Seeing GroEL at 6 A resolution by single particle electron cryomicroscopy

Observation of a single protein by ultrafast X-ray diffraction

The idea of using ultrashort X-ray pulses to obtain images of single proteins frozen in time has fascinated and inspired many. It was one of the arguments for building X-ray free-electron lasers. According to theory, the extremely intense pulses provide sufficient signal to dispense with using crystals as an amplifier, and the ultrashort pulse duration permits capturing the diffraction data before the sample inevitably explodes. This was first demonstrated on biological samples a decade ago on the giant mimivirus. Since then, a large collaboration has been pushing the limit of the smallest sample that can be imaged. The ability to capture snapshots on the timescale of atomic vibrations, while keeping the sample at room temperature, may allow probing the entire conformational phase space of macromolecules. Here we show the first observation of an X-ray diffraction pattern from a single protein, that of Escherichia coli GroEL which at 14 nm in diameter is the smallest biological sample ever imaged by X-rays, and demonstrate that the concept of diffraction before destruction extends to single proteins. From the pattern, it is possible to determine the approximate orientation of the protein. Our experiment demonstrates the feasibility of ultrafast imaging of single proteins, opening the way to single-molecule time-resolved studies on the femtosecond timescale.

Facile hermetic TEM grid preparation for molecular imaging of hydrated biological samples at room temperature

Although structures of vitrified supramolecular complexes have been determined at near-atomic resolution, elucidating in situ molecular structure in living cells remains a challenge. Here, we report a straightforward liquid cell technique, originally developed for real-time visualization of dynamics at a liquid-gas interface using transmission electron microscopy, to image wet biological samples. Due to the scattering effects from the liquid phase, the micrographs display an amplitude contrast comparable to that observed in negatively stained samples. We succeed in resolving subunits within the protein complex GroEL imaged in a buffer solution at room temperature. Additionally, we capture various stages of virus cell entry, a process for which only sparse structural data exists due to their transient nature. To scrutinize the morphological details further, we used individual particle electron tomography for 3D reconstruction of each virus. These findings showcase this approach potential as an efficient, cost-effective complement to other microscopy technique in addressing biological questions at the molecular level.

Cryo-EM image alignment: From pair-wise to joint with deep unsupervised difference learning

Cryo-electron microscopy (cryo-EM) single-particle analysis is a revolutionary imaging technique to resolve and visualize biomacromolecules. Image alignment in cryo-EM is an important and basic step to improve the precision of the image distance calculation. However, it is a very challenging task due to high noise and low signal-to-noise ratio. Therefore, we propose a new deep unsupervised difference learning (UDL) strategy with novel pseudo-label guided learning network architecture and apply it to pair-wise image alignment in cryo-EM. The training framework is fully unsupervised. Furthermore, a variant of UDL called joint UDL (JUDL), is also proposed, which is capable of utilizing the similarity information of the whole dataset and thus further increase the alignment precision. Assessments on both real-world and synthetic cryo-EM single-particle image datasets suggest the new unsupervised joint alignment method can achieve more accurate alignment results. Our method is highly efficient by taking advantages of GPU devices. The source code of our methods is publicly available at "http://www.csbio.sjtu.edu.cn/bioinf/JointUDL/" for academic use.

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

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

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

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

Fast Cryo-EM Image Alignment Algorithm Using Power Spectrum Features

Cryo-electron microscopy (cryo-EM) single-particle image analysis is a powerful technique to resolve structures of biomacromolecules, while the challenge is that the cryo-EM image is of a low signal-to-noise ratio. For both two-dimensional image analysis and three-dimensional density map analysis, image alignment is an important step to improve the precision of the image distance calculation. In this paper, we introduce a new algorithm for performing two-dimensional pairwise alignment for cryo-EM particle images, which is based on the Fourier transform and power spectrum analysis. Compared to the existing heuristic iterative alignment methods, our method utilizes the signal distribution and signal feature on images' power spectrum to directly compute the alignment parameters. It does not require iterative computations and is robust against the cryo-EM image noise. Both theoretical analysis and experimental results suggest that our power-spectrum-feature-based alignment method is highly computational-efficient and is capable of offering effective alignment results. This new alignment algorithm is publicly available at: www.csbio.sjtu.edu.cn/bioinf/EMAF/for academic use.

WITHDRAWN: Structural studies of vitrified biological proteins and macromolecules - A review on the microimaging aspects of cryo-electron microscopy

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Validation of electron microscopy initial models via small angle X-ray scattering curves

MOTIVATION

Cryo electron microscopy (EM) is currently one of the main tools to reveal the structural information of biological macromolecules. The re-construction of three-dimensional (3D) maps is typically carried out following an iterative process that requires an initial estimation of the 3D map to be refined in subsequent steps. Therefore, its determination is key in the quality of the final results, and there are cases in which it is still an open issue in single particle analysis (SPA). Small angle X-ray scattering (SAXS) is a well-known technique applied to structural biology. It is useful from small nanostructures up to macromolecular ensembles for its ability to obtain low resolution information of the biological sample measuring its X-ray scattering curve. These curves, together with further analysis, are able to yield information on the sizes, shapes and structures of the analyzed particles.

RESULTS

In this paper, we show how the low resolution structural information revealed by SAXS is very useful for the validation of EM initial 3D models in SPA, helping the following refinement process to obtain more accurate 3D structures. For this purpose, we approximate the initial map by pseudo-atoms and predict the SAXS curve expected for this pseudo-atomic structure. The match between the predicted and experimental SAXS curves is considered as a good sign of the correctness of the EM initial map.

AVAILABILITY AND IMPLEMENTATION

The algorithm is freely available as part of the Scipion 1.2 software at http://scipion.i2pc.es/.

CFTR structure, stability, function and regulation

Cystic fibrosis transmembrane conductance regulator (CFTR) is a unique member of the ATP-binding cassette family of proteins because it has evolved into a channel. Mutations in CFTR cause cystic fibrosis, the most common genetic disease in people of European origin. The F508del mutation is found in about 90% of patients and here we present data that suggest its main effect is on CFTR stability rather than on the three-dimensional (3D) folded state. A survey of recent cryo-electron microscopy studies was carried out and this highlighted differences in terms of CFTR conformation despite similarities in experimental conditions. We further studied CFTR structure under various phosphorylation states and with the CFTR-interacting protein NHERF1. The coexistence of outward-facing and inward-facing conformations under a range of experimental conditions was suggested from these data. These results are discussed in terms of structural models for channel gating, and favour the model where the mostly disordered regulatory-region of the protein acts as a channel plug.

Computational Protocol for Assessing the Optimal Pixel Size to Improve the Accuracy of Single-particle Cryo-electron Microscopy Maps

Cryo-electron microscopy (cryo-EM) single-particle analysis has come a long way in achieving atomic-level resolution when imaging biomolecules. To obtain the best possible three-dimensional (3D) structure in cryo-EM, many parameters have to be carefully considered. Here we address the often-overlooked parameter of the pixel size, which describes the magnification of the image produced by the experiment. While efforts are made to refine and validate this parameter in the analysis of cryo-EM experimental data, there is no systematic protocol in place. Since the pixel size parameter can have an impact on the resolution and accuracy of a cryo-EM map, and the atomic resolution 3D structure models derived from it, we propose a computational protocol to estimate the appropriate pixel size parameter. In our protocol, we fit and refine atomic structures against cryo-EM maps at multiple pixel sizes. The resulting fitted and refined structures are evaluated using the GOAP (generalized orientation-dependent, all-atom statistical potential) score, which we found to perform better than other commonly used functions, such as Molprobity and the correlation coefficient from refinement. Finally, we describe the efficacy of this protocol in retrieving appropriate pixel sizes for several examples; simulated data based on yeast elongation factor 2 and experimental data from Gro-EL chaperone, beta-galactosidase, and the TRPV1 ion channel.

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

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

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.

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

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

Constrained cyclic coordinate descent for cryo-EM images at medium resolutions: beyond the protein loop closure problem

The cyclic coordinate descent (CCD) method is a popular loop closure method in protein structure modeling. It is a robotics algorithm originally developed for inverse kinematic applications. We demonstrate an effective method of building the backbone of protein structure models using the principle of CCD and a guiding trace. For medium-resolution 3-dimensional (3D) images derived using cryo-electron microscopy (cryo-EM), it is possible to obtain guiding traces of secondary structures and their skeleton connections. Our new method, constrained cyclic coordinate descent (CCCD), builds α-helices, β-strands, and loops quickly and fairly accurately along predefined traces. We show that it is possible to build the entire backbone of a protein fairly accurately when the guiding traces are accurate. In a test of 10 proteins, the models constructed using CCCD show an average of 3.91 Å of backbone root mean square deviation (RMSD). When the CCCD method is incorporated in a simulated annealing framework to sample possible shift, translation, and rotation freedom, the models built with the true topology were ranked high on the list, with an average backbone RMSD100 of 3.76 Å. CCCD is an effective method for modeling atomic structures after secondary structure traces and skeletons are extracted from 3D cryo-EM images.

A Stochastic Hill Climbing Approach for Simultaneous 2D Alignment and Clustering of Cryogenic Electron Microscopy Images

A critical step in the analysis of novel cryogenic electron microscopy (cryo-EM) single-particle datasets is the identification of homogeneous subsets of images. Methods for solving this problem are important for data quality assessment, ab initio 3D reconstruction, and analysis of population diversity due to the heterogeneous nature of macromolecules. Here we formulate a stochastic algorithm for identification of homogeneous subsets of images. The purpose of the method is to generate improved 2D class averages that can be used to produce a reliable 3D starting model in a rapid and unbiased fashion. We show that our method overcomes inherent limitations of widely used clustering approaches and proceed to test the approach on six publicly available experimental cryo-EM datasets. We conclude that, in each instance, ab initio 3D reconstructions of quality suitable for initialization of high-resolution refinement are produced from the cluster centers.

Cellular degradation of 4-hydroxy-2-oxoglutarate aldolase leads to absolute deficiency in primary hyperoxaluria type 3

Primary hyperoxaluria type-3 is characterized by increased oxalate production caused by mutations in the HOGA1 gene encoding 4-hydroxy-2-oxoglutarate aldolase (HOGA1). How the most commonly occurring mutations affect the cellular fates of the expressed HOGA1 mutants is still unknown. We show that two prevalent recombinant HOGA1 mutants are thermally unstable with evidence for chaperone-mediated degradation when expressed in E. coli. In stably transformed HEK-293 cells, protein expression of the Glu315 deletion mutant only becomes detectable during incubation with a 26S proteasome inhibitor. These findings suggest that failure of chaperone-assisted folding leads to targeted cellular degradation and an absolute absence of HOGA1 function.

Particle alignment reliability in single particle electron cryomicroscopy: a general approach

Electron Microscopy is reaching new capabilities thanks to the combined effect of new technologies and new image processing methods. However, the reconstruction process is still complex, requiring many steps and elaborated optimization procedures. Therefore, the possibility to reach a wrong structure exists, justifying the need of robust statistical tests. In this work, we present a conceptually simple alignment test, which does not require tilt-pair images, to evaluate the alignment consistency between a set of projection images with respect to a given 3D density map. We test the approach on a number of problems in 3DEM, especially the ranking and evaluation of initial 3D volumes and high resolution 3D maps, where we show its usefulness in providing an objective evaluation for maps that have recently been subject to a strong controversy in the field. Additionally, this alignment statistical test can be linked to the early stages of structure solving of new complexes, streamlining the whole process.

Electron Microscopy and Image Processing: Essential Tools for Structural Analysis of Macromolecules

Macromolecular electron microscopy typically depicts the structures of macromolecular complexes ranging from ∼200 kDa to hundreds of MDa. The amount of specimen required, a few micrograms, is typically 100 to 1000 times less than needed for X-ray crystallography or nuclear magnetic resonance spectroscopy. Micrographs of frozen-hydrated (cryogenic) specimens portray native structures, but the original images are noisy. Computational averaging reduces noise, and three-dimensional reconstructions are calculated by combining different views of free-standing particles ("single-particle analysis"). Electron crystallography is used to characterize two-dimensional arrays of membrane proteins and very small three-dimensional crystals. Under favorable circumstances, near-atomic resolutions are achieved. For structures at somewhat lower resolution, pseudo-atomic models are obtained by fitting high-resolution components into the density. Time-resolved experiments describe dynamic processes. Electron tomography allows reconstruction of pleiomorphic complexes and subcellular structures and modeling of macromolecules in their cellular context. Significant information is also obtained from metal-coated and dehydrated specimens.

Electron Tomography: A Three-Dimensional Analytic Tool for Hard and Soft Materials Research

Three-dimensional (3D) structural analysis is essential to understand the relationship between the structure and function of an object. Many analytical techniques, such as X-ray diffraction, neutron spectroscopy, and electron microscopy imaging, are used to provide structural information. Transmission electron microscopy (TEM), one of the most popular analytic tools, has been widely used for structural analysis in both physical and biological sciences for many decades, in which 3D objects are projected into two-dimensional (2D) images. In many cases, 2D-projection images are insufficient to understand the relationship between the 3D structure and the function of nanoscale objects. Electron tomography (ET) is a technique that retrieves 3D structural information from a tilt series of 2D projections, and is gradually becoming a mature technology with sub-nanometer resolution. Distinct methods to overcome sample-based limitations have been separately developed in both physical and biological science, although they share some basic concepts of ET. This review discusses the common basis for 3D characterization, and specifies difficulties and solutions regarding both hard and soft materials research. It is hoped that novel solutions based on current state-of-the-art techniques for advanced applications in hybrid matter systems can be motivated.

Efficient initial volume determination from electron microscopy images of single particles

MOTIVATION

Structural information of macromolecular complexes provides key insights into the way they carry out their biological functions. The reconstruction process leading to the final 3D map requires an approximate initial model. Generation of an initial model is still an open and challenging problem in single-particle analysis.

RESULTS

We present a fast and efficient approach to obtain a reliable, low-resolution estimation of the 3D structure of a macromolecule, without any a priori knowledge, addressing the well-known issue of initial volume estimation in the field of single-particle analysis. The input of the algorithm is a set of class average images obtained from individual projections of a biological object at random and unknown orientations by transmission electron microscopy micrographs. The proposed method is based on an initial non-lineal dimensionality reduction approach, which allows to automatically selecting representative small sets of class average images capturing the most of the structural information of the particle under study. These reduced sets are then used to generate volumes from random orientation assignments. The best volume is determined from these guesses using a random sample consensus (RANSAC) approach. We have tested our proposed algorithm, which we will term 3D-RANSAC, with simulated and experimental data, obtaining satisfactory results under the low signal-to-noise conditions typical of cryo-electron microscopy.

AVAILABILITY

The algorithm is freely available as part of the Xmipp 3.1 package [http://xmipp.cnb.csic.es].

CONTACT

jvargas@cnb.csic.es

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Solving the Secondary Structure Matching Problem in Cryo-EM De Novo Modeling Using a Constrained K-Shortest Path Graph Algorithm

Electron cryomicroscopy is becoming a major experimental technique in solving the structures of large molecular assemblies. More and more three-dimensional images have been obtained at the medium resolutions between 5 and 10 Å. At this resolution range, major α-helices can be detected as cylindrical sticks and β-sheets can be detected as plain-like regions. A critical question in de novo modeling from cryo-EM images is to determine the match between the detected secondary structures from the image and those on the protein sequence. We formulate this matching problem into a constrained graph problem and present an O(Δ(2)N(2)2(N)) algorithm to this NP-Hard problem. The algorithm incorporates the dynamic programming approach into a constrained K-shortest path algorithm. Our method, DP-TOSS, has been tested using α-proteins with maximum 33 helices and α-β proteins up to five helices and 12 β-strands. The correct match was ranked within the top 35 for 19 of the 20 α-proteins and all nine α-β proteins tested. The results demonstrate that DP-TOSS improves accuracy, time and memory space in deriving the topologies of the secondary structure elements for proteins with a large number of secondary structures and a complex skeleton.

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

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

Cryo-electron microscopy reveals the membrane insertion mechanism of V. cholerae hemolysin

Vibrio cholerae hemolysin (HlyA) is a 65 kDa pore-forming toxin which causes lysis of target eukaryotic cells by forming heptameric channels in the plasma membrane. Deletion of the 15 kDa C-terminus β-prism carbohydrate-binding domain generates a 50 kDa truncated variant (HlyA50) with 1000-fold-reduced pore-forming activity. Previously, we showed by cryo-electron microscopy that the two toxin oligomers have central channels, but the 65 kDa toxin oligomer is a seven-fold symmetric structure with bowl-, ring-, and arm-like domains, whereas the 50 kDa oligomer is an asymmetric jar-like heptamer. In the present study, we determined three-dimensional(3D) structures of HlyA and HlyA50 in presence of erythrocyte stroma and observed that interaction of the 65 kDa toxin with the stroma induced a significant decrease in the height of the β-barrel oligomer with a change in conformation of the ring- and arm-like domains of HlyA. These features were absent in interaction of HlyA50 with stroma. We propose that this conformational transition is critical for membrane-insertion of the toxin.

Intensity-based skeletonization of CryoEM gray-scale images using a true segmentation-free algorithm

Cryo-electron microscopy is an experimental technique that is able to produce 3D gray-scale images of protein molecules. In contrast to other experimental techniques, cryo-electron microscopy is capable of visualizing large molecular complexes such as viruses and ribosomes. At medium resolution, the positions of the atoms are not visible and the process cannot proceed. The medium-resolution images produced by cryo-electron microscopy are used to derive the atomic structure of the proteins in de novo modeling. The skeletons of the 3D gray-scale images are used to interpret important information that is helpful in de novo modeling. Unfortunately, not all features of the image can be captured using a single segmentation. In this paper, we present a segmentation-free approach to extract the gray-scale curve-like skeletons. The approach relies on a novel representation of the 3D image, where the image is modeled as a graph and a set of volume trees. A test containing 36 synthesized maps and one authentic map shows that our approach can improve the performance of the two tested tools used in de novo modeling. The improvements were 62 and 13 percent for Gorgon and DP-TOSS, respectively.

Computational methods for constructing protein structure models from 3D electron microscopy maps

Protein structure determination by cryo-electron microscopy (EM) has made significant progress in the past decades. Resolutions of EM maps have been improving as evidenced by recently reported structures that are solved at high resolutions close to 3Å. Computational methods play a key role in interpreting EM data. Among many computational procedures applied to an EM map to obtain protein structure information, in this article we focus on reviewing computational methods that model protein three-dimensional (3D) structures from a 3D EM density map that is constructed from two-dimensional (2D) maps. The computational methods we discuss range from de novo methods, which identify structural elements in an EM map, to structure fitting methods, where known high resolution structures are fit into a low-resolution EM map. A list of available computational tools is also provided.

Validation of cryo-EM structure of IP₃R1 channel

About a decade ago, three electron cryomicroscopy (cryo-EM) single-particle reconstructions of IP3R1 were reported at low resolution. It was disturbing that these structures bore little similarity to one another, even at the level of quaternary structure. Recently, we published an improved structure of IP3R1 at ∼1 nm resolution. However, this structure did not bear any resemblance to any of the three previously published structures, leading to the question of why the structure should be considered more reliable than the original three. Here, we apply several methods, including class-average/map comparisons, tilt-pair validation, and use of multiple refinement software packages, to give strong evidence for the reliability of our recent structure. The map resolution and feature resolvability are assessed with the gold standard criterion. This approach is generally applicable to assessing the validity of cryo-EM maps of other molecular machines.

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

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

A Zernike-moment-based non-local denoising filter for cryo-EM images

Cryo-electron microscopy (cryo-EM) plays an important role in determining the structure of proteins, viruses, and even the whole cell. It can capture dynamic structural changes of large protein complexes, which other methods such as X-ray crystallography and nuclear magnetic resonance analysis find difficult. The signal-to-noise ratio of cryo-EM images is low and the contrast is very weak, and therefore, the images are very noisy and require filtering. In this paper, a filtering method based on non-local means and Zernike moments is proposed. The method takes into account the rotational symmetry of some biological molecules to enhance the signal-to-noise ratio of cryo-EM images. The method may be useful in cryo-EM image processing such as the automatic selection of particles, orientation determination, and the building of initial models.

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

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

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

MOTIVATION

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

RESULT

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

Subunit organization of a synechocystis hetero-oligomeric thylakoid FtsH complex involved in photosystem II repair

FtsH metalloproteases are key components of the photosystem II (PSII) repair cycle, which operates to maintain photosynthetic activity in the light. Despite their physiological importance, the structure and subunit composition of thylakoid FtsH complexes remain uncertain. Mutagenesis has previously revealed that the four FtsH homologs encoded by the cyanobacterium Synechocystis sp PCC 6803 are functionally different: FtsH1 and FtsH3 are required for cell viability, whereas FtsH2 and FtsH4 are dispensable. To gain insights into FtsH2, which is involved in selective D1 protein degradation during PSII repair, we used a strain of Synechocystis 6803 expressing a glutathione S-transferase (GST)-tagged derivative (FtsH2-GST) to isolate FtsH2-containing complexes. Biochemical analysis revealed that FtsH2-GST forms a hetero-oligomeric complex with FtsH3. FtsH2 also interacts with FtsH3 in the wild-type strain, and a mutant depleted in FtsH3, like ftsH2(-) mutants, displays impaired D1 degradation. FtsH3 also forms a separate heterocomplex with FtsH1, thus explaining why FtsH3 is more important than FtsH2 for cell viability. We investigated the structure of the isolated FtsH2-GST/FtsH3 complex using transmission electron microscopy and single-particle analysis. The three-dimensional structural model obtained at a resolution of 26 Å revealed that the complex is hexameric and consists of alternating FtsH2/FtsH3 subunits.

EM-fold: de novo atomic-detail protein structure determination from medium-resolution density maps

Electron density maps of membrane proteins or large macromolecular complexes are frequently only determined at medium resolution between 4 Å and 10 Å, either by cryo-electron microscopy or X-ray crystallography. In these density maps, the general arrangement of secondary structure elements (SSEs) is revealed, whereas their directionality and connectivity remain elusive. We demonstrate that the topology of proteins with up to 250 amino acids can be determined from such density maps when combined with a computational protein folding protocol. Furthermore, we accurately reconstruct atomic detail in loop regions and amino acid side chains not visible in the experimental data. The EM-Fold algorithm assembles the SSEs de novo before atomic detail is added using Rosetta. In a benchmark of 27 proteins, the protocol consistently and reproducibly achieves models with root mean square deviation values <3 Å.

Fitting multimeric protein complexes into electron microscopy maps using 3D Zernike descriptors

A novel computational method for fitting high-resolution structures of multiple proteins into a cryoelectron microscopy map is presented. The method named EMLZerD generates a pool of candidate multiple protein docking conformations of component proteins, which are later compared with a provided electron microscopy (EM) density map to select the ones that fit well into the EM map. The comparison of docking conformations and the EM map is performed using the 3D Zernike descriptor (3DZD), a mathematical series expansion of three-dimensional functions. The 3DZD provides a unified representation of the surface shape of multimeric protein complex models and EM maps, which allows a convenient, fast quantitative comparison of the three-dimensional structural data. Out of 19 multimeric complexes tested, near native complex structures with a root-mean-square deviation of less than 2.5 Å were obtained for 14 cases while medium range resolution structures with correct topology were computed for the additional 5 cases.

Structure and size determination of bacteriophage P2 and P4 procapsids: function of size responsiveness mutations

Bacteriophage P4 is dependent on structural proteins supplied by a helper phage, P2, to assemble infectious virions. Bacteriophage P2 normally forms an icosahedral capsid with T=7 symmetry from the gpN capsid protein, the gpO scaffolding protein and the gpQ portal protein. In the presence of P4, however, the same structural proteins are assembled into a smaller capsid with T=4 symmetry. This size determination is effected by the P4-encoded protein Sid, which forms an external scaffold around the small P4 procapsids. Size responsiveness (sir) mutants in gpN fail to assemble small capsids even in the presence of Sid. We have produced large and small procapsids by co-expression of gpN with gpO and Sid, respectively, and applied cryo-electron microscopy and three-dimensional reconstruction methods to visualize these procapsids. gpN has an HK97-like fold and interacts with Sid in an exposed loop where the sir mutations are clustered. The T=7 lattice of P2 has dextro handedness, unlike the laevo lattices of other phages with this fold observed so far.

A 3D image filter for parameter-free segmentation of macromolecular structures from electron tomograms

3D image reconstruction of large cellular volumes by electron tomography (ET) at high (≤ 5 nm) resolution can now routinely resolve organellar and compartmental membrane structures, protein coats, cytoskeletal filaments, and macromolecules. However, current image analysis methods for identifying in situ macromolecular structures within the crowded 3D ultrastructural landscape of a cell remain labor-intensive, time-consuming, and prone to user-bias and/or error. This paper demonstrates the development and application of a parameter-free, 3D implementation of the bilateral edge-detection (BLE) algorithm for the rapid and accurate segmentation of cellular tomograms. The performance of the 3D BLE filter has been tested on a range of synthetic and real biological data sets and validated against current leading filters-the pseudo 3D recursive and Canny filters. The performance of the 3D BLE filter was found to be comparable to or better than that of both the 3D recursive and Canny filters while offering the significant advantage that it requires no parameter input or optimisation. Edge widths as little as 2 pixels are reproducibly detected with signal intensity and grey scale values as low as 0.72% above the mean of the background noise. The 3D BLE thus provides an efficient method for the automated segmentation of complex cellular structures across multiple scales for further downstream processing, such as cellular annotation and sub-tomogram averaging, and provides a valuable tool for the accurate and high-throughput identification and annotation of 3D structural complexity at the subcellular level, as well as for mapping the spatial and temporal rearrangement of macromolecular assemblies in situ within cellular tomograms.

Evolutionary bidirectional expansion for the tracing of alpha helices in cryo-electron microscopy reconstructions

Cryo-electron microscopy (cryo-EM) enables the imaging of macromolecular complexes in near-native environments at resolutions that often permit the visualization of secondary structure elements. For example, alpha helices frequently show consistent patterns in volumetric maps, exhibiting rod-like structures of high density. Here, we introduce VolTrac (Volume Tracer) - a novel technique for the annotation of alpha-helical density in cryo-EM data sets. VolTrac combines a genetic algorithm and a bidirectional expansion with a tabu search strategy to trace helical regions. Our method takes advantage of the stochastic search by using a genetic algorithm to identify optimal placements for a short cylindrical template, avoiding exploration of already characterized tabu regions. These placements are then utilized as starting positions for the adaptive bidirectional expansion that characterizes the curvature and length of the helical region. The method reliably predicted helices with seven or more residues in experimental and simulated maps at intermediate (4-10Å) resolution. The observed success rates, ranging from 70.6% to 100%, depended on the map resolution and validation parameters. For successful predictions, the helical axes were located within 2Å from known helical axes of atomic structures.

Flexible architecture of IP3R1 by Cryo-EM

Inositol 1,4,5-trisphosphate receptors (IP3Rs) play a fundamental role in generating Ca2+ signals that trigger many cellular processes in virtually all eukaryotic cells. Thus far, the three-dimensional (3D) structure of these channels has remained extremely controversial. Here, we report a subnanometer resolution electron cryomicroscopy (cryo-EM) structure of a fully functional type 1 IP3R from cerebellum in the closed state. The transmembrane region reveals a twisted bundle of four α helices, one from each subunit, that form a funnel shaped structure around the 4-fold symmetry axis, strikingly similar to the ion-conduction pore of K+ channels. The lumenal face of IP3R1 has prominent densities that surround the pore entrance and similar to the highly structured turrets of Kir channels. 3D statistical analysis of the cryo-EM density map identifies high variance in the cytoplasmic region. This structural variation could be attributed to genuine structural flexibility of IP3R1.

RANKING VALID TOPOLOGIES OF THE SECONDARY STRUCTURE ELEMENTS USING A CONSTRAINT GRAPH

Electron cryo-microscopy is a fast advancing biophysical technique to derive three-dimensional structures of large protein complexes. Using this technique, many density maps have been generated at intermediate resolution such as 6–10 Å resolution. Although it is challenging to derive the backbone of the protein directly from such density maps, secondary structure elements such as helices and β-sheets can be computationally detected. Our work in this paper provides an approach to enumerate the top-ranked possible topologies instead of enumerating the entire population of the topologies. This approach is particularly practical for large proteins. We developed a directed weighted graph, the topology graph, to represent the secondary structure assignment problem. We prove that the problem of finding the valid topology with the minimum cost is NP hard. We developed an O(N2 2N) dynamic programming algorithm to identify the topology with the minimum cost. The test of 15 proteins suggests that our dynamic programming approach is feasible to work with proteins of much larger size than we could before. The largest protein in the test contains 18 helical sticks detected from the density map out of 33 helices in the protein.

DERIVING TOPOLOGY AND SEQUENCE ALIGNMENT FOR THE HELIX SKELETON IN LOW-RESOLUTION PROTEIN DENSITY MAPS

Cryoelectron microscopy (cryoEM) is an experimental technique to determine the three-dimensional (3D) structure of large protein complexes. Currently, this technique is able to generate protein density maps at 6–9 Å resolution, at which the skeleton of the structure (which is composed of α-helices and β-sheets) can be visualized. As a step towards predicting the entire backbone of the protein from the protein density map, we developed a method to predict the topology and sequence alignment for the skeleton helices. Our method combines the geometrical information of the skeleton helices with the Rosetta ab initio structure prediction method to derive a consensus topology and sequence alignment for the skeleton helices. We tested the method with 60 proteins. For 45 proteins, the majority of the skeleton helices were assigned a correct topology from one of our top ten predictions. The offsets of the alignment for most of the assigned helices were within ±2 amino acids in the sequence. We also analyzed the use of the skeleton helices as a clustering tool for the decoy structures generated by Rosetta. Our comparison suggests that the topology clustering is a better method than a general overlap clustering method to enrich the ranking of decoys, particularly when the decoy pool is small.

A Stochastic Kinematic Model of Class Averaging in Single-Particle Electron Microscopy

Single-particle electron microscopy is an experimental technique that is used to determine the 3D structure of biological macromolecules and the complexes that they form. In general, image processing techniques and reconstruction algorithms are applied to micrographs, which are two-dimensional (2D) images taken by electron microscopes. Each of these planar images can be thought of as a projection of the macromolecular structure of interest from an a priori unknown direction. A class is defined as a collection of projection images with a high degree of similarity, presumably resulting from taking projections along similar directions. In practice, micrographs are very noisy and those in each class are aligned and averaged in order to reduce the background noise. Errors in the alignment process are inevitable due to noise in the electron micrographs. This error results in blurry averaged images. In this paper, we investigate how blurring parameters are related to the properties of the background noise in the case when the alignment is achieved by matching the mass centers and the principal axes of the experimental images. We observe that the background noise in micrographs can be treated as Gaussian. Using the mean and variance of the background Gaussian noise, we derive equations for the mean and variance of translational and rotational misalignments in the class averaging process. This defines a Gaussian probability density on the Euclidean motion group of the plane. Our formulation is validated by convolving the derived blurring function representing the stochasticity of the image alignments with the underlying noiseless projection and comparing with the original blurry image.

Enhancing the contrast of ApoB to locate the surface components in the 3D density map of human LDL

A 26 Å resolution map of the structure of human low-density lipoprotein (LDL) was obtained from electron cryomicroscopy and single-particle image reconstruction. The structure showed a discoidal-shaped LDL particle with high-density regions mainly distributed at the edge of the particle and low-density regions at the flat surface that covers the core region. To determine the chemical components that correspond to these density regions and to delineate the distribution of protein and phospholipid located at the particle surface at the resolution of the map, we used Mono-Sulfo-NHS-Undecagold labeling to increase preferentially the contrast of the apolipoprotein B component on the LDL particle. In the three-dimensional map from the image reconstruction of the undecagold-labeled LDL particles, the high-density region from the undecagold label was distributed mainly at the edge of the particle, and lower density regions were found at the flat surfaces that cover the neutral lipid core. This suggests that apolipoprotein B mainly encircles LDL at the edge of the particle and the phospholipid monolayers are located at the flat surfaces, which are parallel to the cholesterol ester layers in the core and may interact with the core lipid layers through the acyl chains.

Fingerprint-based structure retrieval using electron density

We present a computational approach that can quickly search a large protein structural database to identify structures that fit a given electron density, such as determined by cryo-electron microscopy. We use geometric invariants (fingerprints) constructed using 3D Zernike moments to describe the electron density, and reduce the problem of fitting of the structure to the electron density to simple fingerprint comparison. Using this approach, we are able to screen the entire Protein Data Bank and identify structures that fit two experimental electron densities determined by cryo-electron microscopy.

CFTR three-dimensional structure

CFTR is a member of the ATP-binding cassette family of membrane proteins. This is one of the best characterised membrane protein families in terms of structure and function. CFTR operates as an ion channel, unlike nearly all other family members which are active transporters. Here, we discuss methods that have allowed such data to be obtained for CFTR.

MOTIF-EM: an automated computational tool for identifying conserved regions in CryoEM structures

We present a new, first-of-its-kind, fully automated computational tool MOTIF-EM for identifying regions or domains or motifs in cryoEM maps of large macromolecular assemblies (such as chaperonins, viruses, etc.) that remain conformationally conserved. As a by-product, regions in structures that are not conserved are revealed: this can indicate local molecular flexibility related to biological activity. MOTIF-EM takes cryoEM volumetric maps as inputs. The technique used by MOTIF-EM to detect conserved sub-structures is inspired by a recent breakthrough in 2D object recognition. The technique works by constructing rotationally invariant, low-dimensional representations of local regions in the input cryoEM maps. Correspondences are established between the reduced representations (by comparing them using a simple metric) across the input maps. The correspondences are clustered using hash tables and graph theory is used to retrieve conserved structural domains or motifs. MOTIF-EM has been used to extract conserved domains occurring in large macromolecular assembly maps, including as those of viruses P22 and epsilon 15, Ribosome 70S, GroEL, that remain structurally conserved in different functional states. Our method can also been used to build atomic models for some maps. We also used MOTIF-EM to identify the conserved folds shared among dsDNA bacteriophages HK97, Epsilon 15, and ô29, though they have low-sequence similarity.

Contact:mitul@cs.stanford.edu

Supplementary information:Supplementary data are available at Bioinformatics online.