Modeling experimental image formation for likelihood-based classification of electron microscopy data

Cryo-EM images of phase-separated lipid bilayer vesicles analyzed with a machine-learning approach

Lateral lipid heterogeneity (i.e., raft formation) in biomembranes plays a functional role in living cells. Three-component mixtures of low- and high-melting lipids plus cholesterol offer a simplified experimental model for raft domains in which a liquid-disordered (Ld) phase coexists with a liquid-ordered (Lo) phase. Using such models, we recently showed that cryogenic electron microscopy (cryo-EM) can detect phase separation in lipid vesicles based on differences in bilayer thickness. However, the considerable noise within cryo-EM data poses a significant challenge for accurately determining the membrane phase state at high spatial resolution. To this end, we have developed an image-processing pipeline that utilizes machine learning (ML) to predict the bilayer phase in projection images of lipid vesicles. Importantly, the ML method exploits differences in both the thickness and molecular density of Lo compared to Ld, which leads to improved phase identification. To assess accuracy, we used artificial images of phase-separated lipid vesicles generated from all-atom molecular dynamics simulations of Lo and Ld phases. Synthetic ground-truth data sets mimicking a series of compositions along a tieline of Ld + Lo coexistence were created and then analyzed with various ML models. For all tieline compositions, we find that the ML approach can correctly identify the bilayer phase with >90% accuracy, thus providing a means to isolate the intensity profiles of coexisting Ld and Lo phases, as well as accurately determine domain-size distributions, number of domains, and phase-area fractions. The method described here provides a framework for characterizing nanoscopic lateral heterogeneities in membranes and paves the way for a more detailed understanding of raft properties in biological contexts.

ZART: A novel multiresolution reconstruction algorithm with motion-blur correction for single particle analysis

One of the main purposes of CryoEM Single Particle Analysis is to reconstruct the three-dimensional structure of a macromolecule thanks to the acquisition of many particle images representing different poses of the sample. By estimating the orientation of each projected particle, it is possible to recover the underlying 3D volume by multiple 3D reconstruction methods, usually working either in Fourier or in real space. However, the reconstruction from the projected images works under the assumption that all particles in the dataset correspond to the same conformation of the macromolecule. Although this requisite holds for some macromolecules, it is not true for flexible specimens, leading to motion-induced artefacts in the reconstructed CryoEM maps. In this work, we introduce a new Algebraic Reconstruction Technique called ZART, which is able to include continuous flexibility information during the reconstruction process to improve local resolution and reduce motion blurring. The conformational changes are modelled through Zernike3D polynomials. Our implementation allows for a multiresolution description of the macromolecule adapting itself to the local resolution of the reconstructed map. In addition, ZART has also proven to be a useful algorithm in cases where flexibility is not so dominant, as it improves the overall aspect of the reconstructed maps by improving their local and global resolution.

MEPSi: A tool for simulating tomograms of membrane-embedded proteins

The throughput and fidelity of cryogenic cellular electron tomography (cryo-ET) is constantly increasing through advances in cryogenic electron microscope hardware, direct electron detection devices, and powerful image processing algorithms. However, the need for careful optimization of sample preparations and for access to expensive, high-end equipment, make cryo-ET a costly and time-consuming technique. Generally, only after the last step of the cryo-ET workflow, when reconstructed tomograms are available, it becomes clear whether the chosen imaging parameters were suitable for a specific type of sample in order to answer a specific biological question. Tools for a-priory assessment of the feasibility of samples to answer biological questions and how to optimize imaging parameters to do so would be a major advantage. Here we describe MEPSi (Membrane Embedded Protein Simulator), a simulation tool aimed at rapid and convenient evaluation and optimization of cryo-ET data acquisition parameters for studies of transmembrane proteins in their native environment. We demonstrate the utility of MEPSi by showing how to detangle the influence of different data collection parameters and different orientations in respect to tilt axis and electron beam for two examples: (1) simulated plasma membranes with embedded single-pass transmembrane αIIbβ3 integrin receptors and (2) simulated virus membranes with embedded SARS-CoV-2 spike proteins.

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

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

Machine Learning for Structure Determination in Single-Particle Cryo-Electron Microscopy: A Systematic Review

Recently, single-particle cryo-electron microscopy (cryo-EM) has become an indispensable method for determining macromolecular structures at high resolution to deeply explore the relevant molecular mechanism. Its recent breakthrough is mainly because of the rapid advances in hardware and image processing algorithms, especially machine learning. As an essential support of single-particle cryo-EM, machine learning has powered many aspects of structure determination and greatly promoted its development. In this article, we provide a systematic review of the applications of machine learning in this field. Our review begins with a brief introduction of single-particle cryo-EM, followed by the specific tasks and challenges of its image processing. Then, focusing on the workflow of structure determination, we describe relevant machine learning algorithms and applications at different steps, including particle picking, 2-D clustering, 3-D reconstruction, and other steps. As different tasks exhibit distinct characteristics, we introduce the evaluation metrics for each task and summarize their dynamics of technology development. Finally, we discuss the open issues and potential trends in this promising field.

Cryo-TEM simulations of amorphous radiation-sensitive samples using multislice wave propagation

Image simulation plays a central role in the development and practice of high-resolution electron microscopy, including transmission electron microscopy of frozen-hydrated specimens (cryo-EM). Simulating images with contrast that matches the contrast observed in experimental images remains challenging, especially for amorphous samples. Current state-of-the-art simulators apply post hoc scaling to approximate empirical solvent contrast, attenuated image intensity due to specimen thickness and amplitude contrast. This practice fails for images that require spatially variable scaling, e.g. simulations of a crowded or cellular environment. Modeling both the signal and the noise accurately is necessary to simulate images of biological specimens with contrast that is correct on an absolute scale. The 'frozen plasmon' method is introduced to explicitly model spatially variable inelastic scattering processes in cryo-EM specimens. This approach produces amplitude contrast that depends on the atomic composition of the specimen, reproduces the total inelastic mean free path as observed experimentally and allows for the incorporation of radiation damage in the simulation. These improvements are quantified using the matched filter concept to compare simulation and experiment. The frozen plasmon method, in combination with a new mathematical formulation for accurately sampling the tabulated atomic scattering potentials onto a Cartesian grid, is implemented in the open-source software package cisTEM.

Clustering polymorphs of tau and IAPP fibrils with the CHEP algorithm

Recent steps towards automation have improved the quality and efficiency of the entire cryo-electron microscopy workflow, from sample preparation to image processing. Most of the image processing steps are now quite automated, but there are still a few steps which need the specific intervention of researchers. One such step is the identification and separation of helical protein polymorphs at early stages of image processing. Here, we tested and evaluated our recent clustering approach on three datasets containing amyloid fibrils, demonstrating that the proposed unsupervised clustering method automatically and effectively identifies the polymorphs from cryo-EM images. As an automated polymorph separation method, it has the potential to complement automated helical picking, which typically cannot easily distinguish between polymorphs with subtle differences in morphology, and is therefore a useful tool for the image processing and structure determination of helical proteins.

Likelihood-based structural analysis of electron microscopy images

Likelihood-based analysis of single-particle electron microscopy images has contributed much to the recent improvements in resolution. By treating particle orientations and classes probabilistically, uncertainties in the reconstruction process are explicitly accounted for, and the risk of bias towards the initial model is diminished. As a result, the quality and reliability of the reconstructions have greatly improved at manageable computational cost. Likelihood-based analysis of electron microscopy images also offers a route to direct coordinate refinement for dynamic systems, as an alternative to 3D density reconstruction. Here, we review recent developments in the algorithms used for reconstructions of high-resolution maps, and in the integrative framework of combining likelihood methods with simulations to address conformational variability in cryo-electron microscopy.

The impact of recent improvements in cryo-electron microscopy technology on the understanding of bacterial ribosome assembly

Cryo-electron microscopy (cryo-EM) had played a central role in the study of ribosome structure and the process of translation in bacteria since the development of this technique in the mid 1980s. Until recently cryo-EM structures were limited to ∼10 Å in the best cases. However, the recent advent of direct electron detectors has greatly improved the resolution of cryo-EM structures to the point where atomic resolution is now achievable. This improved resolution will allow cryo-EM to make groundbreaking contributions in essential aspects of ribosome biology, including the assembly process. In this review, we summarize important insights that cryo-EM, in combination with chemical and genetic approaches, has already brought to our current understanding of the ribosomal assembly process in bacteria using previous detector technology. More importantly, we discuss how the higher resolution structures now attainable with direct electron detectors can be leveraged to propose precise testable models regarding this process. These structures will provide an effective platform to develop new antibiotics that target this fundamental cellular process.

Structural Study of Heterogeneous Biological Samples by Cryoelectron Microscopy and Image Processing

In living organisms, biological macromolecules are intrinsically flexible and naturally exist in multiple conformations. Modern electron microscopy, especially at liquid nitrogen temperatures (cryo-EM), is able to visualise biocomplexes in nearly native conditions and in multiple conformational states. The advances made during the last decade in electronic technology and software development have led to the revelation of structural variations in complexes and also improved the resolution of EM structures. Nowadays, structural studies based on single particle analysis (SPA) suggests several approaches for the separation of different conformational states and therefore disclosure of the mechanisms for functioning of complexes. The task of resolving different states requires the examination of large datasets, sophisticated programs, and significant computing power. Some methods are based on analysis of two-dimensional images, while others are based on three-dimensional studies. In this review, we describe the basic principles implemented in the various techniques that are currently used in the analysis of structural conformations and provide some examples of successful applications of these methods in structural studies of biologically significant complexes.

Computational methods for analyzing conformational variability of macromolecular complexes from cryo-electron microscopy images

Thanks to latest technical advances in cryo-electron microscopy (cryo-EM), structures of macromolecular complexes (viruses, ribosomes, etc.) are now often obtained at near-atomic resolution. Also, studies of conformational changes of complexes, in connection with their function, are gaining ground. Conformational variability analysis is usually done by classifying images in a number of discrete classes supposedly representing all conformational states present in the specimen. However, discrete classes cannot be meaningfully defined when the conformational change is continuous (the specimen contains a continuum of states instead of a few discrete states). For such cases, first image analysis methods that explicitly consider continuous conformational changes were recently developed. The latest developments in cryo-EM image analysis methods for conformational variability analysis are the focus of this review.

Cryo-electron Microscopy Analysis of Structurally Heterogeneous Macromolecular Complexes

Cryo-electron microscopy (cryo-EM) has for a long time been a technique of choice for determining structure of large and flexible macromolecular complexes that were difficult to study by other experimental techniques such as X-ray crystallography or nuclear magnetic resonance. However, a fast development of instruments and software for cryo-EM in the last decade has allowed that a large range of complexes can be studied by cryo-EM, and that their structures can be obtained at near-atomic resolution, including the structures of small complexes (e.g., membrane proteins) whose size was earlier an obstacle to cryo-EM. Image analysis to identify multiple coexisting structures in the same specimen (multiconformation reconstruction) is now routinely done both to solve structures at near-atomic resolution and to study conformational dynamics. Methods for multiconformation reconstruction and latest examples of their applications are the focus of this review.

Single particle electron cryomicroscopy: trends, issues and future perspective

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

Processing of Structurally Heterogeneous Cryo-EM Data in RELION

This chapter describes algorithmic advances in the RELION software, and how these are used in high-resolution cryo-electron microscopy (cryo-EM) structure determination. Since the presence of projections of different three-dimensional structures in the dataset probably represents the biggest challenge in cryo-EM data processing, special emphasis is placed on how to deal with structurally heterogeneous datasets. As such, this chapter aims to be of practical help to those who wish to use RELION in their cryo-EM structure determination efforts.

Cryo-EM: A Unique Tool for the Visualization of Macromolecular Complexity

3D cryo-electron microscopy (cryo-EM) is an expanding structural biology technique that has recently undergone a quantum leap progression in its achievable resolution and its applicability to the study of challenging biological systems. Because crystallization is not required, only small amounts of sample are needed, and because images can be classified in a computer, the technique has the potential to deal with compositional and conformational mixtures. Therefore, cryo-EM can be used to investigate complete and fully functional macromolecular complexes in different functional states, providing a richness of biological insight. In this review, we underlie some of the principles behind the cryo-EM methodology of single particle analysis and discuss some recent results of its application to challenging systems of paramount biological importance. We place special emphasis on new methodological developments that are leading to an explosion of new studies, many of which are reaching resolutions that could only be dreamed of just a couple of years ago.

A network of SMG-8, SMG-9 and SMG-1 C-terminal insertion domain regulates UPF1 substrate recruitment and phosphorylation

Mammalian nonsense-mediated mRNA decay (NMD) is a eukaryotic surveillance mechanism that degrades mRNAs containing premature translation termination codons. Phosphorylation of the essential NMD effector UPF1 by the phosphoinositide-3-kinase-like kinase (PIKK) SMG-1 is a key step in NMD and occurs when SMG-1, its two regulatory factors SMG-8 and SMG-9, and UPF1 form a complex at a terminating ribosome. Electron cryo-microscopy of the SMG-1–8–9-UPF1 complex shows the head and arm architecture characteristic of PIKKs and reveals different states of UPF1 docking. UPF1 is recruited to the SMG-1 kinase domain and C-terminal insertion domain, inducing an opening of the head domain that provides access to the active site. SMG-8 and SMG-9 interact with the SMG-1 C-insertion and promote high-affinity UPF1 binding to SMG-1–8–9, as well as decelerated SMG-1 kinase activity and enhanced stringency of phosphorylation site selection. The presence of UPF2 destabilizes the SMG-1–8–9-UPF1 complex leading to substrate release. Our results suggest an intricate molecular network of SMG-8, SMG-9 and the SMG-1 C-insertion domain that governs UPF1 substrate recruitment and phosphorylation by SMG-1 kinase, an event that is central to trigger mRNA decay.

Yeast rvb1 and rvb2 proteins oligomerize as a conformationally variable dodecamer with low frequency

Rvb1 and Rvb2 are conserved AAA+ (ATPases associated with diverse cellular activities) proteins found at the core of large multicomponent complexes that play key roles in chromatin remodeling, integrity of the telomeres, ribonucleoprotein complex biogenesis and other essential cellular processes. These proteins contain an AAA+ domain for ATP binding and hydrolysis and an insertion domain proposed to bind DNA/RNA. Yeast Rvb1 and Rvb2 proteins oligomerize primarily as heterohexameric rings. The six AAA+ core domains form the body of the ring and the insertion domains protrude from one face of the ring. Conversely, human Rvbs form a mixture of hexamers and dodecamers made of two stacked hexamers interacting through the insertion domains. Human dodecamers adopt either a contracted or a stretched conformation. Here, we found that yeast Rvb1/Rvb2 complexes when assembled in vivo mainly form hexamers but they also assemble as dodecamers with a frequency lower than 10%. Yeast dodecamers adopt not only the stretched and contracted structures that have been described for human Rvb1/Rvb2 dodecamers but also intermediate conformations in between these two extreme states. The orientation of the insertion domains of Rvb1 and Rvb2 proteins in these conformers changes as the dodecamer transitions from the stretched structure to a more contracted structure. Finally, we observed that for the yeast proteins, oligomerization as a dodecamer inhibits the ATPase activity of the Rvb1/Rvb2 complex. These results indicate that although human and yeast Rvb1 and Rvb2 proteins share high degree of homology, there are significant differences in their oligomeric behavior and dynamics.

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.

Subunit positioning and stator filament stiffness in regulation and power transmission in the V1 motor of the Manduca sexta V-ATPase

The vacuolar H⁺-ATPase (V-ATPase) is an ATP-driven proton pump essential to the function of eukaryotic cells. Its cytoplasmic V₁ domain is an ATPase, normally coupled to membrane-bound proton pump V_o via a rotary mechanism. How these asymmetric motors are coupled remains poorly understood. Low energy status can trigger release of V₁ from the membrane and curtail ATP hydrolysis. To investigate the molecular basis for these processes, we have carried out cryo-electron microscopy three-dimensional reconstruction of deactivated V₁ from Manduca sexta. In the resulting model, three peripheral stalks that are parts of the mechanical stator of the V-ATPase are clearly resolved as unsupported filaments in the same conformations as in the holoenzyme. They are likely therefore to have inherent stiffness consistent with a role as flexible rods in buffering elastic power transmission between the domains of the V-ATPase. Inactivated V₁ adopted a homogeneous resting state with one open active site adjacent to the stator filament normally linked to the H subunit. Although present at 1:1 stoichiometry with V₁, both recombinant subunit C reconstituted with V₁ and its endogenous subunit H were poorly resolved in three-dimensional reconstructions, suggesting structural heterogeneity in the region at the base of V₁ that could indicate positional variability. If the position of H can vary, existing mechanistic models of deactivation in which it binds to and locks the axle of the V-ATPase rotary motor would need to be re-evaluated.

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Dissociation of vacuolar H⁺-ATPase domains deactivates its V₁ motor.

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V₁ has one “open” catalytic site linked to the stator filament bound by subunit H.

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Movement of subunit H to prevent rotary catalysis is possible.

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Three stator filaments project from deactivated V₁, indicating inherent stiffness.

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This work gives new insight into energetic coupling and control in V-ATPases.

Mechanism of tetracycline resistance by ribosomal protection protein Tet(O)

Tetracycline resistance protein Tet(O), which protects the bacterial ribosome from binding the antibiotic tetracycline, is a translational GTPase with significant similarity in both sequence and structure to the elongation factor EF-G. Here, we present an atomic model of the Tet(O)-bound 70S ribosome based on our cryo-electron microscopic reconstruction at 9.6 Å resolution. This atomic model allowed us to identify the Tet(O)-ribosome binding sites, which involve three characteristic loops in domain 4 of Tet(O). Replacements of the three-amino acid tips of these loops by a single glycine residue result in loss of Tet(O)-mediated tetracycline resistance. On the basis of these findings, the mechanism of Tet(O)-mediated tetracycline resistance can be explained in molecular detail.

Two RNA-binding motifs in eIF3 direct HCV IRES-dependent translation

The initiation of protein synthesis plays an essential regulatory role in human biology. At the center of the initiation pathway, the 13-subunit eukaryotic translation initiation factor 3 (eIF3) controls access of other initiation factors and mRNA to the ribosome by unknown mechanisms. Using electron microscopy (EM), bioinformatics and biochemical experiments, we identify two highly conserved RNA-binding motifs in eIF3 that direct translation initiation from the hepatitis C virus internal ribosome entry site (HCV IRES) RNA. Mutations in the RNA-binding motif of subunit eIF3a weaken eIF3 binding to the HCV IRES and the 40S ribosomal subunit, thereby suppressing eIF2-dependent recognition of the start codon. Mutations in the eIF3c RNA-binding motif also reduce 40S ribosomal subunit binding to eIF3, and inhibit eIF5B-dependent steps downstream of start codon recognition. These results provide the first connection between the structure of the central translation initiation factor eIF3 and recognition of the HCV genomic RNA start codon, molecular interactions that likely extend to the human transcriptome.

Structure of active dimeric human telomerase

Telomerase contains a large RNA subunit TER and a protein catalytic subunit TERT. Whether telomerase functions as monomer or dimer has been a matter of debate. Here we report biochemical and labeling data that show that in vivo assembled human telomerase contains two TERT subunits and binds two telomeric DNA substrates. Importantly, catalytic activity requires both TERT active sites to be functional, demonstrating that human telomerase functions as a dimer. We also present the three-dimensional structure of active, full-length human telomerase dimer, determined by single-particle electron microscopy in negative stain. Telomerase has a bilobal architecture, with the two monomers linked by a flexible interface. The monomer reconstruction at 23Å resolution, and fitting of the atomic structure of the beetle TERT subunit reveals the spatial relationship between RNA and protein subunits, providing insights into the telomerase architecture.

Synthetic lipid membrane channels formed by designed DNA nanostructures

We created nanometer-scale transmembrane channels in lipid bilayers by means of self-assembled DNA-based nanostructures. Scaffolded DNA origami was used to create a stem that penetrated and spanned a lipid membrane, as well as a barrel-shaped cap that adhered to the membrane, in part via 26 cholesterol moieties. In single-channel electrophysiological measurements, we found similarities to the response of natural ion channels, such as conductances on the order of 1 nanosiemens and channel gating. More pronounced gating was seen for mutations in which a single DNA strand of the stem protruded into the channel. Single-molecule translocation experiments show that the synthetic channels can be used to discriminate single DNA molecules.

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

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

A helical processing pipeline for EM structure determination of membrane proteins

Electron crystallography plays a key role in the structural biology of integral membrane proteins (IMPs) by offering one of the most direct means of providing insight into the functional state of these molecular machines in their lipid-associated forms, and also has the potential to facilitate examination of physiologically relevant transitional states and complexes. Helical or tubular crystals, which are the natural product of proteins crystallizing on the surface of a cylindrical vesicle, offer some unique advantages, such as three-dimensional (3D) information from a single view, compared to other crystalline forms. While a number of software packages are available for processing images of helical crystals to produce 3D electron density maps, widespread exploitation of helical image reconstruction is limited by a lack of standardized approaches and the initial effort and specialized expertise required. Our goal is to develop an integrated pipeline to enable structure determination by transmission electron microscopy (TEM) of IMPs in the form of tubular crystals. We describe here the integration of standard Fourier-Bessel helical analysis techniques into Appion, an integrated, database-driven pipeline.

A Bayesian view on cryo-EM structure determination

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

Gating of a G protein-sensitive mammalian Kir3.1 prokaryotic Kir channel chimera in planar lipid bilayers

Kir3 channels control heart rate and neuronal excitability through GTP-binding (G) protein and phosphoinositide signaling pathways. These channels were the first characterized effectors of the βγ subunits of G proteins. Because we currently lack structures of complexes between G proteins and Kir3 channels, their interactions leading to modulation of channel function are not well understood. The recent crystal structure of a chimera between the cytosolic domain of a mammalian Kir3.1 and the transmembrane region of a prokaryotic KirBac1.3 (Kir3.1 chimera) has provided invaluable structural insight. However, it was not known whether this chimera could form functional K(+) channels. Here, we achieved the functional reconstitution of purified Kir3.1 chimera in planar lipid bilayers. The chimera behaved like a bona fide Kir channel displaying an absolute requirement for PIP(2) and Mg(2+)-dependent inward rectification. The channel could also be blocked by external tertiapin Q. The three-dimensional reconstruction of the chimera by single particle electron microscopy revealed a structure consistent with the crystal structure. Channel activity could be stimulated by ethanol and activated G proteins. Remarkably, the presence of both activated Gα and Gβγ subunits was required for gating of the channel. These results confirm the Kir3.1 chimera as a valid structural and functional model of Kir3 channels.

Subtomogram alignment by adaptive Fourier coefficient thresholding

In the past few years, three-dimensional (3D) subtomogram alignment has become an important tool in cryo-electron tomography (CET). This technique allows one to produce higher resolution images of structures which can not be reconstructed using single-particle methods. Building on previous work, we present a new dissimilarity measure between subtomograms that works well for the noisy images that often occur in CET images. A technique that is more robust to noise provides the ability to analyze macromolecules in thicker samples such as whole cells or lower the defocus in thinner samples to push the first zero of the Contrast Transfer Function (CTF). Our method, Threshold Constrained Cross-Correlation (TCCC), uses statistics of the noise to automatically select only a small percentage of the Fourier coefficients to compute the cross-correlation, which has two main advantages: first, it reduces the influence of the noise by looking at only those peaks dominated by signal; and second, it avoids the missing wedge normalization problem since we consider the same number of coefficients for all possible pairs of subtomograms. We present results with synthetic and real data to compare our approach with other existing methods under different SNR and missing wedge conditions, and show that TCCC improves alignment results for datasets with SNR<0.1. We have made our source code freely available for the community.

An adaptive Expectation-Maximization algorithm with GPU implementation for electron cryomicroscopy

Maximum-likelihood (ML) estimation has very desirable properties for reconstructing 3D volumes from noisy cryo-EM images of single macromolecular particles. Current implementations of ML estimation make use of the Expectation-Maximization (EM) algorithm or its variants. However, the EM algorithm is notoriously computation-intensive, as it involves integrals over all orientations and positions for each particle image. We present a strategy to speedup the EM algorithm using domain reduction. Domain reduction uses a coarse grid to evaluate regions in the integration domain that contribute most to the integral. The integral is evaluated with a fine grid in these regions. In the simulations reported in this paper, domain reduction gives speedups which exceed a factor of 10 in early iterations and which exceed a factor of 60 in terminal iterations.

Zernike phase plate cryoelectron microscopy facilitates single particle analysis of unstained asymmetric protein complexes

Single particle reconstruction from cryoelectron microscopy images, though emerging as a powerful means in structural biology, is faced with challenges as applied to asymmetric proteins smaller than megadaltons due to low contrast. Zernike phase plate can improve the contrast by restoring the microscope contrast transfer function. Here, by exploiting simulated Zernike and conventional defocused cryoelectron microscope images with noise characteristics comparable to those of experimental data, we quantified the efficiencies of the steps in single particle analysis of ice-embedded RNA polymerase II (500 kDa), transferrin receptor complex (290 kDa), and T7 RNA polymerase lysozyme (100 kDa). Our results show Zernike phase plate imaging is more effective as to particle identification and also sorting of orientations, conformations, and compositions. Moreover, our analysis on image alignment indicates that Zernike phase plate can, in principle, reduce the number of particles required to attain near atomic resolution by 10-100 fold for proteins between 100 kDa and 500 kDa.

Averaging of electron subtomograms and random conical tilt reconstructions through likelihood optimization

The reference-free averaging of three-dimensional electron microscopy (3D-EM) reconstructions with empty regions in Fourier space represents a pressing problem in electron tomography and single-particle analysis. We present a maximum likelihood algorithm for the simultaneous alignment and classification of subtomograms or random conical tilt (RCT) reconstructions, where the Fourier components in the missing data regions are treated as hidden variables. The behavior of this algorithm was explored using tests on simulated data, while application to experimental data was shown to yield unsupervised class averages for subtomograms of groEL/groES complexes and RCT reconstructions of p53. The latter application served to obtain a reliable de novo structure for p53 that may resolve uncertainties about its quaternary structure.

Conformational rearrangements of SV40 large T antigen during early replication events

The Simian virus 40 (SV40) large tumor antigen (LTag) functions as the replicative helicase and initiator for viral DNA replication. For SV40 replication, the first essential step is the assembly of an LTag double hexamer at the origin DNA that will subsequently melt the origin DNA to initiate fork unwinding. In this study, we used three-dimensional cryo-electron microscopy to visualize early events in the activation of DNA replication in the SV40 model system. We obtained structures of wild-type double-hexamer complexes of LTag bound to SV40 origin DNA, to which atomic structures have been fitted. Wild-type LTag was observed in two distinct conformations: In one conformation, the central module containing the J-domains and the origin binding domains of both hexamers is a compact closed ring. In the other conformation, the central module is an open ring with a gap formed by rearrangement of the N-terminal regions of the two hexamers, potentially allowing for the passage of single-stranded DNA generated from the melted origin DNA. Double-hexamer complexes containing mutant LTag that lacks the N-terminal J-domain show the central module predominantly in the closed-ring state. Analyses of the LTag C-terminal regions reveal that the LTag hexamers bound to the A/T-rich tract origin of replication and early palindrome origin of replication elements are structurally distinct. Lastly, visualization of DNA density protruding from the LTag C-terminal domains suggests that oligomerization of the LTag complex takes place on double-stranded DNA.

An introduction to maximum-likelihood methods in cryo-EM

The maximum-likelihood method provides a powerful approach to many problems in cryo-electron microscopy (cryo-EM) image processing. This contribution aims to provide an accessible introduction to the underlying theory and reviews existing applications in the field. In addition, current developments to reduce computational costs and to improve the statistical description of cryo-EM images are discussed. Combined with the increasing power of modern computers and yet unexplored possibilities provided by theory, these developments are expected to turn the statistical approach into an essential image-processing tool for the electron microscopist.

Visualizing molecular machines in action: Single-particle analysis with structural variability

Many of the electron microscopy (EM) samples that are analyzed by single-particle reconstruction are flexible macromolecular assemblies that adopt multiple structural states in their functioning. Consequently, EM samples often contain a mixture of different structural states. This structural variability has long been regarded as a severe hindrance for single-particle analysis because the combination of projections from different structures into a single reconstruction may cause severe artifacts. This chapter reviews recent developments in image processing that may turn structural variability from an obstacle into an advantage. Modern algorithms now allow classifying projection images according to their underlying three-dimensional (3D) structures, so that multiple reconstructions may be obtained from a single data set. This places 3D-EM in a unique position to study the intricate dynamics of functioning molecular assemblies.

Classification of structural heterogeneity by maximum-likelihood methods

With the advent of computationally feasible approaches to maximum-likelihood (ML) image processing for cryo-electron microscopy, these methods have proven particularly useful in the classification of structurally heterogeneous single-particle data. A growing number of experimental studies have applied these algorithms to study macromolecular complexes with a wide range of structural variability, including nonstoichiometric complex formation, large conformational changes, and combinations of both. This chapter aims to share the practical experience that has been gained from the application of these novel approaches. Current insights on how to prepare the data and how to perform two- or three-dimensional classifications are discussed together with the aspects related to high-performance computing. Thereby, this chapter will hopefully be of practical use for those microscopists wishing to apply ML methods in their own investigations.

Methods for segmentation and interpretation of electron tomographic reconstructions

Electron tomography has become a powerful tool for revealing the molecular architecture of biological cells and tissues. In principle, electron tomography can provide high-resolution mapping of entire proteomes. The achievable resolution (3-8 nm) is capable of bridging the gap between live-cell imaging and atomic resolution structures. However, the relevant information is not readily accessible from the data and needs to be identified, extracted, and processed before it can be used. Because electron tomography imaging and image acquisition technologies have enjoyed major advances in the last few years and continue to increase data throughput, the need for approaches that allow automatic and objective interpretation of electron tomograms becomes more and more urgent. This chapter provides an overview of the state of the art in this field and attempts to identify the major bottlenecks that prevent approaches for interpreting electron tomography data to develop their full potential.

Single-particle applications at intermediate resolution

Electron microscopy together with single-particle image processing is an excellent method for structure determination of biological assemblies that exist in multiple identical copies. Typical assemblies contain several proteins and/or nucleic acids in a defined and reproducible arrangement. Coherent averaging of electron microscopic images of 5000-100,000 copies of these assemblies allows the determination of three-dimensional structures at ca. 1-3-nm resolution. At this intermediate resolution, it is possible to map individual subunits and thus to understand the architecture and quaternary structure of the assemblies. The intermediate resolution structural information gives a solid basis on which pseudo-atomic models of the assemblies can be modeled provided that high-resolution structures of smaller entities are known. The architecture of the assemblies, their pseudo-atomic models, and knowledge on their plasticity during function give a comprehensive understanding of large-scale structural dynamics of multicopy biological complexes. In this review, we will introduce the experimental pipeline and discuss selected examples.

Exploring conformational modes of macromolecular assemblies by multiparticle cryo-EM

Single particle cryo-electron microscopy (cryo-EM) is a technique aimed at structure determination of large macromolecular complexes in their unconstrained, physiological conditions. The power of the method has been demonstrated in selected studies where for highly symmetric molecules the resolution attained permitted backbone tracing. However, most molecular complexes appear to exhibit intrinsic conformational variability necessary to perform their functions. Therefore, it is now increasingly recognized that sample heterogeneity constitutes a major methodological challenge for cryo-EM. To overcome it dedicated experimental and particularly computational multiparticle approaches have been developed. Their applications point to the future of cryo-EM as an experimental method uniquely suited to visualize the conformational modes of large macromolecular complexes and machines.

The advent of near-atomic resolution in single-particle electron microscopy

Single-particle electron microscopy (EM) can provide structural information for a large variety of biological molecules, ranging from small proteins to large macromolecular assemblies, without the need to produce crystals. The year 2008 has become a landmark year for single-particle EM as for the first time density maps have been produced at a resolution that made it possible to trace protein backbones or even to build atomic models. In this review, we highlight some of the recent successes achieved by single-particle EM and describe the individual steps involved in producing a density map by this technique. We also discuss some of the remaining challenges and areas, in which further advances would have a great impact on the results that can be achieved by single-particle EM.

Introducing robustness to maximum-likelihood refinement of electron-microscopy data

An expectation-maximization algorithm for maximum-likelihood refinement of electron-microscopy images is presented that is based on fitting mixtures of multivariate t-distributions. The novel algorithm has intrinsic characteristics for providing robustness against atypical observations in the data, which is illustrated using an experimental test set with artificially generated outliers. Tests on experimental data revealed only minor differences in two-dimensional classifications, while three-dimensional classification with the new algorithm gave stronger elongation factor G density in the corresponding class of a structurally heterogeneous ribosome data set than the conventional algorithm for Gaussian mixtures.

Toward an atomic model of the 26S proteasome

Since the discovery of the 26S proteasome, much progress has been made in determining the structure of this large dynamic protein complex. Until now, a vast amount of structural information of the proteasome has been obtained from all kinds of structure determination techniques, and the function of the protease core is well understood at atomic detail. Yet our understanding of the entire 26S proteasome structure, particularly its 19S regulatory complex, is still limited at a low-resolution blob-ology level. In this review, we highlight the recent progress made in understanding the mechanism of 20S gate opening by the proteasomal activators. We also emphasized the recent methodological advances, particularly in achieving the near atomic resolution by single particle electron cryomicroscopy, and the possible approaches that will enable more detailed structural analysis of the entire 26S proteasome.

Determination of signal-to-noise ratios and spectral SNRs in cryo-EM low-dose imaging of molecules

Attempts to develop efficient classification approaches to the problem of heterogeneity in single-particle reconstruction of macromolecules require phantom data with realistic noise models. We have estimated the signal-to-noise ratios and spectral signal-to-noise ratios for three steps in the electron microscopic image formation from data obtained experimentally. An important result is that structural noise, i.e., the irreproducible component of the object prior to image formation, is substantial, and of the same order of magnitude as the reproducible signal. Based on this result, the noise modeling for testing new classification techniques can be improved.