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

Determining Protein Secondary Structures in Heterogeneous Medium-Resolution Cryo-EM Images Using CryoSSESeg

While the acquisition of cryo-electron microscopy (cryo-EM) at near-atomic resolution is becoming more prevalent, a considerable number of density maps are still resolved only at intermediate resolutions (5-10 Å). Due to the large variation in quality among these medium-resolution density maps, extracting structural information from them remains a challenging task. This study introduces a convolutional neural network (CNN)-based framework, cryoSSESeg, to determine the organization of protein secondary structure elements in medium-resolution cryo-EM images. CryoSSESeg is trained on approximately 1300 protein chains derived from around 500 experimental cryo-EM density maps of varied quality. It demonstrates strong performance with residue-level F 1 scores of 0.76 for helix detection and 0.60 for β-sheet detection on average across a set of testing chains. In comparison to traditional image processing tools like SSETracer, which demand significant manual intervention and preprocessing steps, cryoSSESeg demonstrates comparable or superior performance. Additionally, it demonstrates competitive performance alongside another deep learning-based model, Emap2sec. Furthermore, this study underscores the importance of secondary structure quality, particularly adherence to expected shapes, in detection performance, emphasizing the necessity for careful evaluation of the data quality.

Automatic determination of the handedness of single-particle maps of macromolecules solved by CryoEM

Single-Particle Analysis by Cryo-Electron Microscopy is a well-established technique to elucidate the three-dimensional (3D) structure of biological macromolecules. The orientation of the acquired projection images must be initially estimated without any reference to the final structure. In this step, algorithms may find a mirrored version of all the orientations resulting in a mirrored 3D map. It is as compatible with the acquired images as its unmirrored version from the image processing point of view, only that it is not biologically plausible. In this article, we introduce HaPi (Handedness Pipeline), the first method to automatically determine the hand of electron density maps of macromolecules solved by CryoEM. HaPi is built by training two 3D convolutional neural networks. The first determines α-helices in a map, and the second determines whether the α-helix is left-handed or right-handed. A consensus strategy defines the overall map hand. The pipeline is trained on simulated and experimental data. The handedness can be detected only for maps whose resolution is better than 5 Å. HaPi can identify the hand in 89% of new simulated maps correctly. Moreover, we evaluated all the maps deposited at the Electron Microscopy Data Bank and 11 structures uploaded with the incorrect hand were identified.

Combining Cryo-EM Density Map and Residue Contact for Protein Secondary Structure Topologies

Although atomic structures have been determined directly from cryo-EM density maps with high resolutions, current structure determination methods for medium resolution (5 to 10 Å) cryo-EM maps are limited by the availability of structure templates. Secondary structure traces are lines detected from a cryo-EM density map for α-helices and β-strands of a protein. A topology of secondary structures defines the mapping between a set of sequence segments and a set of traces of secondary structures in three-dimensional space. In order to enhance accuracy in ranking secondary structure topologies, we explored a method that combines three sources of information: a set of sequence segments in 1D, a set of amino acid contact pairs in 2D, and a set of traces in 3D at the secondary structure level. A test of fourteen cases shows that the accuracy of predicted secondary structures is critical for deriving topologies. The use of significant long-range contact pairs is most effective at enriching the rank of the maximum-match topology for proteins with a large number of secondary structures, if the secondary structure prediction is fairly accurate. It was observed that the enrichment depends on the quality of initial topology candidates in this approach. We provide detailed analysis in various cases to show the potential and challenge when combining three sources of information.

A Tool for Segmentation of Secondary Structures in 3D Cryo-EM Density Map Components Using Deep Convolutional Neural Networks

Although cryo-electron microscopy (cryo-EM) has been successfully used to derive atomic structures for many proteins, it is still challenging to derive atomic structures when the resolution of cryo-EM density maps is in the medium resolution range, such as 5-10 Å. Detection of protein secondary structures, such as helices and β-sheets, from cryo-EM density maps provides constraints for deriving atomic structures from such maps. As more deep learning methodologies are being developed for solving various molecular problems, effective tools are needed for users to access them. We have developed an effective software bundle, DeepSSETracer, for the detection of protein secondary structure from cryo-EM component maps in medium resolution. The bundle contains the network architecture and a U-Net model trained with a curriculum and gradient of episodic memory (GEM). The bundle integrates the deep neural network with the visualization capacity provided in ChimeraX. Using a Linux server that is remotely accessed by Windows users, it takes about 6 s on one CPU and one GPU for the trained deep neural network to detect secondary structures in a cryo-EM component map containing 446 amino acids. A test using 28 chain components of cryo-EM maps shows overall residue-level F1 scores of 0.72 and 0.65 to detect helices and β-sheets, respectively. Although deep learning applications are built on software frameworks, such as PyTorch and Tensorflow, our pioneer work here shows that integration of deep learning applications with ChimeraX is a promising and effective approach. Our experiments show that the F1 score measured at the residue level is an effective evaluation of secondary structure detection for individual classes. The test using 28 cryo-EM component maps shows that DeepSSETracer detects β-sheets more accurately than Emap2sec+, with a weighted average residue-level F1 score of 0.65 and 0.42, respectively. It also shows that Emap2sec+ detects helices more accurately than DeepSSETracer with a weighted average residue-level F1 score of 0.77 and 0.72 respectively.

Combine Cryo-EM Density Map and Residue Contact for Protein Structure Prediction - A Case Study

Cryo-electron microscopy is a major structure determination technique for large molecular machines and membrane-associated complexes. Although atomic structures have been determined directly from cryo-EM density maps with high resolutions, current structure determination methods for medium resolution (5 to 10 Å) cryo-EM maps are limited by the availability of structure templates. Secondary structure traces are lines detected from a cryo-EM density map for α-helices and β-strands of a protein. When combined with secondary structure sequence segments predicted from a protein sequence, it is possible to generate a set of likely topologies of α-traces and β-sheet traces. A topology describes the overall folding relationship among secondary structures; it is a critical piece of information for deriving the corresponding atomic structure. We propose a method for protein structure prediction that combines three sources of information: the secondary structure traces detected from the cryo-EM density map, predicted secondary structure sequence segments, and amino acid contact pairs predicted using MULTICOM. A case study shows that using amino acid contact prediction from MULTICOM improves the ranking of the true topology. Our observations convey that using a small set of highly voted secondary structure contact pairs enhances the ranking in all experiments conducted for this case.

Using Curriculum Learning in Pattern Recognition of 3-dimensional Cryo-electron Microscopy Density Maps

Although Cryo-electron microscopy (cryo-EM) has been successfully used to derive atomic structures for many proteins, it is still challenging to derive atomic structure when the resolution of cryo-EM density maps is in the medium range, e.g., 5-10 Å. Studies have attempted to utilize machine learning methods, especially deep neural networks to build predictive models for the detection of protein secondary structures from cryo-EM images, which ultimately helps to derive the atomic structure of proteins. However, the large variation in data quality makes it challenging to train a deep neural network with high prediction accuracy. Curriculum learning has been shown as an effective learning paradigm in machine learning. In this paper, we present a study using curriculum learning as a more effective way to utilize cryo-EM density maps with varying quality. We investigated three distinct training curricula that differ in whether/how images used for training in past are reused while the network was continually trained using new images. A total of 1,382 3-dimensional cryo-EM images were extracted from density maps of Electron Microscopy Data Bank in our study. Our results indicate learning with curriculum significantly improves the performance of the final trained network when the forgetting problem is properly addressed.

Cylindrical Similarity Measurement for Helices in Medium-Resolution Cryo-Electron Microscopy Density Maps

Cryo-electron microscopy (cryo-EM) density maps at medium resolution (5-10 Å) reveal secondary structural features such as α-helices and β-sheets, but they lack the side chain details that would enable a direct structure determination. Among the more than 800 entries in the Electron Microscopy Data Bank (EMDB) of medium-resolution density maps that are associated with atomic models, a wide variety of similarities can be observed between maps and models. To validate such atomic models and to classify structural features, a local similarity criterion, the F1 score, is proposed and evaluated in this study. The F1 score is theoretically normalized to a range from zero to one, providing a local measure of cylindrical agreement between the density and atomic model of a helix. A systematic scan of 30,994 helices (among 3,247 protein chains modeled into medium-resolution density maps) reveals an actual range of observed F1 scores from 0.171 to 0.848, suggesting that the cylindrical fit of the current data is well stratified by the proposed measure. The best (highest) F1 scores tend to be associated with regions that exhibit high and spatially homogeneous local resolution (between 5 Å and 7.5 Å) in the helical density. The proposed F1 scores can be used as a discriminative classifier for validation studies and as a ranking criterion for cryo-EM density features in databases.

Simulation-Based Methods for Model Building and Refinement in Cryoelectron Microscopy

Advances in cryoelectron microscopy (cryo-EM) have revolutionized the structural investigation of large macromolecular assemblies. In this review, we first provide a broad overview of modeling methods used for flexible fitting of molecular models into cryo-EM density maps. We give special attention to approaches rooted in molecular simulations-atomistic molecular dynamics and Monte Carlo. Concise descriptions of the methods are given along with discussion of their advantages, limitations, and most popular alternatives. We also describe recent extensions of the widely used molecular dynamics flexible fitting (MDFF) method and discuss how different model-building techniques could be incorporated into new hybrid modeling schemes and simulation workflows. Finally, we provide two illustrative examples of model-building and refinement strategies employing MDFF, cascade MDFF, and RosettaCM. These examples come from recent cryo-EM studies that elucidated transcription preinitiation complexes and shed light on the functional roles of these assemblies in gene expression and gene regulation.

Exploratory Studies Detecting Secondary Structures in Medium Resolution 3D Cryo-EM Images Using Deep Convolutional Neural Networks

Cryo-electron microscopy (cryo-EM) is an emerging biophysical technique for structural determination of protein complexes. However, accurate detection of secondary structures is still challenging when cryo-EM density maps are at medium resolutions (5-10 Å). Most of existing methods are image processing methods that do not fully utilize available images in the cryo-EM database. In this paper, we present a deep learning approach to segment secondary structure elements as helices and β-sheets from medium-resolution density maps. The proposed 3D convolutional neural network is shown to detect secondary structure locations with an F1 score between 0.79 and 0.88 for six simulated test cases. The architecture was also applied to an experimentally-derived cryo-EM density map with good accuracy.

A Pattern Recognition Tool for Medium-resolution Cryo-EM Density Maps and Low-resolution Cryo-ET Density maps

Cryo-electron microscopy (Cryo-EM) and cryo-electron tomography (cryo-ET) produce 3-D density maps of biological molecules at a range of resolution levels. Pattern recognition tools are important in distinguishing biological components from volumetric maps with the available resolutions. One of the most distinct characters in density maps at medium (5-10 Å) resolution is the visibility of protein secondary structures. Although computational methods have been developed, the accurate detection of helices and β-strands from cryo-EM density maps is still an active research area. We have developed a tool for protein secondary structure detection and evaluation of medium resolution 3-D cryo-EM density maps which combines three computational methods (SSETracer, StrandTwister, and AxisComparison). The program was integrated in UCSF Chimera, a popular visualization software in the cryo-EM community. In related work, we have developed BundleTrac, a computational method to trace filaments in a bundle from lower resolution cryo-ET density maps. It has been applied to actin filament tracing in stereocilia with good accuracy and can be potentially added as a tool in Chimera.

CryoEM-based hybrid modeling approaches for structure determination

Recent advances in cryo-electron microscopy (cryoEM) have dramatically improved the resolutions at which vitrified biological specimens can be studied, revealing new structural and mechanistic insights over a broad range of spatial scales. Bolstered by these advances, much effort has been directed toward the development of hybrid modeling methodologies for the construction and refinement of high-fidelity atomistic models from cryoEM data. In this brief review, we will survey the key elements of cryoEM-based hybrid modeling, providing an overview of available computational tools and strategies as well as several recent applications.

Tracing Actin Filament Bundles in Three-Dimensional Electron Tomography Density Maps of Hair Cell Stereocilia

Cryo-electron tomography (cryo-ET) is a powerful method of visualizing the three-dimensional organization of supramolecular complexes, such as the cytoskeleton, in their native cell and tissue contexts. Due to its minimal electron dose and reconstruction artifacts arising from the missing wedge during data collection, cryo-ET typically results in noisy density maps that display anisotropic XY versus Z resolution. Molecular crowding further exacerbates the challenge of automatically detecting supramolecular complexes, such as the actin bundle in hair cell stereocilia. Stereocilia are pivotal to the mechanoelectrical transduction process in inner ear sensory epithelial hair cells. Given the complexity and dense arrangement of actin bundles, traditional approaches to filament detection and tracing have failed in these cases. In this study, we introduce BundleTrac, an effective method to trace hundreds of filaments in a bundle. A comparison between BundleTrac and manually tracing the actin filaments in a stereocilium showed that BundleTrac accurately built 326 of 330 filaments (98.8%), with an overall cross-distance of 1.3 voxels for the 330 filaments. BundleTrac is an effective semi-automatic modeling approach in which a seed point is provided for each filament and the rest of the filament is computationally identified. We also demonstrate the potential of a denoising method that uses a polynomial regression to address the resolution and high-noise anisotropic environment of the density map.

Quantification of Twist from the Central Lines of β-Strands

Since the discovery of right-handed twist of a β-strand, many studies have been conducted to understand the twist. Given the atomic structure of a protein, twist angles have been defined using atomic positions of the backbone. However, limited study is available to characterize twist when the atomic positions are not available, but the central lines of β-strands are. Recent studies in cryoelectron microscopy show that it is possible to predict the central lines of β-strands from a medium-resolution density map. Accurate measurement of twist angles is important in identification of β-strands from such density maps. We propose an effective method to quantify twist angles from a set of splines. In a data set of 55 pairs of β-strands from 11 β-sheets of 11 proteins, the spline measurement shows comparable results as measured using the discrete method that uses atomic positions directly, particularly in capturing twist angle change along a pair, different levels of twist among different pairs, and the average of twist angles. The proposed method provides an alternative method to characterize twist using the central lines of a β-sheet.

Beta-Barrel Detection for Medium Resolution Cryo-Electron Microscopy Density Maps Using Genetic Algorithms and Ray Tracing

Cryo-electron microscopy (cryo-EM) is a technique that produces three-dimensional density maps of large protein complexes. This allows for the study of the structure of these proteins. Identifying the secondary structures within proteins is vital to understanding the overall structure and function of the protein. The [Formula: see text]-barrel is one such secondary structure, commonly found in lipocalins and membrane proteins. In this article, we present a novel approach that utilizes genetic algorithms, kd-trees, and ray tracing to automatically detect and extract [Formula: see text]-barrels from cryo-EM density maps. This approach was tested on simulated and experimental density maps with zero, one, or multiple barrels in the density map. The results suggest that the proposed approach is capable of performing automatic detection of [Formula: see text]-barrels from medium resolution cryo-EM density maps.

Analysis of β-strand Twist from the 3-dimensional Image of a Protein

Electron cryo-microscopy (Cryo-EM) technique produces density maps that are 3-dimensional (3D) images of molecules. It is challenging to derive atomic structures of proteins from 3D images of medium resolutions. Twist of a β-strand has been studied extensively while little of the known information has been directly obtained from the 3D image of a β-sheet. We describe a method to characterize the twist of β-strands from the 3D image of a protein. An analysis of 11 β-sheet images shows that the Averaged Minimum Twist (AMT) angle is larger for a close set than for a far set of β-traces.

An Effective Computational Method Incorporating Multiple Secondary Structure Predictions in Topology Determination for Cryo-EM Images

A key idea in de novo modeling of a medium-resolution density image obtained from cryo-electron microscopy is to compute the optimal mapping between the secondary structure traces observed in the density image and those predicted on the protein sequence. When secondary structures are not determined precisely, either from the image or from the amino acid sequence of the protein, the computational problem becomes more complex. We present an efficient method that addresses the secondary structure placement problem in presence of multiple secondary structure predictions and computes the optimal mapping. We tested the method using 12 simulated images from α-proteins and two Cryo-EM images of α-β proteins. We observed that the rank of the true topologies is consistently improved by using multiple secondary structure predictions instead of a single prediction. The results show that the algorithm is robust and works well even when errors/misses in the predicted secondary structures are present in the image or the sequence. The results also show that the algorithm is efficient and is able to handle proteins with as many as 33 helices.

Deep Convolutional Neural Networks for Detecting Secondary Structures in Protein Density Maps from Cryo-Electron Microscopy

The detection of secondary structure of proteins using three dimensional (3D) cryo-electron microscopy (cryo-EM) images is still a challenging task when the spatial resolution of cryo-EM images is at medium level (5-10Å ). Prior researches focused on the usage of local features that may not capture the global information of image objects. In this study, we propose to use deep learning methods to extract high representative global features and then automatically detect secondary structures of proteins. In particular, we build a convolutional neural network (CNN) classifier that predicts the probability of label for every individual voxel in 3D cryo-EM image with respect to the secondary structure elements of proteins such as α-helix, β-sheet and background. To effectively incorporate the 3D spatial information in protein structures, we propose to perform 3D convolutions in the convolutional layers of CNNs. We show that the proposed CNN classifier can outperform existing SVM method on identifying the secondary structure elements of proteins from 3D cryo-EM medium resolution images.

Modeling Beta-Traces for Beta-Barrels from Cryo-EM Density Maps

Cryo-electron microscopy (cryo-EM) has produced density maps of various resolutions. Although α-helices can be detected from density maps at 5-8 Å resolutions, β-strands are challenging to detect at such density maps due to close-spacing of β-strands. The variety of shapes of β-sheets adds the complexity of β-strands detection from density maps. We propose a new approach to model traces of β-strands for β-barrel density regions that are extracted from cryo-EM density maps. In the test containing eight β-barrels extracted from experimental cryo-EM density maps at 5.5 Å-8.25 Å resolution, StrandRoller detected about 74.26% of the amino acids in the β-strands with an overall 2.05 Å 2-way distance between the detected β-traces and the observed ones, if the best of the fifteen detection cases is considered.

An Iterative Bézier Method for Fitting Beta-sheet Component of a Cryo-EM Density Map

Cryo-electron microscopy (Cryo-EM) is a powerful technique to produce 3-dimensional density maps for large molecular complexes. Although many atomic structures have been solved from cryo-EM density maps, it is challenging to derive atomic structures when the resolution of density maps is not sufficiently high. Geometrical shape representation of secondary structural components in a medium-resolution density map enhances modeling of atomic structures. We compare two methods in producing surface representation of the β-sheet component of a density map. Given a 3-dimensional volume of β-sheet that is segmented from a density map, the performance of a polynomial fitting was compared with that of an iterative Bézier fitting. The results suggest that the iterative Bézier fitting is more suitable for β-sheets, since it provides more accurate representation of the corners that are naturally twisted in a β-sheet.

Comparing an Atomic Model or Structure to a Corresponding Cryo-electron Microscopy Image at the Central Axis of a Helix

Three-dimensional density maps of biological specimens from cryo-electron microscopy (cryo-EM) can be interpreted in the form of atomic models that are modeled into the density, or they can be compared to known atomic structures. When the central axis of a helix is detectable in a cryo-EM density map, it is possible to quantify the agreement between this central axis and a central axis calculated from the atomic model or structure. We propose a novel arc-length association method to compare the two axes reliably. This method was applied to 79 helices in simulated density maps and six case studies using cryo-EM maps at 6.4-7.7 Å resolution. The arc-length association method is then compared to three existing measures that evaluate the separation of two helical axes: a two-way distance between point sets, the length difference between two axes, and the individual amino acid detection accuracy. The results show that our proposed method sensitively distinguishes lateral and longitudinal discrepancies between the two axes, which makes the method particularly suitable for the systematic investigation of cryo-EM map-model pairs.

CHALLENGES IN MATCHING SECONDARY STRUCTURES IN CRYO-EM: AN EXPLORATION

Cryo-electron microscopy is a fast emerging biophysical technique for structural determination of large protein complexes. While more atomic structures are being determined using this technique, it is still challenging to derive atomic structures from density maps produced at medium resolution when no suitable templates are available. A critical step in structure determination is how a protein chain threads through the 3-dimensional density map. A dynamic programming method was previously developed to generate K best matches of secondary structures between the density map and its protein sequence using shortest paths in a related weighted graph. We discuss challenges associated with the creation of the weighted graph and explore heuristic methods to solve the problem of matching secondary structures.

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

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

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

Comparison of an Atomic Model and Its Cryo-EM Image at the Central Axis of a Helix

Cryo-electron microscopy (cryo-EM) is an important biophysical technique that produces three-dimensional (3D) density maps at different resolutions. Because more and more models are being produced from cryo-EM density maps, validation of the models is becoming important. We propose a method for measuring local agreement between a model and the density map using the central axis of the helix. This method was tested using 19 helices from cryo-EM density maps between 5.5 Å and 7.2 Å resolution and 94 helices from simulated density maps. This method distinguished most of the well-fitting helices, although challenges exist for shorter helices.

Numerical geometry of map and model assessment

We are describing best practices and assessment strategies for the atomic interpretation of cryo-electron microscopy (cryo-EM) maps. Multiscale numerical geometry strategies in the Situs package and in secondary structure detection software are currently evolving due to the recent increases in cryo-EM resolution. Criteria that aim to predict the accuracy of fitted atomic models at low (worse than 8Å) and medium (4-8 Å) resolutions remain challenging. However, a high level of confidence in atomic models can be achieved by combining such criteria. The observed errors are due to map-model discrepancies and due to the effect of imperfect global docking strategies. Extending the earlier motion capture approach developed for flexible fitting, we use simulated fiducials (pseudoatoms) at varying levels of coarse-graining to track the local drift of structural features. We compare three tracking approaches: naïve vector quantization, a smoothly deformable model, and a tessellation of the structure into rigid Voronoi cells, which are fitted using a multi-fragment refinement approach. The lowest error is an upper bound for the (small) discrepancy between the crystal structure and the EM map due to different conditions in their structure determination. When internal features such as secondary structures are visible in medium-resolution EM maps, it is possible to extend the idea of point-based fiducials to more complex geometric representations such as helical axes, strands, and skeletons. We propose quantitative strategies to assess map-model pairs when such secondary structure patterns are prominent.

A Dynamic Programming Algorithm for Finding the Optimal Placement of a Secondary Structure Topology in Cryo-EM Data

The determination of secondary structure topology is a critical step in deriving the atomic structures from the protein density maps obtained from electron cryomicroscopy technique. This step often relies on matching the secondary structure traces detected from the protein density map to the secondary structure sequence segments predicted from the amino acid sequence. Due to inaccuracies in both sources of information, a pool of possible secondary structure positions needs to be sampled. One way to approach the problem is to first derive a small number of possible topologies using existing matching algorithms, and then find the optimal placement for each possible topology. We present a dynamic programming method of Θ(Nq(2)h) to find the optimal placement for a secondary structure topology. We show that our algorithm requires significantly less computational time than the brute force method that is in the order of Θ(q(N) h).

Three-dimensional structure of a protozoal double-stranded RNA virus that infects the enteric pathogen Giardia lamblia

Giardia lamblia virus (GLV) is a small, nonenveloped, nonsegmented double-stranded RNA (dsRNA) virus infecting Giardia lamblia, the most common protozoan pathogen of the human intestine and a major agent of waterborne diarrheal disease worldwide. GLV (genus Giardiavirus) is a member of family Totiviridae, along with several other groups of protozoal or fungal viruses, including Leishmania RNA viruses and Trichomonas vaginalis viruses. Interestingly, GLV is more closely related than other Totiviridae members to a group of recently discovered metazoan viruses that includes penaeid shrimp infectious myonecrosis virus (IMNV). Moreover, GLV is the only known protozoal dsRNA virus that can transmit efficiently by extracellular means, also like IMNV. In this study, we used transmission electron cryomicroscopy and icosahedral image reconstruction to examine the GLV virion at an estimated resolution of 6.0 Å. Its outermost diameter is 485 Å, making it the largest totivirus capsid analyzed to date. Structural comparisons of GLV and other totiviruses highlighted a related "T=2" capsid organization and a conserved helix-rich fold in the capsid subunits. In agreement with its unique capacity as a protozoal dsRNA virus to survive and transmit through extracellular environments, GLV was found to be more thermoresistant than Trichomonas vaginalis virus 1, but no specific protein machinery to mediate cell entry, such as the fiber complexes in IMNV, could be localized. These and other structural and biochemical findings provide a basis for future work to dissect the cell entry mechanism of GLV into a "primitive" (early-branching) eukaryotic host and an important enteric pathogen of humans.

IMPORTANCE

Numerous pathogenic bacteria, including Corynebacterium diphtheriae, Salmonella enterica, and Vibrio cholerae, are infected with lysogenic bacteriophages that contribute significantly to bacterial virulence. In line with this phenomenon, several pathogenic protozoa, including Giardia lamblia, Leishmania species, and Trichomonas vaginalis are persistently infected with dsRNA viruses, and growing evidence indicates that at least some of these protozoal viruses can likewise enhance the pathogenicity of their hosts. Understanding of these protozoal viruses, however, lags far behind that of many bacteriophages. Here, we investigated the dsRNA virus that infects the widespread enteric parasite Giardia lamblia. Using electron cryomicroscopy and icosahedral image reconstruction, we determined the virion structure of Giardia lamblia virus, obtaining new information relating to its assembly, stability, functions in cell entry and transcription, and similarities and differences with other dsRNA viruses. The results of our study set the stage for further mechanistic work on the roles of these viruses in protozoal virulence.

Three-dimensional structure of victorivirus HvV190S suggests coat proteins in most totiviruses share a conserved core

Double-stranded (ds)RNA fungal viruses are currently assigned to six different families. Those from the family Totiviridae are characterized by nonsegmented genomes and single-layer capsids, 300–450 Å in diameter. Helminthosporium victoriae virus 190S (HvV190S), prototype of recently recognized genus Victorivirus, infects the filamentous fungus Helminthosporium victoriae (telomorph: Cochliobolus victoriae), which is the causal agent of Victoria blight of oats. The HvV190S genome is 5179 bp long and encompasses two large, slightly overlapping open reading frames that encode the coat protein (CP, 772 aa) and the RNA-dependent RNA polymerase (RdRp, 835 aa). To our present knowledge, victoriviruses uniquely express their RdRps via a coupled termination–reinitiation mechanism that differs from the well-characterized Saccharomyces cerevisiae virus L-A (ScV-L-A, prototype of genus Totivirus), in which the RdRp is expressed as a CP/RdRp fusion protein due to ribosomal frameshifting. Here, we used transmission electron cryomicroscopy and three-dimensional image reconstruction to determine the structures of HvV190S virions and two types of virus-like particles (capsids lacking dsRNA and capsids lacking both dsRNA and RdRp) at estimated resolutions of 7.1, 7.5, and 7.6 Å, respectively. The HvV190S capsid is thin and smooth, and contains 120 copies of CP arranged in a “T = 2” icosahedral lattice characteristic of ScV-L-A and other dsRNA viruses. For aid in our interpretations, we developed and used an iterative segmentation procedure to define the boundaries of the two, chemically identical CP subunits in each asymmetric unit. Both subunits have a similar fold, but one that differs from ScV-L-A in many details except for a core α-helical region that is further predicted to be conserved among many other totiviruses. In particular, we predict the structures of other victoriviruses to be highly similar to HvV190S and the structures of most if not all totiviruses including, Leishmania RNA virus 1, to be similar as well.

Of the known dsRNA fungal viruses, the best characterized is Saccharomyces cerevisiae virus L-A (ScV-L-A), prototype of the genus Totivirus, family Totiviridae. Until the current study, there have been no subnanometer structures of dsRNA fungal viruses from the genus Victorivirus, which is the largest in family Totiviridae. The 3D cryo-reconstruction presented here of prototype victorivirus Helminthosporium victoriae virus 190S (HvV190S) approaches 7-Å resolution and shows the asymmetric unit of the capsid is a dimer comprising two, chemically identical coat-protein subunits organized in a so called “T = 2” lattice. These HvV190S subunits have a similar fold, but one that differs from ScV-L-A in many details except for a core α-helical region that is further predicted to be conserved among many other totiviruses. In particular, we predict the structures of other victoriviruses to be highly similar to HvV190S and the structures of most if not all totiviruses, including Leishmania RNA virus 1, to be similar as well.

Modeling a ryanodine receptor N-terminal domain connecting the central vestibule and the corner clamp region

Ryanodine receptors (RyRs) form a class of intracellular calcium release channels in various excitable tissues and cells such as muscles and neurons. They are the major cellular mediators of the release of calcium ions from the sarcoplasmic reticulum, an essential step in muscle excitation-contraction coupling. Several crystal structures of skeletal muscle RyR1 peptide fragments have been solved, but these cover less than 15% of the full-length RyR1 sequence. In this study, by combining modeling techniques with sub-nanometer resolution cryo-electron microscopy (cryo-EM) maps, we obtained pseudo-atomic models for RyR fragments consisting of residues 850-1,056 in rabbit RyR1 or residues 861-1,067 in mouse RyR2. These fragments are docked into a domain that connects the central vestibule and corner clamp region of RyR, resulting in a good match of the secondary structure elements in the cryo-EM map and the pseudo-atomic models, which is also consistent with our previous mappings of GFP insertions by cryo-EM and with FRET measurements involving RyR and FK506-binding protein (FKBP). A combined model of the RyR fragment and FKBP docked into the cryo-EM map suggests that the fragment is positioned adjacent to the FKBP-binding site. Its predicted binding interface with FKBP consists primarily of electrostatic contacts and contains several disease-associated mutations. A dynamic interaction between the fragment and an RyR phosphorylation domain, characterized by FRET experiments, also supports the structural predictions of the pseudo-atomic models.

Computational opportunities for remote collaboration and capacity building afforded by Web 2.0 and cloud computing

In this paper, we state our aims and aspirations for building a global network of likeminded people interested in developing and encouraging students in the field of computational biophysics (CB). Global capacity building efforts have uncovered local computational talent in virtually every community regardless of where the students reside. Our vision is to discover and encourage these aspiring investigators by suggesting ways that they and other "garage scientists" can participate in new science even if they have no access to sophisticated research infrastructure. We argue that participatory computing in the "cloud" is particularly suitable for CB and available to any budding computational biophysicist if he or she is provided with open-minded mentors who have the necessary skills and generosity. We recognize that there are barriers to the development of such remote collaborations, and we discuss possible pathways to overcome these barriers. We point out that this Special Issue of Biophysical Reviews provides a much-needed forum for the development of several specific applications of CB.

Developing a denoising filter for electron microscopy and tomography data in the cloud

The low radiation conditions and the predominantly phase-object image formation of cryo-electron microscopy (cryo-EM) result in extremely high noise levels and low contrast in the recorded micrographs. The process of single particle or tomographic 3D reconstruction does not completely eliminate this noise and is even capable of introducing new sources of noise during alignment or when correcting for instrument parameters. The recently developed Digital Paths Supervised Variance (DPSV) denoising filter uses local variance information to control regional noise in a robust and adaptive manner. The performance of the DPSV filter was evaluated in this review qualitatively and quantitatively using simulated and experimental data from cryo-EM and tomography in two and three dimensions. We also assessed the benefit of filtering experimental reconstructions for visualization purposes and for enhancing the accuracy of feature detection. The DPSV filter eliminates high-frequency noise artifacts (density gaps), which would normally preclude the accurate segmentation of tomography reconstructions or the detection of alpha-helices in single-particle reconstructions. This collaborative software development project was carried out entirely by virtual interactions among the authors using publicly available development and file sharing tools.

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.