Computational Methods Toward Unbiased Pattern Mining and Structure Determination in Cryo-Electron Tomography Data

Cryo-electron tomography can uniquely probe the native cellular environment for macromolecular structures. Tomograms feature complex data with densities of diverse, densely crowded macromolecular complexes, low signal-to-noise, and artifacts such as the missing wedge effect. Post-processing of this data generally involves isolating regions or particles of interest from tomograms, organizing them into related groups, and rendering final structures through subtomogram averaging. Template-matching and reference-based structure determination are popular analysis methods but are vulnerable to biases and can often require significant user input. Most importantly, these approaches cannot identify novel complexes that reside within the imaged cellular environment. To reliably extract and resolve structures of interest, efficient and unbiased approaches are therefore of great value. This review highlights notable computational software and discusses how they contribute to making automated structural pattern discovery a possibility. Perspectives emphasizing the importance of features for user-friendliness and accessibility are also presented.     

Visualization of ATP Synthase Dimers in Mitochondria by Electron Cryo-tomography

Electron cryo-tomography is a powerful tool in structural biology, capable of visualizing the three-dimensional structure of biological samples, such as cells, organelles, membrane vesicles, or viruses at molecular detail. To achieve this, the aqueous sample is rapidly vitrified in liquid ethane, which preserves it in a close-to-native, frozen-hydrated state. In the electron microscope, tilt series are recorded at liquid nitrogen temperature, from which 3D tomograms are reconstructed. The signal-to-noise ratio of the tomographic volume is inherently low. Recognizable, recurring features are enhanced by subtomogram averaging, by which individual subvolumes are cut out, aligned and averaged to reduce noise. In this way, 3D maps with a resolution of 2 nm or better can be obtained. A fit of available high-resolution structures to the 3D volume then produces atomic models of protein complexes in their native environment. Here we show how we use electron cryo-tomography to study the in situ organization of large membrane protein complexes in mitochondria. We find that ATP synthases are organized in rows of dimers along highly curved apices of the inner membrane cristae, whereas complex I is randomly distributed in the membrane regions on either side of the rows. By subtomogram averaging we obtained a structure of the mitochondrial ATP synthase dimer within the cristae membrane.     

High-throughput subtomogram alignment and classification by Fourier space constrained fast volumetric matching

Cryo-electron tomography allows the visualization of macromolecular complexes in their cellular environments in close-to-live conditions. The nominal resolution of subtomograms can be significantly increased when individual subtomograms of the same kind are aligned and averaged. A vital step for such a procedure are algorithms that speedup subtomogram alignment and improve its accuracy to allow reference-free subtomogram classifications. Such methods will facilitate automation of tomography analysis and overall high throughput in the data processing. Building on previous work, here we propose a fast rotational alignment method that uses the Fourier equivalent form of a popular constrained correlation measure that considers missing wedge corrections and density variances in the subtomograms. The fast rotational search is based on 3D volumetric matching, which improves the rotational alignment accuracy in particular for highly distorted subtomograms with low SNR and tilt angle ranges in comparison to fast rotational matching of projected 2D spherical images. We further integrate our fast rotational alignment method in a reference-free iterative subtomogram classification scheme, and propose a local feature enhancement strategy in the classification process. As a proof of principle, we can demonstrate that the automatic method can successfully classify a large number of experimental subtomograms without the need of a reference structure.     

Classification and 3D averaging with missing wedge correction in biological electron tomography

Strategies for the determination of 3D structures of biological macromolecules using electron crystallography and single-particle electron microscopy utilize powerful tools for the averaging of information obtained from 2D projection images of structurally homogeneous specimens. In contrast, electron tomographic approaches have often been used to study the 3D structures of heterogeneous, one-of-a-kind objects such as whole cells where image-averaging strategies are not applicable. Complex entities such as cells and viruses, nevertheless, contain multiple copies of numerous macromolecules that can individually be subjected to 3D averaging. Here we present a complete framework for alignment, classification, and averaging of volumes derived by electron tomography that is computationally efficient and effectively accounts for the missing wedge that is inherent to limited-angle electron tomography. Modeling the missing data as a multiplying mask in reciprocal space we show that the effect of the missing wedge can be accounted for seamlessly in all alignment and classification operations. We solve the alignment problem using the convolution theorem in harmonic analysis, thus eliminating the need for approaches that require exhaustive angular search, and adopt an iterative approach to alignment and classification that does not require the use of external references. We demonstrate that our method can be successfully applied for 3D classification and averaging of phantom volumes as well as experimentally obtained tomograms of GroEL where the outcomes of the analysis can be quantitatively compared against the expected results.     

Three-dimensional structure of basal body triplet revealed by electron cryo-tomography

Basal bodies and centrioles play central roles in microtubule (MT)‐organizing centres within many eukaryotes. They share a barrel‐shaped cylindrical structure composed of nine MT triplet blades. Here, we report the structure of the basal body triplet at 33 Å resolution obtained by electron cryo‐tomography and 3D subtomogram averaging. By fitting the atomic structure of tubulin into the EM density, we built a pseudo‐atomic model of the tubulin protofilaments at the core of the triplet. The 3D density map reveals additional densities that represent non‐tubulin proteins attached to the triplet, including a large inner circular structure in the basal body lumen, which functions as a scaffold to stabilize the entire basal body barrel. We found clear longitudinal structural variations along the basal body, suggesting a sequential and coordinated assembly mechanism. We propose a model in which δ‐tubulin and other components participate in the assembly of the basal body.     

Multishot tomography for high-resolution in situ subtomogram averaging

Cryo-electron tomography (cryo-ET) and subtomogram averaging (STA) can resolve protein complexes at near atomic resolution, and when combined with focused ion beam (FIB) milling, macromolecules can be observed within their native context. Unlike single particle acquisition (SPA), cryo-ET can be slow, which may reduce overall project throughput. We here propose a fast, multi-position tomographic acquisition scheme based on beam-tilt corrected beam-shift imaging along the tilt axis, which yields sub-nanometer in situ STA averages.     

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

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

This study presents a complete and detailed step-by-step guide for subtomogram averaging using Dynamo software, with a special focus on particle picking and particle averaging; this will enable efficient processing for all experience levels, and lays a foundation for user-specific projects.     

In Situ Localization of N and C Termini of Subunits of the Flagellar Nexin-Dynein Regulatory Complex (N-DRC) Using SNAP Tag and Cryo-electron Tomography

Cryo-electron tomography (cryo-ET) has reached nanoscale resolution for in situ three-dimensional imaging of macromolecular complexes and organelles. Yet its current resolution is not sufficient to precisely localize or identify most proteins in situ; for example, the location and arrangement of components of the nexin-dynein regulatory complex (N-DRC), a key regulator of ciliary/flagellar motility that is conserved from algae to humans, have remained elusive despite many cryo-ET studies of cilia and flagella. Here, we developed an in situ localization method that combines cryo-ET/subtomogram averaging with the clonable SNAP tag, a widely used cell biological probe to visualize fusion proteins by fluorescence microscopy. Using this hybrid approach, we precisely determined the locations of the N and C termini of DRC3 and the C terminus of DRC4 within the three-dimensional structure of the N-DRC in Chlamydomonas flagella. Our data demonstrate that fusion of SNAP with target proteins allowed for protein localization with high efficiency and fidelity using SNAP-linked gold nanoparticles, without disrupting the native assembly, structure, or function of the flagella. After cryo-ET and subtomogram averaging, we localized DRC3 to the L1 projection of the nexin linker, which interacts directly with a dynein motor, whereas DRC4 was observed to stretch along the N-DRC base plate to the nexin linker. Application of the technique developed here to the N-DRC revealed new insights into the organization and regulatory mechanism of this complex, and provides a valuable tool for the structural dissection of macromolecular complexes in situ.     

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

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

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

Background

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

Results

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

Conclusions

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

     

TomoAlign: A novel approach to correcting sample motion and 3D CTF in CryoET

TomoAlign is a software package that integrates tools to mitigate two important resolution limiting factors in cryoET, namely the beam-induced sample motion and the contrast transfer function (CTF) of the microscope. The package is especially focused on cryoET of thick specimens where fiducial markers are required for accurate tilt-series alignment and sample motion estimation. TomoAlign models the beam-induced sample motion undergone during the tilt-series acquisition. The motion models are used to produce motion-corrected subtilt-series centered on the particles of interest. In addition, the defocus of each particle at each tilt image is determined and can be corrected, resulting in motion-corrected and CTF-corrected subtilt-series from which the subtomograms can be computed. Alternatively, the CTF information can be passed on so that CTF correction can be carried out entirely within external packages like Relion. TomoAlign serves as a versatile tool that can streamline the cryoET workflow from initial alignment of tilt-series to final subtomogram averaging during in situ structure determination.     

A procedure to deposit fiducial markers on vitreous cryo-sections for cellular tomography

We describe a novel approach for the accurate alignment of images in electron tomography of vitreous cryo-sections. Quantum dots, suspended in organic solvents at cryo-temperatures, are applied directly onto the sections and are subsequently used as fiducial markers to align the tilt series. Data collection can be performed from different regions of the vitreous sections, even when the sections touch the grid only at a few places. We present high-resolution tomograms of some organelles in cryo-sections of human skin cells using this method. The average error in image alignment was about 1nm and the resolution was estimated to be 5-7nm. Thus, the use of section-attached quantum dots as fiducial markers in electron tomography of vitreous cryo-sections facilitates high-resolution in situ 3D imaging of organelles and macromolecular complexes in their native hydrated state.     

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

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

Exploring high-resolution cryo-ET and subtomogram averaging capabilities of contemporary DEDs

The potential of energy filtering and direct electron detection for cryo-electron microscopy (cryo-EM) has been well documented. Here, we assess the performance of recently introduced hardware for cryo-electron tomography (cryo-ET) and subtomogram averaging (STA), an increasingly popular structural determination method for complex 3D specimens. We acquired cryo-ET datasets of EIAV virus-like particles (VLPs) on two contemporary cryo-EM systems equipped with different energy filters and direct electron detectors (DED), specifically a Krios G4, equipped with a cold field emission gun (CFEG), Thermo Fisher Scientific Selectris X energy filter, and a Falcon 4 DED; and a Krios G3i, with a Schottky field emission gun (XFEG), a Gatan Bioquantum energy filter, and a K3 DED. We performed constrained cross-correlation-based STA on equally sized datasets acquired on the respective systems. The resulting EIAV CA hexamer reconstructions show that both systems perform comparably in the 4–6 Å resolution range based on Fourier-Shell correlation (FSC). In addition, by employing a recently introduced multiparticle refinement approach, we obtained a reconstruction of the EIAV CA hexamer at 2.9 Å. Our results demonstrate the potential of the new generation of energy filters and DEDs for STA, and the effects of using different processing pipelines on their STA outcomes.     

Integrating on-grid immunogold labeling and cryo-electron tomography to reveal photosystem II structure and spatial distribution in thylakoid membranes

A long-standing challenge in cell biology is elucidating the structure and spatial distribution of individual membrane-bound proteins, protein complexes and their interactions in their native environment. Here, we describe a workflow that combines on-grid immunogold labeling, followed by cryo-electron tomography (cryoET) imaging and structural analyses to identify and characterize the structure of photosystem II (PSII) complexes. Using an antibody specific to a core subunit of PSII, the D1 protein (uniquely found in the water splitting complex in all oxygenic photoautotrophs), we identified PSII complexes in biophysically active thylakoid membranes isolated from a model marine diatom Phaeodactylum tricornutum. Subsequent cryoET analyses of these protein complexes resolved two PSII structures: supercomplexes and dimeric cores. Our integrative approach establishes the structural signature of multimeric membrane protein complexes in their native environment and provides a pathway to elucidate their high-resolution structures.     

Focus gradient correction applied to tilt series image data used in electron tomography

The resolution in 3D reconstructions from tilt series is limited to the information below the first zero of the contrast transfer function unless the signal is corrected computationally. The restoration is usually based on the assumption of a linear space-invariant system and a linear relationship between object mass density and observed image contrast. The space-invariant model is no longer valid when applied to tilted micrographs because the defocus varies in a direction perpendicular to the tilt axis and with it the shape of the associated point spread function. In this paper, a method is presented for determining the defocus gradient in thin specimens such as sections and 2D crystals, and for restoration of the images subsequently used for 3D reconstruction. The alignment procedure for 3D reconstruction includes area matching and tilt geometry refinement. A map with limited resolution computed from uncorrected micrographs is compared to a volume computed from corrected micrographs with extended resolution.     

Single-molecule 3D imaging of human plasma intermediate-density lipoproteins reveals a polyhedral structure

Intermediate-density lipoproteins (IDLs), the remnants of very-low-density lipoproteins via lipolysis, are rich in cholesteryl ester and are associated with cardiovascular disease. Despite pharmacological interest in IDLs, their three-dimensional (3D) structure is still undetermined due to their variation in size, composition, and dynamic structure. To explore the 3D structure of IDLs, we reconstructed 3D density maps from individual IDL particles using cryo-electron microscopy (cryo-EM) and individual-particle electron tomography (IPET, without averaging from different molecules). 3D reconstructions of IDLs revealed an unexpected polyhedral structure that deviates from the generally assumed spherical shape model (Frias et al., 2007; Olson, 1998; Shen et al., 1977). The polyhedral-shaped IDL contains a high-density shell formed by flat surfaces that are similar to those of very-low-density lipoproteins but have sharper dihedral angles between nearby surfaces. These flat surfaces would be less hydrophobic than the curved surface of mature spherical high-density lipoprotein (HDL), leading to a lower binding affinity of IDL to hydrophobic proteins (such as cholesteryl ester transfer protein) than HDL. This is the first visualization of the IDL 3D structure, which could provide fundamental clues for delineating the role of IDL in lipid metabolism and cardiovascular disease.     

High resolution electron tomography and segmentation‐by‐modeling interpretation in Bsoft

Bsoft offers many tools for the processing of tomographic tilt series and the interpretation of tomograms. Since I introduced tomography into Bsoft almost two decades ago, the field has advanced significantly, requiring refinement of old algorithms and development of new ones. The current direct detectors allow us to collect data more efficiently and with better quality, progressing towards automation. The goal is then to also automate alignment of tilt series and reconstruction. I added an estimation of the specimen thickness as well as fiducialless alignment, to augment the existing fiducial‐based alignment. High‐resolution work requires correction for the contrast transfer function, in tomography complicated by the tilted specimen. For this, I developed a method to generate a power spectrum using the whole micrograph, compensating for tilting. This is followed by routine determination of the contrast transfer function, and correction for it during reconstruction. The next steps involve interpretation of the tomogram, either by subtomogram averaging where possible, or by segmentation and modeling otherwise. Such interpretation actually constitutes the main time‐consuming part of tomography and is less amenable to automation compared to the initial reconstruction.     

Research on Location Characteristics and Algorithms based on Frequency Domain for a 2D Underwater Active Electrolocation Positioning System

Weakly electric fish has an ability to generate a low-frequency electric field actively to locate the surrounding object in complete darkness by sensing the change of the electric field.This ability is called active electrolocation.In this paper,we designed a two-dimensional (2D) experimental platform of underwater active electrolocation system by simulating weakly electric fish.On the platform,location characteristics based on frequency domain were investigated.Results indicated that surface shape of 3D location characteristic curves for the 2D underwater active electrolocation positioning system was convex upwards or concave down which was influenced by the material of probed objects and the frequency of the electric field excitation signal.Experiments also confirmed that the amplitude of the electric field excitation signal and the size of the probed object will only influence the amplitude corresponding to 3D location characteristic curves.Based on above location characteristics,we present three location algorithms including Cross Location Algorithm (CLA),Stochastic Location Algorithm (SLA) and Particle Swarm Optimization (PSO) location algorithm in frequency domain and achieved the task of the underwater positioning system.Our work may have reference value for underwater detection study.