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.     

Tomographic subvolume alignment and subvolume classification applied to myosin V and SIV envelope spikes

Electron tomography is a technique for three-dimensional reconstruction, that is widely used for imaging macromolecules, macromolecular assemblies or whole cells. Combined with cryo-electron microscopy, it is capable of visualizing structural detail in a state close to in vivo conditions in the cell. In electron tomography, micrographs are taken while tilting the specimen to different angles about a fixed axis. Due to mechanical constraints, the angular tilt range is limited. As a consequence, the reconstruction of a 3D image is missing data, which for a single axis tilt series is called the “missing wedge”, a region in reciprocal space where Fourier coefficients cannot be obtained experimentally. Tomographic data is analyzed by extracting subvolumes from the raw tomograms, by alignment of the extracted subvolumes, multivariate data analysis, classification, and class-averaging, which results in an increased signal-to-noise ratio and substantial data reduction. Subvolume analysis is a valuable tool to discriminate heterogeneous populations of macromolecules, or conformations of a macromolecule or macromolecular assembly as well as to characterize interactions between macromolecules. However, this analysis is hampered by the lack of data in the original tomograms caused by the missing wedge. Here, we report enhancements of our subvolume processing protocols in which the problem of the missing data in reciprocal space is addressed by using constrained correlation and weighted averaging in reciprocal space. These procedures are applied to the analysis of myosin V and simian immunodeficiency virus (SIV) envelope spikes. We also investigate the effect of the missing wedge on image classification and establish limits of reliability by model calculations with generated phantoms.     

Cross-crystal averaging with search models to improve molecular replacement phases

The application of molecular replacement (MR) in macromolecular crystallography can be limited by the "model bias" problem. Here we propose a strategy to reduce model bias when only part of a new structure is known: after the MR search, structure determination of the unknown part of the new structure can be facilitated by cross-crystal averaging of the known part of the new structure with the search model. This strategy dramatically improves electron density in the unknown part of the new structure. It has enabled us to determine the structures of two coronavirus receptor-binding domains each complexed with their receptor at moderate resolutions. In a test case, it also enabled automated model building when >50% of an antigen-antibody complex was absent. These results suggest that this averaging strategy can be routinely used after MR to enhance the interpretability of electron density associated with missing model.     

Two distinct binding affinities of poliovirus for its cellular receptor

To study the kinetics and equilibrium of poliovirus binding to the poliovirus receptor, we used surface plasmon resonance to examine the interaction of a soluble form of the receptor with poliovirus. Soluble receptor purified from mammalian cells is able to bind poliovirus, neutralize viral infectivity, and induce structural changes in the virus particle. Binding studies revealed that there are two binding sites for the receptor on the poliovirus type 1 capsid, with affinity constants at 20 degrees C of K(D)(1) = 0.67 microm and K(D)(2) = 0.11 microm. The relative abundance of the two binding sites varies with temperature. At 20 degrees C, the K(D)(2) site constitutes approximately 46% of the total binding sites on the sensor chip, and its relative abundance decreased with decreasing temperature such that at 5 degrees C, the relative abundance of the K(D)(2) site is only 12% of the total binding sites. Absolute levels of the K(D)(1) site remained relatively constant at all temperatures tested. The two binding sites may correspond to docking sites for domain 1 of the receptor on the viral capsid, as predicted by a model of the poliovirus-receptor complex. Alternatively, the binding sites may be a consequence of structural breathing, or could result from receptor-induced conformational changes in the virus.     

Maximum likelihood based classification of electron tomographic data

Classification and averaging of sub-tomograms can improve the fidelity and resolution of structures obtained by electron tomography. Here we present a three-dimensional (3D) maximum likelihood algorithm – MLTOMO – which is characterized by integrating 3D alignment and classification into a single, unified processing step. The novelty of our approach lies in the way we calculate the probability of observing an individual sub-tomogram for a given reference structure. We assume that the reference structure is affected by a ‘compound wedge’, resulting from the summation of many individual missing wedges in distinct orientations. The distance metric underlying our probability calculations effectively down-weights Fourier components that are observed less frequently. Simulations demonstrate that MLTOMO clearly outperforms the ‘constrained correlation’ approach and has advantages over existing approaches in cases where the sub-tomograms adopt preferred orientations. Application of our approach to cryo-electron tomographic data of ice-embedded thermosomes revealed distinct conformations that are in good agreement with results obtained by previous single particle studies.     

Classification of cryo-electron sub-tomograms using constrained correlation

Cryo-electron tomography (CET) is currently the only three-dimensional imaging technique capable of visualizing macromolecules in their cellular context at close-to-native conditions with a resolution in the nanometer range. An important component for the analysis of the data is their classification, which should discriminate among various macromolecules, conformational changes and interaction partners. Missing structure factors, typically in a wedge-shaped region in Fourier space if single-axis tilting is performed, hamper classification of cryo-electron tomographic data. Here, we describe a classification method for three-dimensional (3D) sub-tomograms extracted from cryo-electron tomograms, which takes the missing wedge into account and provides reliable results. The similarity of the individually aligned sub-tomograms is scored by constrained correlation. Subsequently, they are clustered based on their pairwise correlation values. In order to demonstrate the feasibility of this approach, we apply the proposed method to simulated tomographic data of the chaperone thermosome in different conformations. By comparison of the principal components of the resulting matrix we show that the proposed metric is significantly less prone to the orientation of the missing wedge compared to the unconstrained correlation. Moreover, we apply our classification method to an experimental dataset of GroEL with and without GroES, where we achieve a distinct discrimination between the putative GroEL and GroEL/GroES complexes.     

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.     

Characterization of the ion channels formed by poliovirus in planar lipid membranes.

The steps in poliovirus infection leading to viral entry and uncoating are not well understood. Current evidence suggests that the virus first binds to a plasma membrane-bound receptor present in viable cells, leading to a conformational rearrangement of the viral proteins such that the virus crosses the membrane and releases the genomic RNA. The studies described in this report were undertaken to determine if poliovirus (160S) as well as one of the subviral particles (135S) could interact with membranes lacking poliovirus receptors in an effort to begin to understand the process of uncoating of the virus. We report that both forms of viral particles, 160S and 135S, interact with lipid membranes and induce the formation of ion-permeable channels in a manner that does not require acid pH. The channels induced by the viral particles 160S have a voltage-dependent conductance which depends on the ionic composition of the medium. Our findings raise the possibility that viral entry into cells may be mediated by direct interaction of viral surface proteins with membrane lipids.     

Substructure of the flagellar basal body of Salmonella typhimurium.

The Salmonella typhimurium basal body, a part of the flagellar rotary motor, consists of four rings (denoted M, S, P and L) and a coaxial rod. Using low-dose electron microscopy and image averaging methods on negatively stained and frozen-hydrated preparations, we examined whole basal body complexes and subcomplexes obtained by dissociation in acid. Dissociation occurs in steps, allowing us to obtain images of substructures lacking the M ring, lacking the M and S rings, and lacking the M and S rings and the proximal portion of the rod. We obtained images of the L and P ring subcomplex. The existence of a subcomplex missing only the M ring suggests either that the S and M rings derive from two different proteins, or that the M ring is a labile domain of a single protein, which makes up both rings. At the 25 to 30 A resolution of our averaged images, the L, P and S rings appear cylindrically symmetric. Images of the M ring show variability that may be due to differences in angular orientation of the grid, but equally could be due to structural variations. Three-dimensional reconstructions of these structures from the averaged images reveal the internal structure and spatial organization of these components.     

An exploration of fixed and random effects selection for longitudinal binary outcomes in the presence of nonignorable dropout

We explore a Bayesian approach to selection of variables that represent fixed and random effects in modeling of longitudinal binary outcomes with missing data caused by dropouts. We show via analytic results for a simple example that nonignorable missing data lead to biased parameter estimates. This bias results in selection of wrong effects asymptotically, which we can confirm via simulations for more complex settings. By jointly modeling the longitudinal binary data with the dropout process that possibly leads to nonignorable missing data, we are able to correct the bias in estimation and selection. Mixture priors with a point mass at zero are used to facilitate variable selection. We illustrate the proposed approach using a clinical trial for acute ischemic stroke.     

Neutralization of poliovirus by cell receptors expressed in insect cells.

To examine the interaction of the poliovirus receptor (PVR) with virus and the role of the PVR in virus entry, the PVR was expressed in insect cells. Poliovirus bound to insect cells infected with a recombinant baculovirus (AcPVR) carrying cDNA encoding the PVR. Antibodies raised against PVR expressed in bacteria immunoprecipitated a 67-kilodalton polypeptide from cytoplasmic extracts of AcPVR-infected cells. Treatment of AcPVR-infected cells with tunicamycin revealed that the PVR is a glycoprotein containing N-glycosidic linkages and that carbohydrate accounts for nearly 50% of its molecular weight as estimated by sodium dodecyl sulfate-polyacrylamide gel electrophoresis. When PVR was solubilized from AcPVR-infected insect cells and incubated with poliovirus, viral infectivity was neutralized. Sedimentation analysis revealed that irreversibly altered 135S particles were formed after incubation of poliovirus at 37 degrees C with solubilized extracts of AcPVR-infected insect cells. These results demonstrate that poliovirus eclipse may result from interaction with the cell receptor at neutral pH in the absence of membranes and suggest that soluble receptors may be effective antiviral agents against picornaviruses.     

Poliovirus proteins induce membrane association of GTPase ADP-ribosylation factor

Poliovirus infection results in the disintegration of intracellular membrane structures and formation of specific vesicles that serve as sites for replication of viral RNA. The mechanism of membrane rearrangement has not been clearly defined. Replication of poliovirus is sensitive to brefeldin A (BFA), a fungal metabolite known to prevent normal function of the ADP-ribosylation factor (ARF) family of small GTPases. During normal membrane trafficking in uninfected cells, ARFs are involved in vesicle formation from different intracellular sites through interaction with numerous regulatory and coat proteins as well as in regulation of phospholipase D activity and cytoskeleton modifications. We demonstrate here that ARFs 3 and 5, but not ARF6, are translocated to membranes in HeLa cell extracts that are engaged in translation of poliovirus RNA. The accumulation of ARFs on membranes correlates with active replication of poliovirus RNA in vitro, whereas ARF translocation to membranes does not occur in the presence of BFA. ARF translocation can be induced independently by synthesis of poliovirus 3A or 3CD proteins, and we describe mutations that abolished this activity. In infected HeLa cells, an ARF1-enhanced green fluorescent protein fusion redistributes from Golgi stacks to the perinuclear region, where poliovirus RNA replication occurs. Taken together, the data suggest an involvement of ARF in poliovirus RNA replication.     

Intracellular topology and epitope shielding of poliovirus 3A protein

The poliovirus RNA replication complex comprises multiple viral and possibly cellular proteins assembled on the cytoplasmic surface of rearranged intracellular membranes. Viral proteins 3A and 3AB perform several functions during the poliovirus replicative cycle, including significant roles in rearranging membranes, anchoring the viral polymerase to these membranes, inhibiting host protein secretion, and possibly providing the 3B protein primer for RNA synthesis. During poliovirus infection, the immunofluorescence signal of an amino-terminal epitope of 3A-containing proteins is markedly shielded compared to 3A protein expressed in the absence of other poliovirus proteins. This is not due to luminal orientation of all or a subset of the 3A-containing polypeptides, as shown by immunofluorescence following differential permeabilization and proteolysis experiments. Shielding of the 3A epitope is more pronounced in cells infected with wild-type poliovirus than in cells with temperature-sensitive mutant virus that contains a mutation in the 3D polymerase coding region adjacent to the 3AB binding site. Therefore, it is likely that direct binding of the poliovirus RNA-dependent RNA polymerase occludes the amino terminus of 3A-containing polypeptides in the RNA replication complex.     

A Semiparametric Missing‐Data‐Induced Intensity Method for Missing Covariate Data in Individually Matched Case–Control Studies

Summary In individually matched case–control studies, when some covariates are incomplete, an analysis based on the complete data may result in a large loss of information both in the missing and completely observed variables. This usually results in a bias and loss of efficiency. In this article, we propose a new method for handling the problem of missing covariate data based on a missing‐data‐induced intensity approach when the missingness mechanism does not depend on case–control status and show that this leads to a generalization of the missing indicator method. We derive the asymptotic properties of the estimates from the proposed method and, using an extensive simulation study, assess the finite sample performance in terms of bias, efficiency, and 95% confidence coverage under several missing data scenarios. We also make comparisons with complete‐case analysis (CCA) and some missing data methods that have been proposed previously. Our results indicate that, under the assumption of predictable missingness, the suggested method provides valid estimation of parameters, is more efficient than CCA, and is competitive with other, more complex methods of analysis. A case–control study of multiple myeloma risk and a polymorphism in the receptor Inter‐Leukin‐6 (IL‐6‐α) is used to illustrate our findings.     

Visualization of alpha-helical features in a density map constructed using 9 molecular images of the 1.8 MDa icosahedral core of pyruvate dehydrogenase

Strategies to achieve the highest resolutions in structures of protein complexes determined by cryo-electron microscopy generally involve averaging information from large numbers of individual molecular images. However, significant limitations are posed by heterogeneity in image quality and in protein conformation that are inherent to large data sets of images. Here, we demonstrate that the combination of iterative refinement and stringent molecular sorting is an effective method to obtain substantial improvements in map quality of the 1.8 MDa icosahedral catalytic core of the pyruvate dehydrogenase complex from Bacillus stearothermophilus. From a starting set of 42,945 images of the core complex, we show that using only the best 139 particles in the data set produces a map that is superior to those constructed with greater numbers of images, and that the location of many of the alpha-helices in the structure can be unambiguously visualized in a map constructed from as few as 9 particles.     

Graph identification of proteins in tomograms (GRIP-Tomo)

In this study, we present a method of pattern mining based on network theory that enables the identification of protein structures or complexes from synthetic volume densities, without the knowledge of predefined templates or human biases for refinement. We hypothesized that the topological connectivity of protein structures is invariant, and they are distinctive for the purpose of protein identification from distorted data presented in volume densities. Three-dimensional densities of a protein or a complex from simulated tomographic volumes were transformed into mathematical graphs as observables. We systematically introduced data distortion or defects such as missing fullness of data, the tumbling effect, and the missing wedge effect into the simulated volumes, and varied the distance cutoffs in pixels to capture the varying connectivity between the density cluster centroids in the presence of defects. A similarity score between the graphs from the simulated volumes and the graphs transformed from the physical protein structures in point data was calculated by comparing their network theory order parameters including node degrees, betweenness centrality, and graph densities. By capturing the essential topological features defining the heterogeneous morphologies of a network, we were able to accurately identify proteins and homo-multimeric complexes from 10 topologically distinctive samples without realistic noise added. Our approach empowers future developments of tomogram processing by providing pattern mining with interpretability, to enable the classification of single-domain protein native topologies as well as distinct single-domain proteins from multimeric complexes within noisy volumes.     

CD44 is not required for poliovirus replication.

The identification of a monoclonal antibody, AF3, which recognizes a single isoform of the cell surface protein CD44 and preferentially blocks binding of serotype 2 poliovirus to HeLa cells, suggested that CD44 might be an accessory molecule to Pvr, the cell receptor for poliovirus, and that it could play a role in the function of the poliovirus receptor site. We show here that only AF3 blocks binding of serotype 2 poliovirus to HeLa cells and, in contrast to a previously published report, that the anti-CD44 monoclonal antibodies A3D8 and IM7 are unable to block binding of poliovirus. To determine whether CD44 is involved in poliovirus infection, we analyzed the replication of all three serotypes of poliovirus in human neuroblastoma cells which lack or express CD44 and in mouse neuroblastoma cells which lack Pgp-1, the mouse homolog of human CD44, and which express Pvr. All three poliovirus serotypes replicate with normal kinetics and to normal levels in the absence or presence of CD44 or in the absence of Pgp-1. Furthermore, the binding affinity constants of all three poliovirus serotypes for Pvr are unaffected by the presence or absence of CD44 in the human neuroblastoma cell line. We conclude that CD44 and Pgp-1 are not required for poliovirus replication and are unlikely to be involved in poliovirus pathogenesis.     

Multi-Task Linear Programming Discriminant Analysis for the Identification of Progressive MCI Individuals

Accurately identifying mild cognitive impairment (MCI) individuals who will progress to Alzheimer''s disease (AD) is very important for making early interventions. Many classification methods focus on integrating multiple imaging modalities such as magnetic resonance imaging (MRI) and fluorodeoxyglucose positron emission tomography (FDG-PET). However, the main challenge for MCI classification using multiple imaging modalities is the existence of a lot of missing data in many subjects. For example, in the Alzheimer''s Disease Neuroimaging Initiative (ADNI) study, almost half of the subjects do not have PET images. In this paper, we propose a new and flexible binary classification method, namely Multi-task Linear Programming Discriminant (MLPD) analysis, for the incomplete multi-source feature learning. Specifically, we decompose the classification problem into different classification tasks, i.e., one for each combination of available data sources. To solve all different classification tasks jointly, our proposed MLPD method links them together by constraining them to achieve the similar estimated mean difference between the two classes (under classification) for those shared features. Compared with the state-of-the-art incomplete Multi-Source Feature (iMSF) learning method, instead of constraining different classification tasks to choose a common feature subset for those shared features, MLPD can flexibly and adaptively choose different feature subsets for different classification tasks. Furthermore, our proposed MLPD method can be efficiently implemented by linear programming. To validate our MLPD method, we perform experiments on the ADNI baseline dataset with the incomplete MRI and PET images from 167 progressive MCI (pMCI) subjects and 226 stable MCI (sMCI) subjects. We further compared our method with the iMSF method (using incomplete MRI and PET images) and also the single-task classification method (using only MRI or only subjects with both MRI and PET images). Experimental results show very promising performance of our proposed MLPD method.     

Symmetry and dimensions of membrane-bound nicotinic acetylcholine receptors from Torpedo californica electric tissue: rapid rearrangement to two-dimensional ordered lattices

Computer-aided image-averaging methods are applied to different preparations of membrane-bound nicotinic acetylcholine receptor. Circular harmonic averaging (CHA), a novel, reference-independent averaging method developed by W. Kunath and H. Sack-Kongehl [1989) Ultramicroscopy 27:171-184) allows analyzing images of single molecules of the receptor in its native membrane-bound state. The five subunits of the receptor are clearly resolved. At the resolution obtained (approximately 20 A) no differences were observed with resting and agonist-desensitized receptors. A method is proposed for rapidly arranging the acetylcholine receptors to ordered lattices. Depending on the conditions, tetragonal or hexagonal, two-dimensional lattices can be obtained within 2 to 6 days at 4 degrees C. Analysis by CHA shows that the receptor molecules preserve their gross structure and dimensions in these membranes, but that they are randomly oriented. Both lattices, therefore, do not represent true two-dimensional crystals.     

The poliovirus replication machinery can escape inhibition by an antiviral drug that targets a host cell protein

Viral replication depends on specific interactions with host factors. For example, poliovirus RNA replication requires association with intracellular membranes. Brefeldin A (BFA), which induces a major rearrangement of the cellular secretory apparatus, is a potent inhibitor of poliovirus RNA replication. Most aspects governing the relationship between viral replication complex and the host membranes remain poorly defined. To explore these interactions, we used a genetic approach and isolated BFA-resistant poliovirus variants. Mutations within viral proteins 2C and 3A render poliovirus resistant to BFA. In the absence of BFA, viruses containing either or both of these mutations replicated similarly to wild type. In the presence of BFA, viruses carrying a single mutation in 2C or 3A exhibited an intermediate-growth phenotype, while the double mutant was fully resistant. The viral proteins 2C and 3A have critical roles in both RNA replication and vesicle formation. The identification of BFA resistant mutants may facilitate the identification of cellular membrane-associated proteins necessary for induction of vesicle formation and RNA replication. Importantly, our data underscore the dramatic plasticity of the host-virus interactions required for successful viral replication.