Contact Map Overlap Research Articles

An interactive visualization tool for educational outreach in protein contact map overlap analysis.

Recent advancements in contact map-based protein three-dimensional (3D) structure prediction have been driven by the evolution of deep learning algorithms. However, the gap in accessible software tools for novices in this domain remains a significant challenge. This study introduces GoFold, a novel, standalone graphical user interface (GUI) designed for beginners to perform contact map overlap (CMO) problems for better template selection. Unlike existing tools that cater more to research needs or assume foundational knowledge, GoFold offers an intuitive, user-friendly platform with comprehensive tutorials. It stands out in its ability to visually represent the CMO problem, allowing users to input proteins in various formats and explore the CMO problem. The educational value of GoFold is demonstrated through benchmarking against the state-of-the-art contact map overlap method, map_align, using two datasets: PSICOV and CAMEO. GoFold exhibits superior performance in terms of TM-score and Z-score metrics across diverse qualities of contact maps and target difficulties. Notably, GoFold runs efficiently on personal computers without any third-party dependencies, thereby making it accessible to the general public for promoting citizen science. The tool is freely available for download for macOS, Linux, and Windows.

Selecting Near-Native Protein Structures from Predicted Decoy Sets Using Ordered Graphlet Degree Similarity.

Effective prediction of protein tertiary structure from sequence is an important and challenging problem in computational structural biology. Ab initio protein structure prediction is based on amino acid sequence alone, thus, it has a wide application area. With the ab initio method, a large number of candidate protein structures called decoy set can be predicted, however, it is a difficult problem to select a good near-native structure from the predicted decoy set. In this work we propose a new method for selecting the near-native structure from the decoy set based on both contact map overlap (CMO) and graphlets. By generalizing graphlets to ordered graphs, and using a dynamic programming to select the optimal alignment with an introduced gap penalty, a GR_score is defined for calculating the similarity between the three-dimensional (3D) decoy structures. The proposed method was applied to all 54 single-domain targets in CASP11 and all 43 targets in CASP10, and ensemble clustering was used to cluster the protein decoy structures based on the computed CR_scores. The most popular centroid structure was selected as the near-native structure. The experiments showed that compared to the SPICKER method, which is used in I-TASSER, the proposed method can usually select better near-native structures in terms of the similarity between the selected structure and the true native structure.

Adaptive distributed modified extremal optimisation for maximising contact map overlap and its performance evaluation

Maximising the contact map overlap (CMO) problem is one of the simplest yet most robust techniques for finding optimal protein structure alignment. This optimisation is known as the CMO problem, and is also known as NP-hard. We have been developing bio-inspired heuristics using distributed modified extremal optimisation (DMEO) for the CMO problem. DMEO is a hybrid of population-based modified extremal optimisation (PMEO) and the island model. In our previous work, we proposed a DMEO-based bio-inspired heuristic, i.e., DMEO with different evolutionary strategies (DMEODES) to maintain the population diversity of evolution. DMEODES efficiently maintains population diversity; however, once the population falls into local optimal solutions, there is no mechanism for getting out of them. In this paper, we propose a novel heuristic model to improve the DMEO's ability to prevent evolution stagnation. The new model integrates an adaptive generation alternation mechanism in DMEO called ADMEO. The experimental results show that ADMEO outperforms DMEODES.

Adaptive distributed modified extremal optimisation for maximising contact map overlap and its performance evaluation

Maximising the contact map overlap (CMO) problem is one of the simplest yet most robust techniques for finding optimal protein structure alignment. This optimisation is known as the CMO problem, and is also known as NP-hard. We have been developing bio-inspired heuristics using distributed modified extremal optimisation (DMEO) for the CMO problem. DMEO is a hybrid of population-based modified extremal optimisation (PMEO) and the island model. In our previous work, we proposed a DMEO-based bio-inspired heuristic, i.e., DMEO with different evolutionary strategies (DMEODES) to maintain the population diversity of evolution. DMEODES efficiently maintains population diversity; however, once the population falls into local optimal solutions, there is no mechanism for getting out of them. In this paper, we propose a novel heuristic model to improve the DMEO's ability to prevent evolution stagnation. The new model integrates an adaptive generation alternation mechanism in DMEO called ADMEO. The experimental results show that ADMEO outperforms DMEODES.

A New Heuristic Algorithm for Protein Folding in the HP Model.

This article presents an efficient heuristic for protein folding. The protein folding problem is to predict the compact three-dimensional structure of a protein based on its amino acid sequence. The focus is on an original integer programming model derived from a platform used for Contact Map Overlap problem.

Automatic Classification of Protein Structure Using the Maximum Contact Map Overlap Metric

In this work, we propose a new distance measure for comparing two protein structures based on their contact map representations. We show that our novel measure, which we refer to as the maximum contact map overlap (max-CMO) metric, satisfies all properties of a metric on the space of protein representations. Having a metric in that space allows one to avoid pairwise comparisons on the entire database and, thus, to significantly accelerate exploring the protein space compared to no-metric spaces. We show on a gold standard superfamily classification benchmark set of 6759 proteins that our exact k-nearest neighbor (k-NN) scheme classifies up to 224 out of 236 queries correctly and on a larger, extended version of the benchmark with 60; 850 additional structures, up to 1361 out of 1369 queries. Our k-NN classification thus provides a promising approach for the automatic classification of protein structures based on flexible contact map overlap alignments.

Divide and Conquer Approach to Contact Map Overlap Problem Using 2D-Pattern Mining of Protein Contact Networks.

A novel approach to Contact Map Overlap (CMO) problem is proposed using the two dimensional clusters present in the contact maps. Each protein is represented as a set of the non-trivial clusters of contacts extracted from its contact map. The approach involves finding matching regions between the two contact maps using approximate 2D-pattern matching algorithm and dynamic programming technique. These matched pairs of small contact maps are submitted in parallel to a fast heuristic CMO algorithm. The approach facilitates parallelization at this level since all the pairs of contact maps can be submitted to the algorithm in parallel. Then, a merge algorithm is used in order to obtain the overall alignment. As a proof of concept, MSVNS, a heuristic CMO algorithm is used for global as well as local alignment. The divide and conquer approach is evaluated for two benchmark data sets that of Skolnick and Ding et al. It is interesting to note that along with achieving saving of time, better overlap is also obtained for certain protein folds.

GR-Align: fast and flexible alignment of protein 3D structures using graphlet degree similarity

Protein structure alignment is key for transferring information from well-studied proteins to less studied ones. Structural alignment identifies the most precise mapping of equivalent residues, as structures are more conserved during evolution than sequences. Among the methods for aligning protein structures, maximum Contact Map Overlap (CMO) has received sustained attention during the past decade. Yet, known algorithms exhibit modest performance and are not applicable for large-scale comparison. Graphlets are small induced subgraphs that are used to design sensitive topological similarity measures between nodes and networks. By generalizing graphlets to ordered graphs, we introduce GR-Align, a CMO heuristic that is suited for database searches. On the Proteus_300 set (44 850 protein domain pairs), GR-Align is several orders of magnitude faster than the state-of-the-art CMO solvers Apurva, MSVNS and AlEigen7, and its similarity score is in better agreement with the structural classification of proteins. On a large-scale experiment on the Gold-standard benchmark dataset (3 207 270 protein domain pairs), GR-Align is several orders of magnitude faster than the state-of-the-art protein structure comparison tools TM-Align, DaliLite, MATT and Yakusa, while achieving similar classification performances. Finally, we illustrate the difference between GR-Align's flexible alignments and the traditional ones by querying a flexible protein in the Astral-40 database (11 154 protein domains). In this experiment, GR-Align's top scoring alignments are not only in better agreement with structural classification of proteins, but also that they allow transferring more information across proteins.

ClusCo: clustering and comparison of protein models

BackgroundThe development, optimization and validation of protein modeling methods require efficient tools for structural comparison. Frequently, a large number of models need to be compared with the target native structure. The main reason for the development of Clusco software was to create a high-throughput tool for all-versus-all comparison, because calculating similarity matrix is the one of the bottlenecks in the protein modeling pipeline.ResultsClusco is fast and easy-to-use software for high-throughput comparison of protein models with different similarity measures (cRMSD, dRMSD, GDT_TS, TM-Score, MaxSub, Contact Map Overlap) and clustering of the comparison results with standard methods: K-means Clustering or Hierarchical Agglomerative Clustering.ConclusionsThe application was highly optimized and written in C/C++, including the code for parallel execution on CPU and GPU, which resulted in a significant speedup over similar clustering and scoring computation programs.

CSA: comprehensive comparison of pairwise protein structure alignments.

CSA is a web server for the computation, evaluation and comprehensive comparison of pairwise protein structure alignments. Its exact alignment engine computes either optimal, top-scoring alignments or heuristic alignments with quality guarantee for the inter-residue distance-based scorings of contact map overlap, PAUL, DALI and MATRAS. These and additional, uploaded alignments are compared using a number of quality measures and intuitive visualizations. CSA brings new insight into the structural relationship of the protein pairs under investigation and is a valuable tool for studying structural similarities. It is available at http://csa.project.cwi.nl.

A similarity matrix-based hybrid algorithm for the contact map overlaps problem

This paper proposes a similarity matrix-based hybrid algorithm for the contact map overlap (CMO) problem in protein structure alignment. In this algorithm, Genetic Algorithm (GA) is used as a framework, in which the initial solutions are constructed with similarity matrix heuristic, and Extremal Optimization (EO) is embedded as a mutated operator. In this process, EO quickly approaches near-optimal solutions and GA generates improved global approximations. Five similarity measurements including ratio, inner product, cosine function, Jaccard index and Dice coefficient have been exploited to compute the similarity matrix between two contact maps. The simulations demonstrate that our algorithm is significantly faster and gets better results for most of the test sets.

Maximum Contact Map Overlap Revisited

Among the measures for quantifying the similarity between three-dimensional (3D) protein structures, maximum contact map overlap (CMO) received sustained attention during the past decade. Despite this, the known algorithms exhibit modest performance and are not applicable for large-scale comparison. This article offers a clear advance in this respect. We present a new integer programming model for CMO and propose an exact branch-and-bound algorithm with bounds obtained by a novel Lagrangian relaxation. The efficiency of the approach is demonstrated on a popular small benchmark (Skolnick set, 40 domains). On this set, our algorithm significantly outperforms the best existing exact algorithms. Many hard CMO instances have been solved for the first time. To further assess our approach, we constructed a large-scale set of 300 protein domains. Computing the similarity measure for any of the 44850 pairs, we obtained a classification in excellent agreement with SCOP. Supplementary Material is available at www.liebertonline.com/cmb.

Towards optimal alignment of protein structure distance matrices

Structural alignments of proteins are important for identification of structural similarities, homology detection and functional annotation. The structural alignment problem is well studied and computationally difficult. Many different scoring schemes for structural similarity as well as many algorithms for finding high-scoring alignments have been proposed. Algorithms using contact map overlap (CMO) as scoring function are currently the only practical algorithms able to compute provably optimal alignments. We propose a new mathematical model for the alignment of inter-residue distance matrices, building upon previous work on maximum CMO. Our model includes all elements needed to emulate various scoring schemes for the alignment of protein distance matrices. The algorithm that we use to compute alignments is practical only for sparse distance matrices. Therefore, we propose a more effective scoring function, which uses a distance threshold and only positive structural scores. We show that even under these restrictions our approach is in terms of alignment accuracy competitive with state-of-the-art structural alignment algorithms, whereas it additionally either proves the optimality of an alignment or returns bounds on the optimal score. Our novel method is freely available and constitutes an important promising step towards truly provably optimal structural alignments of proteins. An executable of our program PAUL is available at http://planet-lisa.net/.

Fast overlapping of protein contact maps by alignment of eigenvectors

Searching for structural similarity is a key issue of protein functional annotation. The maximum contact map overlap (CMO) is one of the possible measures of protein structure similarity. Exact and approximate methods known to optimize the CMO are computationally expensive and this hampers their applicability to large-scale comparison of protein structures. In this article, we describe a heuristic algorithm (Al-Eigen) for finding a solution to the CMO problem. Our approach relies on the approximation of contact maps by eigendecomposition. We obtain good overlaps of two contact maps by computing the optimal global alignment of few principal eigenvectors. Our algorithm is simple, fast and its running time is independent of the amount of contacts in the map. Experimental testing indicates that the algorithm is comparable to exact CMO methods in terms of the overlap quality, to structural alignment methods in terms of structure similarity detection and it is fast enough to be suited for large-scale comparison of protein structures. Furthermore, our preliminary tests indicates that it is quite robust to noise, which makes it suitable for structural similarity detection also for noisy and incomplete contact maps. Available at http://bioinformatics.cs.unibo.it/Al-Eigen.

Toward High-Throughput, Multicriteria Protein-Structure Comparison and Analysis

Protein-structure comparison (PSC) is an essential component of biomedical research as it impacts on, e.g., drug design, molecular docking, protein folding and structure prediction algorithms as well as being essential to the assessment of these predictions. Each of these applications, as well as many others where molecular comparison plays an important role, requires a different notion of similarity that naturally lead to the multicriteria PSC (MC-PSC) problem. Protein (Structure) Comparison, Knowledge, Similarity, and Information (ProCKSI) (www.procksi.org) provides algorithmic solutions for the MC-PSC problem by means of an enhanced structural comparison that relies on the principled application of information fusion to similarity assessments derived from multiple comparison methods. Current MC-PSC works well for moderately sized datasets and it is time consuming as it provides public service to multiple users. Many of the structural bioinformatics applications mentioned above would benefit from the ability to perform, for a dedicated user, thousands or tens of thousands of comparisons through multiple methods in real time, a capacity beyond our current technology. In this paper, we take a key step into that direction by means of a high-throughput distributed reimplementation of ProCKSI for very large datasets. The core of the proposed framework lies in the design of an innovative distributed algorithm that runs on each compute node in a cluster/grid environment to perform structure comparison of a given subset of input structures using some of the most popular PSC methods [e.g., universal similarity metric (USM), maximum contact map overlap (MaxCMO), fast alignment and search tool (FAST), distance alignment (DaliLite), combinatorial extension (CE), template modeling alignment (TMAlign)]. We follow this with a procedure of distributed consensus building. Thus, the new algorithms proposed here achieve ProCKSI's similarity assessment quality but with a fraction of the time required by it. Our results show that the proposed distributed method can be used efficiently to compare: 1) a particular protein against a very large protein structures dataset (target-against-all comparison), and 2) a particular very large-scale dataset against itself or against another very large-scale dataset (all-against-all comparison). We conclude the paper by enumerating some of the outstanding challenges for real-time MC-PSC.

Optimal contact definition for reconstruction of Contact Maps

BackgroundContact maps have been extensively used as a simplified representation of protein structures. They capture most important features of a protein's fold, being preferred by a number of researchers for the description and study of protein structures. Inspired by the model's simplicity many groups have dedicated a considerable amount of effort towards contact prediction as a proxy for protein structure prediction. However a contact map's biological interest is subject to the availability of reliable methods for the 3-dimensional reconstruction of the structure.ResultsWe use an implementation of the well-known distance geometry protocol to build realistic protein 3-dimensional models from contact maps, performing an extensive exploration of many of the parameters involved in the reconstruction process. We try to address the questions: a) to what accuracy does a contact map represent its corresponding 3D structure, b) what is the best contact map representation with regard to reconstructability and c) what is the effect of partial or inaccurate contact information on the 3D structure recovery. Our results suggest that contact maps derived from the application of a distance cutoff of 9 to 11Å around the Cβ atoms constitute the most accurate representation of the 3D structure. The reconstruction process does not provide a single solution to the problem but rather an ensemble of conformations that are within 2Å RMSD of the crystal structure and with lower values for the pairwise average ensemble RMSD. Interestingly it is still possible to recover a structure with partial contact information, although wrong contacts can lead to dramatic loss in reconstruction fidelity.ConclusionsThus contact maps represent a valid approximation to the structures with an accuracy comparable to that of experimental methods. The optimal contact definitions constitute key guidelines for methods based on contact maps such as structure prediction through contacts and structural alignments based on maximum contact map overlap.

A simple and fast heuristic for protein structure comparison

BackgroundProtein structure comparison is a key problem in bioinformatics. There exist several methods for doing protein comparison, being the solution of the Maximum Contact Map Overlap problem (MAX-CMO) one of the alternatives available. Although this problem may be solved using exact algorithms, researchers require approximate algorithms that obtain good quality solutions using less computational resources than the formers.ResultsWe propose a variable neighborhood search metaheuristic for solving MAX-CMO. We analyze this strategy in two aspects: 1) from an optimization point of view the strategy is tested on two different datasets, obtaining an error of 3.5%(over 2702 pairs) and 1.7% (over 161 pairs) with respect to optimal values; thus leading to high accurate solutions in a simpler and less expensive way than exact algorithms; 2) in terms of protein structure classification, we conduct experiments on three datasets and show that is feasible to detect structural similarities at SCOP's family and CATH's architecture levels using normalized overlap values. Some limitations and the role of normalization are outlined for doing classification at SCOP's fold level.ConclusionWe designed, implemented and tested.a new tool for solving MAX-CMO, based on a well-known metaheuristic technique. The good balance between solution's quality and computational effort makes it a valuable tool. Moreover, to the best of our knowledge, this is the first time the MAX-CMO measure is tested at SCOP's fold and CATH's architecture levels with encouraging results.Software is available for download at .

ProCKSI: a decision support system for Protein (structure) Comparison, Knowledge, Similarity and Information.

BackgroundWe introduce the decision support system for Protein (Structure) Comparison, Knowledge, Similarity and Information (ProCKSI). ProCKSI integrates various protein similarity measures through an easy to use interface that allows the comparison of multiple proteins simultaneously. It employs the Universal Similarity Metric (USM), the Maximum Contact Map Overlap (MaxCMO) of protein structures and other external methods such as the DaliLite and the TM-align methods, the Combinatorial Extension (CE) of the optimal path, and the FAST Align and Search Tool (FAST). Additionally, ProCKSI allows the user to upload a user-defined similarity matrix supplementing the methods mentioned, and computes a similarity consensus in order to provide a rich, integrated, multicriteria view of large datasets of protein structures.ResultsWe present ProCKSI's architecture and workflow describing its intuitive user interface, and show its potential on three distinct test-cases. In the first case, ProCKSI is used to evaluate the results of a previous CASP competition, assessing the similarity of proposed models for given targets where the structures could have a large deviation from one another. To perform this type of comparison reliably, we introduce a new consensus method. The second study deals with the verification of a classification scheme for protein kinases, originally derived by sequence comparison by Hanks and Hunter, but here we use a consensus similarity measure based on structures. In the third experiment using the Rost and Sander dataset (RS126), we investigate how a combination of different sets of similarity measures influences the quality and performance of ProCKSI's new consensus measure. ProCKSI performs well with all three datasets, showing its potential for complex, simultaneous multi-method assessment of structural similarity in large protein datasets. Furthermore, combining different similarity measures is usually more robust than relying on one single, unique measure.ConclusionBased on a diverse set of similarity measures, ProCKSI computes a consensus similarity profile for the entire protein set. All results can be clustered, visualised, analysed and easily compared with each other through a simple and intuitive interface.ProCKSI is publicly available at for academic and non-commercial use.

A Reduction-Based Exact Algorithm for the Contact Map Overlap Problem

Aligning proteins based on their structural similarity is a fundamental problem in molecular biology with applications in many settings, including structure classification, database search, function prediction, and assessment of folding prediction methods. Structural alignment can be done via several methods, including contact map overlap (CMO) maximization that aligns proteins in a way that maximizes the number of common residue contacts. In this paper, we develop a reduction-based exact algorithm for the CMO problem. Our approach solves CMO directly rather than after transformation to other combinatorial optimization problems. We exploit the mathematical structure of the problem in order to develop a number of efficient lower bounding, upper bounding, and reduction schemes. Computational experiments demonstrate that our algorithm runs significantly faster than existing exact algorithms and solves some hard CMO instances that were not solved in the past. In addition, the algorithm produces protein clusters that are in excellent agreement with the SCOP classification. An implementation of our algorithm is accessible as an on-line server at http://eudoxus.scs.uiuc.edu/cmos/cmos.html.

Fast Molecular Shape Matching Using Contact Maps

In this paper, we study the problem of computing the similarity of two protein structures by measuring their contact-map overlap. Contact-map overlap abstracts the problem of computing the similarity of two polygonal chains as a graph-theoretic problem. In R3, we present the first polynomial time algorithm with any guarantee on the approximation ratio for the 3-dimensional problem. More precisely, we give an algorithm for the contact-map overlap problem with an approximation ratio of sigma where sigma = min{sigma(P1), sigma(P2)} <or= O(n(1/2)) is a decomposition parameter depending on the input polygonal chains P1 and P2. In R2, we improve the running time of the previous best known approximation algorithm from O(n(6)) to O(n(3) log n) at the cost of decreasing the approximation ratio by half. We also give hardness results for the problem in three dimensions, suggesting that approximating it better than O(n(epsilon)), for some epsilon > 0, is hard.