Heterogeneity of large macromolecular complexes revealed by 3D cryo-EM variance analysis

Exploring the Structural Variability of Dynamic Biological Complexes by Single-Particle Cryo-Electron Microscopy

Biological macromolecules and assemblies precisely rearrange their atomic 3D structures to execute cellular functions. Understanding the mechanisms by which these molecular machines operate requires insight into the ensemble of structural states they occupy during the functional cycle. Single-particle cryo-electron microscopy (cryo-EM) has become the preferred method to provide near-atomic resolution, structural information about dynamic biological macromolecules elusive to other structure determination methods. Recent advances in cryo-EM methodology have allowed structural biologists not only to probe the structural intermediates of biochemical reactions, but also to resolve different compositional and conformational states present within the same dataset. This article reviews newly developed sample preparation and single-particle analysis (SPA) techniques for high-resolution structure determination of intrinsically dynamic and heterogeneous samples, shedding light upon the intricate mechanisms employed by molecular machines and helping to guide drug discovery efforts.

Data-driven determination of number of discrete conformations in single-particle cryo-EM

BACKGROUND AND OBJECTIVE

One of the strengths of single-particle cryo-EM compared to other structural determination techniques is its ability to image heterogeneous samples containing multiple molecular species, different oligomeric states or distinct conformations. This is achieved using routines for in-silico 3D classification that are now well established in the field and have successfully been used to characterize the structural heterogeneity of important biomolecules. These techniques, however, rely on expert-user knowledge and trial-and-error experimentation to determine the correct number of conformations, making it a labor intensive, subjective, and difficult to reproduce procedure.

METHODS

We propose an approach to address the problem of automatically determining the number of discrete conformations present in heterogeneous single-particle cryo-EM datasets. We do this by systematically evaluating all possible partitions of the data and selecting the result that maximizes the average variance of similarities measured between particle images and the corresponding 3D reconstructions.

RESULTS

Using this strategy, we successfully analyzed datasets of heterogeneous protein complexes, including: 1) in-silico mixtures obtained by combining closely related antibody-bound HIV-1 Env trimers and other important membrane channels, and 2) naturally occurring mixtures from diverse and dynamic protein complexes representing varying degrees of structural heterogeneity and conformational plasticity.

CONCLUSIONS

The availability of unsupervised strategies for 3D classification combined with existing approaches for fully automatic pre-processing and 3D refinement, represents an important step towards converting single-particle cryo-EM into a high-throughput technique.

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.

NUDIM: A non-uniform fast Fourier transform based dual-space constraint iterative reconstruction method in biological electron tomography

Electron tomography, a powerful imaging tool for studying 3D structures of macromolecular assemblies, always suffers from imperfect reconstruction with limited resolution due to the intrinsic low signal-to-noise ratio (SNR) and inaccessibility to certain tilt angles induced by radiation damage or mechanical limitation. In order to compensate for such insufficient data with low SNR and further improve imaging resolution, prior knowledge constraints about the objects in both real space and reciprocal space are thus exploited during tomographic reconstruction. However, direct Fast Fourier transform (FFT) between real space and reciprocal space remains extraordinarily challenging owing to their inconsistent grid sampling modes, e.g. regular and uniform grid sampling in real space whereas radial or polar grid sampling in reciprocal space. In order to solve such problem, a technique of non-uniform fast Fourier transform (NFFT) has been developed to transform efficiently between non-uniformly sampled grids in real and reciprocal space with sufficient accuracy. In this work, a Non-Uniform fast Fourier transform based Dual-space constraint Iterative reconstruction Method (NUDIM) applicable to biological electron tomography is proposed with a combination of basic concepts from equally sloped tomography (EST) and NFFT based reconstruction. In NUDIM, the use of NFFT can circumvent such grid sampling inconsistency and thus alleviate the stringent equally-sloped sampling requirement in EST reconstruction, while the dual-space constraint iterative procedure can dramatically enhance reconstruction quality. In comparison with conventional reconstruction methods, NUDIM is numerically and experimentally demonstrated to produce superior reconstruction quality with higher contrast, less noise and reduced missing wedge artifacts. More importantly, it is also capable of retrieving part of missing information from a limited number of projections.

Advances in methods for atomic resolution macromolecular structure determination

Recent technical advances have dramatically increased the power and scope of structural biology. New developments in high-resolution cryo-electron microscopy, serial X-ray crystallography, and electron diffraction have been especially transformative. Here we highlight some of the latest advances and current challenges at the frontiers of atomic resolution methods for elucidating the structures and dynamical properties of macromolecules and their complexes.

Computational Methods for Single-Particle Electron Cryomicroscopy

Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for elucidating the three-dimensional structure of proteins and other biologically significant complexes at near-atomic resolution. It is an imaging method that does not require crystallization and can capture molecules in their native states. In single-particle cryo-EM, the three-dimensional molecular structure needs to be determined from many noisy two-dimensional tomographic projections of individual molecules, whose orientations and positions are unknown. The high level of noise and the unknown pose parameters are two key elements that make reconstruction a challenging computational problem. Even more challenging is the inference of structural variability and flexible motions when the individual molecules being imaged are in different conformational states. This review discusses computational methods for structure determination by single-particle cryo-EM and their guiding principles from statistical inference, machine learning, and signal processing that also play a significant role in many other data science applications.

Reconstruction of Stochastic 3D Signals With Symmetric Statistics From 2D Projection Images Motivated by Cryo-Electron Microscopy

Cryo-electron microscopy provides 2D projection images of the 3D electron scattering intensity of many instances of the particle under study (e.g., a virus). Both symmetry (rotational point groups) and heterogeneity are important aspects of biological particles and both aspects can be combined by describing the electron scattering intensity of the particle as a stochastic process with a symmetric probability law and, therefore, symmetric moments. A maximum likelihood estimator implemented by an expectation-maximization algorithm is described, which estimates the unknown statistics of the electron scattering intensity stochastic process from the images of instances of the particle. The algorithm is demonstrated on the bacteriophage HK97 and the virus [Formula: see text]. The results are contrasted with the existing algorithms, which assume that each instance of the particle has the symmetry rather than the less restrictive assumption that the probability law has the symmetry.

Single-Molecule 3D Images of "Hole-Hole" IgG1 Homodimers by Individual-Particle Electron Tomography

The engineering of immunoglobulin-G molecules (IgGs) is of wide interest for improving therapeutics, for example by modulating the activity or multiplexing the specificity of IgGs to recognize more than one antigen. Optimization of engineered IgG requires knowledge of three-dimensional (3D) structure of synthetic IgG. However, due to flexible nature of the molecules, their structural characterization is challenging. Here, we use our reported individual-particle electron tomography (IPET) method with optimized negative-staining (OpNS) for direct 3D reconstruction of individual IgG hole-hole homodimer molecules. The hole-hole homodimer is an undesired variant generated during the production of a bispecific antibody using the knob-into-hole heterodimer technology. A total of 64 IPET 3D density maps at ~15 Å resolutions were reconstructed from 64 individual molecules, revealing 64 unique conformations. In addition to the known Y-shaped conformation, we also observed an unusual X-shaped conformation. The 3D structure of the X-shaped conformation contributes to our understanding of the structural details of the interaction between two heavy chains in the Fc domain. The IPET approach, as an orthogonal technique to characterize the 3D structure of therapeutic antibodies, provides insight into the 3D structural variety and dynamics of heterogeneous IgG molecules.

MBIR: A cryo-ET 3D reconstruction method that effectively minimizes missing wedge artifacts and restores missing information

Cryo-Electron Tomography (cryo-ET) has become an essential technique in revealing cellular and macromolecular assembly structures in their native states. However, due to radiation damage and the limited tilt range, cryo-ET suffers from low contrast and missing wedge artifacts, which limits the tomograms to low resolution and hinders further biological interpretation. In this study, we applied the Model-Based Iterative Reconstruction (MBIR) method to obtain tomographic 3D reconstructions of experimental cryo-ET datasets and demonstrated the advantages of MBIR in contrast improvement, missing wedge artifacts reduction, missing information restoration, and subtomogram averaging compared with other reconstruction approaches. Considering the outstanding reconstruction quality, MBIR has a great potential in the determination of high resolution biological structures with cryo-ET.

Survey of the analysis of continuous conformational variability of biological macromolecules by electron microscopy

Single-particle analysis by electron microscopy is a well established technique for analyzing the three-dimensional structures of biological macromolecules. Besides its ability to produce high-resolution structures, it also provides insights into the dynamic behavior of the structures by elucidating their conformational variability. Here, the different image-processing methods currently available to study continuous conformational changes are reviewed.

Allosteric effects in bacteriophage HK97 procapsids revealed directly from covariance analysis of cryo EM data

The information content of cryo EM data sets exceeds that of the electron scattering potential (cryo EM) density initially derived for structure determination. Previously we demonstrated the power of data variance analysis for characterizing regions of cryo EM density that displayed functionally important variance anomalies associated with maturation cleavage events in Nudaurelia Omega Capensis Virus and the presence or absence of a maturation protease in bacteriophage HK97 procapsids. Here we extend the analysis in two ways. First, instead of imposing icosahedral symmetry on every particle in the data set during the variance analysis, we only assume that the data set as a whole has icosahedral symmetry. This change removes artifacts of high variance along icosahedral symmetry axes, but retains all of the features previously reported in the HK97 data set. Second we present a covariance analysis that reveals correlations in structural dynamics (variance) between the interior of the HK97 procapsid with the protease and regions of the exterior (not seen in the absence of the protease). The latter analysis corresponds well with hydrogen deuterium exchange studies previously published that reveal the same correlation.

Particle segmentation algorithm for flexible single particle reconstruction

As single particle cryo-electron microscopy has evolved to a new era of atomic resolution, sample heterogeneity still imposes a major limit to the resolution of many macromolecular complexes, especially those with continuous conformational flexibility. Here, we describe a particle segmentation algorithm towards solving structures of molecules composed of several parts that are relatively flexible with each other. In this algorithm, the different parts of a target molecule are segmented from raw images according to their alignment information obtained from a preliminary 3D reconstruction and are subjected to single particle processing in an iterative manner. This algorithm was tested on both simulated and experimental data and showed improvement of 3D reconstruction resolution of each segmented part of the molecule than that of the entire molecule.

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.

Unsupervised Cryo-EM Data Clustering through Adaptively Constrained K-Means Algorithm

In single-particle cryo-electron microscopy (cryo-EM), K-means clustering algorithm is widely used in unsupervised 2D classification of projection images of biological macromolecules. 3D ab initio reconstruction requires accurate unsupervised classification in order to separate molecular projections of distinct orientations. Due to background noise in single-particle images and uncertainty of molecular orientations, traditional K-means clustering algorithm may classify images into wrong classes and produce classes with a large variation in membership. Overcoming these limitations requires further development on clustering algorithms for cryo-EM data analysis. We propose a novel unsupervised data clustering method building upon the traditional K-means algorithm. By introducing an adaptive constraint term in the objective function, our algorithm not only avoids a large variation in class sizes but also produces more accurate data clustering. Applications of this approach to both simulated and experimental cryo-EM data demonstrate that our algorithm is a significantly improved alterative to the traditional K-means algorithm in single-particle cryo-EM analysis.

Identifying and Visualizing Macromolecular Flexibility in Structural Biology

Structural biology comprises a variety of tools to obtain atomic resolution data for the investigation of macromolecules. Conventional structural methodologies including crystallography, NMR and electron microscopy often do not provide sufficient details concerning flexibility and dynamics, even though these aspects are critical for the physiological functions of the systems under investigation. However, the increasing complexity of the molecules studied by structural biology (including large macromolecular assemblies, integral membrane proteins, intrinsically disordered systems, and folding intermediates) continuously demands in-depth analyses of the roles of flexibility and conformational specificity involved in interactions with ligands and inhibitors. The intrinsic difficulties in capturing often subtle but critical molecular motions in biological systems have restrained the investigation of flexible molecules into a small niche of structural biology. Introduction of massive technological developments over the recent years, which include time-resolved studies, solution X-ray scattering, and new detectors for cryo-electron microscopy, have pushed the limits of structural investigation of flexible systems far beyond traditional approaches of NMR analysis. By integrating these modern methods with powerful biophysical and computational approaches such as generation of ensembles of molecular models and selective particle picking in electron microscopy, more feasible investigations of dynamic systems are now possible. Using some prominent examples from recent literature, we review how current structural biology methods can contribute useful data to accurately visualize flexibility in macromolecular structures and understand its important roles in regulation of biological processes.

Single-Particle Refinement and Variability Analysis in EMAN2.1

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

Continuous changes in structure mapped by manifold embedding of single-particle data in cryo-EM

Cryo-electron microscopy, when combined with single-particle reconstruction, is a powerful method for studying macromolecular structure. Recent developments in detector technology have pushed the resolution into a range comparable to that of X-ray crystallography. However, cryo-EM is able to separate and thus recover the structure of each of several discrete structures present in the sample. For the more general case involving continuous structural changes, a novel technique employing manifold embedding has been recently demonstrated. Potentially, the entire work-cycle of a molecular machine may be observed as it passes through a continuum of states, and its free-energy landscape may be mapped out. This technique will be outlined and discussed in the context of its application to a large single-particle dataset of yeast ribosomes.

A local-optimization refinement algorithm in single particle analysis for macromolecular complex with multiple rigid modules

Single particle analysis, which can be regarded as an average of signals from thousands or even millions of particle projections, is an efficient method to study the three-dimensional structures of biological macromolecules. An intrinsic assumption in single particle analysis is that all the analyzed particles must have identical composition and conformation. Thus specimen heterogeneity in either composition or conformation has raised great challenges for high-resolution analysis. For particles with multiple conformations, inaccurate alignments and orientation parameters will yield an averaged map with diminished resolution and smeared density. Besides extensive classification approaches, here based on the assumption that the macromolecular complex is made up of multiple rigid modules whose relative orientations and positions are in slight fluctuation around equilibriums, we propose a new method called as local optimization refinement to address this conformational heterogeneity for an improved resolution. The key idea is to optimize the orientation and shift parameters of each rigid module and then reconstruct their three-dimensional structures individually. Using simulated data of 80S/70S ribosomes with relative fluctuations between the large (60S/50S) and the small (40S/30S) subunits, we tested this algorithm and found that the resolutions of both subunits are significantly improved. Our method provides a proof-of-principle solution for high-resolution single particle analysis of macromolecular complexes with dynamic conformations.

3D Structural Fluctuation of IgG1 Antibody Revealed by Individual Particle Electron Tomography

Commonly used methods for determining protein structure, including X-ray crystallography and single-particle reconstruction, often provide a single and unique three-dimensional (3D) structure. However, in these methods, the protein dynamics and flexibility/fluctuation remain mostly unknown. Here, we utilized advances in electron tomography (ET) to study the antibody flexibility and fluctuation through structural determination of individual antibody particles rather than averaging multiple antibody particles together. Through individual-particle electron tomography (IPET) 3D reconstruction from negatively-stained ET images, we obtained 120 ab-initio 3D density maps at an intermediate resolution (~1-3 nm) from 120 individual IgG1 antibody particles. Using these maps as a constraint, we derived 120 conformations of the antibody via structural flexible docking of the crystal structure to these maps by targeted molecular dynamics simulations. Statistical analysis of the various conformations disclosed the antibody 3D conformational flexibility through the distribution of its domain distances and orientations. This blueprint approach, if extended to other flexible proteins, may serve as a useful methodology towards understanding protein dynamics and functions.

Cryogenic electron microscopy and single-particle analysis

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

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.

A national facility for biological cryo-electron microscopy

Three-dimensional electron microscopy is an enormously powerful tool for structural biologists. It is now able to provide an understanding of the molecular machinery of cells, disease processes and the actions of pathogenic organisms from atomic detail through to the cellular context. However, cutting-edge research in this field requires very substantial resources for equipment, infrastructure and expertise. Here, a brief overview is provided of the plans for a UK national three-dimensional electron-microscopy facility for integrated structural biology to enable internationally leading research on the machinery of life. State-of-the-art equipment operated with expert support will be provided, optimized for both atomic-level single-particle analysis of purified macromolecules and complexes and for tomography of cell sections. The access to and organization of the facility will be modelled on the highly successful macromolecular crystallography (MX) synchrotron beamlines, and will be embedded at the Diamond Light Source, facilitating the development of user-friendly workflows providing near-real-time experimental feedback.

Structure of β-galactosidase at 3.2-Å resolution obtained by cryo-electron microscopy

We report the solution structure of Escherichia coli β-galactosidase (∼465 kDa), solved at ∼3.2-Å resolution by using single-particle cryo-electron microscopy (cryo-EM). Densities for most side chains, including those of residues in the active site, and a catalytic Mg(2+) ion can be discerned in the map obtained by cryo-EM. The atomic model derived from our cryo-EM analysis closely matches the 1.7-Å crystal structure with a global rmsd of ∼0.66 Å. There are significant local differences throughout the protein, with clear evidence for conformational changes resulting from contact zones in the crystal lattice. Inspection of the map reveals that although densities for residues with positively charged and neutral side chains are well resolved, systematically weaker densities are observed for residues with negatively charged side chains. We show that the weaker densities for negatively charged residues arise from their greater sensitivity to radiation damage from electron irradiation as determined by comparison of density maps obtained by using electron doses ranging from 10 to 30 e(-)/Å(2). In summary, we establish that it is feasible to use cryo-EM to determine near-atomic resolution structures of protein complexes (<500 kDa) with low symmetry, and that the residue-specific radiation damage that occurs with increasing electron dose can be monitored by using dose fractionation tools available with direct electron detector technology.

Iterative reconstruction of cryo-electron tomograms using nonuniform fast Fourier transforms

Algorithms for three-dimensional (3D) reconstruction of objects based on their projections are essential in various biological and medical imaging modalities. In cryo-electron tomography (CET) a major challenge for reconstruction is the limited range of projection angles, which manifests itself as a "missing wedge" of data in Fourier space making the reconstruction problem ill-posed. Here, we apply an iterative reconstruction method that makes use of nonuniform fast Fourier transform (NUFFT) to the reconstruction of cryo-electron tomograms. According to several measures the reconstructions are superior to those obtained using conventional methods, most notably weighted backprojection. Most importantly, we show that it is possible to fill in partially the unsampled region in Fourier space with meaningful information without making assumptions about the data or applying prior knowledge. As a consequence, particles of known structure can be localized with higher confidence in cryotomograms and subtomogram averaging yields higher resolution densities.

Hepatitis-C-virus-like internal ribosome entry sites displace eIF3 to gain access to the 40S subunit

Hepatitis C virus (HCV) and classical swine fever virus (CSFV) messenger RNAs contain related (HCV-like) internal ribosome entry sites (IRESs) that promote 5'-end independent initiation of translation, requiring only a subset of the eukaryotic initiation factors (eIFs) needed for canonical initiation on cellular mRNAs. Initiation on HCV-like IRESs relies on their specific interaction with the 40S subunit, which places the initiation codon into the P site, where it directly base-pairs with eIF2-bound initiator methionyl transfer RNA to form a 48S initiation complex. However, all HCV-like IRESs also specifically interact with eIF3 (refs 2, 5-7, 9-12), but the role of this interaction in IRES-mediated initiation has remained unknown. During canonical initiation, eIF3 binds to the 40S subunit as a component of the 43S pre-initiation complex, and comparison of the ribosomal positions of eIF3 and the HCV IRES revealed that they overlap, so that their rearrangement would be required for formation of ribosomal complexes containing both components. Here we present a cryo-electron microscopy reconstruction of a 40S ribosomal complex containing eIF3 and the CSFV IRES. Remarkably, although the position and interactions of the CSFV IRES with the 40S subunit in this complex are similar to those of the HCV IRES in the 40S-IRES binary complex, eIF3 is completely displaced from its ribosomal position in the 43S complex, and instead interacts through its ribosome-binding surface exclusively with the apical region of domain III of the IRES. Our results suggest a role for the specific interaction of HCV-like IRESs with eIF3 in preventing ribosomal association of eIF3, which could serve two purposes: relieving the competition between the IRES and eIF3 for a common binding site on the 40S subunit, and reducing formation of 43S complexes, thereby favouring translation of viral mRNAs.

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.

Structure of the mammalian ribosomal 43S preinitiation complex bound to the scanning factor DHX29

Eukaryotic translation initiation begins with assembly of a 43S preinitiation complex. First, methionylated initiator methionine transfer RNA (Met-tRNAi(Met)), eukaryotic initiation factor (eIF) 2, and guanosine triphosphate form a ternary complex (TC). The TC, eIF3, eIF1, and eIF1A cooperatively bind to the 40S subunit, yielding the 43S preinitiation complex, which is ready to attach to messenger RNA (mRNA) and start scanning to the initiation codon. Scanning on structured mRNAs additionally requires DHX29, a DExH-box protein that also binds directly to the 40S subunit. Here, we present a cryo-electron microscopy structure of the mammalian DHX29-bound 43S complex at 11.6 Å resolution. It reveals that eIF2 interacts with the 40S subunit via its α subunit and supports Met-tRNAi(Met) in an unexpected P/I orientation (eP/I). The structural core of eIF3 resides on the back of the 40S subunit, establishing two principal points of contact, whereas DHX29 binds around helix 16. The structure provides insights into eukaryote-specific aspects of translation, including the mechanism of action of DHX29.

Single particle electron microscopy

Single particle electron microscopy is a versatile technique for the structural analysis of protein complexes in near-native conditions. While tremendous progress has been made during the past few decades in techniques for specimen preparation, imaging, and image analysis, the field is still in development. In the context of this volume on electron crystallography, the following chapter gives practical guidelines on how to begin single particle EM studies, including preparing specimens, selecting imaging conditions, and choosing which of the many approaches to image analysis are appropriate for a specific sample.

High-resolution cryo-electron microscopy structure of the Trypanosoma brucei ribosome

Ribosomes, the protein factories of living cells, translate genetic information carried by messenger RNAs into proteins, and are thus involved in virtually all aspects of cellular development and maintenance. The few available structures of the eukaryotic ribosome reveal that it is more complex than its prokaryotic counterpart, owing mainly to the presence of eukaryote-specific ribosomal proteins and additional ribosomal RNA insertions, called expansion segments. The structures also differ among species, partly in the size and arrangement of these expansion segments. Such differences are extreme in kinetoplastids, unicellular eukaryotic parasites often infectious to humans. Here we present a high-resolution cryo-electron microscopy structure of the ribosome of Trypanosoma brucei, the parasite that is transmitted by the tsetse fly and that causes African sleeping sickness. The atomic model reveals the unique features of this ribosome, characterized mainly by the presence of unusually large expansion segments and ribosomal-protein extensions leading to the formation of four additional inter-subunit bridges. We also find additional rRNA insertions, including one large rRNA domain that is not found in other eukaryotes. Furthermore, the structure reveals the five cleavage sites of the kinetoplastid large ribosomal subunit (LSU) rRNA chain, which is known to be cleaved uniquely into six pieces, and suggests that the cleavage is important for the maintenance of the T. brucei ribosome in the observed structure. We discuss several possible implications of the large rRNA expansion segments for the translation-regulation process. The structure could serve as a basis for future experiments aimed at understanding the functional importance of these kinetoplastid-specific ribosomal features in protein-translation regulation, an essential step towards finding effective and safe kinetoplastid-specific drugs.

Optimal noise reduction in 3D reconstructions of single particles using a volume-normalized filter

The high noise level found in single-particle electron cryo-microscopy (cryo-EM) image data presents a special challenge for three-dimensional (3D) reconstruction of the imaged molecules. The spectral signal-to-noise ratio (SSNR) and related Fourier shell correlation (FSC) functions are commonly used to assess and mitigate the noise-generated error in the reconstruction. Calculation of the SSNR and FSC usually includes the noise in the solvent region surrounding the particle and therefore does not accurately reflect the signal in the particle density itself. Here we show that the SSNR in a reconstructed 3D particle map is linearly proportional to the fractional volume occupied by the particle. Using this relationship, we devise a novel filter (the "single-particle Wiener filter") to minimize the error in a reconstructed particle map, if the particle volume is known. Moreover, we show how to approximate this filter even when the volume of the particle is not known, by optimizing the signal within a representative interior region of the particle. We show that the new filter improves on previously proposed error-reduction schemes, including the conventional Wiener filter as well as figure-of-merit weighting, and quantify the relationship between all of these methods by theoretical analysis as well as numeric evaluation of both simulated and experimentally collected data. The single-particle Wiener filter is applicable across a broad range of existing 3D reconstruction techniques, but is particularly well suited to the Fourier inversion method, leading to an efficient and accurate implementation.

Repair complexes of FEN1 endonuclease, DNA, and Rad9-Hus1-Rad1 are distinguished from their PCNA counterparts by functionally important stability

Processivity clamps such as proliferating cell nuclear antigen (PCNA) and the checkpoint sliding clamp Rad9/Rad1/Hus1 (9-1-1) act as versatile scaffolds in the coordinated recruitment of proteins involved in DNA replication, cell-cycle control, and DNA repair. Association and handoff of DNA-editing enzymes, such as flap endonuclease 1 (FEN1), with sliding clamps are key processes in biology, which are incompletely understood from a mechanistic point of view. We have used an integrative computational and experimental approach to define the assemblies of FEN1 with double-flap DNA substrates and either proliferating cell nuclear antigen or the checkpoint sliding clamp 9-1-1. Fully atomistic models of these two ternary complexes were developed and refined through extensive molecular dynamics simulations to expose their conformational dynamics. Clustering analysis revealed the most dominant conformations accessible to the complexes. The cluster centroids were subsequently used in conjunction with single-particle electron microscopy data to obtain a 3D EM reconstruction of the human 9-1-1/FEN1/DNA assembly at 18-Å resolution. Comparing the structures of the complexes revealed key differences in the orientation and interactions of FEN1 and double-flap DNA with the two clamps that are consistent with their respective functions in providing inherent flexibility for lagging strand DNA replication or inherent stability for DNA repair.

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

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

Real-space processing of helical filaments in SPARX

We present a major revision of the iterative helical real-space refinement (IHRSR) procedure and its implementation in the SPARX single particle image processing environment. We built on over a decade of experience with IHRSR helical structure determination and we took advantage of the flexible SPARX infrastructure to arrive at an implementation that offers ease of use, flexibility in designing helical structure determination strategy, and high computational efficiency. We introduced the 3D projection matching code which now is able to work with non-cubic volumes, the geometry better suited for long helical filaments, we enhanced procedures for establishing helical symmetry parameters, and we parallelized the code using distributed memory paradigm. Additional features include a graphical user interface that facilitates entering and editing of parameters controlling the structure determination strategy of the program. In addition, we present a novel approach to detect and evaluate structural heterogeneity due to conformer mixtures that takes advantage of helical structure redundancy.

An adaptation of the Wiener filter suitable for analyzing images of isolated single particles

The Wiener filter is a standard means of optimizing the signal in sums of aligned, noisy images obtained by electron cryo-microscopy (cryo-EM). However, estimation of the resolution-dependent ("spectral") signal-to-noise ratio (SSNR) from the input data has remained problematic, and error reduction due to specific application of the SSNR term within a Wiener filter has not been reported. Here we describe an adjustment to the Wiener filter for optimal summation of images of isolated particles surrounded by large regions of featureless background, as is typically the case in single-particle cryo-EM applications. We show that the density within the particle area can be optimized, in the least-squares sense, by scaling the SSNR term found in the conventional Wiener filter by a factor that reflects the fraction of the image field occupied by the particle. We also give related expressions that allow the SSNR to be computed for application in this new filter, by incorporating a masking step into a Fourier Ring Correlation (FRC), a standard resolution measure. Furthermore, we show that this masked FRC estimation scheme substantially improves on the accuracy of conventional SSNR estimation methods. We demonstrate the validity of our new approach in numeric tests with simulated data corresponding to realistic cryo-EM imaging conditions. This variation of the Wiener filter and accompanying derivation should prove useful for a variety of single-particle cryo-EM applications, including 3D reconstruction.

Atomic resolution cryo electron microscopy of macromolecular complexes

Single-particle cryo electron microscopy (cryoEM) is a technique for determining three-dimensional (3D) structures from projection images of molecular complexes preserved in their "native," noncrystalline state. Recently, atomic or near-atomic resolution structures of several viruses and protein assemblies have been determined by single-particle cryoEM, allowing ab initio atomic model building by following the amino acid side chains or nucleic acid bases identifiable in their cryoEM density maps. In particular, these cryoEM structures have revealed extended arms contributing to molecular interactions that are otherwise not resolved by the conventional structural method of X-ray crystallography at similar resolutions. High-resolution cryoEM requires careful consideration of a number of factors, including proper sample preparation to ensure structural homogeneity, optimal configuration of electron imaging conditions to record high-resolution cryoEM images, accurate determination of image parameters to correct image distortions, efficient refinement and computation to reconstruct a 3D density map, and finally appropriate choice of modeling tools to construct atomic models for functional interpretation. This progress illustrates the power of cryoEM and ushers it into the arsenal of structural biology, alongside conventional techniques of X-ray crystallography and NMR, as a major tool (and sometimes the preferred one) for the studies of molecular interactions in supramolecular assemblies or machines.

Separating and visualising protein assemblies by means of preparative mass spectrometry and microscopy

Many multi-protein assemblies exhibit characteristics which hamper their structural and dynamical characterization. These impediments include low copy number, heterogeneity, polydispersity, hydrophobicity, and intrinsic disorder. It is becoming increasingly apparent that both novel and hybrid structural biology approaches need to be developed to tackle the most challenging targets. Nanoelectrospray mass spectrometry has matured over the last decade to enable the elucidation of connectivity and composition of large protein assemblies. Moreover, comparing mass spectrometry data with transmission electron microscopy images has enabled the mapping of subunits within topological models. Here we describe a preparative form of mass spectrometry designed to isolate specific protein complexes from within a heterogeneous ensemble, and to 'soft-land' these target complexes for ex situ imaging. By building a retractable probe incorporating a versatile target holder, and modifying the ion optics of a commercial mass spectrometer, we show that we can steer the macromolecular ion beam onto a target for imaging by means of transmission electron microscopy and atomic force microscopy. Our data for the tetradecameric chaperonin GroEL show that not only are the molecular volumes of the landed particles consistent with the overall dimensions of the complex, but also that their gross topological features can be maintained.

Visualizing ribosome biogenesis: parallel assembly pathways for the 30S subunit

Ribosomes are self-assembling macromolecular machines that translate DNA into proteins, and an understanding of ribosome biogenesis is central to cellular physiology. Previous studies on the Escherichia coli 30S subunit suggest that ribosome assembly occurs via multiple parallel pathways rather than through a single rate-limiting step, but little mechanistic information is known about this process. Discovery single-particle profiling (DSP), an application of time-resolved electron microscopy, was used to obtain more than 1 million snapshots of assembling 30S subunits, identify and visualize the structures of 14 assembly intermediates, and monitor the population flux of these intermediates over time. DSP results were integrated with mass spectrometry data to construct the first ribosome-assembly mechanism that incorporates binding dependencies, rate constants, and structural characterization of populated intermediates.

Single-particle electron microscopy of animal fatty acid synthase describing macromolecular rearrangements that enable catalysis

We have used macromolecular electron microscopy (EM) to characterize the conformational flexibility of the animal fatty acid synthase (FAS). Here we describe in detail methods employed for image collection and analysis. We also provide an account of how EM results were interpreted by considering a high-resolution static FAS X-ray structure and functional data to arrive at a molecular understanding of the way in which conformational pliability enables fatty acid synthesis.

Matching structural densities from different biophysical origins with gain and bias

The registration of volumetric structures in real space involves geometric and density transformations that align a target map and a probe map in the best way possible. Many computational docking strategies exist for finding the geometric transformations that superimpose maps, but the problem of finding an optimal density transformation, for the purposes of difference calculations or segmentation, has received little attention in the literature. We report results based on simulated and experimental electron microscopy maps, showing that a single scale factor (gain) may be insufficient when it comes to minimizing the density discrepancy between an aligned target and probe. We propose an affine transformation, with gain and bias, that is parameterized by known surface isovalues and by an interactive centering of the "cancellation peak" in the surface thresholded difference map histogram. The proposed approach minimizes discrepancies across a wide range of interior densities. Owing to having only two parameters, it avoids overfitting and requires only minimal knowledge of the probe and target maps. The linear transformation also preserves phases and relative amplitudes in Fourier space. The histogram matching strategy was implemented in the newly revised volhist tool of the Situs package, version 2.6.

Structure and dynamics of a processive Brownian motor: the translating ribosome

There is mounting evidence indicating that protein synthesis is driven and regulated by mechanisms that direct stochastic, large-scale conformational fluctuations of the translational apparatus. This mechanistic paradigm implies that a free-energy landscape governs the conformational states that are accessible to and sampled by the translating ribosome. This scenario presents interdependent opportunities and challenges for structural and dynamic studies of protein synthesis. Indeed, the synergism between cryogenic electron microscopic and X-ray crystallographic structural studies, on the one hand, and single-molecule fluorescence resonance energy transfer (smFRET) dynamic studies, on the other, is emerging as a powerful means for investigating the complex free-energy landscape of the translating ribosome and uncovering the mechanisms that direct the stochastic conformational fluctuations of the translational machinery. In this review, we highlight the principal insights obtained from cryogenic electron microscopic, X-ray crystallographic, and smFRET studies of the elongation stage of protein synthesis and outline the emerging themes, questions, and challenges that lie ahead in mechanistic studies of translation.