Methods for aligning and for averaging 3D volumes with missing data

The visibility and resolution of a tomographic reconstruction containing multiple copies of discrete particles can be enhanced by averaging subtomograms after they are corrected aligned. However, the “missing wedge” in electron tomography can easily lead to erroneous alignment. We have explored a Fourier space cross-correlation method with a proper weighting scheme to align and average different sets of volumetric data, each of which has different missing data due to the limited specimen tilts. This approach depends neither on a preexisting template, nor an exact knowledge of the geometry, orientation, or amount of the missing data. This paper introduces a procedure where the missing data might be gradually “filled in” by consecutively aligning and averaging volumes with different orientations of their missing data. We have validated these techniques by a set of simulated data with various symmetries and extent of missing data. We have also successfully applied these procedures to experimental cryo-electron tomographic data [Chang, J.T., Schmid, M.F., Rixon, F.J., and Chiu, W., 2007. Electron cryotomography reveals the portal in the herpesvirus capsid. J. Virol. 81, 2065–2068; Schmid, M.F., Paredes, A.M., Khant, H.A., Soyer, F., Aldrich, H.C., Chiu, W., and Shively, J.M., 2006. Structure of Halothiobacillus neapolitanus carboxysomes by cryo-electron tomography. J. Mol. Biol. 364, 526–535].     

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.     

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.     

In vivo virus structures: simultaneous classification, resolution enhancement, and noise reduction in whole-cell electron tomography

Hutchinson-Gilford progeria syndrome (HGPS) is a premature aging syndrome caused by the expression and accumulation of a mutant form of lamin A, Δ50 lamin A. As a component of the cell's nucleoskeleton, lamin A plays an important role in the mechanical stabilization of the nuclear envelope and in other nuclear functions. It is largely unknown how the characteristic 50 amino acid deletion affects the conformation of the mostly intrinsically disordered tail domain of lamin A. Here we perform replica exchange molecular dynamics simulations of the tail domain and determine an ensemble of semi-stable structures. Based on these structures we show that the ZMPSTE 24 cleavage site on the precursor form of the lamin A tail domain orients itself in such a way as to facilitate cleavage during the maturation process. We confirm our simulated structures by comparing the thermodynamic properties of the ensemble structures to in vitro stability measurements. Using this combination of experimental and computational techniques, we compare the size, heterogeneity of size, thermodynamic stability of the Ig-fold, as well as the mechanisms of force-induced denaturation. Our data shows that the Δ50 lamin A tail domain is more compact and displays less heterogeneity than the mature lamin A tail domain. Altogether these results suggest that the altered structure and stability of the tail domain can explain changed protein-protein and protein-DNA interactions and may represent an etiology of the disease. Also, this study provides the first molecular structure(s) of the lamin A tail domain, which is confirmed by thermodynamic tests in experiment.     

Compressed sensing for electron cryotomography and high-resolution subtomogram averaging of biological specimens

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Capturing actin assemblies in cells using in situ cryo-electron tomography

Actin contributes to an exceptionally wide range of cellular processes through the assembly and disassembly of highly dynamic and ordered structures. Visualizing these structures in cells can help us understand how the molecular players of the actin machinery work together to produce force-generating systems. In recent years, cryo-electron tomography (cryo-ET) has become the method of choice for structural analysis of the cell interior at the molecular scale. Here we review advances in cryo-ET workflows that have enabled this transformation, especially the automation of sample preparation procedures, data collection, and processing. We discuss new structural analyses of dynamic actin assemblies in cryo-preserved cells, which have provided mechanistic insights into actin assembly and function at the nanoscale. Finally, we highlight the latest visual proteomics studies of actin filaments and their interactors reaching sub-nanometer resolutions in cells.     

Unique structures in a tumor herpesvirus revealed by cryo-electron tomography and microscopy

Gammaherpesviruses, including the human pathogens Epstein–Barr virus and Kaposi’s sarcoma-associated herpesvirus, are causative agents of lymphomas and other malignancies. The structural characterization of these viruses has been limited due to difficulties in obtaining adequate amount of virion particles. Here we report the first three-dimensional structural characterization of a whole gammaherpesvirus virion by an emerging integrated approach of cryo-electron tomography combined with single-particle cryo-electron microscopy, using murine gammaherpesvirus-68 (MHV-68) as a model system. We found that the MHV-68 virion consists of distinctive envelope and tegument compartments, and a highly conserved nucleocapsid. Two layers of tegument are identified: an inner tegument layer tethered to the underlying capsid and an outer, flexible tegument layer conforming to the overlying, pleomorphic envelope, consistent with the sequential viral tegumentation process inside host cells. Surprisingly, comparison of the MHV-68 virion and capsid reconstructions shows that the interactions between the capsid and inner tegument proteins are completely different from those observed in alpha and betaherpesviruses. These observations support the notion that the inner layer tegument across different subfamilies of herpesviruses has evolved significantly to confer specific characteristics related to viral–host interactions, in contrast to a highly conserved capsid for genome encapsidation and protection.     

Stereology meets electron tomography: towards quantitative 3D electron microscopy

Stereological tools are the gold standard for accurate (i.e., unbiased) and precise quantification of any microscopic sample. The past decades have provided a broad spectrum of tools to estimate a variety of parameters such as volumes, surfaces, lengths, and numbers. Some of them require pairs of parallel sections that can be produced by either physical or optical sectioning, with optical sectioning being much more efficient when applicable. Unfortunately, transmission electron microscopy could not fully profit from these riches, mainly because of the large depth of field. Hence, optical sectioning was a long-time desire for electron microscopists. This desire was fulfilled with the development of electron tomography that yield stacks of slices from electron microscopic sections. Now, parallel optical slices of a previously unimagined small thickness (2-5 nm axial resolution) can be produced. These optical slices minimize problems related to overprojection effects, and allow for direct stereological analysis, e.g., volume estimation with the Cavalieri principle and number estimation with the optical disector method. Here, we demonstrate that the symbiosis of stereology and electron tomography is an easy and efficient way for quantitative analysis at the electron microscopic level. We call this approach quantitative 3D electron microscopy.     

Tools for correlative cryo-fluorescence microscopy and cryo-electron tomography applied to whole mitochondria in human endothelial cells

Cryo-electron tomography (cryo-ET) allows for the visualization of biological material in a close-to-native state, in three dimensions and with nanometer scale resolution. However, due to the low signal-to-noise ratio inherent to imaging of the radiation-sensitive frozen-hydrated samples, it appears oftentimes impossible to localize structures within heterogeneous samples. Because a major potential for cryo-ET is thereby left unused, we set out to combine cryo-ET with cryo-fluorescence microscopy (cryo-FM), in order to facilitate the search for structures of interest. We describe a cryo-FM setup and workflow for correlative cryo-fluorescence and cryo-electron microscopy (cryo-CLEM) that can be easily implemented. Cells are grown on finder grids, vitally labeled with one or two fluorescent dyes, and vitrified. After a structure is located by cryo-FM (with 0.4 μm resolution), its image coordinates are translated to cryo-ET stage coordinates via a home-built software routine. We tested our workflow on whole mount primary human umbilical vein endothelial cells. The correlative routine enabled us to investigate mitochondrial ultrastructure for the first time on intact human mitochondria, and led us to find mitochondrial cristae that were connected to the intermembrane space via large slits, which challenges the current view that such connections are established exclusively via small circular pores. Taken together, this study emphasizes that cryo-CLEM can be a routinely used technique that opens up exciting new possibilities for cryo-ET.     

猪动脉内皮细胞胞膜小窝的电子断层三维结构分析

利用电子断层三维重构技术对猪动脉内皮细胞 (porcine aorta endothelial cell,PAE cell) 胞膜小窝的三维结构进行了初步研究,发现胞膜小窝在细胞膜表面呈不均匀分布并在局部形成聚集,胞膜小窝膜内外表面都由宽度约14～16 nm的条纹状结构所环绕,推测该条纹状结构主要由小窝蛋白和胆固醇构成,狭窄的胞膜小窝颈部区域存在高密度的丝状结构．三维结构显示胞膜小窝与纤维丝体网络(推测为微管网络)相互作用,暗示了细胞内吞可能的运输途径．     

A novel approach for intracellular 3D immuno-labeling for electron tomography

Electron tomography (ET) is an indispensable high-resolution tool for three dimensional (3D) imaging in cell biology. When applied to immuno-labeled cells, ET can provide essential insights in both the cellular architecture and the dynamics. Current protocols for 3D immuno-labeling of intracellular antigens include permeabilization steps that cause random, extensive cell membrane disruption. This permeabilization results in a poor cell ultrastructure, limiting the usefulness of the specimens for high-resolution studies. Here we describe a novel method, based on a well-controlled permeabilization by targeted laser cell perforation, that allows for the 3D immuno-localization of cytoplasmic antigens in cultured cells. The approach is unique since it is applicable to both chemically and cryo-fixed cells and leads to a superior ultrastructural preservation for electron microscopy and tomography.     

3D imaging of diatoms with ion-abrasion scanning electron microscopy

Ion-abrasion scanning electron microscopy (IASEM) takes advantage of focused ion beams to abrade thin sections from the surface of bulk specimens, coupled with SEM to image the surface of each section, enabling 3D reconstructions of subcellular architecture at 30 nm resolution. Here, we report the first application of IASEM for imaging a biomineralizing organism, the marine diatom Thalassiosira pseudonana. Diatoms have highly patterned silica-based cell wall structures that are unique models for the study and application of directed nanomaterials synthesis by biological systems. Our study provides new insights into the architecture and assembly principles of both the “hard” (siliceous) and “soft” (organic) components of the cell. From 3D reconstructions of developmentally synchronized diatoms captured at different stages, we show that both micro- and nanoscale siliceous structures can be visualized at specific stages in their formation. We show that not only are structures visualized in a whole-cell context, but demonstrate that fragile, early-stage structures are visible, and that this can be combined with elemental mapping in the exposed slice. We demonstrate that the 3D architectures of silica structures, and the cellular components that mediate their creation and positioning can be visualized simultaneously, providing new opportunities to study and manipulate mineral nanostructures in a genetically tractable system.     

Light and electron microscopy continuum-resolution imaging of 3D cell cultures

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Automated 3D tree-ring detection and measurement from X-ray computed tomography

Tree ring analysis is essential to reveal the environmental information encoded in the wood structure. It provides quantitative data on the anatomical structure which can be used, for example, to measure the impact of the fluctuating environment on the tree growth, to support global vegetation models and for the dendrochronological analysis of archaeological wooden artefacts. Currently, several imaging-based methods for tree-ring detection and tree-ring feature estimation exist. However, despite advances in computer vision and edge recognition algorithms, detection of tree-rings is mostly limited to two-dimensional (2D) datasets and performed manually in some cases. This paper describes a new approach to estimate the three-dimensional (3D) structure of tree rings and their width automatically from X-ray computed tomography data. This approach relies on a modified Canny edge detection algorithm, which is capable of detecting fully connected tree-ring edges throughout the image stack. Our results show that this approach performs well on six tree species having conifer, ring-porous and diffuse-porous ring boundary structures. In our study, image denoising proved to be a critical step to achieve accurate results. A major advantage of this procedure is that it requires very little to no user interaction rendering it a reproducible procedure for tree-ring width measurements. As it also provides 3D representations of the ring edges, it also may be used in the future for the inspection of anatomical features.     

Imputation and variable selection in linear regression models with missing covariates

Across multiply imputed data sets, variable selection methods such as stepwise regression and other criterion-based strategies that include or exclude particular variables typically result in models with different selected predictors, thus presenting a problem for combining the results from separate complete-data analyses. Here, drawing on a Bayesian framework, we propose two alternative strategies to address the problem of choosing among linear regression models when there are missing covariates. One approach, which we call "impute, then select" (ITS) involves initially performing multiple imputation and then applying Bayesian variable selection to the multiply imputed data sets. A second strategy is to conduct Bayesian variable selection and missing data imputation simultaneously within one Gibbs sampling process, which we call "simultaneously impute and select" (SIAS). The methods are implemented and evaluated using the Bayesian procedure known as stochastic search variable selection for multivariate normal data sets, but both strategies offer general frameworks within which different Bayesian variable selection algorithms could be used for other types of data sets. A study of mental health services utilization among children in foster care programs is used to illustrate the techniques. Simulation studies show that both ITS and SIAS outperform complete-case analysis with stepwise variable selection and that SIAS slightly outperforms ITS.     

Automated tracing of filaments in 3D electron tomography reconstructions using Sculptor and Situs

The molecular graphics program Sculptor and the command-line suite Situs are software packages for the integration of biophysical data across spatial resolution scales. Herein, we provide an overview of recently developed tools relevant to cryo-electron tomography (cryo-ET), with an emphasis on functionality supported by Situs 2.7.1 and Sculptor 2.1.1. We describe a work flow for automatically segmenting filaments in cryo-ET maps including denoising, local normalization, feature detection, and tracing. Tomograms of cellular actin networks exhibit both cross-linked and bundled filament densities. Such filamentous regions in cryo-ET data sets can then be segmented using a stochastic template-based search, VolTrac. The approach combines a genetic algorithm and a bidirectional expansion with a tabu search strategy to localize and characterize filamentous regions. The automated filament segmentation by VolTrac compares well to a manual one performed by expert users, and it allows an efficient and reproducible analysis of large data sets. The software is free, open source, and can be used on Linux, Macintosh or Windows computers.     

Analyzing a randomized trial on breast self-examination with noncompliance and missing outcomes

Recently, instrumental variables methods have been used to address non-compliance in randomized experiments. Complicating such analyses is often the presence of missing data. The standard model for missing data, missing at random (MAR), has some unattractive features in this context. In this paper we compare MAR-based estimates of the complier average causal effect (CACE) with an estimator based on an alternative, nonignorable model for the missing data process, developed by Frangakis and Rubin (1999, Biometrika, 86, 365-379). We also introduce a new missing data model that, like the Frangakis-Rubin model, is specially suited for models with instrumental variables, but makes different substantive assumptions. We analyze these issues in the context of a randomized trial of breast self-examination (BSE). In the study two methods of teaching BSE, consisting of either mailed information about BSE (the standard treatment) or the attendance of a course involving theoretical and practical sessions (the new treatment), were compared with the aim of assessing whether teaching programs could increase BSE practice and improve examination skills. The study was affected by the two sources of bias mentioned above: only 55% of women assigned to receive the new treatment complied with their assignment and 35% of the women did not respond to the post-test questionnaire. Comparing the causal estimand of the new treatment using the MAR, Frangakis-Rubin, and our new approach, the results suggest that for these data the MAR assumption appears least plausible, and that the new model appears most plausible among the three choices.     

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.     

Numerical equivalence of imputing scores and weighted estimators in regression analysis with missing covariates

Imputation, weighting, direct likelihood, and direct Bayesian inference (Rubin, 1976) are important approaches for missing data regression. Many useful semiparametric estimators have been developed for regression analysis of data with missing covariates or outcomes. It has been established that some semiparametric estimators are asymptotically equivalent, but it has not been shown that many are numerically the same. We applied some existing methods to a bladder cancer case-control study and noted that they were the same numerically when the observed covariates and outcomes are categorical. To understand the analytical background of this finding, we further show that when observed covariates and outcomes are categorical, some estimators are not only asymptotically equivalent but also actually numerically identical. That is, although their estimating equations are different, they lead numerically to exactly the same root. This includes a simple weighted estimator, an augmented weighted estimator, and a mean-score estimator. The numerical equivalence may elucidate the relationship between imputing scores and weighted estimation procedures.     

Methods for identifying and averaging variable molecular conformations in tomograms of actively contracting insect flight muscle

During active muscle contraction, tension is generated through many simultaneous, independent interactions between the molecular motor myosin and the actin filaments. The ensemble of myosin motors displays heterogeneous conformations reflecting different mechanochemical steps of the ATPase pathway. We used electron tomography of actively contracting insect flight muscle fast-frozen, freeze substituted, Araldite embedded, thin-sectioned and stained, to obtain 3D snapshots of the multiplicity of actin-attached myosin structures. We describe procedures for alignment of the repeating lattice of sub-volumes (38.7 nm cross-bridge repeats bounded by troponin) and multivariate data analysis to identify self-similar repeats for computing class averages. Improvements in alignment and classification of repeat sub-volumes reveals (for the first time in active muscle images) the helix of actin subunits in the thin filament and the troponin density with sufficient clarity that a quasiatomic model of the thin filament can be built into the class averages independent of the myosin cross-bridges. We show how quasiatomic model building can identify both strong and weak myosin attachments to actin. We evaluate the accuracy of image classification to enumerate the different types of actin–myosin attachments.