle tomography in EMAN2

Single particle tomography (SPT or subtomogram averaging) offers a powerful alternative to traditional 2-D single particle reconstruction for studying conformationally or compositionally heterogeneous macromolecules. It can also provide direct observation (without labeling or staining) of complexes inside cells at nanometer resolution. The development of computational methods and tools for SPT remains an area of active research. Here we present the EMAN2.1 SPT toolbox, which offers a full SPT processing pipeline, from particle picking to post-alignment analysis of subtomogram averages, automating most steps. Different algorithm combinations can be applied at each step, providing versatility and allowing for procedural cross-testing and specimen-specific strategies. Alignment methods include all-vs-all, binary tree, iterative single-model refinement, multiple-model refinement, and self-symmetry alignment. An efficient angular search, Graphic Processing Unit (GPU) acceleration and both threaded and distributed parallelism are provided to speed up processing. Finally, automated simulations, per particle reconstruction of subtiltseries, and per-particle Contrast Transfer Function (CTF) correction have been implemented. Processing examples using both real and simulated data are shown for several structures.

Covariance Matrix Estimation for the Cryo-EM Heterogeneity Problem

In cryo-electron microscopy (cryo-EM), a microscope generates a top view of a sample of randomly oriented copies of a molecule. The problem of single particle reconstruction (SPR) from cryo-EM is to use the resulting set of noisy two-dimensional projection images taken at unknown directions to reconstruct the three-dimensional (3D) structure of the molecule. In some situations, the molecule under examination exhibits structural variability, which poses a fundamental challenge in SPR. The heterogeneity problem is the task of mapping the space of conformational states of a molecule. It has been previously suggested that the leading eigenvectors of the covariance matrix of the 3D molecules can be used to solve the heterogeneity problem. Estimating the covariance matrix is challenging, since only projections of the molecules are observed, but not the molecules themselves. In this paper, we formulate a general problem of covariance estimation from noisy projections of samples. This problem has intimate connections with matrix completion problems and high-dimensional principal component analysis. We propose an estimator and prove its consistency. When there are finitely many heterogeneity classes, the spectrum of the estimated covariance matrix reveals the number of classes. The estimator can be found as the solution to a certain linear system. In the cryo-EM case, the linear operator to be inverted, which we term the projection covariance transform, is an important object in covariance estimation for tomographic problems involving structural variation. Inverting it involves applying a filter akin to the ramp filter in tomography. We design a basis in which this linear operator is sparse and thus can be tractably inverted despite its large size. We demonstrate via numerical experiments on synthetic datasets the robustness of our algorithm to high levels of noise.

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.

Toward a high-resolution structure of IP₃R channel

The ability of cells to maintain low levels of Ca(2+) under resting conditions and to create rapid and transient increases in Ca(2+) upon stimulation is a fundamental property of cellular Ca(2+) signaling mechanism. An increase of cytosolic Ca(2+) level in response to diverse stimuli is largely accounted for by the inositol 1,4,5-trisphosphate receptor (IP3R) present in the endoplasmic reticulum membranes of virtually all eukaryotic cells. Extensive information is currently available on the function of IP3Rs and their interaction with modulators. Very little, however, is known about their molecular architecture and therefore most critical issues surrounding gating of IP3R channels are still ambiguous, including the central question of how opening of the IP3R pore is initiated by IP3 and Ca(2+). Membrane proteins such as IP3R channels have proven to be exceptionally difficult targets for structural analysis due to their large size, their location in the membrane environment, and their dynamic nature. To date, a 3D structure of complete IP3R channel is determined by single-particle cryo-EM at intermediate resolution, and the best crystal structures of IP3R are limited to a soluble portion of the cytoplasmic region representing ∼15% of the entire channel protein. Together these efforts provide the important structural information for this class of ion channels and serve as the basis for further studies aiming at understanding of the IP3R function.

GPU-accelerated analysis and visualization of large structures solved by molecular dynamics flexible fitting

Hybrid structure fitting methods combine data from cryo-electron microscopy and X-ray crystallography with molecular dynamics simulations for the determination of all-atom structures of large biomolecular complexes. Evaluating the quality-of-fit obtained from hybrid fitting is computationally demanding, particularly in the context of a multiplicity of structural conformations that must be evaluated. Existing tools for quality-of-fit analysis and visualization have previously targeted small structures and are too slow to be used interactively for large biomolecular complexes of particular interest today such as viruses or for long molecular dynamics trajectories as they arise in protein folding. We present new data-parallel and GPU-accelerated algorithms for rapid interactive computation of quality-of-fit metrics linking all-atom structures and molecular dynamics trajectories to experimentally-determined density maps obtained from cryo-electron microscopy or X-ray crystallography. We evaluate the performance and accuracy of the new quality-of-fit analysis algorithms vis-à-vis existing tools, examine algorithm performance on GPU-accelerated desktop workstations and supercomputers, and describe new visualization techniques for results of hybrid structure fitting methods.

Spherical deconvolution improves quality of single particle reconstruction

One single-particle reconstruction technique is the reconstruction of macromolecules from projection images of randomly oriented particles (SPRR). In SPRR the reliability and consequent interpretation of the final reconstruction is affected by errors arising from incorrect assignment of projection angles to individual particles. In order to improve the resolution of SPRR we studied the influence of imperfect assignment on 3D blurring. We find that this blurring can be described as a Point Spread Function (PSF) that depends on the distance from geometrical center of the reconstructed volume and that blurring is higher at the periphery. This particular PSF can be described by an almost pure tangential angular function with a negligible radial component. We have developed a reliable algorithm for spherical deconvolution of the 3D reconstruction. This spherical deconvolution operation was tested on reconstructions of GroEL and mitochondrial ribosomes. We show that spherical deconvolution improves the quality of SPRR by reducing blurring and enhancing high frequency components, particularly near the periphery of the reconstruction.

Atomic model of the F420-reducing [NiFe] hydrogenase by electron cryo-microscopy using a direct electron detector

The introduction of direct electron detectors with higher detective quantum efficiency and fast read-out marks the beginning of a new era in electron cryo-microscopy. Using the FEI Falcon II direct electron detector in video mode, we have reconstructed a map at 3.36 Å resolution of the 1.2 MDa F420-reducing hydrogenase (Frh) from methanogenic archaea from only 320,000 asymmetric units. Videos frames were aligned by a combination of image and particle alignment procedures to overcome the effects of beam-induced motion. The reconstructed density map shows all secondary structure as well as clear side chain densities for most residues. The full coordination of all cofactors in the electron transfer chain (a [NiFe] center, four [4Fe4S] clusters and an FAD) is clearly visible along with a well-defined substrate access channel. From the rigidity of the complex we conclude that catalysis is diffusion-limited and does not depend on protein flexibility or conformational changes. DOI: http://dx.doi.org/10.7554/eLife.01963.001.

The joys and perils of flexible fitting

While performing their functions, biological macromolecules often form large, dynamically changing macromolecular assemblies. Only a relatively small number of such assemblies have been accessible to the atomic-resolution techniques X-ray crystallography and NMR. Electron microscopy in conjunction with image reconstruction has become the preferred alternative for revealing the structures of such macromolecular complexes. However, for most assemblies the achievable resolution is too low to allow accurate atomic modeling directly from the data. Yet, useful models often can be obtained by fitting atomic models of individual components into a low-resolution reconstruction of the entire assembly. Several algorithms for achieving optimal fits in this context were developed recently, many allowing considerable degrees of flexibility to account for binding-induced conformational changes of the assembly components. This chapter describes the advantages and potential pitfalls of these methods and puts them into perspective with alternative approaches such as iterative modular fitting of rigid-body domains.

Cryo-EM techniques to resolve the structure of HSV-1 capsid-associated components

Electron cryo-microscopy has become a routine technique to determine the structure of biochemically purified herpes simplex virus capsid particles. This chapter describes the procedures of specimen preparation by cryopreservation; low dose and low temperature imaging in an electron cryo-microscope; and data processing for reconstruction. This methodology has yielded subnanometer resolution structures of the icosahedral capsid shell where α-helices and β-sheets of individual subunits can be recognized. A relaxation of the symmetry in the reconstruction steps allows us to resolve the DNA packaging protein located at one of the 12 vertices in the capsid.

Molecular mechanism of TRP channels

Transient receptor potential (TRP) channels are cellular sensors for a wide spectrum of physical and chemical stimuli. They are involved in the formation of sight, hearing, touch, smell, taste, temperature, and pain sensation. TRP channels also play fundamental roles in cell signaling and allow the host cell to respond to benign or harmful environmental changes. As TRP channel activation is controlled by very diverse processes and, in many cases, exhibits complex polymodal properties, understanding how each TRP channel responds to its unique forms of activation energy is both crucial and challenging. The past two decades witnessed significant advances in understanding the molecular mechanisms that underlie TRP channels activation. This review focuses on our current understanding of the molecular determinants for TRP channel activation.

Bayesian analysis of individual electron microscopy images: towards structures of dynamic and heterogeneous biomolecular assemblies

We develop a method to extract structural information from electron microscopy (EM) images of dynamic and heterogeneous molecular assemblies. To overcome the challenge of disorder in the imaged structures, we analyze each image individually, avoiding information loss through clustering or averaging. The Bayesian inference of EM (BioEM) method uses a likelihood-based probabilistic measure to quantify the consistency between each EM image and given structural models. The likelihood function accounts for uncertainties in the molecular position and orientation, variations in the relative intensities and noise in the experimental images. The BioEM formalism is physically intuitive and mathematically simple. We show that for experimental GroEL images, BioEM correctly identifies structures according to the functional state. The top-ranked structure is the corresponding X-ray crystal structure, followed by an EM structure generated previously from a superset of the EM images used here. To analyze EM images of highly flexible molecules, we propose an ensemble refinement procedure, and validate it with synthetic EM maps of the ESCRT-I-II supercomplex. Both the size of the ensemble and its structural members are identified correctly. BioEM offers an alternative to 3D-reconstruction methods, extracting accurate population distributions for highly flexible structures and their assemblies. We discuss limitations of the method, and possible applications beyond ensemble refinement, including the cross-validation and unbiased post-assessment of model structures, and the structural characterization of systems where traditional approaches fail. Overall, our results suggest that the BioEM framework can be used to analyze EM images of both ordered and disordered molecular systems.

Cryo-EM structure of a molluscan hemocyanin suggests its allosteric mechanism

Hemocyanins are responsible for transporting O2 in the arthropod and molluscan hemolymph. Haliotis diversicolor molluscan hemocyanin isoform 1 (HdH1) is an 8 MDa oligomer. Each subunit is made up of eight functional units (FUs). Each FU contains two Cu ions, which can reversibly bind an oxygen molecule. Here, we report a 4.5 A° cryo-EM structure of HdH1. The structure clearly shows ten asymmetric units arranged with D5 symmetry. Each asymmetric unit contains two structurally distinct but chemically identical subunits. The map is sufficiently resolved to trace the entire subunit Ca backbone and to visualize densities corresponding to some large side chains, Cu ion pairs, and interaction networks of adjacent subunits. A FU topology path intertwining between the two subunits of the asymmetric unit is unambiguously determined. Our observations suggest a structural mechanism for the stability of the entire hemocyanin didecamer and 20 ‘‘communication clusters’’ across asymmetric units responsible for its allosteric property upon oxygen binding.

Electron microscopy analysis of a disaccharide analog complex reveals receptor interactions of adeno-associated virus

Mechanistic studies of macromolecular complexes often feature X-ray structures of complexes with bound ligands. The attachment of adeno-associated virus (AAV) to cell surface glycosaminoglycans (GAGs) is an example that has not proven amenable to crystallography, because the binding of GAG analogs disrupts lattice contacts. The interactions of AAV with GAGs are of interest in mediating the cell specificity of AAV-based gene therapy vectors. Previous electron microscopy led to differing conclusions on the exact binding site and the existence of large ligand-induced conformational changes in the virus. Conformational changes are expected during cell entry, but it has remained unclear whether the electron microscopy provided evidence of their induction by GAG-binding. Taking advantage of automated data collection, careful processing and new methods of structure refinement, the structure of AAV-DJ complexed with sucrose octasulfate is determined by electron microscopy difference map analysis to 4.8Å resolution. At this higher resolution, individual sulfate groups are discernible, providing a stereochemical validation of map interpretation, and highlighting interactions with two surface arginines that have been implicated in genetic studies. Conformational changes induced by the SOS are modest and limited to the loop most directly interacting with the ligand. While the resolution attainable will depend on sample order and other factors, there are an increasing number of macromolecular complexes that can be studied by cryo-electron microscopy at resolutions beyond 5Å, for which the approaches used here could be used to characterize the binding of inhibitors and other small molecule effectors when crystallography is not tractable.

Validated near-atomic resolution structure of bacteriophage epsilon15 derived from cryo-EM and modeling

High-resolution structures of viruses have made important contributions to modern structural biology. Bacteriophages, the most diverse and abundant organisms on earth, replicate and infect all bacteria and archaea, making them excellent potential alternatives to antibiotics and therapies for multidrug-resistant bacteria. Here, we improved upon our previous electron cryomicroscopy structure of Salmonella bacteriophage epsilon15, achieving a resolution sufficient to determine the tertiary structures of both gp7 and gp10 protein subunits that form the T = 7 icosahedral lattice. This study utilizes recently established best practice for near-atomic to high-resolution (3-5 Å) electron cryomicroscopy data evaluation. The resolution and reliability of the density map were cross-validated by multiple reconstructions from truly independent data sets, whereas the models of the individual protein subunits were validated adopting the best practices from X-ray crystallography. Some sidechain densities are clearly resolved and show the subunit-subunit interactions within and across the capsomeres that are required to stabilize the virus. The presence of the canonical phage and jellyroll viral protein folds, gp7 and gp10, respectively, in the same virus suggests that epsilon15 may have emerged more recently relative to other bacteriophages.

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.

Novel convergence-oriented approach for evaluation and optimization of workflow in single-particle two-dimensional averaging of electron microscope images

Three-dimensional (3D) protein structures facilitate the understanding of their biological functions and provide valuable information for developing medicines. Single-particle analysis (SPA) from electron microscopy (EM) is a structure determination method suitable for macromolecules. To achieve a high resolution using combinations of several SPA software packages, 'workflow' optimization and comparative evaluation by scoring results are essential. Two-dimensional (2D) averaging is a key step for 3D reconstruction. The integrated convergence-evaluation oriented system (IC-EOS) proposed here provides an effective tool for customizing 2D averaging. This assesses the behavior and characteristics of workflows and evaluates the convergence of iteration steps without human intervention. We chose five base measurements for quantifying convergence: resolution, variance, similarity, shift-distance and rotation-angle. Curve fitting to history graphs scored their stability. We call this score 'fluctuation'. The number of particle images discarded from the library and the number of classification groups were examined to see their effects on optimization levels and fluctuation of measurements, allowing the IC-EOS to select the most appropriate workflow for the target. A case study using a bacterial sodium channel and a simulation study using GroEL showed that resolution of 2D averaging improved with relatively stricter particle selection. With fewer groups, resolutions of class averages improved, but similarities between class-averages and their constituent particle images degraded. Fluctuation was useful for selecting adequate conditions, even when achieved values alone were not conclusive. The vote method, using fluctuation, was robust against noise and enabled a decision without exhaustive search trials. Thus, the IC-EOS is a step toward full automation of SPA.

De novo modeling of the F(420)-reducing [NiFe]-hydrogenase from a methanogenic archaeon by cryo-electron microscopy

Methanogenic archaea use a [NiFe]-hydrogenase, Frh, for oxidation/reduction of F420, an important hydride carrier in the methanogenesis pathway from H2 and CO2. Frh accounts for about 1% of the cytoplasmic protein and forms a huge complex consisting of FrhABG heterotrimers with each a [NiFe] center, four Fe-S clusters and an FAD. Here, we report the structure determined by near-atomic resolution cryo-EM of Frh with and without bound substrate F420. The polypeptide chains of FrhB, for which there was no homolog, was traced de novo from the EM map. The 1.2-MDa complex contains 12 copies of the heterotrimer, which unexpectedly form a spherical protein shell with a hollow core. The cryo-EM map reveals strong electron density of the chains of metal clusters running parallel to the protein shell, and the F420-binding site is located at the end of the chain near the outside of the spherical structure. DOI:http://dx.doi.org/10.7554/eLife.00218.001.

Assembly of anthrax toxin pore: lethal-factor complexes into lipid nanodiscs

We have devised a procedure to incorporate the anthrax protective antigen (PA) pore complexed with the N-terminal domain of anthrax lethal factor (LFN ) into lipid nanodiscs and analyzed the resulting complexes by negative-stain electron microscopy. Insertion into nanodiscs was performed without relying on primary and secondary detergent screens. The preparations were relatively pure, and the percentage of PA pore inserted into nanodiscs on EM grids was high (∼43%). Three-dimensional analysis of negatively stained single particles revealed the LFN -PA nanodisc complex mirroring the previous unliganded PA pore nanodisc structure, but with additional protein density consistent with multiple bound LFN molecules on the PA cap region. The assembly procedure will facilitate collection of higher resolution cryo-EM LFN -PA nanodisc structures and use of advanced automated particle selection methods.

FOLD-EM: automated fold recognition in medium- and low-resolution (4-15 Å) electron density maps

MOTIVATION

Owing to the size and complexity of large multi-component biological assemblies, the most tractable approach to determining their atomic structure is often to fit high-resolution radiographic or nuclear magnetic resonance structures of isolated components into lower resolution electron density maps of the larger assembly obtained using cryo-electron microscopy (cryo-EM). This hybrid approach to structure determination requires that an atomic resolution structure of each component, or a suitable homolog, is available. If neither is available, then the amount of structural information regarding that component is limited by the resolution of the cryo-EM map. However, even if a suitable homolog cannot be identified using sequence analysis, a search for structural homologs should still be performed because structural homology often persists throughout evolution even when sequence homology is undetectable, As macromolecules can often be described as a collection of independently folded domains, one way of searching for structural homologs would be to systematically fit representative domain structures from a protein domain database into the medium/low resolution cryo-EM map and return the best fits. Taken together, the best fitting non-overlapping structures would constitute a 'mosaic' backbone model of the assembly that could aid map interpretation and illuminate biological function.

RESULT

Using the computational principles of the Scale-Invariant Feature Transform (SIFT), we have developed FOLD-EM-a computational tool that can identify folded macromolecular domains in medium to low resolution (4-15 Å) electron density maps and return a model of the constituent polypeptides in a fully automated fashion. As a by-product, FOLD-EM can also do flexible multi-domain fitting that may provide insight into conformational changes that occur in macromolecular assemblies.

Nhs: network-based hierarchical segmentation for cryo-electron microscopy density maps

Cryo-electron microscopy (cryo-EM) experiments yield low-resolution (3-30 Å) 3D-density maps of macromolecules. These density maps are segmented to identify structurally distinct proteins, protein domains, and subunits. Such partitioning aids the inference of protein motions and guides fitting of high-resolution atomistic structures. Cryo-EM density map segmentation has traditionally required tedious and subjective manual partitioning or semisupervised computational methods, whereas validation of resulting segmentations has remained an open problem in this field. We introduce a network-based hierarchical segmentation (Nhs) method, that provides a multi-scale partitioning, reflecting local and global clustering, while requiring no user input. This approach models each map as a graph, where map voxels constitute nodes and weighted edges connect neighboring voxels. Nhs initiates Markov diffusion (or random walk) on the weighted graph. As Markov probabilities homogenize through diffusion, an intrinsic segmentation emerges. We validate the segmentations with ground-truth maps based on atomistic models. When implemented on density maps in the 2010 Cryo-EM Modeling Challenge, Nhs efficiently and objectively partitions macromolecules into structurally and functionally relevant subregions at multiple scales.

Gorgon and pathwalking: macromolecular modeling tools for subnanometer resolution density maps

The complex interplay of proteins and other molecules, often in the form of large transitory assemblies, are critical to cellular function. Today, X-ray crystallography and electron cryo-microscopy (cryo-EM) are routinely used to image these macromolecular complexes, though often at limited resolutions. Despite the rapidly growing number of macromolecular structures, few tools exist for modeling and annotating structures in the range of 3-10 Å resolution. To address this need, we have developed a number of utilities specifically targeting subnanometer resolution density maps. As part of the 2010 Cryo-EM Modeling Challenge, we demonstrated two of our latest de novo modeling tools, Pathwalking and Gorgon, as well as a tool for secondary structure identification (SSEHunter) and a new rigid-body/flexible fitting tool in Gorgon. In total, we submitted 30 structural models from ten different subnanometer resolution data sets in four of the six challenge categories. Each of our utlities produced accurate structural models and annotations across the various density maps. In the end, the utilities that we present here offer users a robust toolkit for analyzing and modeling protein structure in macromolecular assemblies at non-atomic resolutions.