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Bernard C, Postic G, Ghannay S, Tahi F. State-of-the-RNArt: benchmarking current methods for RNA 3D structure prediction. NAR Genom Bioinform 2024; 6:lqae048. [PMID: 38745991 PMCID: PMC11091930 DOI: 10.1093/nargab/lqae048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2024] [Revised: 04/05/2024] [Accepted: 05/08/2024] [Indexed: 05/16/2024] Open
Abstract
RNAs are essential molecules involved in numerous biological functions. Understanding RNA functions requires the knowledge of their 3D structures. Computational methods have been developed for over two decades to predict the 3D conformations from RNA sequences. These computational methods have been widely used and are usually categorised as either ab initio or template-based. The performances remain to be improved. Recently, the rise of deep learning has changed the sight of novel approaches. Deep learning methods are promising, but their adaptation to RNA 3D structure prediction remains difficult. In this paper, we give a brief review of the ab initio, template-based and novel deep learning approaches. We highlight the different available tools and provide a benchmark on nine methods using the RNA-Puzzles dataset. We provide an online dashboard that shows the predictions made by benchmarked methods, freely available on the EvryRNA platform: https://evryrna.ibisc.univ-evry.fr/evryrna/state_of_the_rnart/.
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Affiliation(s)
- Clément Bernard
- Université Paris-Saclay, Univ. Evry, IBISC, 91020 Evry-Courcouronnes, France
- LISN - CNRS/Université Paris-Saclay, 91400 Orsay, France
| | - Guillaume Postic
- Université Paris-Saclay, Univ. Evry, IBISC, 91020 Evry-Courcouronnes, France
| | - Sahar Ghannay
- LISN - CNRS/Université Paris-Saclay, 91400 Orsay, France
| | - Fariza Tahi
- Université Paris-Saclay, Univ. Evry, IBISC, 91020 Evry-Courcouronnes, France
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2
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Quadrini M, Tesei L, Merelli E. Automatic generation of pseudoknotted RNAs taxonomy. BMC Bioinformatics 2023; 23:575. [PMID: 37322429 DOI: 10.1186/s12859-023-05362-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Accepted: 05/25/2023] [Indexed: 06/17/2023] Open
Abstract
BACKGROUND The ability to compare RNA secondary structures is important in understanding their biological function and for grouping similar organisms into families by looking at evolutionarily conserved sequences such as 16S rRNA. Most comparison methods and benchmarks in the literature focus on pseudoknot-free structures due to the difficulty of mapping pseudoknots in classical tree representations. Some approaches exist that permit to cluster pseudoknotted RNAs but there is not a general framework for evaluating their performance. RESULTS We introduce an evaluation framework based on a similarity/dissimilarity measure obtained by a comparison method and agglomerative clustering. Their combination automatically partition a set of molecules into groups. To illustrate the framework we define and make available a benchmark of pseudoknotted (16S and 23S) and pseudoknot-free (5S) rRNA secondary structures belonging to Archaea, Bacteria and Eukaryota. We also consider five different comparison methods from the literature that are able to manage pseudoknots. For each method we clusterize the molecules in the benchmark to obtain the taxa at the rank phylum according to the European Nucleotide Archive curated taxonomy. We compute appropriate metrics for each method and we compare their suitability to reconstruct the taxa.
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Affiliation(s)
- Michela Quadrini
- School of Sciences and Technology, University of Camerino, Via Madonna delle Carceri 7, 62032, Camerino, MC, Italy
| | - Luca Tesei
- School of Sciences and Technology, University of Camerino, Via Madonna delle Carceri 7, 62032, Camerino, MC, Italy.
| | - Emanuela Merelli
- School of Sciences and Technology, University of Camerino, Via Madonna delle Carceri 7, 62032, Camerino, MC, Italy
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3
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Zhou L, Wang X, Yu S, Tan YL, Tan ZJ. FebRNA: An automated fragment-ensemble-based model for building RNA 3D structures. Biophys J 2022; 121:3381-3392. [PMID: 35978551 PMCID: PMC9515226 DOI: 10.1016/j.bpj.2022.08.017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2022] [Revised: 07/19/2022] [Accepted: 08/15/2022] [Indexed: 11/23/2022] Open
Abstract
Knowledge of RNA three-dimensional (3D) structures is critical to understanding the important biological functions of RNAs. Although various structure prediction models have been developed, the high-accuracy predictions of RNA 3D structures are still limited to the RNAs with short lengths or with simple topology. In this work, we proposed a new model, namely FebRNA, for building RNA 3D structures through fragment assembly based on coarse-grained (CG) fragment ensembles. Specifically, FebRNA is composed of four processes: establishing the library of different types of non-redundant CG fragment ensembles regardless of the sequences, building CG 3D structure ensemble through fragment assembly, identifying top-scored CG structures through a specific CG scoring function, and rebuilding the all-atom structures from the top-scored CG ones. Extensive examination against different types of RNA structures indicates that FebRNA consistently gives the reliable predictions on RNA 3D structures, including pseudoknots, three-way junctions, four-way and five-way junctions, and RNAs in the RNA-Puzzles. FebRNA is available on the Web site: https://github.com/Tan-group/FebRNA.
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Affiliation(s)
- Li Zhou
- Department of Physics and Key Laboratory of Artificial Micro & Nano-structures of Education, School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Xunxun Wang
- Department of Physics and Key Laboratory of Artificial Micro & Nano-structures of Education, School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Shixiong Yu
- Department of Physics and Key Laboratory of Artificial Micro & Nano-structures of Education, School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Ya-Lan Tan
- Research Center of Nonlinear Science, School of Mathematical and Physical Sciences, Wuhan Textile University, Wuhan 430073, China.
| | - Zhi-Jie Tan
- Department of Physics and Key Laboratory of Artificial Micro & Nano-structures of Education, School of Physics and Technology, Wuhan University, Wuhan 430072, China.
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4
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Zakh R, Churkin A, Totzeck F, Parr M, Tuller T, Etzion O, Dahari H, Roggendorf M, Frishman D, Barash D. A Mathematical Analysis of HDV Genotypes: From Molecules to Cells. MATHEMATICS (BASEL, SWITZERLAND) 2021; 9:2063. [PMID: 34540628 PMCID: PMC8445514 DOI: 10.3390/math9172063] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Hepatitis D virus (HDV) is classified according to eight genotypes. The various genotypes are included in the HDVdb database, where each HDV sequence is specified by its genotype. In this contribution, a mathematical analysis is performed on RNA sequences in HDVdb. The RNA folding predicted structures of the Genbank HDV genome sequences in HDVdb are classified according to their coarse-grain tree-graph representation. The analysis allows discarding in a simple and efficient way the vast majority of the sequences that exhibit a rod-like structure, which is important for the virus replication, to attempt to discover other biological functions by structure consideration. After the filtering, there remain only a small number of sequences that can be checked for their additional stem-loops besides the main one that is known to be responsible for virus replication. It is found that a few sequences contain an additional stem-loop that is responsible for RNA editing or other possible functions. These few sequences are grouped into two main classes, one that is well-known experimentally belonging to genotype 3 for patients from South America associated with RNA editing, and the other that is not known at present belonging to genotype 7 for patients from Cameroon. The possibility that another function besides virus replication reminiscent of the editing mechanism in HDV genotype 3 exists in HDV genotype 7 has not been explored before and is predicted by eigenvalue analysis. Finally, when comparing native and shuffled sequences, it is shown that HDV sequences belonging to all genotypes are accentuated in their mutational robustness and thermodynamic stability as compared to other viruses that were subjected to such an analysis.
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Affiliation(s)
- Rami Zakh
- Department of Computer Science, Ben-Gurion University, Beer-Sheva 8410501, Israel
| | - Alexander Churkin
- Department of Software Engineering, Sami Shamoon College of Engineering, Beer-Sheva 8410501, Israel
| | - Franziska Totzeck
- Department of Bioinformatics, Wissenschaftszentrum Weihenstephan, Technische Universität München, Maximus-von-Imhof-Forum 3, 85354 Freising, Germany
| | - Marina Parr
- Department of Bioinformatics, Wissenschaftszentrum Weihenstephan, Technische Universität München, Maximus-von-Imhof-Forum 3, 85354 Freising, Germany
| | - Tamir Tuller
- Department of Biomedical Engineering, Tel-Aviv University, Tel-Aviv 6997801, Israel
| | - Ohad Etzion
- Soroka University Medical Center, Ben-Gurion University, Beer-Sheva 8410501, Israel
| | - Harel Dahari
- Stritch School of Medicine, Loyola University Chicago, Maywood, IL 60153, USA
| | - Michael Roggendorf
- Institute of Virology, Technische Universität München, 81675 Munich, Germany
| | - Dmitrij Frishman
- Department of Bioinformatics, Wissenschaftszentrum Weihenstephan, Technische Universität München, Maximus-von-Imhof-Forum 3, 85354 Freising, Germany
| | - Danny Barash
- Department of Computer Science, Ben-Gurion University, Beer-Sheva 8410501, Israel
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5
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Jahn K, Beerenwinkel N, Zhang L. The Bourque distances for mutation trees of cancers. Algorithms Mol Biol 2021; 16:9. [PMID: 34112201 PMCID: PMC8193869 DOI: 10.1186/s13015-021-00188-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Accepted: 06/02/2021] [Indexed: 12/02/2022] Open
Abstract
Background Mutation trees are rooted trees in which nodes are of arbitrary degree and labeled with a mutation set. These trees, also referred to as clonal trees, are used in computational oncology to represent the mutational history of tumours. Classical tree metrics such as the popular Robinson–Foulds distance are of limited use for the comparison of mutation trees. One reason is that mutation trees inferred with different methods or for different patients often contain different sets of mutation labels. Results We generalize the Robinson–Foulds distance into a set of distance metrics called Bourque distances for comparing mutation trees. We show the basic version of the Bourque distance for mutation trees can be computed in linear time. We also make a connection between the Robinson–Foulds distance and the nearest neighbor interchange distance. Supplementary Information The online version contains supplementary material available at 10.1186/s13015-021-00188-3.
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Mak CH, Phan ENH. Diagrammatic approaches to RNA structures with trinucleotide repeats. Biophys J 2021; 120:2343-2354. [PMID: 33887227 PMCID: PMC8390803 DOI: 10.1016/j.bpj.2021.04.010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2020] [Revised: 04/07/2021] [Accepted: 04/09/2021] [Indexed: 11/30/2022] Open
Abstract
Trinucleotide repeat expansion disorders are associated with the overexpansion of (CNG) repeats on the genome. Messenger RNA transcripts of sequences with greater than 60–100 (CNG) tandem units have been implicated in trinucleotide repeat expansion disorder pathogenesis. In this work, we develop a diagrammatic theory to study the structural diversity of these (CNG)n RNA sequences. Representing structural elements on the chain’s conformation by a set of graphs and employing elementary diagrammatic methods, we have formulated a renormalization procedure to re-sum these graphs and arrive at a closed-form expression for the ensemble partition function. With a simple approximation for the renormalization and applied to extended (CNG)n sequences, this theory can comprehensively capture an infinite set of conformations with any number and any combination of duplexes, hairpins, multiway junctions, and quadruplexes. To quantify the diversity of different (CNG)n ensembles, the analytical equations derived from the diagrammatic theory were solved numerically to derive equilibrium estimates for the secondary structural contents of the chains. The results suggest that the structural ensembles of (CNG)n repeat sequence with n ∼60 are surprisingly diverse, and the distribution is sensitive to the ability of the N nucleotide to make noncanonical pairs and whether the (CNG)n sequence can sustain stable quadruplexes. The results show how perturbations in the form of biases on the stabilities of the various structural motifs, duplexes, junctions, helices, and quadruplexes could affect the secondary structures of the chains and how these structures may switch when they are perturbed.
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Affiliation(s)
- Chi H Mak
- Department of Chemistry, Center of Applied Mathematical Sciences and Department of Quantitative and Computational Biology, University of Southern California, Los Angeles, California.
| | - Ethan N H Phan
- Department of Chemistry, University of Southern California, Los Angeles, California
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7
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Abstract
Novel RNA motif design is of great practical importance for technology and medicine. Increasingly, computational design plays an important role in such efforts. Our coarse-grained RAG (RNA-As-Graphs) framework offers strategies for enumerating the universe of RNA 2D folds, selecting "RNA-like" candidates for design, and determining sequences that fold onto these candidates. In RAG, RNA secondary structures are represented as tree or dual graphs. Graphs with known RNA structures are called "existing", and the others are labeled "hypothetical". By using simplified features for RNA graphs, we have clustered the hypothetical graphs into "RNA-like" and "non-RNA-like" groups and proposed RNA-like graphs as candidates for design. Here, we propose a new way of designing graph features by using Fiedler vectors. The new features reflect graph shapes better, and they lead to a more clustered organization of existing graphs. We show significant increases in K-means clustering accuracy by using the new features (e.g., up to 95% and 98% accuracy for tree and dual graphs, respectively). In addition, we propose a scoring model for top graph candidate selection. This scoring model allows users to set a threshold for candidates, and it incorporates weighing of existing graphs based on their corresponding number of known RNAs. We include a list of top scored RNA-like candidates, which we hope will stimulate future novel RNA design.
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Affiliation(s)
- Qiyao Zhu
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, United States
| | - Tamar Schlick
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, United States
- Department of Chemistry, New York University, New York, New York 10003, United States
- NYU-ECNU Center for Computational Chemistry, NYU Shanghai, Shanghai 200062, P. R. China
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8
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Jain S, Zhu Q, Paz ASP, Schlick T. Identification of novel RNA design candidates by clustering the extended RNA-As-Graphs library. Biochim Biophys Acta Gen Subj 2020; 1864:129534. [PMID: 31954797 DOI: 10.1016/j.bbagen.2020.129534] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2019] [Revised: 01/10/2020] [Accepted: 01/14/2020] [Indexed: 12/31/2022]
Abstract
BACKGROUND We re-evaluate our RNA-As-Graphs clustering approach, using our expanded graph library and new RNA structures, to identify potential RNA-like topologies for design. Our coarse-grained approach represents RNA secondary structures as tree and dual graphs, with vertices and edges corresponding to RNA helices and loops. The graph theoretical framework facilitates graph enumeration, partitioning, and clustering approaches to study RNA structure and its applications. METHODS Clustering graph topologies based on features derived from graph Laplacian matrices and known RNA structures allows us to classify topologies into 'existing' or hypothetical, and the latter into, 'RNA-like' or 'non RNA-like' topologies. Here we update our list of existing tree graph topologies and RAG-3D database of atomic fragments to include newly determined RNA structures. We then use linear and quadratic regression, optionally with dimensionality reduction, to derive graph features and apply several clustering algorithms on our tree-graph library and recently expanded dual-graph library to classify them into the three groups. RESULTS The unsupervised PAM and K-means clustering approaches correctly classify 72-77% of all existing graph topologies and 75-82% of newly added ones as RNA-like. For supervised k-NN clustering, the cross-validation accuracy ranges from 57 to 81%. CONCLUSIONS Using linear regression with unsupervised clustering, or quadratic regression with supervised clustering, provides better accuracies than supervised/linear clustering. All accuracies are better than random, especially for newly added existing topologies, thus lending credibility to our approach. GENERAL SIGNIFICANCE Our updated RAG-3D database and motif classification by clustering present new RNA substructures and RNA-like motifs as novel design candidates.
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Affiliation(s)
- Swati Jain
- Department of Chemistry, New York University, 1021 Silver, 100 Washington Square East, New York, NY 10003, USA
| | - Qiyao Zhu
- Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
| | - Amiel S P Paz
- NYU Shanghai, 1555 Century Avenue, Shanghai 200135, China; NYU-ECNU Center for Computational Chemistry, NYU Shanghai, 3663 Zhongshang Road North, Shanghai 200062, China
| | - Tamar Schlick
- Department of Chemistry, New York University, 1021 Silver, 100 Washington Square East, New York, NY 10003, USA; Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA; NYU-ECNU Center for Computational Chemistry, NYU Shanghai, 3663 Zhongshang Road North, Shanghai 200062, China.
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9
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Inverse folding with RNA-As-Graphs produces a large pool of candidate sequences with target topologies. J Struct Biol 2019; 209:107438. [PMID: 31874236 DOI: 10.1016/j.jsb.2019.107438] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2019] [Revised: 12/18/2019] [Accepted: 12/19/2019] [Indexed: 02/07/2023]
Abstract
We present an RNA-As-Graphs (RAG) based inverse folding algorithm, RAG-IF, to design novel RNA sequences that fold onto target tree graph topologies. The algorithm can be used to enhance our recently reported computational design pipeline (Jain et al., NAR 2018). The RAG approach represents RNA secondary structures as tree and dual graphs, where RNA loops and helices are coarse-grained as vertices and edges, opening the usage of graph theory methods to study, predict, and design RNA structures. Our recently developed computational pipeline for design utilizes graph partitioning (RAG-3D) and atomic fragment assembly (F-RAG) to design sequences to fold onto RNA-like tree graph topologies; the atomic fragments are taken from existing RNA structures that correspond to tree subgraphs. Because F-RAG may not produce the target folds for all designs, automated mutations by RAG-IF algorithm enhance the candidate pool markedly. The crucial residues for mutation are identified by differences between the predicted and the target topology. A genetic algorithm then mutates the selected residues, and the successful sequences are optimized to retain only the minimal or essential mutations. Here we evaluate RAG-IF for 6 RNA-like topologies and generate a large pool of successful candidate sequences with a variety of minimal mutations. We find that RAG-IF adds robustness and efficiency to our RNA design pipeline, making inverse folding motivated by graph topology rather than secondary structure more productive.
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10
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Kimchi O, Cragnolini T, Brenner MP, Colwell LJ. A Polymer Physics Framework for the Entropy of Arbitrary Pseudoknots. Biophys J 2019; 117:520-532. [PMID: 31353036 PMCID: PMC6697467 DOI: 10.1016/j.bpj.2019.06.037] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2018] [Revised: 06/21/2019] [Accepted: 06/27/2019] [Indexed: 11/18/2022] Open
Abstract
The accurate prediction of RNA secondary structure from primary sequence has had enormous impact on research from the past 40 years. Although many algorithms are available to make these predictions, the inclusion of non-nested loops, termed pseudoknots, still poses challenges arising from two main factors: 1) no physical model exists to estimate the loop entropies of complex intramolecular pseudoknots, and 2) their NP-complete enumeration has impeded their study. Here, we address both challenges. First, we develop a polymer physics model that can address arbitrarily complex pseudoknots using only two parameters corresponding to concrete physical quantities-over an order of magnitude fewer than the sparsest state-of-the-art phenomenological methods. Second, by coupling this model to exhaustive enumeration of the set of possible structures, we compute the entire free energy landscape of secondary structures resulting from a primary RNA sequence. We demonstrate that for RNA structures of ∼80 nucleotides, with minimal heuristics, the complete enumeration of possible secondary structures can be accomplished quickly despite the NP-complete nature of the problem. We further show that despite our loop entropy model's parametric sparsity, it performs better than or on par with previously published methods in predicting both pseudoknotted and non-pseudoknotted structures on a benchmark data set of RNA structures of ≤80 nucleotides. We suggest ways in which the accuracy of the model can be further improved.
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Affiliation(s)
- Ofer Kimchi
- Harvard Graduate Program in Biophysics, Harvard University, Cambridge, Massachusetts.
| | - Tristan Cragnolini
- Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
| | - Michael P Brenner
- School of Engineering and Applied Sciences, Cambridge, Massachusetts; Kavli Institute for Bionano Science and Technology, Harvard University, Cambridge, Massachusetts
| | - Lucy J Colwell
- Department of Chemistry, University of Cambridge, Cambridge, United Kingdom.
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11
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Jain S, Laederach A, Ramos SBV, Schlick T. A pipeline for computational design of novel RNA-like topologies. Nucleic Acids Res 2019; 46:7040-7051. [PMID: 30137633 PMCID: PMC6101589 DOI: 10.1093/nar/gky524] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2017] [Accepted: 05/24/2018] [Indexed: 12/11/2022] Open
Abstract
Designing novel RNA topologies is a challenge, with important therapeutic and industrial applications. We describe a computational pipeline for design of novel RNA topologies based on our coarse-grained RNA-As-Graphs (RAG) framework. RAG represents RNA structures as tree graphs and describes RNA secondary (2D) structure topologies (currently up to 13 vertices, ≈260 nucleotides). We have previously identified novel graph topologies that are RNA-like among these. Here we describe a systematic design pipeline and illustrate design for six broad design problems using recently developed tools for graph-partitioning and fragment assembly (F-RAG). Following partitioning of the target graph, corresponding atomic fragments from our RAG-3D database are combined using F-RAG, and the candidate atomic models are scored using a knowledge-based potential developed for 3D structure prediction. The sequences of the top scoring models are screened further using available tools for 2D structure prediction. The results indicate that our modular approach based on RNA-like topologies rather than specific 2D structures allows for greater flexibility in the design process, and generates a large number of candidate sequences quickly. Experimental structure probing using SHAPE-MaP for two sequences agree with our predictions and suggest that our combined tools yield excellent candidates for further sequence and experimental screening.
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Affiliation(s)
- Swati Jain
- Department of Chemistry, New York University, 1001 Silver, 100 Washington Square East, New York, NY 10003, USA
| | - Alain Laederach
- Department of Biology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
| | - Silvia B V Ramos
- Department of Biochemistry and Biophysics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
| | - Tamar Schlick
- Department of Chemistry, New York University, 1001 Silver, 100 Washington Square East, New York, NY 10003, USA.,Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA.,NYU-ECNU Center for Computational Chemistry at New York University Shanghai, Room 340, Geography Building, North Zhongshan Road, 3663 Shanghai, China
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12
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Mak CH, Phan ENH. Topological Constraints and Their Conformational Entropic Penalties on RNA Folds. Biophys J 2019; 114:2059-2071. [PMID: 29742400 PMCID: PMC5961522 DOI: 10.1016/j.bpj.2018.03.035] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2017] [Revised: 03/08/2018] [Accepted: 03/22/2018] [Indexed: 02/01/2023] Open
Abstract
Functional RNAs can fold into intricate structures using a number of different secondary and tertiary structural motifs. Many factors contribute to the overall free energy of the target fold. This study aims at quantifying the entropic costs coming from the loss of conformational freedom when the sugar-phosphate backbone is subjected to constraints imposed by secondary and tertiary contacts. Motivated by insights from topology theory, we design a diagrammatic scheme to represent different types of RNA structures so that constraints associated with a folded structure may be segregated into mutually independent subsets, enabling the total conformational entropy loss to be easily calculated as a sum of independent terms. We used high-throughput Monte Carlo simulations to simulate large ensembles of single-stranded RNA sequences in solution to validate the assumptions behind our diagrammatic scheme, examining the entropic costs for hairpin initiation and formation of many multiway junctions. Our diagrammatic scheme aids in the factorization of secondary/tertiary constraints into distinct topological classes and facilitates the discovery of interrelationships among multiple constraints on RNA folds. This perspective, which to our knowledge is novel, leads to useful insights into the inner workings of some functional RNA sequences, demonstrating how they might operate by transforming their structures among different topological classes.
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Affiliation(s)
- Chi H Mak
- Department of Chemistry, University of Southern California, Los Angeles, California; Center of Applied Mathematical Sciences, University of Southern California, Los Angeles, California; Department of Biological Sciences, University of Southern California, Los Angeles, California.
| | - Ethan N H Phan
- Department of Chemistry, University of Southern California, Los Angeles, California
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13
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Jain S, Saju S, Petingi L, Schlick T. An extended dual graph library and partitioning algorithm applicable to pseudoknotted RNA structures. Methods 2019; 162-163:74-84. [PMID: 30928508 DOI: 10.1016/j.ymeth.2019.03.022] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2019] [Revised: 02/28/2019] [Accepted: 03/22/2019] [Indexed: 12/18/2022] Open
Abstract
Exploring novel RNA topologies is imperative for understanding RNA structure and pursuing its design. Our RNA-As-Graphs (RAG) approach exploits graph theory tools and uses coarse-grained tree and dual graphs to represent RNA helices and loops by vertices and edges. Only dual graphs represent pseudoknotted RNAs fully. Here we develop a dual graph enumeration algorithm to generate an expanded library of dual graph topologies for 2-9 vertices, and extend our dual graph partitioning algorithm to identify all possible RNA subgraphs. Our enumeration algorithm connects smaller-vertex graphs, using all possible edge combinations, to build larger-vertex graphs and retain all non-isomorphic graph topologies, thereby more than doubling the size of our prior library to a total of 110,667 dual graph topologies. We apply our dual graph partitioning algorithm, which keeps pseudoknots and junctions intact, to all existing RNA structures to identify all possible substructures up to 9 vertices. In addition, our expanded dual graph library assigns graph topologies to all RNA graphs and subgraphs, rectifying prior inconsistencies. We update our RAG-3Dual database of RNA atomic fragments with all newly identified substructures and their graph IDs, increasing its size by more than 50 times. The enlarged dual graph library and RAG-3Dual database provide a comprehensive repertoire of graph topologies and atomic fragments to study yet undiscovered RNA molecules and design RNA sequences with novel topologies, including a variety of pseudoknotted RNAs.
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Affiliation(s)
- Swati Jain
- Department of Chemistry, New York University, 1021 Silver, 100 Washington Square East, New York, NY 10003, USA
| | - Sera Saju
- Department of Chemistry, New York University, 1021 Silver, 100 Washington Square East, New York, NY 10003, USA
| | - Louis Petingi
- Computer Science Department, College of Staten Island, City University of New York, Staten Island, New York, NY 10314, USA
| | - Tamar Schlick
- Department of Chemistry, New York University, 1021 Silver, 100 Washington Square East, New York, NY 10003, USA; Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA; NYU-East China Normal University Center for Computational Chemistry at New York University Shanghai, Room 340, Geography Building, North Zhongshan Road, 3663 Shanghai, China.
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14
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Jain S, Bayrak CS, Petingi L, Schlick T. Dual Graph Partitioning Highlights a Small Group of Pseudoknot-Containing RNA Submotifs. Genes (Basel) 2018; 9:E371. [PMID: 30044451 PMCID: PMC6115904 DOI: 10.3390/genes9080371] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2018] [Revised: 06/26/2018] [Accepted: 06/26/2018] [Indexed: 12/31/2022] Open
Abstract
RNA molecules are composed of modular architectural units that define their unique structural and functional properties. Characterization of these building blocks can help interpret RNA structure/function relationships. We present an RNA secondary structure motif and submotif library using dual graph representation and partitioning. Dual graphs represent RNA helices as vertices and loops as edges. Unlike tree graphs, dual graphs can represent RNA pseudoknots (intertwined base pairs). For a representative set of RNA structures, we construct dual graphs from their secondary structures, and apply our partitioning algorithm to identify non-separable subgraphs (or blocks) without breaking pseudoknots. We report 56 subgraph blocks up to nine vertices; among them, 22 are frequently occurring, 15 of which contain pseudoknots. We then catalog atomic fragments corresponding to the subgraph blocks to define a library of building blocks that can be used for RNA design, which we call RAG-3Dual, as we have done for tree graphs. As an application, we analyze the distribution of these subgraph blocks within ribosomal RNAs of various prokaryotic and eukaryotic species to identify common subgraphs and possible ancestry relationships. Other applications of dual graph partitioning and motif library can be envisioned for RNA structure analysis and design.
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Affiliation(s)
- Swati Jain
- Department of Chemistry, New York University, New York, NY 10003, USA.
| | - Cigdem S Bayrak
- Department of Chemistry, New York University, New York, NY 10003, USA.
| | - Louis Petingi
- Computer Science Department, College of Staten Island, City University of New York, Staten Island, New York, NY 10314, USA.
| | - Tamar Schlick
- Department of Chemistry, New York University, New York, NY 10003, USA.
- Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA.
- NYU-East China Normal University Center for Computational Chemistry, New York University Shanghai, Shanghai 3663, China.
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15
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Abstract
The structure of RNA has been a natural subject for mathematical modeling, inviting many innovative computational frameworks. This single-stranded polynucleotide chain can fold upon itself in numerous ways to form hydrogen-bonded segments, imperfect with single-stranded loops. Illustrating these paired and non-paired interaction networks, known as RNA's secondary (2D) structure, using mathematical graph objects has been illuminating for RNA structure analysis. Building upon such seminal work from the 1970s and 1980s, graph models are now used to study not only RNA structure but also describe RNA's recurring modular units, sample the conformational space accessible to RNAs, predict RNA's three-dimensional folds, and apply the combined aspects to novel RNA design. In this article, we outline the development of the RNA-As-Graphs (or RAG) approach and highlight current applications to RNA structure prediction and design.
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Affiliation(s)
- Tamar Schlick
- Department of Chemistry, 100 Washington Square East, Silver Building, New York University, New York, NY 10003, USA; Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012, USA; New York University ECNU - Center for Computational Chemistry at NYU Shanghai, 3663 North Zhongshan Road, Shanghai, 200062, China.
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16
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Jain S, Schlick T. F-RAG: Generating Atomic Coordinates from RNA Graphs by Fragment Assembly. J Mol Biol 2017; 429:3587-3605. [PMID: 28988954 PMCID: PMC5693719 DOI: 10.1016/j.jmb.2017.09.017] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2017] [Revised: 09/12/2017] [Accepted: 09/22/2017] [Indexed: 10/18/2022]
Abstract
Coarse-grained models represent attractive approaches to analyze and simulate ribonucleic acid (RNA) molecules, for example, for structure prediction and design, as they simplify the RNA structure to reduce the conformational search space. Our structure prediction protocol RAGTOP (RNA-As-Graphs Topology Prediction) represents RNA structures as tree graphs and samples graph topologies to produce candidate graphs. However, for a more detailed study and analysis, construction of atomic from coarse-grained models is required. Here we present our graph-based fragment assembly algorithm (F-RAG) to convert candidate three-dimensional (3D) tree graph models, produced by RAGTOP into atomic structures. We use our related RAG-3D utilities to partition graphs into subgraphs and search for structurally similar atomic fragments in a data set of RNA 3D structures. The fragments are edited and superimposed using common residues, full atomic models are scored using RAGTOP's knowledge-based potential, and geometries of top scoring models is optimized. To evaluate our models, we assess all-atom RMSDs and Interaction Network Fidelity (a measure of residue interactions) with respect to experimentally solved structures and compare our results to other fragment assembly programs. For a set of 50 RNA structures, we obtain atomic models with reasonable geometries and interactions, particularly good for RNAs containing junctions. Additional improvements to our protocol and databases are outlined. These results provide a good foundation for further work on RNA structure prediction and design applications.
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Affiliation(s)
- Swati Jain
- Department of Chemistry, New York University, 1001 Silver, 100 Washington Square East, New York, NY 10003, USA
| | - Tamar Schlick
- Department of Chemistry, New York University, 1001 Silver, 100 Washington Square East, New York, NY 10003, USA; Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA; New York University-East China Normal University Center for Computational Chemistry at New York University Shanghai, Room 340, Geography Building, North Zhongshan Road, 3663 Shanghai, China.
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17
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Bayrak CS, Kim N, Schlick T. Using sequence signatures and kink-turn motifs in knowledge-based statistical potentials for RNA structure prediction. Nucleic Acids Res 2017; 45:5414-5422. [PMID: 28158755 PMCID: PMC5435971 DOI: 10.1093/nar/gkx045] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2016] [Accepted: 01/22/2017] [Indexed: 12/15/2022] Open
Abstract
Kink turns are widely occurring motifs in RNA, located in internal loops and associated with many biological functions including translation, regulation and splicing. The associated sequence pattern, a 3-nt bulge and G-A, A-G base-pairs, generates an angle of ∼50° along the helical axis due to A-minor interactions. The conserved sequence and distinct secondary structures of kink-turns (k-turn) suggest computational folding rules to predict k-turn-like topologies from sequence. Here, we annotate observed k-turn motifs within a non-redundant RNA dataset based on sequence signatures and geometrical features, analyze bending and torsion angles, and determine distinct knowledge-based potentials with and without k-turn motifs. We apply these scoring potentials to our RAGTOP (RNA-As-Graph-Topologies) graph sampling protocol to construct and sample coarse-grained graph representations of RNAs from a given secondary structure. We present graph-sampling results for 35 RNAs, including 12 k-turn and 23 non k-turn internal loops, and compare the results to solved structures and to RAGTOP results without special k-turn potentials. Significant improvements are observed with the updated scoring potentials compared to the k-turn-free potentials. Because k-turns represent a classic example of sequence/structure motif, our study suggests that other such motifs with sequence signatures and unique geometrical features can similarly be utilized for RNA structure prediction and design.
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Affiliation(s)
- Cigdem Sevim Bayrak
- Department of Chemistry and Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
| | - Namhee Kim
- Department of Chemistry and Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
| | - Tamar Schlick
- Department of Chemistry and Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
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18
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Bharath K, Kambadur P, Dey DK, Rao A, Baladandayuthapani V. Statistical Tests for Large Tree-Structured Data. J Am Stat Assoc 2017; 112:1733-1743. [PMID: 37013199 PMCID: PMC10066867 DOI: 10.1080/01621459.2016.1240081] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Abstract
We develop a general statistical framework for the analysis and inference of large tree-structured data, with a focus on developing asymptotic goodness-of-fit tests. We first propose a consistent statistical model for binary trees, from which we develop a class of invariant tests. Using the model for binary trees, we then construct tests for general trees by using the distributional properties of the Continuum Random Tree, which arises as the invariant limit for a broad class of models for tree-structured data based on conditioned Galton-Watson processes. The test statistics for the goodness-of-fit tests are simple to compute and are asymptotically distributed as χ 2 and F random variables. We illustrate our methods on an important application of detecting tumour heterogeneity in brain cancer. We use a novel approach with tree-based representations of magnetic resonance images and employ the developed tests to ascertain tumor heterogeneity between two groups of patients.
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Affiliation(s)
- Karthik Bharath
- School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
| | | | - Dipak. K. Dey
- Department of Statistics, University of Connecticut, Storrs, CT
| | - Arvind Rao
- Department of Bioinformatics and Computational Biology, The University of Texas MD Anderson Cancer Center, Houston, TX
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19
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Schlick T, Pyle AM. Opportunities and Challenges in RNA Structural Modeling and Design. Biophys J 2017; 113:225-234. [PMID: 28162235 PMCID: PMC5529161 DOI: 10.1016/j.bpj.2016.12.037] [Citation(s) in RCA: 50] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2016] [Revised: 12/08/2016] [Accepted: 12/19/2016] [Indexed: 01/27/2023] Open
Abstract
We describe opportunities and challenges in RNA structural modeling and design, as recently discussed during the second Telluride Science Research Center workshop organized in June 2016. Topics include fundamental processes of RNA, such as structural assemblies (hierarchical folding, multiple conformational states and their clustering), RNA motifs, and chemical reactivity of RNA, as used for structural prediction and functional inference. We also highlight the software and database issues associated with RNA structures, such as the multiple approaches for motif annotation, the need for frequent database updating, and the importance of quality control of RNA structures. We discuss various modeling approaches for structure prediction, mechanistic analysis of RNA reactions, and RNA design, and the complementary roles that both atomistic and coarse-grained approaches play in such simulations. Collectively, as scientists from varied disciplines become familiar and drawn into these unique challenges, new approaches and collaborative efforts will undoubtedly be catalyzed.
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Affiliation(s)
- Tamar Schlick
- Department of Chemistry, New York University, New York, New York; Courant Institute of Mathematical Sciences, New York University, New York, New York.
| | - Anna Marie Pyle
- Department of Molecular and Cellular and Developmental Biology and Department of Chemistry, Yale University; Howard Hughes Medical Institute, New Haven, Connecticut.
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20
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Rogers E, Heitsch C. New insights from cluster analysis methods for RNA secondary structure prediction. WILEY INTERDISCIPLINARY REVIEWS-RNA 2016; 7:278-94. [PMID: 26971529 DOI: 10.1002/wrna.1334] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2015] [Revised: 12/03/2015] [Accepted: 12/17/2015] [Indexed: 01/12/2023]
Abstract
A widening gap exists between the best practices for RNA secondary structure prediction developed by computational researchers and the methods used in practice by experimentalists. Minimum free energy predictions, although broadly used, are outperformed by methods which sample from the Boltzmann distribution and data mine the results. In particular, moving beyond the single structure prediction paradigm yields substantial gains in accuracy. Furthermore, the largest improvements in accuracy and precision come from viewing secondary structures not at the base pair level but at lower granularity/higher abstraction. This suggests that random errors affecting precision and systematic ones affecting accuracy are both reduced by this 'fuzzier' view of secondary structures. Thus experimentalists who are willing to adopt a more rigorous, multilayered approach to secondary structure prediction by iterating through these levels of granularity will be much better able to capture fundamental aspects of RNA base pairing. WIREs RNA 2016, 7:278-294. doi: 10.1002/wrna.1334 For further resources related to this article, please visit the WIREs website.
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Affiliation(s)
- Emily Rogers
- School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0765, USA
| | - Christine Heitsch
- School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA
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21
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Baba N, Elmetwaly S, Kim N, Schlick T. Predicting Large RNA-Like Topologies by a Knowledge-Based Clustering Approach. J Mol Biol 2015; 428:811-821. [PMID: 26478223 DOI: 10.1016/j.jmb.2015.10.009] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2015] [Accepted: 10/06/2015] [Indexed: 11/19/2022]
Abstract
An analysis and expansion of our resource for classifying, predicting, and designing RNA structures, RAG (RNA-As-Graphs), is presented, with the goal of understanding features of RNA-like and non-RNA-like motifs and exploiting this information for RNA design. RAG was first reported in 2004 for cataloging RNA secondary structure motifs using graph representations. In 2011, the RAG resource was updated with the increased availability of RNA structures and was improved by utilities for analyzing RNA structures, including substructuring and search tools. We also classified RNA structures as graphs up to 10 vertices (~200 nucleotides) into three classes: existing, RNA-like, and non-RNA-like using clustering approaches. Here, we focus on the tree graphs and evaluate the newly founded RNAs since 2011, which also support our refined predictions of RNA-like motifs. We expand the RAG resource for large tree graphs up to 13 vertices (~260 nucleotides), thereby cataloging more than 10 times as many secondary structures. We apply clustering algorithms based on features of RNA secondary structures translated from known tertiary structures to suggest which hypothetical large RNA motifs can be considered "RNA-like". The results by the PAM (Partitioning Around Medoids) approach, in particular, reveal good accuracy, with small error for the largest cases. The RAG update here up to 13 vertices offers a useful graph-based tool for exploring RNA motifs and suggesting large RNA motifs for design.
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Affiliation(s)
- Naoto Baba
- Department of Chemistry and Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA; Department of Chemistry, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8601, Japan
| | - Shereef Elmetwaly
- Department of Chemistry and Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
| | - Namhee Kim
- Department of Chemistry and Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
| | - Tamar Schlick
- Department of Chemistry and Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA; NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai, 200062, China.
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22
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Boudard M, Bernauer J, Barth D, Cohen J, Denise A. GARN: Sampling RNA 3D Structure Space with Game Theory and Knowledge-Based Scoring Strategies. PLoS One 2015; 10:e0136444. [PMID: 26313379 PMCID: PMC4551674 DOI: 10.1371/journal.pone.0136444] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2015] [Accepted: 08/03/2015] [Indexed: 11/19/2022] Open
Abstract
Cellular processes involve large numbers of RNA molecules. The functions of these RNA molecules and their binding to molecular machines are highly dependent on their 3D structures. One of the key challenges in RNA structure prediction and modeling is predicting the spatial arrangement of the various structural elements of RNA. As RNA folding is generally hierarchical, methods involving coarse-grained models hold great promise for this purpose. We present here a novel coarse-grained method for sampling, based on game theory and knowledge-based potentials. This strategy, GARN (Game Algorithm for RNa sampling), is often much faster than previously described techniques and generates large sets of solutions closely resembling the native structure. GARN is thus a suitable starting point for the molecular modeling of large RNAs, particularly those with experimental constraints. GARN is available from: http://garn.lri.fr/.
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Affiliation(s)
- Mélanie Boudard
- PRiSM, CNRS UMR 8144, Université de Versailles-St-Quentin-en-Yvelines, 78000 Versailles, France
- LRI, CNRS UMR 8623, Université Paris-Sud, 91405 Orsay, France
- * E-mail: (MB); (JC)
| | - Julie Bernauer
- AMIB, Inria Saclay-Ile de France, 91120 Palaiseau, France
- LIX, CNRS UMR 7161, Ecole Polytechnique, 91120 Palaiseau, France
| | - Dominique Barth
- PRiSM, CNRS UMR 8144, Université de Versailles-St-Quentin-en-Yvelines, 78000 Versailles, France
| | - Johanne Cohen
- LRI, CNRS UMR 8623, Université Paris-Sud, 91405 Orsay, France
- * E-mail: (MB); (JC)
| | - Alain Denise
- LRI, CNRS UMR 8623, Université Paris-Sud, 91405 Orsay, France
- AMIB, Inria Saclay-Ile de France, 91120 Palaiseau, France
- I2BC, CNRS, Université Paris-Sud, 91405 Orsay, France
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23
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Graph-based sampling for approximating global helical topologies of RNA. Proc Natl Acad Sci U S A 2014; 111:4079-84. [PMID: 24591615 DOI: 10.1073/pnas.1318893111] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
A current challenge in RNA structure prediction is the description of global helical arrangements compatible with a given secondary structure. Here we address this problem by developing a hierarchical graph sampling/data mining approach to reduce conformational space and accelerate global sampling of candidate topologies. Starting from a 2D structure, we construct an initial graph from size measures deduced from solved RNAs and junction topologies predicted by our data-mining algorithm RNAJAG trained on known RNAs. We sample these graphs in 3D space guided by knowledge-based statistical potentials derived from bending and torsion measures of internal loops as well as radii of gyration for known RNAs. Graph sampling results for 30 representative RNAs are analyzed and compared with reference graphs from both solved structures and predicted structures by available programs. This comparison indicates promise for our graph-based sampling approach for characterizing global helical arrangements in large RNAs: graph rmsds range from 2.52 to 28.24 Å for RNAs of size 25-158 nucleotides, and more than half of our graph predictions improve upon other programs. The efficiency in graph sampling, however, implies an additional step of translating candidate graphs into atomic models. Such models can be built with the same idea of graph partitioning and build-up procedures we used for RNA design.
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24
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Combinatorial Insights into RNA Secondary Structure. DISCRETE AND TOPOLOGICAL MODELS IN MOLECULAR BIOLOGY 2014. [DOI: 10.1007/978-3-642-40193-0_7] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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25
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Laing C, Jung S, Kim N, Elmetwaly S, Zahran M, Schlick T. Predicting helical topologies in RNA junctions as tree graphs. PLoS One 2013; 8:e71947. [PMID: 23991010 PMCID: PMC3753280 DOI: 10.1371/journal.pone.0071947] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2013] [Accepted: 07/05/2013] [Indexed: 01/11/2023] Open
Abstract
RNA molecules are important cellular components involved in many fundamental biological processes. Understanding the mechanisms behind their functions requires knowledge of their tertiary structures. Though computational RNA folding approaches exist, they often require manual manipulation and expert intuition; predicting global long-range tertiary contacts remains challenging. Here we develop a computational approach and associated program module (RNAJAG) to predict helical arrangements/topologies in RNA junctions. Our method has two components: junction topology prediction and graph modeling. First, junction topologies are determined by a data mining approach from a given secondary structure of the target RNAs; second, the predicted topology is used to construct a tree graph consistent with geometric preferences analyzed from solved RNAs. The predicted graphs, which model the helical arrangements of RNA junctions for a large set of 200 junctions using a cross validation procedure, yield fairly good representations compared to the helical configurations in native RNAs, and can be further used to develop all-atom models as we show for two examples. Because junctions are among the most complex structural elements in RNA, this work advances folding structure prediction methods of large RNAs. The RNAJAG module is available to academic users upon request.
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Affiliation(s)
- Christian Laing
- Department of Biology, Wilkes University, Wilkes-Barre, Pennsylvania, United States of America
- Department of Mathematics and Computer Science, Wilkes University, Wilkes-Barre, Pennsylvania, United States of America
| | - Segun Jung
- Department of Chemistry, New York University, New York, United States of America
| | - Namhee Kim
- Department of Chemistry, New York University, New York, United States of America
| | - Shereef Elmetwaly
- Department of Chemistry, New York University, New York, United States of America
| | - Mai Zahran
- Department of Chemistry, New York University, New York, United States of America
| | - Tamar Schlick
- Department of Chemistry, New York University, New York, United States of America
- Courant Institute of Mathematical Sciences, New York University, New York, United States of America
- * E-mail:
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26
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Milo N, Zakov S, Katzenelson E, Bachmat E, Dinitz Y, Ziv-Ukelson M. Unrooted unordered homeomorphic subtree alignment of RNA trees. Algorithms Mol Biol 2013; 8:13. [PMID: 23590940 PMCID: PMC3765143 DOI: 10.1186/1748-7188-8-13] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2012] [Accepted: 02/05/2013] [Indexed: 11/17/2022] Open
Abstract
We generalize some current approaches for RNA tree alignment, which are traditionally confined to ordered rooted mappings, to also consider unordered unrooted mappings. We define the Homeomorphic Subtree Alignment problem (HSA), and present a new algorithm which applies to several modes, combining global or local, ordered or unordered, and rooted or unrooted tree alignments. Our algorithm generalizes previous algorithms that either solved the problem in an asymmetric manner, or were restricted to the rooted and/or ordered cases. Focusing here on the most general unrooted unordered case, we show that for input trees T and S, our algorithm has an O(nTnS + min(dT,dS)LTLS) time complexity, where nT,LT and dT are the number of nodes, the number of leaves, and the maximum node degree in T, respectively (satisfying dT ≤ LT ≤ nT), and similarly for nS,LS and dS with respect to the tree S. This improves the time complexity of previous algorithms for less general variants of the problem. In order to obtain this time bound for HSA, we developed new algorithms for a generalized variant of the Min-Cost Bipartite Matching problem (MCM), as well as to two derivatives of this problem, entitled All-Cavity-MCM and All-Pairs-Cavity-MCM. For two input sets of size n and m, where n ≤ m, MCM and both its cavity derivatives are solved in O(n3 + nm) time, without the usage of priority queues (e.g. Fibonacci heaps) or other complex data structures. This gives the first cubic time algorithm for All-Pairs-Cavity-MCM, and improves the running times of MCM and All-Cavity-MCM problems in the unbalanced case where n ≪ m. We implemented the algorithm (in all modes mentioned above) as a graphical software tool which computes and displays similarities between secondary structures of RNA given as input, and employed it to a preliminary experiment in which we ran all-against-all inter-family pairwise alignments of RNAse P and Hammerhead RNA family members, exposing new similarities which could not be detected by the traditional rooted ordered alignment approaches. The results demonstrate that our approach can be used to expose structural similarity between some RNAs with higher sensitivity than the traditional rooted ordered alignment approaches. Source code and web-interface for our tool can be found in http://www.cs.bgu.ac.il/\~negevcb/FRUUT.
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27
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Churkin A, Barash D. RNA dot plots: an image representation for RNA secondary structure analysis and manipulations. WILEY INTERDISCIPLINARY REVIEWS-RNA 2013; 4:205-16. [PMID: 23386427 DOI: 10.1002/wrna.1154] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
Dot plots were originally introduced in bioinformatics as dot-containing images used to compare biological sequences and identify regions of close similarity between them. In addition to similarity, dot plots were extended to possibly represent interactions between building blocks of biological sequences, where the dots can vary in size or color according to desired features. In this survey, we first review their use in representing an RNA secondary structure, which has mostly been applied for displaying the output secondary structures as a result of running RNA folding prediction algorithms. Such a result may often contain suboptimal solutions in addition to the optimal one, which can be easily incorporated in the dot plot. We then proceed from their passive use of providing RNA secondary structure snapshots to their active use of illustrating RNA secondary structure manipulations in beneficial ways. While comparison between RNA secondary structures can mostly be done efficiently using a string representation, there are notable advantages in using dot plots for analyzing the suboptimal solutions that convey important information about the structure of the RNA molecule. In addition, structure-based alignment of dot plots has been advanced considerably and the filtering of dot plots that considers chemical and enzymatic data from structure determination experiments has been suggested. We discuss these procedures and how they can be enhanced in the future by using an image representation to analyze RNA secondary structures and examine their manipulations.
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Affiliation(s)
- Alexander Churkin
- Department of Computer Science, Ben-Gurion University, Beer-Sheva, Israel
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28
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Ray SS, Pal SK. RNA secondary structure prediction using soft computing. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2013; 10:2-17. [PMID: 23702539 DOI: 10.1109/tcbb.2012.159] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Prediction of RNA structure is invaluable in creating new drugs and understanding genetic diseases. Several deterministic algorithms and soft computing-based techniques have been developed for more than a decade to determine the structure from a known RNA sequence. Soft computing gained importance with the need to get approximate solutions for RNA sequences by considering the issues related with kinetic effects, cotranscriptional folding, and estimation of certain energy parameters. A brief description of some of the soft computing-based techniques, developed for RNA secondary structure prediction, is presented along with their relevance. The basic concepts of RNA and its different structural elements like helix, bulge, hairpin loop, internal loop, and multiloop are described. These are followed by different methodologies, employing genetic algorithms, artificial neural networks, and fuzzy logic. The role of various metaheuristics, like simulated annealing, particle swarm optimization, ant colony optimization, and tabu search is also discussed. A relative comparison among different techniques, in predicting 12 known RNA secondary structures, is presented, as an example. Future challenging issues are then mentioned.
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29
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Churkin A, Gabdank I, Barash D. On topological indices for small RNA graphs. Comput Biol Chem 2012; 41:35-40. [PMID: 23147564 DOI: 10.1016/j.compbiolchem.2012.10.004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2012] [Revised: 10/11/2012] [Accepted: 10/12/2012] [Indexed: 11/29/2022]
Abstract
The secondary structure of RNAs can be represented by graphs at various resolutions. While it was shown that RNA secondary structures can be represented by coarse grain tree-graphs and meaningful topological indices can be used to distinguish between various structures, small RNAs are needed to be represented by full graphs. No meaningful topological index has yet been suggested for the analysis of such type of RNA graphs. Recalling that the second eigenvalue of the Laplacian matrix can be used to track topological changes in the case of coarse grain tree-graphs, it is plausible to assume that a topological index such as the Wiener index that represents all Laplacian eigenvalues may provide a similar guide for full graphs. However, by its original definition, the Wiener index was defined for acyclic graphs. Nevertheless, similarly to cyclic chemical graphs, small RNA graphs can be analyzed using elementary cuts, which enables the calculation of topological indices for small RNAs in an intuitive way. We show how to calculate a structural descriptor that is suitable for cyclic graphs, the Szeged index, for small RNA graphs by elementary cuts. We discuss potential uses of such a procedure that considers all eigenvalues of the associated Laplacian matrices to quantify the topology of small RNA graphs.
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Affiliation(s)
- Alexander Churkin
- Department of Computer Science, Ben-Gurion University, 84105 Beer-Sheva, Israel
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30
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Abstract
MOTIVATION Mass spectrometry allows sensitive, automated and high-throughput analysis of small molecules such as metabolites. One major bottleneck in metabolomics is the identification of 'unknown' small molecules not in any database. Recently, fragmentation tree alignments have been introduced for the automated comparison of the fragmentation patterns of small molecules. Fragmentation pattern similarities are strongly correlated with the chemical similarity of the molecules, and allow us to cluster compounds based solely on their fragmentation patterns. RESULTS Aligning fragmentation trees is computationally hard. Nevertheless, we present three exact algorithms for the problem: a dynamic programming (DP) algorithm, a sparse variant of the DP, and an Integer Linear Program (ILP). Evaluation of our methods on three different datasets showed that thousands of alignments can be computed in a matter of minutes using DP, even for 'challenging' instances. Running times of the sparse DP were an order of magnitude better than for the classical DP. The ILP was clearly outperformed by both DP approaches. We also found that for both DP algorithms, computing the 1% slowest alignments required as much time as computing the 99% fastest.
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Affiliation(s)
- Franziska Hufsky
- Chair for Bioinformatics, Friedrich-Schiller-University, Jena, Germany
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Lai D, Proctor JR, Zhu JYA, Meyer IM. R-CHIE: a web server and R package for visualizing RNA secondary structures. Nucleic Acids Res 2012; 40:e95. [PMID: 22434875 PMCID: PMC3384350 DOI: 10.1093/nar/gks241] [Citation(s) in RCA: 88] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022] Open
Abstract
Visually examining RNA structures can greatly aid in understanding their potential functional roles and in evaluating the performance of structure prediction algorithms. As many functional roles of RNA structures can already be studied given the secondary structure of the RNA, various methods have been devised for visualizing RNA secondary structures. Most of these methods depict a given RNA secondary structure as a planar graph consisting of base-paired stems interconnected by roundish loops. In this article, we present an alternative method of depicting RNA secondary structure as arc diagrams. This is well suited for structures that are difficult or impossible to represent as planar stem-loop diagrams. Arc diagrams can intuitively display pseudo-knotted structures, as well as transient and alternative structural features. In addition, they facilitate the comparison of known and predicted RNA secondary structures. An added benefit is that structure information can be displayed in conjunction with a corresponding multiple sequence alignments, thereby highlighting structure and primary sequence conservation and variation. We have implemented the visualization algorithm as a web server R-chie as well as a corresponding R package called R4RNA, which allows users to run the software locally and across a range of common operating systems.
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Affiliation(s)
- Daniel Lai
- Department of Computer Science, Centre for High-Throughput Biology, University of British Columbia, Vancouver V6T 1Z4, Canada
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Avihoo A, Churkin A, Barash D. RNAexinv: An extended inverse RNA folding from shape and physical attributes to sequences. BMC Bioinformatics 2011; 12:319. [PMID: 21813013 PMCID: PMC3176266 DOI: 10.1186/1471-2105-12-319] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2011] [Accepted: 08/03/2011] [Indexed: 11/17/2022] Open
Abstract
Background RNAexinv is an interactive java application that performs RNA sequence design, constrained to yield a specific RNA shape and physical attributes. It is an extended inverse RNA folding program with the rationale behind that the generated sequences should not only fold into a desired structure, but they should also exhibit favorable attributes such as thermodynamic stability and mutational robustness. RNAexinv considers not only the secondary structure in order to design sequences, but also the mutational robustness and the minimum free energy. The sequences that are generated may not fully conform with the given RNA secondary structure, but they will strictly conform with the RNA shape of the given secondary structure and thereby take into consideration the recommended values of thermodynamic stability and mutational robustness that are provided. Results The output consists of designed sequences that are generated by the proposed method. Selecting a sequence displays the secondary structure drawings of the target and the predicted fold of the sequence, including some basic information about the desired and achieved thermodynamic stability and mutational robustness. RNAexinv can be used successfully without prior experience, simply specifying an initial RNA secondary structure in dot-bracket notation and numerical values for the desired neutrality and minimum free energy. The package runs under LINUX operating system. Secondary structure predictions are performed using the Vienna RNA package. Conclusions RNAexinv is a user friendly tool that can be used for RNA sequence design. It is especially useful in cases where a functional stem-loop structure of a natural sequence should be strictly kept in the designed sequences but a distant motif in the rest of the structure may contain one more or less nucleotide at the expense of another, as long as the global shape is preserved. This allows the insertion of physical observables as constraints. RNAexinv is available at http://www.cs.bgu.ac.il/~RNAexinv.
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Affiliation(s)
- Assaf Avihoo
- Department of Computer Science, Ben-Gurion University, 84105 Beer Sheva, Israel
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Churkin A, Gabdank I, Barash D. The RNAmute web server for the mutational analysis of RNA secondary structures. Nucleic Acids Res 2011; 39:W92-9. [PMID: 21478166 PMCID: PMC3125725 DOI: 10.1093/nar/gkr207] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
Abstract
RNA mutational analysis at the secondary-structure level can be useful to a wide-range of biological applications. It can be used to predict an optimal site for performing a nucleotide mutation at the single molecular level, as well as to analyze basic phenomena at the systems level. For the former, as more sequence modification experiments are performed that include site-directed mutagenesis to find and explore functional motifs in RNAs, a pre-processing step that helps guide in planning the experiment becomes vital. For the latter, mutations are generally accepted as a central mechanism by which evolution occurs, and mutational analysis relating to structure should gain a better understanding of system functionality and evolution. In the past several years, the program RNAmute that is structure based and relies on RNA secondary-structure prediction has been developed for assisting in RNA mutational analysis. It has been extended from single-point mutations to treat multiple-point mutations efficiently by initially calculating all suboptimal solutions, after which only the mutations that stabilize the suboptimal solutions and destabilize the optimal one are considered as candidates for being deleterious. The RNAmute web server for mutational analysis is available at http://www.cs.bgu.ac.il/~xrnamute/XRNAmute.
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Affiliation(s)
- Alexander Churkin
- Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel
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34
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Hower V, Heitsch CE. Parametric Analysis of RNA Branching Configurations. Bull Math Biol 2011; 73:754-76. [DOI: 10.1007/s11538-010-9607-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2009] [Accepted: 11/04/2010] [Indexed: 01/30/2023]
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Koessler DR, Knisley DJ, Knisley J, Haynes T. A predictive model for secondary RNA structure using graph theory and a neural network. BMC Bioinformatics 2010; 11 Suppl 6:S21. [PMID: 20946605 PMCID: PMC3026369 DOI: 10.1186/1471-2105-11-s6-s21] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
Background Determining the secondary structure of RNA from the primary structure is a challenging computational problem. A number of algorithms have been developed to predict the secondary structure from the primary structure. It is agreed that there is still room for improvement in each of these approaches. In this work we build a predictive model for secondary RNA structure using a graph-theoretic tree representation of secondary RNA structure. We model the bonding of two RNA secondary structures to form a larger secondary structure with a graph operation we call merge. We consider all combinatorial possibilities using all possible tree inputs, both those that are RNA-like in structure and those that are not. The resulting data from each tree merge operation is represented by a vector. We use these vectors as input values for a neural network and train the network to recognize a tree as RNA-like or not, based on the merge data vector. The network estimates the probability of a tree being RNA-like. Results The network correctly assigned a high probability of RNA-likeness to trees previously identified as RNA-like and a low probability of RNA-likeness to those classified as not RNA-like. We then used the neural network to predict the RNA-likeness of the unclassified trees. Conclusions There are a number of secondary RNA structure prediction algorithms available online. These programs are based on finding the secondary structure with the lowest total free energy. In this work, we create a predictive tool for secondary RNA structures using graph-theoretic values as input for a neural network. The use of a graph operation to theoretically describe the bonding of secondary RNA is novel and is an entirely different approach to the prediction of secondary RNA structures. Our method correctly predicted trees to be RNA-like or not RNA-like for all known cases. In addition, our results convey a measure of likelihood that a tree is RNA-like or not RNA-like. Given that the majority of secondary RNA folding algorithms return more than one possible outcome, our method provides a means of determining the best or most likely structures among all of the possible outcomes.
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Affiliation(s)
- Denise R Koessler
- Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN 37614, USA
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36
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Barash D, Churkin A. Mutational analysis in RNAs: comparing programs for RNA deleterious mutation prediction. Brief Bioinform 2010; 12:104-14. [DOI: 10.1093/bib/bbq059] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
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Laing C, Schlick T. Computational approaches to 3D modeling of RNA. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:283101. [PMID: 21399271 PMCID: PMC6286080 DOI: 10.1088/0953-8984/22/28/283101] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Many exciting discoveries have recently revealed the versatility of RNA and its importance in a variety of functions within the cell. Since the structural features of RNA are of major importance to their biological function, there is much interest in predicting RNA structure, either in free form or in interaction with various ligands, including proteins, metabolites and other molecules. In recent years, an increasing number of researchers have developed novel RNA algorithms for predicting RNA secondary and tertiary structures. In this review, we describe current experimental and computational advances and discuss recent ideas that are transforming the traditional view of RNA folding. To evaluate the performance of the most recent RNA 3D folding algorithms, we provide a comparative study in order to test the performance of available 3D structure prediction algorithms for an RNA data set of 43 structures of various lengths and motifs. We find that the algorithms vary widely in terms of prediction quality across different RNA lengths and topologies; most predictions have very large root mean square deviations from the experimental structure. We conclude by outlining some suggestions for future RNA folding research.
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Affiliation(s)
- Christian Laing
- Department of Chemistry and Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
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38
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Wang S, Tian F, Qiu Y, Liu X. Bilateral similarity function: a novel and universal method for similarity analysis of biological sequences. J Theor Biol 2010; 265:194-201. [PMID: 20399215 DOI: 10.1016/j.jtbi.2010.04.013] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2009] [Revised: 04/11/2010] [Accepted: 04/12/2010] [Indexed: 11/26/2022]
Abstract
Bilateral similarity function is designed for analyzing the similarities of biological sequences such as DNA, RNA secondary structure or protein in this paper. The defined function can perform comprehensive comparison between sequences remarkably well, both in terms of the Hamming distance of two compared sequences and the corresponding location difference. Compared with the existing methods for similarity analysis, the examination of similarities/dissimilarities illustrates that the proposed method with the computational complexity of O(N) is effective for these three kinds of biological sequences, and bears the universality for them.
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Affiliation(s)
- Shiyuan Wang
- College of Communication Engineering, Chongqing University, Chongqing 400044, China.
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39
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Liao B, Chen W, Sun X, Zhu W. A binary coding method of RNA secondary structure and its application. J Comput Chem 2010; 30:2205-12. [PMID: 19242960 DOI: 10.1002/jcc.21227] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
According to the three classifications of nucleotides, we introduce a sort of binary coding method of RNA secondary structures. On the basis of this representation, we can reduce a RNA secondary structure into three binary digit sequences. We also propose coding rules based on the exclusive-OR operation. Associating with the proposed coding rules, we can judge the mutation between bases or between base and base pair, and make sequence alignment easily.
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Affiliation(s)
- Bo Liao
- School of Computer and Communication, Hunan University, Changsha, Hunan Province 410082, China.
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40
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Biomolecular Structure and Modeling: Historical Perspective. INTERDISCIPLINARY APPLIED MATHEMATICS 2010. [PMCID: PMC7124002 DOI: 10.1007/978-1-4419-6351-2_1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/01/2022]
Abstract
physics, chemistry, and biology have been connected by a web of causal explanation organized by induction-based theories that telescope into one another. … Thus, quantum theory underlies atomic physics, which is the foundation of reagent chemistry and its specialized offshoot biochemistry, which interlock with molecular biology — essentially, the chemistry of organic macromolecules — and hence, through successively higher levels of organization, cellular, organismic, and evolutionary biology. … Such is the unifying and highly productive understanding of the world that has evolved in the natural sciences.
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41
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Protein Structure Hierarchy. INTERDISCIPLINARY APPLIED MATHEMATICS 2010. [PMCID: PMC7139416 DOI: 10.1007/978-1-4419-6351-2_4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The complexity of protein structures requires a description of their structural components. This chapter describes the elements of protein secondary structure — regular local structural patterns — such as helices, sheets, turns, and loops. Helices and sheets tend to fall into specific regions in the {ϕ, ψ} space of the Ramachandran plot (see Figures 28 and 29). The corresponding width and shape of each region reflects the spread of that motif as found in proteins.
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42
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Nucleotide's bilinear indices: novel bio-macromolecular descriptors for bioinformatics studies of nucleic acids. I. Prediction of paromomycin's affinity constant with HIV-1 Psi-RNA packaging region. J Theor Biol 2009; 259:229-41. [PMID: 19272394 DOI: 10.1016/j.jtbi.2009.02.021] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2008] [Revised: 02/24/2009] [Accepted: 02/25/2009] [Indexed: 02/03/2023]
Abstract
A new set of nucleotide-based bio-macromolecular descriptors are presented. This novel approach to bio-macromolecular design from a linear algebra point of view is relevant to nucleic acids quantitative structure-activity relationship (QSAR) studies. These bio-macromolecular indices are based on the calculus of bilinear maps on Re(n)[b(mk)(x (m),y (m)):Re(n) x Re(n)-->Re] in canonical basis. Nucleic acid's bilinear indices are calculated from kth power of non-stochastic and stochastic nucleotide's graph-theoretic electronic-contact matrices, M(m)(k) and (s)M(m)(k), respectively. That is to say, the kth non-stochastic and stochastic nucleic acid's bilinear indices are calculated using M(m)(k) and (s)M(m)(k) as matrix operators of bilinear transformations. Moreover, biochemical information is codified by using different pair combinations of nucleotide-base properties as weightings (experimental molar absorption coefficient epsilon(260) at 260 nm and pH=7.0, first (Delta E(1)) and second (Delta E(2)) single excitation energies in eV, and first (f(1)) and second (f(2)) oscillator strength values (of the first singlet excitation energies) of the nucleotide DNA-RNA bases. As example of this approach, an interaction study of the antibiotic paromomycin with the packaging region of the HIV-1 Psi-RNA have been performed and it have been obtained several linear models in order to predict the interaction strength. The best linear model obtained by using non-stochastic bilinear indices explains about 91% of the variance of the experimental Log K (R=0.95 and s=0.08 x 10(-4)M(-1)) as long as the best stochastic bilinear indices-based equation account for 93% of the Log K variance (R=0.97 and s=0.07 x 10(-4)M(-1)). The leave-one-out (LOO) press statistics, evidenced high predictive ability of both models (q(2)=0.86 and s(cv)=0.09 x 10(-4)M(-1) for non-stochastic and q(2)=0.91 and s(cv)=0.08 x 10(-4)M(-1) for stochastic bilinear indices). The nucleic acid's bilinear indices-based models compared favorably with other nucleic acid's indices-based approaches reported nowadays. These models also permit the interpretation of the driving forces of the interaction process. In this sense, developed equations involve short-reaching (k<or=3), middle-reaching (4<k<9), and far-reaching (k=10 or greater) nucleotide's bilinear indices. This situation points to electronic and topologic nucleotide's backbone interactions control of the stability profile of paromomycin-RNA complexes. Consequently, the present approach represents a novel and rather promising way to theoretical-biology studies.
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Lozano A, Pinter RY, Rokhlenko O, Valiente G, Ziv-Ukelson M. Seeded tree alignment. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2008; 5:503-513. [PMID: 18989038 DOI: 10.1109/tcbb.2008.59] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
The optimal transformation of one tree into another by means of elementary edit operations is an important algorithmic problem that has several interesting applications to computational biology. Here we introduce a constrained form of this problem in which a partial mapping of a set of nodes (the "seeds") in one tree to a corresponding set of nodes in the other tree is given, and present efficient algorithms for both ordered and unordered trees. Whereas ordered tree matching based on seeded nodes has applications in pattern matching of RNA structures, unordered tree matching based on seeded nodes has applications in co-speciation and phylogeny reconciliation. The latter involves the solution of the planar tanglegram layout problem, for which a polynomial-time algorithm is given here.
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Affiliation(s)
- Antoni Lozano
- Logic and Programming Research Group, Department of Software, Technical University of Catalonia, Jordi Girona, 1-3 Modul Omega, Campus Nord, E-08034 Barcelona, Spain.
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Dromi N, Avihoo A, Barash D. Reconstruction of natural RNA sequences from RNA shape, thermodynamic stability, mutational robustness, and linguistic complexity by evolutionary computation. J Biomol Struct Dyn 2008; 26:147-62. [PMID: 18533734 DOI: 10.1080/07391102.2008.10507231] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Abstract
The process of designing novel RNA sequences by inverse RNA folding, available in tools such as RNAinverse and InfoRNA, can be thought of as a reconstruction of RNAs from secondary structure. In this reconstruction problem, no physical measures are considered as additional constraints that are independent of structure, aside of the goal to reach the same secondary structure as the input using energy minimization methods. An extension of the reconstruction problem can be formulated since in many cases of natural RNAs, it is desired to analyze the sequence and structure of RNA molecules using various physical quantifiable measures. In prior works that used secondary structure predictions, it has been shown that natural RNAs differ significantly from random RNAs in some of these measures. Thus, we relax the problem of reconstructing RNAs from secondary structure into reconstructing RNAs from shapes, and in turn incorporate physical quantities as constraints. This allows for the design of novel RNA sequences by inverse folding while considering various physical quantities of interest such as thermodynamic stability, mutational robustness, and linguistic complexity. At the expense of altering the number of nucleotides in stems and loops, for example, physical measures can be taken into account. We use evolutionary computation for the new reconstruction problem and illustrate the procedure on various natural RNAs.
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Affiliation(s)
- N Dromi
- Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel
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45
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Dai Q, Wang T. Use of linear regression model to compare RNA secondary structures. J Theor Biol 2008; 253:854-60. [DOI: 10.1016/j.jtbi.2008.04.023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2008] [Revised: 04/17/2008] [Accepted: 04/17/2008] [Indexed: 11/25/2022]
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Abstract
We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of Large Numbers for the distribution of vertex degrees in a large random tree. Our motivation for this study comes from the analysis of RNA secondary structures.
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47
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Li C, Xing L, Wang X. Analysis of similarity of RNA secondary structures based on a 2D graphical representation. Chem Phys Lett 2008. [DOI: 10.1016/j.cplett.2008.04.112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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48
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Shu W, Bo X, Zheng Z, Wang S. A novel representation of RNA secondary structure based on element-contact graphs. BMC Bioinformatics 2008; 9:188. [PMID: 18402706 PMCID: PMC2373570 DOI: 10.1186/1471-2105-9-188] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2007] [Accepted: 04/11/2008] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Depending on their specific structures, noncoding RNAs (ncRNAs) play important roles in many biological processes. Interest in developing new topological indices based on RNA graphs has been revived in recent years, as such indices can be used to compare, identify and classify RNAs. Although the topological indices presented before characterize the main topological features of RNA secondary structures, information on RNA structural details is ignored to some degree. Therefore, it is necessity to identify topological features with low degeneracy based on complete and fine-grained RNA graphical representations. RESULTS In this study, we present a complete and fine scheme for RNA graph representation as a new basis for constructing RNA topological indices. We propose a combination of three vertex-weighted element-contact graphs (ECGs) to describe the RNA element details and their adjacent patterns in RNA secondary structure. Both the stem and loop topologies are encoded completely in the ECGs. The relationship among the three typical topological index families defined by their ECGs and RNA secondary structures was investigated from a dataset of 6,305 ncRNAs. The applicability of topological indices is illustrated by three application case studies. Based on the applied small dataset, we find that the topological indices can distinguish true pre-miRNAs from pseudo pre-miRNAs with about 96% accuracy, and can cluster known types of ncRNAs with about 98% accuracy, respectively. CONCLUSION The results indicate that the topological indices can characterize the details of RNA structures and may have a potential role in identifying and classifying ncRNAs. Moreover, these indices may lead to a new approach for discovering novel ncRNAs. However, further research is needed to fully resolve the challenging problem of predicting and classifying noncoding RNAs.
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Affiliation(s)
- Wenjie Shu
- Beijing Institute of Radiation Medicine, Beijing 100850, China.
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49
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Veksler-Lublinsky I, Ziv-Ukelson M, Barash D, Kedem K. A structure-based flexible search method for motifs in RNA. J Comput Biol 2008; 14:908-26. [PMID: 17803370 DOI: 10.1089/cmb.2007.0061] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
The discovery of non-coding RNA (ncRNA) motifs and their role in regulating gene expression has recently attracted considerable attention. The goal is to discover these motifs in a sequence database. Current RNA motif search methods start from the primary sequence and only then take into account secondary structure considerations. One can think of developing a flexible structure-based motif search method that will filter datasets based on secondary structure first, while allowing extensive primary sequence factors and additional factors such as potential pseudoknots as constraints. Since different motifs vary in structure rigidity and in local sequence constraints, there is a need for algorithms and tools that can be fine-tuned according to the searched RNA motif, but differ in their approach from the RNAMotif descriptor language. We present an RNA motif search tool called STRMS (Structural RNA Motif Search), which takes as input the secondary structure of the query, including local sequence and structure constraints, and a target sequence database. It reports all occurrences of the query in the target, ranked by their similarity to the query, and produces an html file that displays graphical images of the predicted structures for both the query and the candidate hits. Our tool is flexible and takes into account a large number of sequence options and existence of potential pseudoknots as dictated by specific queries. Our approach combines pre-folding and an O(m n) RNA pattern matching algorithm based on subtree homeomorphism for ordered, rooted trees. An O(n(2) log n) extension is described that allows the search engine to take into account the pseudoknots typical to riboswitches. We employed STRMS in search for both new and known RNA motifs (riboswitches and tRNAs) in large target databases. Our results point to a number of additional purine bacterial riboswitch candidates in newly sequenced bacteria, and demonstrate high sensitivity on known riboswitches and tRNAs. Code and data are available at www.cs.bgu.ac.il/vaksler/STRMS.
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50
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Dai Q, Wang TM. Use of statistical measures for analyzing RNA secondary structures. J Comput Chem 2008; 29:1292-305. [PMID: 18172840 DOI: 10.1002/jcc.20891] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
With more and more RNA secondary structures accumulated, the need for comparing different RNA secondary structures often arises in function prediction and evolutionary analysis. Numerous efficient algorithms were developed for comparing different RNA secondary structures, but challenges remain. In this article, a new statistical measure extending the notion of relative entropy based on the proposed stochastic model is evaluated for RNA secondary structures. The results obtained from several experiments on real datasets have shown the effectiveness of the proposed approach. Moreover, the time complexity of our method is favorable by comparing with that of the existing methods which solve the similar problem.
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Affiliation(s)
- Qi Dai
- Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, People's Republic of China.
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