This work provides new evidence of the utility of deep learning-based protein structure prediction approaches, specifically AlphaFold2, in the interpretation of 4-6 Å resolution cryo-EM maps. We describe the dependencies, as well as the strengths and limitations, of integrating experimental and AI-based approaches to building accurate models, even from poorly resolved density maps. The test followed recent work that implemented a refinement protocol in the Phenix program, which successfully refined AlphaFold2 models in high-resolution maps but which at lower resolution relied on simulated "hybrid density maps". To study the noise and imperfections present in experimental cryo-EM maps more realistically, in this work, we selected only experimental map/model pairs in the 4-6 Å resolution range where refinement performance starts to degrade. Most of the AlphaFold2 predicted models are highly accurate, particularly for the 9 larger chains (226-373 residues long) of the 10 cases, exhibiting TM-scores above 0.9. A small chain of 115 residues in length containing three helices was poorly predicted, with a TM-score of 0.52. The observed success of the subsequent refinement step depends significantly on the quality of the AlphaFold2 prediction, the quality of the experimental cryo-EM data, and the quality of the alignment of the model with the density.

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 resolution range such as 5-10 A. Although multiple neural networks have been proposed for the problem of secondary structure detection from cryo-EM 3D images, loss functions used in the existing networks are primarily based on cross entropy loss (CE). In order to study the behavior of various loss functions in the secondary structure detection problem, we investigated five loss functions and compared their performances. Using a U-net architecture in DeepSSETracer and a test set of 65 protein chains of atomic structures and their corresponding cryo-EM density component maps, we found that the combined function with focal cross entropy loss (FCE) and Dice loss (DL) provides the best overall detection of secondary structures. In particular, the combined loss function has a significant enhancement of an overall F1score of 6.7% when compared to CE in detection of $\beta-$sheet voxels that are generally much harder to be detected accurately than for helix voxels. Our work shows the potential of designing effective loss functions to enhance the detection of hard cases in the segmentation of secondary structure problem.

filopodia makes identifying filaments within noisy cryo-electron tomograms extremely challenging. In this work, we present a computationally efficient dynamic programming-based framework for tracing arbitrarily oriented actin filaments. Starting from locally determined seed points, it accumulates densities along paths of a particular length within 45° of the three Cartesian coordinate axes. This novel approach covers all possible orientations, so there is no need to assume a dominant direction as in earlier work. For each seed point, the path with the highest density value is selected, and it acts as a candidate filament segment (CFS) that is likely to form a part of a filament when it has a high path density value. The subsequent stages involve identifying groups of CFSs with high path densities by binning and merging them. The merging step considers the relative orientations and distances of CFSs to connect them. In addition, the CFSs are extended to fill the noise-induced gaps to some extent. In the current prototype software, we focused on the proof of the concept, using a noisy simulated tomogram with a known ground truth that closely mimics the appearance of an experimental map. We achieved an almost perfect precision score of 0.999, but this success came at the expense of a lower recall score 0.462 due to false negatives. We discuss the dependencies as well as the limitations of the current filament merging that need to be overcome to achieve a higher recall score in the future.

We propose a fast, dynamic programming-based framework for tracing actin filaments in 3D maps of subcellular components in cryo-electron tomography. The approach can identify high-density filament segments in various orientations, but it takes advantage of the arrangement of actin filaments within cells into more or less tightly aligned bundles. Assuming that the tomogram can be rotated such that the filaments can be oriented to be directed in a dominant direction (i.e., the X, Y, or Z axis), the proposed framework first identifies local seed points that form the origin of candidate filament segments (CFSs), which are then grown from the seeds using a fast dynamic programming algorithm. The CFS length l can be tuned to the nominal resolution of the tomogram or the separation of desired features, or it can be used to restrict the curvature of filaments that deviate from the overall bundle direction. In subsequent steps, the CFSs are filtered based on backward tracing and path density analysis. Finally, neighboring CFSs are fused based on a collinearity criterion to bridge any noise artifacts in the 3D map that would otherwise fractionalize the tracing. We validate our proposed framework on simulated tomograms that closely mimic the features and appearance of experimental maps.

As automated filament tracing algorithms in cryo-electron tomography (cryo-ET) continue to improve, the validation of these approaches has become more incumbent. Having a known ground truth on which to base predictions is crucial to reliably test predicted cytoskeletal filaments because the detailed structure of the filaments in experimental tomograms is obscured by a low resolution, as well as by noise and missing Fourier space wedge artifacts. We present a software tool for the realistic simulation of tomographic maps (TomoSim) based on a known filament trace. The parameters of the simulated map are automatically matched to those of a corresponding experimental map. We describe the computational details of the first prototype of our approach, which includes wedge masking in Fourier space, noise color, and signal-to-noise matching. We also discuss current and potential future applications of the approach in the validation of concurrent filament tracing methods in cryo-ET.

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.

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.

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.

Protein structure prediction is one of the most important subjects in computational structural biology. In the process of protein structure prediction, many structure decoys are obtained. It has remained an unsolved and challenging problem to select the best model from the structure decoys that are closest to the native structure. One of the important methods for selecting the near-native structure is by clustering the structure decoys. The traditional methods simply use clustering methods which are usually not appropriate in the high dimensional conformation space. Here we propose a method based on maximal cliques in graph theory to solve this problem. The similarities between the decoys are first computed using TM-score, and a graph is built using the shared nearest neighbor (SNN) information among the decoys. Then the maximal cliques of the graph are found and the centroids of these maximal cliques are selected as near-native structures. The experiments show that, compared to the traditional methods, the proposed method can select better near-native structures which have higher similarities with the native structures.

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.

Electron cryomicroscopy is becoming a major experimental technique in solving the structures of large molecular assemblies. More and more three-dimensional images have been obtained at the medium resolutions between 5 and 10 Å. At this resolution range, major α-helices can be detected as cylindrical sticks and β-sheets can be detected as plain-like regions. A critical question in de novo modeling from cryo-EM images is to determine the match between the detected secondary structures from the image and those on the protein sequence. We formulate this matching problem into a constrained graph problem and present an O(Δ(2)N(2)2(N)) algorithm to this NP-Hard problem. The algorithm incorporates the dynamic programming approach into a constrained K-shortest path algorithm. Our method, DP-TOSS, has been tested using α-proteins with maximum 33 helices and α-β proteins up to five helices and 12 β-strands. The correct match was ranked within the top 35 for 19 of the 20 α-proteins and all nine α-β proteins tested. The results demonstrate that DP-TOSS improves accuracy, time and memory space in deriving the topologies of the secondary structure elements for proteins with a large number of secondary structures and a complex skeleton.

Cryo-electron microscopy is an experimental technique that is able to produce 3D gray-scale images of protein molecules. In contrast to other experimental techniques, cryo-electron microscopy is capable of visualizing large molecular complexes such as viruses and ribosomes. At medium resolution, the positions of the atoms are not visible and the process cannot proceed. The medium-resolution images produced by cryo-electron microscopy are used to derive the atomic structure of the proteins in de novo modeling. The skeletons of the 3D gray-scale images are used to interpret important information that is helpful in de novo modeling. Unfortunately, not all features of the image can be captured using a single segmentation. In this paper, we present a segmentation-free approach to extract the gray-scale curve-like skeletons. The approach relies on a novel representation of the 3D image, where the image is modeled as a graph and a set of volume trees. A test containing 36 synthesized maps and one authentic map shows that our approach can improve the performance of the two tested tools used in de novo modeling. The improvements were 62 and 13 percent for Gorgon and DP-TOSS, respectively.

The determination of the secondary structure topology is a critical step in deriving the atomic structure from the protein density map obtained from electron cryo-microscopy technique. This step often relies on the matching of two sources of information. One source comes from the secondary structures detected from the protein density map at the medium resolution, such as 5-10 A. The other source comes from the predicted secondary structures from the amino acid sequence. Due to the uncertainty in either source of information, a pool of possible secondary structure positions has to be sampled in order to include the true answer. A naive way to find the native topology is to exhaustively map the pool of possible secondary structures detected in the density map with the pool of the secondary structures predicted from the sequence and search for the topology with the lowest cost. This paper studies the question that is how to reduce the computation of the mapping when the uncertainty of the secondary structure predictions is considered. We present a method that combines the concept of dynamic graph with our previous work of using constrained shortest path to identify the topology of the secondary structures. We show a reduction of about 34.55% time as comparison to the naive way of handling the inaccuracies. To our knowledge, this is the Is computationally effective exact algorithm to identify the optimal topology of the secondary structures when the inaccuracy of the predicted data is considered.

BACKGROUND: The current advances in electron cryo-microscopy technique have made it possible to obtain protein density maps at about 6-10 A resolution. Although it is hard to derive the protein chain directly from such a low resolution map, the location of the secondary structures such as helices and strands can be computationally detected. It has been demonstrated that such low-resolution map can be used during the protein structure prediction process to enhance the structure prediction. RESULTS: We have developed an approach to predict the 3-dimensional structure for the helical skeletons that can be detected from the low resolution protein density map. This approach does not require the construction of the entire chain and distinguishes the structures based on the conformation of the helices. A test with 35 low resolution density maps shows that the highest ranked structure with the correct topology can be found within the top 1% of the list ranked by the effective energy formed by the helices. CONCLUSION: The results in this paper suggest that it is possible to eliminate the great majority of the bad conformations of the helices even without the construction of the entire chain of the protein. For many proteins, the effective contact energy formed by the secondary structures alone can distinguish a small set of likely structures from the pool.

BACKGROUND: Electron cryomicroscopy is a fast developing technique aiming at the determination of the 3-dimensional structures of large protein complexes. Using this technique, protein density maps can be generated with 6 to 10 A resolution. At such resolutions, the secondary structure elements such as helices and beta-strands appear to be skeletons and can be computationally detected. However, it is not known which segment of the protein sequence corresponds to which of the skeletons. The topology in this paper refers to the linear order and the directionality of the secondary structures. For a protein with N helices and M strands, there are (N!2N)(M!2M) different topologies, each of which maps N helix segments and M strand segments on the protein sequence to N helix and M strand skeletons. Since the backbone position is not available in the skeleton, each topology of the skeletons corresponds to additional freedom to position the atoms in the skeletons. RESULTS: We have developed a method to construct the possible atomic structures for the helix skeletons by sampling the solution space of all the possible topologies of the skeletons. Our method also ranks the possible structures based on the contact energy formed by the secondary structures, rather than the entire chain. If we assume that the backbone atomic positions are known for the skeletons, then the native topology of the secondary structures can be found in the top 30% of the ranked list of all possible topologies for all the 30 proteins tested, and within the top 5% for most of the 30 proteins. Without assuming the backbone location of the skeletons, the possible atomic structures of the skeletons can be constructed using the axis of the skeleton and the sequence segments. The best constructed structure for the skeletons has RMSD to native between 4 and 5 A for the four tested alpha-proteins. These best constructed structures were ranked the 17th, 31st, 16th and 5th respectively for the four proteins out of 32066, 391833, 98755 and 192935 possible assignments in the pool. CONCLUSION: Our work suggested that the direct estimation of the contact energy formed by the secondary structures is quite effective in reducing the topological space to a small subset that includes a near native structure for the skeletons.