Maximum likelihood based classification of electron tomographic data

Learning structural heterogeneity from cryo-electron sub-tomograms with tomoDRGN

Cryo-electron tomography (cryo-ET) enables observation of macromolecular complexes in their native, spatially contextualized cellular environment. Cryo-ET processing software to visualize such complexes at nanometer resolution via iterative alignment and averaging are well developed but rely upon assumptions of structural homogeneity among the complexes of interest. Recently developed tools allow for some assessment of structural diversity but have limited capacity to represent highly heterogeneous structures, including those undergoing continuous conformational changes. Here we extend the highly expressive cryoDRGN (Deep Reconstructing Generative Networks) deep learning architecture, originally created for single-particle cryo-electron microscopy analysis, to cryo-ET. Our new tool, tomoDRGN, learns a continuous low-dimensional representation of structural heterogeneity in cryo-ET datasets while also learning to reconstruct heterogeneous structural ensembles supported by the underlying data. Using simulated and experimental data, we describe and benchmark architectural choices within tomoDRGN that are uniquely necessitated and enabled by cryo-ET. We additionally illustrate tomoDRGN's efficacy in analyzing diverse datasets, using it to reveal high-level organization of human immunodeficiency virus (HIV) capsid complexes assembled in virus-like particles and to resolve extensive structural heterogeneity among ribosomes imaged in situ.

MDSPACE and MDTOMO Software for Extracting Continuous Conformational Landscapes from Datasets of Single Particle Images and Subtomograms Based on Molecular Dynamics Simulations: Latest Developments in ContinuousFlex Software Package

Cryo electron microscopy (cryo-EM) instrumentation allows obtaining 3D reconstruction of the structure of biomolecular complexes in vitro (purified complexes studied by single particle analysis) and in situ (complexes studied in cells by cryo electron tomography). Standard cryo-EM approaches allow high-resolution reconstruction of only a few conformational states of a molecular complex, as they rely on data classification into a given number of classes to increase the resolution of the reconstruction from the most populated classes while discarding all other classes. Such discrete classification approaches result in a partial picture of the full conformational variability of the complex, due to continuous conformational transitions with many, uncountable intermediate states. In this article, we present the software with a user-friendly graphical interface for running two recently introduced methods, namely, MDSPACE and MDTOMO, to obtain continuous conformational landscapes of biomolecules by analyzing in vitro and in situ cryo-EM data (single particle images and subtomograms) based on molecular dynamics simulations of an available atomic model of one of the conformations. The MDSPACE and MDTOMO software is part of the open-source ContinuousFlex software package (starting from version 3.4.2 of ContinuousFlex), which can be run as a plugin of the Scipion software package (version 3.1 and later), broadly used in the cryo-EM field.

Computational methods for in situ structural studies with cryogenic electron tomography

Cryo-electron tomography (cryo-ET) plays a critical role in imaging microorganisms in situ in terms of further analyzing the working mechanisms of viruses and drug exploitation, among others. A data processing workflow for cryo-ET has been developed to reconstruct three-dimensional density maps and further build atomic models from a tilt series of two-dimensional projections. Low signal-to-noise ratio (SNR) and missing wedge are two major factors that make the reconstruction procedure challenging. Because only few near-atomic resolution structures have been reconstructed in cryo-ET, there is still much room to design new approaches to improve universal reconstruction resolutions. This review summarizes classical mathematical models and deep learning methods among general reconstruction steps. Moreover, we also discuss current limitations and prospects. This review can provide software and methods for each step of the entire procedure from tilt series by cryo-ET to 3D atomic structures. In addition, it can also help more experts in various fields comprehend a recent research trend in cryo-ET. Furthermore, we hope that more researchers can collaborate in developing computational methods and mathematical models for high-resolution three-dimensional structures from cryo-ET datasets.

Learning structural heterogeneity from cryo-electron sub-tomograms with tomoDRGN

Cryo-electron tomography (cryo-ET) allows one to observe macromolecular complexes in their native, spatially contextualized environment. Tools to visualize such complexes at nanometer resolution via iterative alignment and averaging are well-developed but rely on assumptions of structural homogeneity among the complexes under consideration. Recently developed downstream analysis tools allow for some assessment of macromolecular diversity but have limited capacity to represent highly heterogeneous macromolecules, including those undergoing continuous conformational changes. Here, we extend the highly expressive cryoDRGN deep learning architecture, originally created for cryo-electron microscopy single particle analysis, to sub-tomograms. Our new tool, tomoDRGN, learns a continuous low-dimensional representation of structural heterogeneity in cryo-ET datasets while also learning to reconstruct a large, heterogeneous ensemble of structures supported by the underlying data. Using simulated and experimental data, we describe and benchmark architectural choices within tomoDRGN that are uniquely necessitated and enabled by cryo-ET data. We additionally illustrate tomoDRGN's efficacy in analyzing an exemplar dataset, using it to reveal extensive structural heterogeneity among ribosomes imaged in situ.

Subtomogram analysis: The sum of a tomogram's particles reveals molecular structure in situ

Cryo-electron tomography is uniquely suited to provide insights into the molecular architecture of cells and tissue in the native state. While frozen hydrated specimens tolerate sufficient electron doses to distinguish different types of particles in a tomogram, the accumulating beam damage does not allow resolving their detailed molecular structure individually. Statistical methods for subtomogram averaging and classification that coherently enhance the signal of particles corresponding to copies of the same type of macromolecular allow obtaining much higher resolution insights into macromolecules. Here, I review the developments in subtomogram analysis at Wolfgang Baumeister's laboratory that make the dream of structural biology in the native cell become reality.

TomoFlow: Analysis of Continuous Conformational Variability of Macromolecules in Cryogenic Subtomograms based on 3D Dense Optical Flow

Cryogenic Electron Tomography (cryo-ET) allows structural and dynamics studies of macromolecules in situ. Averaging different copies of imaged macromolecules is commonly used to obtain their structure at higher resolution and discrete classification to analyze their dynamics. Instrumental and data processing developments are progressively equipping cryo-ET studies with the ability to escape the trap of classification into a complete continuous conformational variability analysis. In this work, we propose TomoFlow, a method for analyzing macromolecular continuous conformational variability in cryo-ET subtomograms based on a three-dimensional dense optical flow (OF) approach. The resultant lower-dimensional conformational space allows generating movies of macromolecular motion and obtaining subtomogram averages by grouping conformationally similar subtomograms. The animations and the subtomogram group averages reveal accurate trajectories of macromolecular motion based on a novel mathematical model that makes use of OF properties. This paper describes TomoFlow with tests on simulated datasets generated using different techniques, namely Normal Mode Analysis and Molecular Dynamics Simulation. It also shows an application of TomoFlow on a dataset of nucleosomes in situ, which provided promising results coherent with previous findings using the same dataset but without imposing any prior knowledge on the analysis of the conformational variability. The method is discussed with its potential uses and limitations.

Step-by-step guide to efficient subtomogram averaging of virus-like particles with Dynamo

Subtomogram averaging (STA) is a powerful image processing technique in electron tomography used to determine the 3D structure of macromolecular complexes in their native environments. It is a fast growing technique with increasing importance in structural biology. The computational aspect of STA is very complex and depends on a large number of variables. We noticed a lack of detailed guides for STA processing. Also, current publications in this field often lack a documentation that is practical enough to reproduce the results with reasonable effort, which is necessary for the scientific community to grow. We therefore provide a complete, detailed, and fully reproducible processing protocol that covers all aspects of particle picking and particle alignment in STA. The command line-based workflow is fully based on the popular Dynamo software for STA. Within this workflow, we also demonstrate how large parts of the processing pipeline can be streamlined and automatized for increased throughput. This protocol is aimed at users on all levels. It can be used for training purposes, or it can serve as basis to design user-specific projects by taking advantage of the flexibility of Dynamo by modifying and expanding the given pipeline. The protocol is successfully validated using the Electron Microscopy Public Image Archive (EMPIAR) database entry 10164 from immature HIV-1 virus-like particles (VLPs) that describe a geometry often seen in electron tomography.

Coming of Age: Cryo-Electron Tomography as a Versatile Tool to Generate High-Resolution Structures at Cellular/Biological Interfaces

Over the last few years, cryo electron microscopy has become the most important method in structural biology. While 80% of deposited maps are from single particle analysis, electron tomography has grown to become the second most important method. In particular sub-tomogram averaging has matured as a method, delivering structures between 2 and 5 Å from complexes in cells as well as in vitro complexes. While this resolution range is not standard, novel developments point toward a promising future. Here, we provide a guide for the workflow from sample to structure to gain insight into this emerging field.

Current data processing strategies for cryo-electron tomography and subtomogram averaging

Cryo-electron tomography (cryo-ET) can be used to reconstruct three-dimensional (3D) volumes, or tomograms, from a series of tilted two-dimensional images of biological objects in their near-native states in situ or in vitro. 3D subvolumes, or subtomograms, containing particles of interest can be extracted from tomograms, aligned, and averaged in a process called subtomogram averaging (STA). STA overcomes the low signal to noise ratio within the individual subtomograms to generate structures of the particle(s) of interest. In recent years, cryo-ET with STA has increasingly been capable of reaching subnanometer resolution due to improvements in microscope hardware and data processing strategies. There has also been an increase in the number and quality of software packages available to process cryo-ET data with STA. In this review, we describe and assess the data processing strategies available for cryo-ET data and highlight the recent software developments which have enabled the extraction of high-resolution information from cryo-ET datasets.

HEMNMA-3D: Cryo Electron Tomography Method Based on Normal Mode Analysis to Study Continuous Conformational Variability of Macromolecular Complexes

Cryogenic electron tomography (cryo-ET) allows structural determination of biomolecules in their native environment (in situ). Its potential of providing information on the dynamics of macromolecular complexes in cells is still largely unexploited, due to the challenges of the data analysis. The crowded cell environment and continuous conformational changes of complexes make difficult disentangling the data heterogeneity. We present HEMNMA-3D, which is, to the best of our knowledge, the first method for analyzing cryo electron subtomograms in terms of continuous conformational changes of complexes. HEMNMA-3D uses a combination of elastic and rigid-body 3D-to-3D iterative alignments of a flexible 3D reference (atomic structure or electron microscopy density map) to match the conformation, orientation, and position of the complex in each subtomogram. The elastic matching combines molecular mechanics simulation (Normal Mode Analysis of the 3D reference) and experimental, subtomogram data analysis. The rigid-body alignment includes compensation for the missing wedge, due to the limited tilt angle of cryo-ET. The conformational parameters (amplitudes of normal modes) of the complexes in subtomograms obtained through the alignment are processed to visualize the distribution of conformations in a space of lower dimension (typically, 2D or 3D) referred to as space of conformations. This allows a visually interpretable insight into the dynamics of the complexes, by calculating 3D averages of subtomograms with similar conformations from selected (densest) regions and by recording movies of the 3D reference's displacement along selected trajectories through the densest regions. We describe HEMNMA-3D and show its validation using synthetic datasets. We apply HEMNMA-3D to an experimental dataset describing in situ nucleosome conformational variability. HEMNMA-3D software is available freely (open-source) as part of ContinuousFlex plugin of Scipion V3.0 (http://scipion.i2pc.es).

The promise and the challenges of cryo-electron tomography

Structural biologists have traditionally approached cellular complexity in a reductionist manner in which the cellular molecular components are fractionated and purified before being studied individually. This 'divide and conquer' approach has been highly successful. However, awareness has grown in recent years that biological functions can rarely be attributed to individual macromolecules. Most cellular functions arise from their concerted action, and there is thus a need for methods enabling structural studies performed in situ, ideally in unperturbed cellular environments. Cryo-electron tomography (Cryo-ET) combines the power of 3D molecular-level imaging with the best structural preservation that is physically possible to achieve. Thus, it has a unique potential to reveal the supramolecular architecture or 'molecular sociology' of cells and to discover the unexpected. Here, we review state-of-the-art Cryo-ET workflows, provide examples of biological applications, and discuss what is needed to realize the full potential of Cryo-ET.

In situ structure determination by subtomogram averaging

Cryo-tomography and subtomogram averaging are increasingly popular techniques for structural determination of macromolecular complexes in situ. They have the potential to achieve high-resolution views of native complexes, together with the details of their location relative to interacting molecules. The subtomogram averaging (StA) pipelines are well-established, with current developments aiming to optimise each step by reducing manual intervention and user decisions, following similar trends in single-particle approaches that have dramatically increased their popularity. Here, we review the main steps of typical StA workflows. We focus on considerations arising from the fact that the objects of study are embedded within unique crowded environments, and we emphasise those steps where careful decisions need to be made by the user.

Subtomogram averaging from cryo-electron tomograms

Cryo-electron tomography (cryo-ET) allows three-dimensional (3D) visualization of frozen-hydrated biological samples, such as protein complexes and cell organelles, in near-native environments at nanometer scale. Protein complexes that are present in multiple copies in a set of tomograms can be extracted, mutually aligned, and averaged to yield a signal-enhanced 3D structure up to sub-nanometer or even near-atomic resolution. This technique, called subtomogram averaging (StA), is powered by improvements in EM hardware and image processing software. Importantly, StA provides unique biological insights into the structure and function of cellular machinery in close-to-native contexts. In this chapter, we describe the principles and key steps of StA. We briefly cover sample preparation and data collection with an emphasis on image processing procedures related to tomographic reconstruction, subtomogram alignment, averaging, and classification. We conclude by summarizing current limitations and future directions of this technique with a focus on high-resolution StA.

Visualizing membrane trafficking through the electron microscope: cryo-tomography of coat complexes

Coat proteins mediate vesicular transport between intracellular compartments, which is essential for the distribution of molecules within the eukaryotic cell. The global arrangement of coat proteins on the membrane is key to their function, and cryo-electron tomography and subtomogram averaging have been used to study membrane-bound coat proteins, providing crucial structural insight. This review outlines a workflow for the structural elucidation of coat proteins, incorporating recent developments in the collection and processing of cryo-electron tomography data. Recent work on coat protein I, coat protein II and retromer performed on in vitro reconstitutions or in situ is summarized. These studies have answered long-standing questions regarding the mechanisms of membrane binding, polymerization and assembly regulation of coat proteins.

Big data in cryoEM: automated collection, processing and accessibility of EM data

The scope and complexity of cryogenic electron microscopy (cryoEM) data has greatly increased, and will continue to do so, due to recent and ongoing technical breakthroughs that have led to much improved resolutions for macromolecular structures solved using this method. This big data explosion includes single particle data as well as tomographic tilt series, both generally acquired as direct detector movies of ∼10-100 frames per image or per tilt-series. We provide a brief survey of the developments leading to the current status, and describe existing cryoEM pipelines, with an emphasis on the scope of data acquisition, methods for automation, and use of cloud storage and computing.

Cryo-electron microscopy for structural analysis of dynamic biological macromolecules

BACKGROUND

Since the introduction of what became today's standard for cryo-embedding of biological macromolecules at native conditions more than 30years ago, techniques and equipment have been drastically improved and the structure of biomolecules can now be studied at near atomic resolution by cryo-electron microscopy (cryo-EM) while capturing multiple dynamic states. Here we review the recent progress in cryo-EM for structural studies of dynamic biological macromolecules.

SCOPE OF REVIEW

We provide an overview of the cryo-EM method and introduce contemporary studies to investigate biomolecular structure and dynamics, including examples from the recent literature.

MAJOR CONCLUSIONS

Cryo-EM is a powerful tool for the investigation of biological macromolecular structures including analysis of their dynamics by using advanced image-processing algorithms. The method has become even more widely applicable with present-day single particle analysis and electron tomography.

GENERAL SIGNIFICANCE

The cryo-EM method can be used to determine the three-dimensional structure of biomacromolecules in near native condition at close to atomic resolution, and has the potential to reveal conformations of dynamic molecular complexes. This article is part of a Special Issue entitled "Biophysical Exploration of Dynamical Ordering of Biomolecular Systems" edited by Dr. Koichi Kato.

The advent of structural biology in situ by single particle cryo-electron tomography

Single particle tomography (SPT), also known as subtomogram averaging, is a powerful technique uniquely poised to address questions in structural biology that are not amenable to more traditional approaches like X-ray crystallography, nuclear magnetic resonance, and conventional cryoEM single particle analysis. Owing to its potential for in situ structural biology at subnanometer resolution, SPT has been gaining enormous momentum in the last five years and is becoming a prominent, widely used technique. This method can be applied to unambiguously determine the structures of macromolecular complexes that exhibit compositional and conformational heterogeneity, both in vitro and in situ. Here we review the development of SPT, highlighting its applications and identifying areas of ongoing development.

The integrative role of cryo electron microscopy in molecular and cellular structural biology

After gradually moving away from preparation methods prone to artefacts such as plastic embedding and negative staining for cell sections and single particles, the field of cryo electron microscopy (cryo-EM) is now heading off at unprecedented speed towards high-resolution analysis of biological objects of various sizes. This 'revolution in resolution' is happening largely thanks to new developments of new-generation cameras used for recording the images in the cryo electron microscope which have much increased sensitivity being based on complementary metal oxide semiconductor devices. Combined with advanced image processing and 3D reconstruction, the cryo-EM analysis of nucleoprotein complexes can provide unprecedented insights at molecular and atomic levels and address regulatory mechanisms in the cell. These advances reinforce the integrative role of cryo-EM in synergy with other methods such as X-ray crystallography, fluorescence imaging or focussed-ion beam milling as exemplified here by some recent studies from our laboratory on ribosomes, viruses, chromatin and nuclear receptors. Such multi-scale and multi-resolution approaches allow integrating molecular and cellular levels when applied to purified or in situ macromolecular complexes, thus illustrating the trend of the field towards cellular structural biology.

A simple and fast approach for missing-wedge invariant classification of subtomograms extracted from filamentous structures

Unsupervised classification of subtomograms extracted from cryo-electron tomograms is often challenging due to the presence of a missing wedge in tomographic data. Here, we propose a simple new approach to classify subtomograms extracted from cryo-electron tomograms of filamentous objects. This unsupervised classification approach uses the 1D projections of the subtomograms for classification and works independently of the orientations of the missing wedge. We applied this approach to subtomograms from eukaryotic cilia and successfully detected heterogeneity including structural polymorphism of dynein molecules.

Cryo-Electron Tomography and Subtomogram Averaging

Cryo-electron tomography (cryo-ET) allows 3D volumes to be reconstructed from a set of 2D projection images of a tilted biological sample. It allows densities to be resolved in 3D that would otherwise overlap in 2D projection images. Cryo-ET can be applied to resolve structural features in complex native environments, such as within the cell. Analogous to single-particle reconstruction in cryo-electron microscopy, structures present in multiple copies within tomograms can be extracted, aligned, and averaged, thus increasing the signal-to-noise ratio and resolution. This reconstruction approach, termed subtomogram averaging, can be used to determine protein structures in situ. It can also be applied to facilitate more conventional 2D image analysis approaches. In this chapter, we provide an introduction to cryo-ET and subtomogram averaging. We describe the overall workflow, including tomographic data collection, preprocessing, tomogram reconstruction, subtomogram alignment and averaging, classification, and postprocessing. We consider theoretical issues and practical considerations for each step in the workflow, along with descriptions of recent methodological advances and remaining limitations.

Alignment algorithms and per-particle CTF correction for single particle cryo-electron tomography

Single particle cryo-electron tomography (cryoSPT) extracts features from cryo-electron tomograms, followed by 3D classification, alignment and averaging to generate improved 3D density maps of such features. Robust methods to correct for the contrast transfer function (CTF) of the electron microscope are necessary for cryoSPT to reach its resolution potential. Many factors can make CTF correction for cryoSPT challenging, such as lack of eucentricity of the specimen stage, inherent low dose per image, specimen charging, beam-induced specimen motions, and defocus gradients resulting both from specimen tilting and from unpredictable ice thickness variations. Current CTF correction methods for cryoET make at least one of the following assumptions: that the defocus at the center of the image is the same across the images of a tiltseries, that the particles all lie at the same Z-height in the embedding ice, and/or that the specimen, the cryo-electron microscopy (cryoEM) grid and/or the carbon support are flat. These experimental conditions are not always met. We have developed a CTF correction algorithm for cryoSPT without making any of the aforementioned assumptions. We also introduce speed and accuracy improvements and a higher degree of automation to the subtomogram averaging algorithms available in EMAN2. Using motion-corrected images of isolated virus particles as a benchmark specimen, recorded with a DE20 direct detection camera, we show that our CTF correction and subtomogram alignment routines can yield subtomogram averages close to 4/5 Nyquist frequency of the detector under our experimental conditions.

cellPACK: a virtual mesoscope to model and visualize structural systems biology

cellPACK assembles computational models of the biological mesoscale, an intermediate scale (10⁻⁷–10⁻⁸m) between molecular and cellular biology. cellPACK’s modular architecture unites existing and novel packing algorithms to generate, visualize and analyze comprehensive 3D models of complex biological environments that integrate data from multiple experimental systems biology and structural biology sources. cellPACK is currently available as open source code, with tools for validation of models and with recipes and models for five biological systems: blood plasma, cytoplasm, synaptic vesicles, HIV and a mycoplasma cell. We have applied cellPACK to model distributions of HIV envelope protein to test several hypotheses for consistency with experimental observations. Biologists, educators, and outreach specialists can interact with cellPACK models, develop new recipes and perform packing experiments through scripting and graphical user interfaces at http://cellPACK.org.

Structural analysis of supramolecular assemblies by cryo-electron tomography

Structural analysis of macromolecular assemblies in their physiological environment is a challenging task that is instrumental in answering fundamental questions in cellular and molecular structural biology. The continuous development of computational and analytical tools for cryo-electron tomography (cryo-ET) enables the study of these assemblies at a resolution of a few nanometers. Through the implementation of thinning procedures, cryo-ET can now be applied to the reconstruction of macromolecular structures located inside thick regions of vitrified cells and tissues, thus becoming a central tool for structural determinations in various biological disciplines. Here, we focus on the successful in situ applications of cryo-ET to reveal structures of macromolecular complexes within eukaryotic cells.

Optimal and fast rotational alignment of volumes with missing data in Fourier space

Electron tomography of intact cells has the potential to reveal the entire cellular content at a resolution corresponding to individual macromolecular complexes. Characterization of macromolecular complexes in tomograms is nevertheless an extremely challenging task due to the high level of noise, and due to the limited tilt angle that results in missing data in Fourier space. By identifying particles of the same type and averaging their 3D volumes, it is possible to obtain a structure at a more useful resolution for biological interpretation. Currently, classification and averaging of sub-tomograms is limited by the speed of computational methods that optimize alignment between two sub-tomographic volumes. The alignment optimization is hampered by the fact that the missing data in Fourier space has to be taken into account during the rotational search. A similar problem appears in single particle electron microscopy where the random conical tilt procedure may require averaging of volumes with a missing cone in Fourier space. We present a fast implementation of a method guaranteed to find an optimal rotational alignment that maximizes the constrained cross-correlation function (cCCF) computed over the actual overlap of data in Fourier space.

One number does not fit all: mapping local variations in resolution in cryo-EM reconstructions

The resolution of density maps from single particle analysis is usually measured in terms of the highest spatial frequency to which consistent information has been obtained. This calculation represents an average over the entire reconstructed volume. In practice, however, substantial local variations in resolution may occur, either from intrinsic properties of the specimen or for technical reasons such as a non-isotropic distribution of viewing orientations. To address this issue, we propose the use of a space-frequency representation, the short-space Fourier transform, to assess the quality of a density map, voxel-by-voxel, i.e. by local resolution mapping. In this approach, the experimental volume is divided into small subvolumes and the resolution determined for each of them. It is illustrated in applications both to model data and to experimental density maps. Regions with lower-than-average resolution may be mobile components or ones with incomplete occupancy or result from multiple conformational states. To improve the interpretability of reconstructions, we propose an adaptive filtering approach that reconciles the resolution to which individual features are calculated with the results of the local resolution map.

Projection-based volume alignment

When heterogeneous samples of macromolecular assemblies are being examined by 3D electron microscopy (3DEM), often multiple reconstructions are obtained. For example, subtomograms of individual particles can be acquired from tomography, or volumes of multiple 2D classes can be obtained by random conical tilt reconstruction. Of these, similar volumes can be averaged to achieve higher resolution. Volume alignment is an essential step before 3D classification and averaging. Here we present a projection-based volume alignment (PBVA) algorithm. We select a set of projections to represent the reference volume and align them to a second volume. Projection alignment is achieved by maximizing the cross-correlation function with respect to rotation and translation parameters. If data are missing, the cross-correlation functions are normalized accordingly. Accurate alignments are obtained by averaging and quadratic interpolation of the cross-correlation maximum. Comparisons of the computation time between PBVA and traditional 3D cross-correlation methods demonstrate that PBVA outperforms the traditional methods. Performance tests were carried out with different signal-to-noise ratios using modeled noise and with different percentages of missing data using a cryo-EM dataset. All tests show that the algorithm is robust and highly accurate. PBVA was applied to align the reconstructions of a subcomplex of the NADH: ubiquinone oxidoreductase (Complex I) from the yeast Yarrowia lipolytica, followed by classification and averaging.

A collaborative framework for 3D alignment and classification of heterogeneous subvolumes in cryo-electron tomography

The limitation of using low electron doses in non-destructive cryo-electron tomography of biological specimens can be partially offset via averaging of aligned and structurally homogeneous subsets present in tomograms. This type of sub-volume averaging is especially challenging when multiple species are present. Here, we tackle the problem of conformational separation and alignment with a "collaborative" approach designed to reduce the effect of the "curse of dimensionality" encountered in standard pair-wise comparisons. Our new approach is based on using the nuclear norm as a collaborative similarity measure for alignment of sub-volumes, and by exploiting the presence of symmetry early in the processing. We provide a strict validation of this method by analyzing mixtures of intact simian immunodeficiency viruses SIV mac239 and SIV CP-MAC. Electron microscopic images of these two virus preparations are indistinguishable except for subtle differences in conformation of the envelope glycoproteins displayed on the surface of each virus particle. By using the nuclear norm-based, collaborative alignment method presented here, we demonstrate that the genetic identity of each virus particle present in the mixture can be assigned based solely on the structural information derived from single envelope glycoproteins displayed on the virus surface.

Electron tomography of paracrystalline 2D arrays

Paracrystalline arrays possess specific types of disorder that reduce the structural information as well as resolution when spatially averaged over repeating motifs. Electron tomography combined with motif classification and averaging can solve the heterogeneity problem and provide information on the structural elements that give rise to the disorder. This chapter describes procedures that would be used in a typical tomography application to identify and characterize a paracrystalline specimen. Particular emphasis is given to actively contracting insect flight muscle, a specimen with particularly difficult to characterize structural heterogeneity and 2D paracrystalline arrays of myosin-V, from which a particularly high resolution motif average was obtained. All aspects of the study are described including data collection, merging of micrographs to produce the tomogram, alignment to an invariant structural element, classification and averaging of heterogeneous structures, and reassembly of focused class averages into high signal-to-noise ratio representations of the original raw repeats. Particular emphasis is placed on limitations of the various processes to produce the final class averages.

Cryo-electron microscopy--a primer for the non-microscopist

Cryo-electron microscopy (cryo-EM) is increasingly becoming a mainstream technology for studying the architecture of cells, viruses and protein assemblies at molecular resolution. Recent developments in microscope design and imaging hardware, paired with enhanced image processing and automation capabilities, are poised to further advance the effectiveness of cryo-EM methods. These developments promise to increase the speed and extent of automation, and to improve the resolutions that may be achieved, making this technology useful to determine a wide variety of biological structures. Additionally, established modalities for structure determination, such as X-ray crystallography and nuclear magnetic resonance spectroscopy, are being routinely integrated with cryo-EM density maps to achieve atomic-resolution models of complex, dynamic molecular assemblies. In this review, which is directed towards readers who are not experts in cryo-EM methodology, we provide an overview of emerging themes in the application of this technology to investigate diverse questions in biology and medicine. We discuss the ways in which these methods are being used to study structures of macromolecular assemblies that range in size from whole cells to small proteins. Finally, we include a description of how the structural information obtained by cryo-EM is deposited and archived in a publicly accessible database.

Unraveling the structure of membrane proteins in situ by transfer function corrected cryo-electron tomography

Cryo-electron tomography in combination with subtomogram averaging allows to investigate the structure of protein assemblies in their natural environment in a close to live state. To make full use of the structural information contained in tomograms it is necessary to analyze the contrast transfer function (CTF) of projections and to restore the phases of higher spatial frequencies. CTF correction is however hampered by the difficulty of determining the actual defocus values from tilt series data, which is due to the low signal-to-noise ratio of electron micrographs. In this study, an extended acquisition scheme is introduced that enables an independent CTF determination. Two high-dose images are recorded along the tilt axis on both sides of each projection, which allow an accurate determination of the defocus values of these images. These values are used to calculate the CTF for each image of the tilt series. We applied this scheme to the mycobacterial outer membrane protein MspA reconstituted in lipid vesicles and tested several variants of CTF estimation in combination with subtomogram averaging and correction of the modulation transfer function (MTF). The 3D electron density map of MspA was compared with a structure previously determined by X-ray crystallography. We were able to demonstrate that structural information up to a resolution of 16.8Å can be recovered using our CTF correction approach, whereas the uncorrected 3D map had a resolution of only 26.2Å.

Creating an infrastructure for high-throughput high-resolution cryogenic electron microscopy

New instrumentation for three-dimensional electron microscopy is facilitating an increase in the throughput of data collection and reconstruction. The increase in throughput creates bottlenecks in the workflow for storing and processing the image data. Here we describe the creation and quantify the throughput of a high-throughput infrastructure supporting collection of three-dimensional data collection.

High precision alignment of cryo-electron subtomograms through gradient-based parallel optimization

BACKGROUND

Cryo-electron tomography emerges as an important component for structural system biology. It not only allows the structural characterization of macromolecular complexes, but also the detection of their cellular localizations in near living conditions. However, the method is hampered by low resolution, missing data and low signal-to-noise ratio (SNR). To overcome some of these difficulties and enhance the nominal resolution one can align and average a large set of subtomograms. Existing methods for obtaining the optimal alignments are mostly based on an exhaustive scanning of all but discrete relative rigid transformations (i.e. rotations and translations) of one subtomogram with respect to the other.

RESULTS

In this paper, we propose gradient-guided alignment methods based on two popular subtomogram similarity measures, a real space as well as a Fourier-space constrained score. We also propose a stochastic parallel refinement method that increases significantly the efficiency for the simultaneous refinement of a set of alignment candidates. We estimate that our stochastic parallel refinement is on average about 20 to 40 fold faster in comparison to the standard independent refinement approach. Results on simulated data of model complexes and experimental structures of protein complexes show that even for highly distorted subtomograms and with only a small number of very sparsely distributed initial alignment seeds, our combined methods can accurately recover true transformations with a substantially higher precision than the scanning based alignment methods.

CONCLUSIONS

Our methods increase significantly the efficiency and accuracy for subtomogram alignments, which is a key factor for the systematic classification of macromolecular complexes in cryo-electron tomograms of whole cells.

Computational separation of conformational heterogeneity using cryo-electron tomography and 3D sub-volume averaging

We have previously used cryo-electron tomography combined with sub-volume averaging and classification to obtain 3D structures of macromolecular assemblies in cases where a single dominant species was present, and applied these methods to the analysis of a variety of trimeric HIV-1 and SIV envelope glycoproteins (Env). Here, we extend these studies by demonstrating automated, iterative, missing wedge-corrected 3D image alignment and classification methods to distinguish multiple conformations that are present simultaneously. We present a method for measuring the spatial distribution of the vector elements representing distinct conformational states of Env. We identify data processing strategies that allow clear separation of the previously characterized closed and open conformations, as well as unliganded and antibody-liganded states of Env when they are present in mixtures. We show that identifying and removing spikes with the lowest signal-to-noise ratios improves the overall accuracy of alignment between individual Env sub-volumes, and that alignment accuracy, in turn, determines the success of image classification in assessing conformational heterogeneity in heterogeneous mixtures. We validate these procedures for computational separation by successfully separating and reconstructing distinct 3D structures for unliganded and antibody-liganded as well as open and closed conformations of Env present simultaneously in mixtures.

Dynamo: a flexible, user-friendly development tool for subtomogram averaging of cryo-EM data in high-performance computing environments

Dynamo is a new software package for subtomogram averaging of cryo Electron Tomography (cryo-ET) data with three main goals: first, Dynamo allows user-transparent adaptation to a variety of high-performance computing platforms such as GPUs or CPU clusters. Second, Dynamo implements user-friendliness through GUI interfaces and scripting resources. Third, Dynamo offers user-flexibility through a plugin API. Besides the alignment and averaging procedures, Dynamo includes native tools for visualization and analysis of results and data, as well as support for third party visualization software, such as Chimera UCSF or EMAN2. As a demonstration of these functionalities, we studied bacterial flagellar motors and showed automatically detected classes with absent and present C-rings. Subtomogram averaging is a common task in current cryo-ET pipelines, which requires extensive computational resources and follows a well-established workflow. However, due to the data diversity, many existing packages offer slight variations of the same algorithm to improve results. One of the main purposes behind Dynamo is to provide explicit tools to allow the user the insertion of custom designed procedures - or plugins - to replace or complement the native algorithms in the different steps of the processing pipeline for subtomogram averaging without the burden of handling parallelization. Custom scripts that implement new approaches devised by the user are integrated into the Dynamo data management system, so that they can be controlled by the GUI or the scripting capacities. Dynamo executables do not require licenses for third party commercial software. Sources, executables and documentation are freely distributed on http://www.dynamo-em.org.

PyTom: a python-based toolbox for localization of macromolecules in cryo-electron tomograms and subtomogram analysis

Cryo-electron tomography (CET) is a three-dimensional imaging technique for structural studies of macromolecules under close-to-native conditions. In-depth analysis of macromolecule populations depicted in tomograms requires identification of subtomograms corresponding to putative particles, averaging of subtomograms to enhance their signal, and classification to capture the structural variations among them. Here, we introduce the open-source platform PyTom that unifies standard tomogram processing steps in a python toolbox. For subtomogram averaging, we implemented an adaptive adjustment of scoring and sampling that clearly improves the resolution of averages compared to static strategies. Furthermore, we present a novel stochastic classification method that yields significantly more accurate classification results than two deterministic approaches in simulations. We demonstrate that the PyTom workflow yields faithful results for alignment and classification of simulated and experimental subtomograms of ribosomes and GroEL(14)/GroEL(14)GroES(7), respectively, as well as for the analysis of ribosomal 60S subunits in yeast cell lysate. PyTom enables parallelized processing of large numbers of tomograms, but also provides a convenient, sustainable environment for algorithmic development.

Putting structure into context: fitting of atomic models into electron microscopic and electron tomographic reconstructions

A complete understanding of complex dynamic cellular processes such as cell migration or cell adhesion requires the integration of atomic level structural information into the larger cellular context. While direct atomic-level information at the cellular level remains inaccessible, electron microscopy, electron tomography and their associated computational image processing approaches have now matured to a point where sub-cellular structures can be imaged in three dimensions at the nanometer scale. Atomic-resolution information obtained by other means can be combined with this data to obtain three-dimensional models of large macromolecular assemblies in their cellular context. This article summarizes some recent advances in this field.

Interaction of complexes I, III, and IV within the bovine respirasome by single particle cryoelectron tomography

The respirasome is a multisubunit supercomplex of the respiratory chain in mitochondria. Here we report the 3D reconstruction of the bovine heart respirasome, composed of dimeric complex III and single copies of complex I and IV, at about 2.2-nm resolution, determined by cryoelectron tomography and subvolume averaging. Fitting of X-ray structures of single complexes I, III(2), and IV with high fidelity allows interpretation of the model at the level of secondary structures and shows how the individual complexes interact within the respirasome. Surprisingly, the distance between cytochrome c binding sites of complexes III(2) and IV is about 10 nm. Modeling indicates a loose interaction between the three complexes and provides evidence that lipids are gluing them at the interfaces.

Classification of electron sub-tomograms with neural networks and its application to template-matching

Classification of electron sub-tomograms is a challenging task, due the missing-wedge and the low signal-to-noise ratio of the data. Classification algorithms tend to classify data according to their orientation to the missing-wedge, rather than to the underlying signal. Here we use a neural network approach, called the Kernel Density Estimator Self-Organizing Map (KerDenSOM3D), which we have implemented in three-dimensions (3D), also having compensated for the missing-wedge, and we comprehensively compare it to other classification methods. For this purpose, we use various simulated macromolecules, as well as tomographically reconstructed in vitro GroEL and GroEL/GroES molecules. We show that the performance of this classification method is superior to previously used algorithms. Furthermore, we show how this algorithm can be used to provide an initial cross-validation of template-matching approaches. For the example of sub-tomogram classification extracted from cellular tomograms of Mycoplasma pneumonia and Spiroplasma melliferum cells, we show the bias of template-matching, and by using differing search and classification areas, we demonstrate how the bias can be significantly reduced.