LPTD: a novel linear programming-based topology determination method for cryo-EM maps.

SUMMARY: Topology determination is one of the most important intermediate steps toward building the atomic structure of proteins from their medium-resolution cryo-electron microscopy (cryo-EM) map. The main goal in the topology determination is to identify correct matches (i.e. assignment and direction) between secondary structure elements (SSEs) (α-helices and ß-sheets) detected in a protein sequence and cryo-EM density map. Despite many recent advances in molecular biology technologies, the problem remains a challenging issue. To overcome the problem, this article proposes a linear programming-based topology determination (LPTD) method to solve the secondary structure topology problem in three-dimensional geometrical space. Through modeling of the protein's sequence with the aid of extracting highly reliable features and a distance-based scoring function, the secondary structure matching problem is transformed into a complete weighted bipartite graph matching problem. Subsequently, an algorithm based on linear programming is developed as a decision-making strategy to extract the true topology (native topology) between all possible topologies. The proposed automatic framework is verified using 12 experimental and 15 simulated α-ß proteins. Results demonstrate that LPTD is highly efficient and extremely fast in such a way that for 77% of cases in the dataset, the native topology has been detected in the first rank topology in <2 s. Besides, this method is able to successfully handle large complex proteins with as many as 65 SSEs. Such a large number of SSEs have never been solved with current tools/methods. AVAILABILITY AND IMPLEMENTATION: The LPTD package (source code and data) is publicly available at https://github.com/B-Behkamal/LPTD. Moreover, two test samples as well as the instruction of utilizing the graphical user interface have been provided in the shared readme file. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Detection of Partially Structural Collapse Using Long-Term Small Displacement Data from Satellite Images.

The development of satellite sensors and interferometry synthetic aperture radar (InSAR) technology has enabled the exploitation of their benefits for long-term structural health monitoring (SHM). However, some restrictions cause this process to provide a small number of images leading to the problem of small data for SAR-based SHM. Conversely, the major challenge of the long-term monitoring of civil structures pertains to variations in their inherent properties by environmental and/or operational variability. This article aims to propose new hybrid unsupervised learning methods for addressing these challenges. The methods in this work contain three main parts: (i) data augmentation by the Markov Chain Monte Carlo algorithm, (ii) feature normalization, and (iii) decision making via Mahalanobis-squared distance. The first method presented in this work develops an artificial neural network-based feature normalization by proposing an iterative hyperparameter selection of hidden neurons of the network. The second method is a novel unsupervised teacher-student learning by combining an undercomplete deep neural network and an overcomplete single-layer neural network. A small set of long-term displacement samples extracted from a few SAR images of TerraSAR-X is applied to validate the proposed methods. The results show that the methods can effectively deal with the major challenges in the SAR-based SHM applications.

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 ß-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.

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 ß-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.