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

Three-Dimensional Graph Matching to Identify Secondary Structure Correspondence of Medium-Resolution Cryo-EM Density Maps

Cryo-electron microscopy (cryo-EM) is a structural technique that has played a significant role in protein structure determination in recent years. Compared to the traditional methods of X-ray crystallography and NMR spectroscopy, cryo-EM is capable of producing images of much larger protein complexes. However, cryo-EM reconstructions are limited to medium-resolution (~4-10 Å) for some cases. At this resolution range, a cryo-EM density map can hardly be used to directly determine the structure of proteins at atomic level resolutions, or even at their amino acid residue backbones. At such a resolution, only the position and orientation of secondary structure elements (SSEs) such as α-helices and β-sheets are observable. Consequently, finding the mapping of the secondary structures of the modeled structure (SSEs-A) to the cryo-EM map (SSEs-C) is one of the primary concerns in cryo-EM modeling. To address this issue, this study proposes a novel automatic computational method to identify SSEs correspondence in three-dimensional (3D) space. Initially, through a modeling of the target sequence with the aid of extracting highly reliable features from a generated 3D model and map, the SSEs matching problem is formulated as a 3D vector matching problem. Afterward, the 3D vector matching problem is transformed into a 3D graph matching problem. Finally, a similarity-based voting algorithm combined with the principle of least conflict (PLC) concept is developed to obtain the SSEs correspondence. To evaluate the accuracy of the method, a testing set of 25 experimental and simulated maps with a maximum of 65 SSEs is selected. Comparative studies are also conducted to demonstrate the superiority of the proposed method over some state-of-the-art techniques. The results demonstrate that the method is efficient, robust, and works well in the presence of errors in the predicted secondary structures of the cryo-EM images.

Solving the α-helix correspondence problem at medium-resolution Cryo-EM maps through modeling and 3D matching

Cryo-electron microscopy (cryo-EM) has recently emerged as a prominent biophysical method for macromolecular structure determination. Many research efforts have been devoted to produce cryo-EM images, density maps, at near-atomic resolution. Despite many advances in technology, the resolution of the generated density maps may not be sufficiently adequate and informative to directly construct the atomic structure of proteins. At medium-resolution (∼4-10 Å), secondary structure elements (α-helices and β-sheets) are discernible, whereas finding the correspondence of secondary structure elements detected in the density map with those on the sequence remains a challenging problem. In this paper, an automatic framework is proposed to solve α-helix correspondence problem in three-dimensional space. Through modeling of the sequence with the aid of a novel strategy, the α-helix correspondence problem is initially transformed into a complete weighted bipartite graph matching problem. An innovative correlation-based scoring function based on a well-known and robust statistical method is proposed for weighting the graph. Moreover, two local optimization algorithms, which are Greedy and Improved Greedy algorithms, have been presented to find α-helix correspondence. A widely used data set including 16 reconstructed and 4 experimental cryo-EM maps were chosen to verify the accuracy and reliability of the proposed automatic method. The experimental results demonstrate that the automatic method is highly efficient (86.25% accuracy), robust (11.3% error rate), fast (∼1.4 s), and works independently from cryo-EM skeleton.

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.

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.

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.

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.