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.

     

A feature-guided,focused 3D signal permutation method for subtomogram averaging

Advances in electron microscope instrumentation, cryo-electron tomography data collection, and subtomogram averaging have allowed for the in-situ visualization of molecules and their complexes in their native environment. Current data processing pipelines commonly extract subtomograms as a cubic subvolume with the key assumption that the selected object of interest is discrete from its surroundings. However, in instances when the object is in its native environment, surrounding densities may negatively affect the subsequent alignment and refinement processes, leading to loss of information due to misalignment. For example, the strong densities from surrounding membranes may dominate the alignment process for membrane proteins. Here, we developed methods for feature-guided subtomogram alignment and 3D signal permutation for subtomogram averaging. Our 3D signal permutation method randomizes and filters voxels outside a mask of any shape and blurs the boundary of the mask that encapsulates the object of interest. The randomization preserves global statistical properties such as mean density and standard deviation of voxel density values, effectively producing a featureless background surrounding the object of interest. This signal permutation process can be repeatedly applied with intervening alignments of the 3D signal-permuted subvolumes, recentering of the mask, and optional adjustments of the shape of the mask. We have implemented these methods in a new processing pipeline which starts from tomograms, contains feature-guided subtomogram extraction and alignment, 3D signal-permutation, and subtomogram visualization tools. As an example, feature-guided alignment and 3D signal permutation leads to improved subtomogram average maps for a dataset of synaptic protein complexes in their native environment.     

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.     

2D fast rotational matching for image processing of biophysical data

In 3D single particle reconstruction, which involves the translational and rotational matching of a large number of electron microscopy (EM) images, the algorithmic performance is largely dependent on the efficiency and accuracy of the underlying 2D image alignment kernel. We present a novel fast rotational matching kernel for 2D images (FRM2D) that significantly reduces the cost of this alignment. The alignment problem is formulated using one translational and two rotational degrees of freedom. This allows us to take advantage of fast Fourier transforms (FFTs) in rotational space to accelerate the search of the two angular parameters, while the remaining translational parameter is explored, within a limited range, by exhaustive search. Since there are no boundary effects in FFTs of cyclic angular variables, we avoid the expensive zero padding associated with Fourier transforms in linear space. To verify the robustness of our method, efficiency and accuracy tests were carried out over a range of noise levels in realistic simulations of EM images. Performance tests against two standard alignment methods, resampling to polar coordinates and self-correlation, demonstrate that FRM2D compares very favorably to the traditional methods. FRM2D exhibits a comparable or higher robustness against noise and a significant gain in efficiency that depends on the fineness of the angular sampling and linear search range.     

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

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

Fast rotational matching of single-particle images

The presence of noise and absence of contrast in electron micrographs lead to a reduced resolution of the final 3D reconstruction, due to the inherent limitations of single-particle image alignment. The fast rotational matching (FRM) algorithm was introduced recently for an accurate alignment of 2D images under such challenging conditions. Here, we implemented this algorithm for the first time in a standard 3D reconstruction package used in electron microscopy. This allowed us to carry out exhaustive tests of the robustness and reliability in iterative orientation determination, classification, and 3D reconstruction on simulated and experimental image data. A classification test on GroEL chaperonin images demonstrates that FRM assigns up to 13% more images to their correct reference orientation, compared to the classical self-correlation function method. Moreover, at sub-nanometer resolution, GroEL and rice dwarf virus reconstructions exhibit a remarkable resolution gain of 10-20% that is attributed to the novel image alignment kernel.     

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.     

Automatic alignment of transmission electron microscope tilt series without fiducial markers

Accurate image alignment is needed for computing three-dimensional reconstructions from transmission electron microscope tilt series. So far, the best results have been obtained by using colloidal gold beads as fiducial markers. If their use has not been possible for some reason, the only option has been the automatic cross-correlation-based registration methods. However, the latter methods are inaccurate and, as we will show, inappropriate for the whole problem. Conversely, we propose a novel method that uses the actual 3D motion model but works without any fiducial markers in the images. The method is based on matching and tracking some interest points of the intensity surface by first solving the underlying geometrical constraint of consecutive images in the tilt series. The results show that our method is near the gold marker alignment in the level of accuracy and hence opens the way for new opportunities in the analysis of electron tomography reconstructions, especially when markers cannot be used.     

The human nuclear pore complex as revealed by cryo-electron tomography

Nuclear pore complexes (NPCs) are the sole passage through the nuclear envelope, connecting the cytoplasm to the nucleoplasm. These gigantic molecular machines, over 100 MDa in molecular weight, allow free diffusion of small molecules and ions while mediating selective energy-dependent nucleocytoplasmic transport of large macromolecules. Here, we applied cryo-electron tomography to human fibroblast cells, reconstructing their nuclear envelopes without applying any purification steps. From these reconstructions, we extracted subtomograms containing individual NPCs and utilized in silico subtomogram averaging procedures to determine the structure of the mammalian pore complex at a resolution of ～6.6?nm. Beyond revealing the canonical features of the human NPC, our analysis identified inner lateral channels and fusing bridge-like structures, suggesting alternative routes of peripheral nuclear passage. Finally, we concluded from our structural analysis that the human NPC is structurally distinct from that of lower eukaryotes in terms of dimension and organization but resembles its amphibian (frog) counterpart.     

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.     

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.     

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

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

Multiphase method for automatic alignment of transmission electron microscope images using markers

In order to successfully perform the 3D reconstruction in electron tomography, transmission electron microscope images must be accurately aligned or registered. So far, the problem is solved by either manually showing the corresponding fiducial markers from the set of images or automatically using simple correlation between the images on several rotations and scales. The present solutions, however, share the problem of being inefficient and/or inaccurate. We therefore propose a method in which the registration is automated using conventional colloidal gold particles as reference markers between images. We approach the problem from the computer vision viewpoint; hence, the alignment problem is divided into several subproblems: (1) finding initial matches from successive images, (2) estimating the epipolar geometry between consecutive images, (3) finding and localizing the gold particles with subpixel accuracy in each image, (4) predicting the probable matching gold particles using the epipolar constraint and its uncertainty, (5) matching and tracking the gold beads through the tilt series, and (6) optimizing the transformation parameters for the whole image set. The results show not only the reliability of the suggested method but also a high level of accuracy in alignment, since practically all the visible gold markers can be used.     

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.     

Reference-free particle selection enhanced with semi-supervised machine learning for cryo-electron microscopy

Reference-based methods have dominated the approaches to the particle selection problem, proving fast, and accurate on even the most challenging micrographs. A reference volume, however, is not always available and compiling a set of reference projections from the micrographs themselves requires significant effort to attain the same level of accuracy. We propose a reference-free method to quickly extract particles from the micrograph. The method is augmented with a new semi-supervised machine-learning algorithm to accurately discriminate particles from contaminants and noise.     

Efficient Alignment of RNAs with Pseudoknots Using Sequence Alignment Constraints

When aligning RNAs, it is important to consider both the secondary structure similarity and primary sequence similarity to find an accurate alignment. However, algorithms that can handle RNA secondary structures typically have high computational complexity that limits their utility. For this reason, there have been a number of attempts to find useful alignment constraints that can reduce the computations without sacrificing the alignment accuracy. In this paper, we propose a new method for finding effective alignment constraints for fast and accurate structural alignment of RNAs, including pseudoknots. In the proposed method, we use a profile-HMM to identify the “seedâ€� regions that can be aligned with high confidence. We also estimate the position range of the aligned bases that are located outside the seed regions. The location of the seed regions and the estimated range of the alignment positions are then used to establish the sequence alignment constraints. We incorporated the proposed constraints into the profile context-sensitive HMM (profile-csHMM) based RNA structural alignment algorithm. Experiments indicate that the proposed method can make the alignment speed up to 11 times faster without degrading the accuracy of the RNA alignment.     

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.     

UPSEC: an algorithm for classifying unaligned protein sequences into functional families.

To classify proteins into functional families based on their primary sequences, popular algorithms such as the k-NN-, HMM-, and SVM-based algorithms are often used. For many of these algorithms to perform their tasks, protein sequences need to be properly aligned first. Since the alignment process can be error-prone, protein classification may not be performed very accurately. To improve classification accuracy, we propose an algorithm, called the Unaligned Protein SEquence Classifier (UPSEC), which can perform its tasks without sequence alignment. UPSEC makes use of a probabilistic measure to identify residues that are useful for classification in both positive and negative training samples, and can handle multi-class classification with a single classifier and a single pass through the training data. UPSEC has been tested with real protein data sets. Experimental results show that UPSEC can effectively classify unaligned protein sequences into their corresponding functional families, and the patterns it discovers during the training process can be biologically meaningful.     

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.     

Cross-correlation and merging of crystallographic reflections derived from cryoelectron micrographs of 3D crystals: application to the Limulus acrosomal bundle

A method is described for merging in reciprocal space of electron microscopic data from three-dimensional crystals of the acrosomal bundle. Permutation of indices was required to find the proper alignment of data from different bundles. The method utilizes a statistical evaluation of the significance of the cross-correlation results to indicate the proper order for merging. The three-dimensional (3D) merging is a reference-free operation that does not depend on choosing a "zero-tilt" user-defined starting point. Results from the merging are given and the merged 3D data to 9.5A resolution is evaluated for coherence. General issues such as statistical significance of cross-correlation function peaks, symmetry evaluation, and phase coherence as a function of amplitude are discussed.