Unsupervised classification of single particles by cluster tracking in multi-dimensional space

Focused classifications and refinements in high-resolution single particle cryo-EM analysis

Recent advances in cryo electron microscopy (cryo-EM) and image processing provide new opportunities to analyse drug targets at high resolution. However, structural heterogeneity limits resolution in many practical cases, hence restricting the level at which structural details can be analysed and drug design be performed. As structural disorder is not spread throughout the entire structure of a given macromolecular complex but instead is found in certain regions that move with respect to others and covering molecular scales from domain conformational changes up to the level of side chain conformations in ligand binding pockets, it is possible to focus the attention on those regions and the associated relative movements. Here we show how the usage of focused classifications and refinements provide insights into global conformational arrangements, exemplified on the human ribosome and on the cannabinoid G protein coupled receptor (GPCR), and how they can improve the local map resolution from an essentially disordered region to the 3-4 Å and finally to the 2 Å resolution range. A systematic analysis with variable spherical masks during focused refinement is presented showing that the choice of an optimal mask size helps refining to high resolution. This study covers several practical approaches on 4 examples illustrating how important mask size & shape and including neighbouring structural elements are for a focused analysis of a macromolecular complex. Such methods will be crucial for cryo-EM structure-based drug design of various medical targets and are applicable to single particle cryo-EM and electron tomography data.

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).

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.

StructMap: Elastic Distance Analysis of Electron Microscopy Maps for Studying Conformational Changes

Single-particle electron microscopy (EM) has been shown to be very powerful for studying structures and associated conformational changes of macromolecular complexes. In the context of analyzing conformational changes of complexes, distinct EM density maps obtained by image analysis and three-dimensional (3D) reconstruction are usually analyzed in 3D for interpretation of structural differences. However, graphic visualization of these differences based on a quantitative analysis of elastic transformations (deformations) among density maps has not been done yet due to a lack of appropriate methods. Here, we present an approach that allows such visualization. This approach is based on statistical analysis of distances among elastically aligned pairs of EM maps (one map is deformed to fit the other map), and results in visualizing EM maps as points in a lower-dimensional distance space. The distances among points in the new space can be analyzed in terms of clusters or trajectories of points related to potential conformational changes. The results of the method are shown with synthetic and experimental EM maps at different resolutions.

Dissecting random and systematic differences between noisy composite data sets

A multidimensional scaling analysis of pairwise correlation coefficients is presented which positions data sets in a sphere with unit radius of an abstract, low-dimensional space at radii inversely proportional to their levels of random error and at spherical angles related to their mutual systematic differences. This reduction in dimensionality can not only be used for classification purposes, but also to derive data-set relations on a continuous scale.

Composite data sets measured on different objects are usually affected by random errors, but may also be influenced by systematic (genuine) differences in the objects themselves, or the experimental conditions. If the individual measurements forming each data set are quantitative and approximately normally distributed, a correlation coefficient is often used to compare data sets. However, the relations between data sets are not obvious from the matrix of pairwise correlations since the numerical value of the correlation coefficient is lowered by both random and systematic differences between the data sets. This work presents a multidimensional scaling analysis of the pairwise correlation coefficients which places data sets into a unit sphere within low-dimensional space, at a position given by their CC* values [as defined by Karplus & Diederichs (2012 ▸), Science, 336, 1030–1033] in the radial direction and by their systematic differences in one or more angular directions. This dimensionality reduction can not only be used for classification purposes, but also to derive data-set relations on a continuous scale. Projecting the arrangement of data sets onto the subspace spanned by systematic differences (the surface of a unit sphere) allows, irrespective of the random-error levels, the identification of clusters of closely related data sets. The method gains power with increasing numbers of data sets. It is illustrated with an example from low signal-to-noise ratio image processing, and an application in macromolecular crystallography is shown, but the approach is completely general and thus should be widely applicable.

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

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

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.

Cryo-electron Microscopy Analysis of Structurally Heterogeneous Macromolecular Complexes

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

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.

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

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

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.

Trajectories of the ribosome as a Brownian nanomachine

A Brownian machine, a tiny device buffeted by the random motions of molecules in the environment, is capable of exploiting these thermal motions for many of the conformational changes in its work cycle. Such machines are now thought to be ubiquitous, with the ribosome, a molecular machine responsible for protein synthesis, increasingly regarded as prototypical. Here we present a new analytical approach capable of determining the free-energy landscape and the continuous trajectories of molecular machines from a large number of snapshots obtained by cryogenic electron microscopy. We demonstrate this approach in the context of experimental cryogenic electron microscope images of a large ensemble of nontranslating ribosomes purified from yeast cells. The free-energy landscape is seen to contain a closed path of low energy, along which the ribosome exhibits conformational changes known to be associated with the elongation cycle. Our approach allows model-free quantitative analysis of the degrees of freedom and the energy landscape underlying continuous conformational changes in nanomachines, including those important for biological function.

Hybrid Electron Microscopy Normal Mode Analysis graphical interface and protocol

This article presents an integral graphical interface to the Hybrid Electron Microscopy Normal Mode Analysis (HEMNMA) approach that was developed for capturing continuous motions of large macromolecular complexes from single-particle EM images. HEMNMA was shown to be a good approach to analyze multiple conformations of a macromolecular complex but it could not be widely used in the EM field due to a lack of an integral interface. In particular, its use required switching among different software sources as well as selecting modes for image analysis was difficult without the graphical interface. The graphical interface was thus developed to simplify the practical use of HEMNMA. It is implemented in the open-source software package Xmipp 3.1 (http://xmipp.cnb.csic.es) and only a small part of it relies on MATLAB that is accessible through the main interface. Such integration provides the user with an easy way to perform the analysis of macromolecular dynamics and forms a direct connection to the single-particle reconstruction process. A step-by-step HEMNMA protocol with the graphical interface is given in full details in Supplementary material. The graphical interface will be useful to experimentalists who are interested in studies of continuous conformational changes of macromolecular complexes beyond the modeling of continuous heterogeneity in single particle reconstruction.

Surface-Constrained 3D Reconstruction in Cryo-EM

Random spherically-constrained (RSC) reconstruction is a new form of single particle reconstruction (SPR) using cryo-EM images of membrane proteins embedded in spherical lipid vesicles to generate a 3D protein structure. The method has many advantages over conventional SPR, including a more native environment for protein particles and an initial estimate of the particle's angular orientation. These advances allow us to determine structures of membrane proteins such as ion channels and derive more reliable structure estimates. We present an algorithm that relates conventional SPR to the RSC model, and generally, to projection images of particles embedded with an axis parallel to the local normal of a general 2D manifold. We illustrate the performance of this algorithm in the spherical system using synthetic data.

tmRNA on its way through the ribosome: two steps of resume, and what next?

Trans-translation is a universal quality-control process eubacteria use to degrade incompletely synthesized proteins and rescue ribosome stalled on defective mRNAs. This process is facilitated by a ribonucleoprotein complex composed of transfer-messenger RNA (tmRNA)-a chimera made of a tRNA-like molecule and a short open reading frame (ORF) -and small protein B (SmpB). Determination of the structure of tmRNA and SmpB in complex with the ribosome, at the stage when translation has resumed on tmRNA, has provided an increased understanding of the structure of tmRNA as it transits the ribosome, and unique insights into the complex mechanism of template switching on the ribosome and SmpB-driven selection of the correct reading frame on tmRNA's ORF.

Accurate modeling of single-particle cryo-EM images quantitates the benefits expected from using Zernike phase contrast

The use of a Zernike-type phase plate in biologic cryo-electron microscopy allows the imaging, without using defocus, of what are predominantly phase objects. It is thought that such phase-plate implementations might result in higher quality images, free from the problems of CTF correction that occur when images must be recorded at extremely high values of defocus. In single-particle cryo-electron microscopy it is hoped that these improvements in image quality will facilitate work on structures that have proved difficult to study, either because of their relatively small size or because the structures are not completely homogeneous. There is still a need, however, to quantitate how much improvement can be gained by using a phase plate for single-particle cryo-electron microscopy. We present a method for quantitatively modeling the images recorded with 200keV electrons, for single particles embedded in vitreous ice. We then investigate what difference the use of a phase-plate device could have on the processing of single-particle data. We confirm that using a phase plate results in single-particle datasets in which smaller molecules can be detected, particles can be more accurately aligned and problems of heterogeneity can be more easily addressed.

Single molecule microscopy methods for the study of DNA origami structures

Single molecule microscopy techniques play an important role in the investigation of advanced DNA structures such as those created by the DNA origami method. Three single molecule microscopy techniques are particularly interesting for the investigation of complex self-assembled three-dimensional (3D) DNA nanostructures, namely single molecule fluorescence microscopy, atomic force microscopy (AFM), and cryogenic transmission electron microscopy (cryo-EM). Here we discuss the strengths of these three techniques and demonstrate how their interplay can yield very important and unique new insights into the structure and conformation of advanced biological nanostructures. The applications of the three single molecule microscopy techniques are illustrated by focusing on a self-assembled DNA origami 3D box nanostructure. Its size and structure were studied by AFM and cryo-EM, while the lid opening, which can be controlled by the addition of oligonucleotide keys, was recorded by Förster/fluorescence resonance energy transfer (FRET) spectroscopy.

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.

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

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

Automated multi-model reconstruction from single-particle electron microscopy data

Biological macromolecules can adopt multiple conformational and compositional states due to structural flexibility and alternative subunit assemblies. This structural heterogeneity poses a major challenge in the study of macromolecular structure using single-particle electron microscopy. We propose a fully automated, unsupervised method for the three-dimensional reconstruction of multiple structural models from heterogeneous data. As a starting reference, our method employs an initial structure that does not account for any heterogeneity. Then, a multi-stage clustering is used to create multiple models representative of the heterogeneity within the sample. The multi-stage clustering combines an existing approach based on Multivariate Statistical Analysis to perform clustering within individual Euler angles, and a newly developed approach to sort out class averages from individual Euler angles into homogeneous groups. Structural models are computed from individual clusters. The whole data classification is further refined using an iterative multi-model projection-matching approach. We tested our method on one synthetic and three distinct experimental datasets. The tests include the cases where a macromolecular complex exhibits structural flexibility and cases where a molecule is found in ligand-bound and unbound states. We propose the use of our approach as an efficient way to reconstruct distinct multiple models from heterogeneous data.

Methods for three-dimensional reconstruction of heterogeneous assemblies

Electron microscopy (EM) has developed into an important method for determining the three-dimensional (3D) structures of biological complexes, in particular of isolated macromolecular complexes in vitrified solution (cryo-EM of "single particles"). One of the consequences of studying complexes in solution rather than in a crystal lattice is that they are less constrained to adopt a single conformation. It is a common problem in single-particle analysis that samples of purified macromolecules can be structurally heterogeneous, with molecules adopting different conformations, corresponding to different functional states. In the case of multisubunit assemblies, there may also be heterogeneity of assembly or ligand binding. Heterogeneity limits the accuracy and resolution of 3D structures, since different conformations will contribute to a single 3D map and variable parts of the structure will be smeared out. Therefore, a new group of image processing methods has been developed to deal with the problems of detecting and sorting structural heterogeneity. The basic problem is to discriminate the source of image variations, and then to separate the images into homogeneous subsets for separate reconstruction. Variations in image features can arise from different particle orientations, variations in conformation and/or ligand binding, and noise fluctuations in the low signal-to-noise ratio images typical of cryo-EM. Here, we present a review of approaches developed to deal with these problems, along with examples of the application of a method based on multivariate statistical analysis to both model and real data. The methods have been used to discriminate small differences in size, conformation and ligand binding, and to obtain high quality, reliable reconstructions of multiple structures from mixed data sets.

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

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

Exploring conformational modes of macromolecular assemblies by multiparticle cryo-EM

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

Chapter 1 Visualizing functional flexibility by three-dimensional electron microscopy reconstructing complex I of the mitochondrial respiratory chain

Complex I is the major entry point in the bacterial and mitochondrial respiratory chain. Structural knowledge of the enzyme is still limited because of its large size and complicated architecture. Only the structure of the hydrophilic domain of a bacterial Complex I has been solved to high resolution by X-ray crystallography. To date, no X-ray structure of the complete enzyme has been reported, and most structural information of the holoenzyme has been obtained by 3-D electron microscopy. In this chapter the methods are described used for determining the 3-D reconstruction of Complex I that revealed for the first time a detailed and reproducible domain structure. Complex I is a highly flexible molecule, and methods for calculating the 3-D reconstruction from electron micrographs must take into account this heterogeneity. The techniques described in this chapter can be modified and adapted for the study of more heterogeneous preparations, such as functionalized Complex I. In addition, these techniques are not restricted to the structure determination of Complex I but are appropriate for the 3-D reconstruction of macromolecular assemblies from electron micrographs when inhomogeneities may be present.

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

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

A method for the alignment of heterogeneous macromolecules from electron microscopy

We propose a feature-based image alignment method for single-particle electron microscopy that is able to accommodate various similarity scoring functions while efficiently sampling the two-dimensional transformational space. We use this image alignment method to evaluate the performance of a scoring function that is based on the Mutual Information (MI) of two images rather than one that is based on the cross-correlation function. We show that alignment using MI for the scoring function has far less model-dependent bias than is found with cross-correlation based alignment. We also demonstrate that MI improves the alignment of some types of heterogeneous data, provided that the signal-to-noise ratio is relatively high. These results indicate, therefore, that use of MI as the scoring function is well suited for the alignment of class-averages computed from single-particle images. Our method is tested on data from three model structures and one real dataset.

Problems in fitting high resolution structures into electron microscopic reconstructions

Great advances have been made in electron microscopy (EM) over the past decade, with the result that a number of protein complexes have been solved at near-atomic resolution using EM imaging. However, only a limited number of such complexes are expected to have the high degree of internal order needed to achieve this type of resolution. Many other complexes and polymers will be visualized and reconstructed by EM at an intermediate level of resolution, where the polypeptide chain cannot be directly traced. Crystal and nuclear magnetic resonance structures for components or subunits of these higher-order assemblies are frequently available. One of the greatest strengths of EM continues to be the ability to dock high-resolution structures of components into low or intermediate resolution reconstructions of assemblies to build pseudoatomic models for quaternary structure. This review discusses the strengths and limitations of this approach, with particular emphasis on protein polymers. I discuss how limitations in resolution can lead to ambiguities in building models, and these cannot be always be resolved with available data. The use of homology models for quaternary structure are particularly problematic, given accumulating evidence for the divergence of quaternary structures at the same time that tertiary structure can be conserved.

Folding and assembly of large macromolecular complexes monitored by hydrogen-deuterium exchange and mass spectrometry

Recent advances in protein mass spectrometry (MS) have enabled determinations of hydrogen deuterium exchange (HDX) in large macromolecular complexes. HDX-MS became a valuable tool to follow protein folding, assembly and aggregation. The methodology has a wide range of applications in biotechnology ranging from quality control for over-expressed proteins and their complexes to screening of potential ligands and inhibitors. This review provides an introduction to protein folding and assembly followed by the principles of HDX and MS detection, and concludes with selected examples of applications that might be of interest to the biotechnology community.

Cross-correlation of common lines: a novel approach for single-particle reconstruction of a structure containing a flexible domain

We describe a novel approach to sorting class averages of a structure in multiple conformational states in order to generate 3D reconstructions that account for conformational variability present in the sample. The method assumes that the relative Euler angles between class averages are known, then uses a common lines approach to match any given class against a set of distinct conformations from a selected view of the structure. We show the effectiveness of the method both on model data and on an experimental dataset for which the conformational variability is limited to a defined region within the structure. During our studies of hepatitis C virus (HCV) internal ribosome entry site (IRES) interaction with the human translation initiation factor eIF3, we observed that the IRES RNA included a flexible region holding multiple conformations. While current classification methods were used to produce two-dimensional averages of the complex showing these different conformations, no method existed for relating these averages in three dimensions. Our approach overcame these limitations, giving us structural insight that was previously not possible.

Classification of heterogeneous electron microscopic projections into homogeneous subsets

The co-existence of different states of a macromolecular complex in samples used by three-dimensional electron microscopy (3D-EM) constitutes a serious challenge. The single particle method applied directly to such heterogeneous sets is unable to provide useful information about the encountered conformational diversity and produces reconstructions with severely reduced resolution. One approach to solving this problem is to partition heterogeneous projection set into homogeneous components and apply existing reconstruction techniques to each of them. Due to the nature of the projection images and the high noise level present in them, this classification task is difficult. A method is presented to achieve the desired classification by using a novel image similarity measure and solving the corresponding optimization problem. Unlike the majority of competing approaches, the presented method employs unsupervised classification (it does not require any prior knowledge about the objects being classified) and does not involve a 3D reconstruction procedure. We demonstrate a fast implementation of this method, capable of classifying projection sets that originate from 3D-EM. The method's performance is evaluated on synthetically generated data sets produced by projecting 3D objects that resemble biological structures.