1
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Tarafder S, Bhattacharya D. lociPARSE: a locality-aware invariant point attention model for scoring RNA 3D structures. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2023.11.04.565599. [PMID: 37961488 PMCID: PMC10635153 DOI: 10.1101/2023.11.04.565599] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/15/2023]
Abstract
A scoring function that can reliably assess the accuracy of a 3D RNA structural model in the absence of experimental structure is not only important for model evaluation and selection but also useful for scoring-guided conformational sampling. However, high-fidelity RNA scoring has proven to be difficult using conventional knowledge-based statistical potentials and currently-available machine learning-based approaches. Here we present lociPARSE, a locality-aware invariant point attention architecture for scoring RNA 3D structures. Unlike existing machine learning methods that estimate superposition-based root mean square deviation (RMSD), lociPARSE estimates Local Distance Difference Test (lDDT) scores capturing the accuracy of each nucleotide and its surrounding local atomic environment in a superposition-free manner, before aggregating information to predict global structural accuracy. Tested on multiple datasets including CASP15, lociPARSE significantly outperforms existing statistical potentials (rsRNASP, cgRNASP, DFIRE-RNA, and RASP) and machine learning methods (ARES and RNA3DCNN) across complementary assessment metrics. lociPARSE is freely available at https://github.com/Bhattacharya-Lab/lociPARSE.
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Affiliation(s)
- Sumit Tarafder
- Department of Computer Science, Virginia Tech, Blacksburg, Virginia, 24061, USA
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2
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Gren BA, Antczak M, Zok T, Sulkowska JI, Szachniuk M. Knotted artifacts in predicted 3D RNA structures. PLoS Comput Biol 2024; 20:e1011959. [PMID: 38900780 PMCID: PMC11218946 DOI: 10.1371/journal.pcbi.1011959] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2024] [Revised: 07/02/2024] [Accepted: 06/01/2024] [Indexed: 06/22/2024] Open
Abstract
Unlike proteins, RNAs deposited in the Protein Data Bank do not contain topological knots. Recently, admittedly, the first trefoil knot and some lasso-type conformations have been found in experimental RNA structures, but these are still exceptional cases. Meanwhile, algorithms predicting 3D RNA models have happened to form knotted structures not so rarely. Interestingly, machine learning-based predictors seem to be more prone to generate knotted RNA folds than traditional methods. A similar situation is observed for the entanglements of structural elements. In this paper, we analyze all models submitted to the CASP15 competition in the 3D RNA structure prediction category. We show what types of topological knots and structure element entanglements appear in the submitted models and highlight what methods are behind the generation of such conformations. We also study the structural aspect of susceptibility to entanglement. We suggest that predictors take care of an evaluation of RNA models to avoid publishing structures with artifacts, such as unusual entanglements, that result from hallucinations of predictive algorithms.
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Affiliation(s)
- Bartosz A. Gren
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
| | - Maciej Antczak
- Institute of Computing Science, Poznan University of Technology, Poznan, Poland
- Institute of Bioorganic Chemistry, Polish Academy of Sciences, Poznan, Poland
| | - Tomasz Zok
- Institute of Computing Science, Poznan University of Technology, Poznan, Poland
| | | | - Marta Szachniuk
- Institute of Computing Science, Poznan University of Technology, Poznan, Poland
- Institute of Bioorganic Chemistry, Polish Academy of Sciences, Poznan, Poland
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3
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Niemyska W, Mukherjee S, Gren BA, Niewieczerzal S, Bujnicki JM, Sulkowska JI. Discovery of a trefoil knot in the RydC RNA: Challenging previous notions of RNA topology. J Mol Biol 2024; 436:168455. [PMID: 38272438 DOI: 10.1016/j.jmb.2024.168455] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2023] [Revised: 01/16/2024] [Accepted: 01/18/2024] [Indexed: 01/27/2024]
Abstract
Knots are very common in polymers, including DNA and protein molecules. Yet, no genuine knot has been identified in natural RNA molecules to date. Upon re-examining experimentally determined RNA 3D structures, we discovered a trefoil knot 31, the most basic non-trivial knot, in the RydC RNA. This knotted RNA is a member of a small family of short bacterial RNAs, whose secondary structure is characterized by an H-type pseudoknot. Molecular dynamics simulations suggest a folding pathway of the RydC RNA that starts with a native twisted loop. Based on sequence analyses and computational RNA 3D structure predictions, we postulate that this trefoil knot is a conserved feature of all RydC-related RNAs. The first discovery of a knot in a natural RNA molecule introduces a novel perspective on RNA 3D structure formation and on fundamental research on the relationship between function and spatial structure of biopolymers.
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Affiliation(s)
- Wanda Niemyska
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland; Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland.
| | - Sunandan Mukherjee
- Laboratory of Bioinformatics and Protein Engineering, International Institute of Molecular and Cell Biology in Warsaw, Trojdena 4, 02-109 Warsaw, Poland
| | - Bartosz A Gren
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
| | - Szymon Niewieczerzal
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
| | - Janusz M Bujnicki
- Laboratory of Bioinformatics and Protein Engineering, International Institute of Molecular and Cell Biology in Warsaw, Trojdena 4, 02-109 Warsaw, Poland.
| | - Joanna I Sulkowska
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland.
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4
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Luwanski K, Hlushchenko V, Popenda M, Zok T, Sarzynska J, Martsich D, Szachniuk M, Antczak M. RNAspider: a webserver to analyze entanglements in RNA 3D structures. Nucleic Acids Res 2022; 50:W663-W669. [PMID: 35349710 PMCID: PMC9252836 DOI: 10.1093/nar/gkac218] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2022] [Revised: 03/04/2022] [Accepted: 03/22/2022] [Indexed: 12/12/2022] Open
Abstract
Advances in experimental and computational techniques enable the exploration of large and complex RNA 3D structures. These, in turn, reveal previously unstudied properties and motifs not characteristic for small molecules with simple architectures. Examples include entanglements of structural elements in RNA molecules and knot-like folds discovered, among others, in the genomes of RNA viruses. Recently, we presented the first classification of entanglements, determined by their topology and the type of entangled structural elements. Here, we introduce RNAspider - a web server to automatically identify, classify, and visualize primary and higher-order entanglements in RNA tertiary structures. The program applies to evaluate RNA 3D models obtained experimentally or by computational prediction. It supports the analysis of uncommon topologies in the pseudoknotted RNA structures. RNAspider is implemented as a publicly available tool with a user-friendly interface and can be freely accessed at https://rnaspider.cs.put.poznan.pl/.
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Affiliation(s)
- Kamil Luwanski
- Institute of Computing Science and European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
| | - Vladyslav Hlushchenko
- Institute of Computing Science and European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
| | - Mariusz Popenda
- Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704 Poznan, Poland
| | - Tomasz Zok
- Institute of Computing Science and European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
| | - Joanna Sarzynska
- Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704 Poznan, Poland
| | - Daniil Martsich
- Institute of Computing Science and European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
| | - Marta Szachniuk
- Institute of Computing Science and European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
- Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704 Poznan, Poland
| | - Maciej Antczak
- Institute of Computing Science and European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
- Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704 Poznan, Poland
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5
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Popenda M, Zok T, Sarzynska J, Korpeta A, Adamiak R, Antczak M, Szachniuk M. Entanglements of structure elements revealed in RNA 3D models. Nucleic Acids Res 2021; 49:9625-9632. [PMID: 34432024 PMCID: PMC8464073 DOI: 10.1093/nar/gkab716] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2021] [Revised: 08/02/2021] [Accepted: 08/06/2021] [Indexed: 01/14/2023] Open
Abstract
Computational methods to predict RNA 3D structure have more and more practical applications in molecular biology and medicine. Therefore, it is crucial to intensify efforts to improve the accuracy and quality of predicted three-dimensional structures. A significant role in this is played by the RNA-Puzzles initiative that collects, evaluates, and shares RNAs built computationally within currently nearly 30 challenges. RNA-Puzzles datasets, subjected to multi-criteria analysis, allow revealing the strengths and weaknesses of computer prediction methods. Here, we study the issue of entangled RNA fragments in the predicted RNA 3D structure models. By entanglement, we mean an arrangement of two structural elements such that one of them passes through the other. We propose the classification of entanglements driven by their topology and components. It distinguishes two general classes, interlaces and lassos, and subclasses characterized by element types-loops, dinucleotide steps, open single-stranded fragments-and puncture multiplicity. Our computational pipeline for entanglement detection, applied for 1,017 non-redundant models from RNA-Puzzles, has shown the frequency of different entanglements and allowed identifying 138 structures with intersected assemblies.
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Affiliation(s)
- Mariusz Popenda
- Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704 Poznan, Poland
| | - Tomasz Zok
- Institute of Computing Science & European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
| | - Joanna Sarzynska
- Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704 Poznan, Poland
| | - Agnieszka Korpeta
- Institute of Computing Science & European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
| | - Ryszard W Adamiak
- Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704 Poznan, Poland
- Institute of Computing Science & European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
| | - Maciej Antczak
- Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704 Poznan, Poland
- Institute of Computing Science & European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
| | - Marta Szachniuk
- Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704 Poznan, Poland
- Institute of Computing Science & European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
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6
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Jarmolinska AI, Gambin A, Sulkowska JI. Knot_pull-python package for biopolymer smoothing and knot detection. Bioinformatics 2019; 36:953-955. [PMID: 31504154 PMCID: PMC9883683 DOI: 10.1093/bioinformatics/btz644] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2019] [Revised: 08/08/2019] [Accepted: 08/13/2019] [Indexed: 02/03/2023] Open
Abstract
SUMMARY The biggest hurdle in studying topology in biopolymers is the steep learning curve for actually seeing the knots in structure visualization. Knot_pull is a command line utility designed to simplify this process-it presents the user with a smoothing trajectory for provided structures (any number and length of protein, RNA or chromatin chains in PDB, CIF or XYZ format), and calculates the knot type (including presence of any links, and slipknots when a subchain is specified). AVAILABILITY AND IMPLEMENTATION Knot_pull works under Python >=2.7 and is system independent. Source code and documentation are available at http://github.com/dzarmola/knot_pull under GNU GPL license and include also a wrapper script for PyMOL for easier visualization. Examples of smoothing trajectories can be found at: https://www.youtube.com/watch?v=IzSGDfc1vAY. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Affiliation(s)
| | - Anna Gambin
- Department of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw 02-097, Poland
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7
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Zok T, Antczak M, Zurkowski M, Popenda M, Blazewicz J, Adamiak RW, Szachniuk M. RNApdbee 2.0: multifunctional tool for RNA structure annotation. Nucleic Acids Res 2019; 46:W30-W35. [PMID: 29718468 PMCID: PMC6031003 DOI: 10.1093/nar/gky314] [Citation(s) in RCA: 70] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2018] [Accepted: 04/14/2018] [Indexed: 01/07/2023] Open
Abstract
In the field of RNA structural biology and bioinformatics, an access to correctly annotated RNA structure is of crucial importance, especially in the secondary and 3D structure predictions. RNApdbee webserver, introduced in 2014, primarily aimed to address the problem of RNA secondary structure extraction from the PDB files. Its new version, RNApdbee 2.0, is a highly advanced multifunctional tool for RNA structure annotation, revealing the relationship between RNA secondary and 3D structure given in the PDB or PDBx/mmCIF format. The upgraded version incorporates new algorithms for recognition and classification of high-ordered pseudoknots in large RNA structures. It allows analysis of isolated base pairs impact on RNA structure. It can visualize RNA secondary structures—including that of quadruplexes—with depiction of non-canonical interactions. It also annotates motifs to ease identification of stems, loops and single-stranded fragments in the input RNA structure. RNApdbee 2.0 is implemented as a publicly available webserver with an intuitive interface and can be freely accessed at http://rnapdbee.cs.put.poznan.pl/
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Affiliation(s)
- Tomasz Zok
- Institute of Computing Science, and European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland.,Poznan Supercomputing and Networking Center, Jana Pawla II 10, 61-139 Poznan, Poland
| | - Maciej Antczak
- Institute of Computing Science, and European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
| | - Michal Zurkowski
- Institute of Computing Science, and European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
| | - Mariusz Popenda
- Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704 Poznan, Poland
| | - Jacek Blazewicz
- Institute of Computing Science, and European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland.,Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704 Poznan, Poland
| | - Ryszard W Adamiak
- Institute of Computing Science, and European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland.,Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704 Poznan, Poland
| | - Marta Szachniuk
- Institute of Computing Science, and European Centre for Bioinformatics and Genomics, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland.,Institute of Bioorganic Chemistry, Polish Academy of Sciences, Noskowskiego 12/14, 61-704 Poznan, Poland
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8
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Grosberg AY. Ensemble View of RNAs and Proteins: Loops, Knots, Territories, and Evolution. Biophys J 2019; 110:2289-2290. [PMID: 27276246 DOI: 10.1016/j.bpj.2016.04.021] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2016] [Accepted: 04/18/2016] [Indexed: 11/30/2022] Open
Affiliation(s)
- Alexander Y Grosberg
- Department of Physics and Center for Soft Matter Research, New York University, New York, New York.
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9
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Iubini S, Orlandini E, Michieletto D, Baiesi M. Topological Sieving of Rings According to Their Rigidity. ACS Macro Lett 2018; 7:1408-1412. [PMID: 35651235 DOI: 10.1021/acsmacrolett.8b00719] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
We present a novel mechanism for resolving the mechanical rigidity of nanoscopic circular polymers that flow in a complex environment. The emergence of a regime of negative differential mobility induced by topological interactions between the rings and the substrate is the key mechanism for selective sieving of circular polymers with distinct flexibilities. A simple model accurately describes the sieving process observed in molecular dynamics simulations and yields experimentally verifiable analytical predictions, which can be used as a reference guide for improving filtration procedures of circular filaments. The topological sieving mechanism we propose ought to be relevant also in probing the microscopic details of complex substrates.
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Affiliation(s)
- Stefano Iubini
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Enzo Orlandini
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, U.K
| | - Marco Baiesi
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
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10
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Dabrowski-Tumanski P, Sulkowska JI. The APS-bracket – A topological tool to classify lasso proteins, RNAs and other tadpole-like structures. REACT FUNCT POLYM 2018. [DOI: 10.1016/j.reactfunctpolym.2018.09.005] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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11
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Cardelli C, Tubiana L, Bianco V, Nerattini F, Dellago C, Coluzza I. Heteropolymer Design and Folding of Arbitrary Topologies Reveals an Unexpected Role of Alphabet Size on the Knot Population. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b01359] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Chiara Cardelli
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Luca Tubiana
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Valentino Bianco
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Francesca Nerattini
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Christoph Dellago
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Ivan Coluzza
- CIC biomaGUNE, Paseo Miramon 182, 20014 San Sebastian, Spain
- IKERBASQUE,
Basque
Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
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12
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Tubiana L, Polles G, Orlandini E, Micheletti C. KymoKnot: A web server and software package to identify and locate knots in trajectories of linear or circular polymers. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:72. [PMID: 29884956 DOI: 10.1140/epje/i2018-11681-0] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2018] [Accepted: 05/18/2018] [Indexed: 06/08/2023]
Abstract
The KymoKnot software package and web server identifies and locates physical knots or proper knots in a series of polymer conformations. It is mainly intended as an analysis tool for trajectories of linear or circular polymers, but it can be used on single instances too, e.g. protein structures in PDB format. A key element of the software package is the so-called minimally interfering chain closure algorithm that is used to detect physical knots in open chains and to locate the knotted region in both open and closed chains. The web server offers a user-friendly graphical interface that identifies the knot type and highlights the knotted region on each frame of the trajectory, which the user can visualize interactively from various viewpoints. The dynamical evolution of the knotted region along the chain contour is presented as a kymograph. All data can be downloaded in text format. The KymoKnot package is licensed under the BSD 3-Clause licence. The server is publicly available at http://kymoknot.sissa.it/kymoknot/interactive.php .
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Affiliation(s)
- Luca Tubiana
- Computational Physics Department, University of Vienna, Sensengasse 8/10, 1090, Vienna, Austria.
| | - Guido Polles
- Molecular and Computational Biology, Department of Biological Sciences, University of Southern California, 90089, Los Angeles, CA, USA
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia and Sezione INFN, Università di Padova, Via Marzolo 8, 35131, Padova, Italy
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, Via Bonomea 265, I-34136, Trieste, Italy
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13
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Abstract
The first synthetic molecular trefoil knot was prepared in the late 1980s. However, it is only in the last few years that more complex small-molecule knot topologies have been realized through chemical synthesis. The steric restrictions imposed on molecular strands by knotting can impart significant physical and chemical properties, including chirality, strong and selective ion binding, and catalytic activity. As the number and complexity of accessible molecular knot topologies increases, it will become increasingly useful for chemists to adopt the knot terminology employed by other disciplines. Here we give an overview of synthetic strategies towards molecular knots and outline the principles of knot, braid, and tangle theory appropriate to chemistry and molecular structure.
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Affiliation(s)
| | - David A. Leigh
- School of ChemistryUniversity of ManchesterOxford RoadManchesterM13 9PLUK
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14
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Affiliation(s)
- Stephen D. P. Fielden
- School of Chemistry; University of Manchester; Oxford Road Manchester M13 9PL Großbritannien
| | - David A. Leigh
- School of Chemistry; University of Manchester; Oxford Road Manchester M13 9PL Großbritannien
| | - Steffen L. Woltering
- School of Chemistry; University of Manchester; Oxford Road Manchester M13 9PL Großbritannien
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15
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Liu L, Hyeon C. Contact Statistics Highlight Distinct Organizing Principles of Proteins and RNA. Biophys J 2017; 110:2320-2327. [PMID: 27276250 DOI: 10.1016/j.bpj.2016.04.020] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2016] [Revised: 03/15/2016] [Accepted: 04/01/2016] [Indexed: 11/18/2022] Open
Abstract
Although both RNA and proteins have densely packed native structures, chain organizations of these two biopolymers are fundamentally different. Motivated by the recent discoveries in chromatin folding that interphase chromosomes have territorial organization with signatures pointing to metastability, we analyzed the biomolecular structures deposited in the Protein Data Bank and found that the intrachain contact probabilities, P(s) as a function of the arc length s, decay in power-law ∼s(-γ) over the intermediate range of s, 10 ≲ s ≲ 110. We found that the contact probability scaling exponent is γ ≈ 1.11 for large RNA (N > 110), γ ≈ 1.41 for small-sized RNA (N < 110), and γ ≈ 1.65 for proteins. Given that Gaussian statistics is expected for a fully equilibrated chain in polymer melts, the deviation of γ-value from γ = 1.5 for the subchains of large RNA in the native state suggests that the chain configuration of RNA is not fully equilibrated. It is visually clear that folded structures of large-sized RNA (N ≳ 110) adopt crumpled structures, partitioned into modular multidomains assembled by proximal sequences along the chain, whereas the polypeptide chain of folded proteins looks better mixed with the rest of the structure. Our finding of γ ≈ 1 for large RNA might be an ineluctable consequence of the hierarchical ordering of the secondary to tertiary elements in the folding process.
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Affiliation(s)
- Lei Liu
- School of Computational Sciences, Korea Institute for Advanced Study, Seoul, Republic of Korea
| | - Changbong Hyeon
- School of Computational Sciences, Korea Institute for Advanced Study, Seoul, Republic of Korea.
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16
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Synthesizing topological structures containing RNA. Nat Commun 2017; 8:14936. [PMID: 28361879 PMCID: PMC5381007 DOI: 10.1038/ncomms14936] [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: 08/22/2016] [Accepted: 02/15/2017] [Indexed: 12/27/2022] Open
Abstract
Though knotting and entanglement have been observed in DNA and proteins, their existence in RNA remains an enigma. Synthetic RNA topological structures are significant for understanding the physical and biological properties pertaining to RNA topology, and these properties in turn could facilitate identifying naturally occurring topologically nontrivial RNA molecules. Here we show that topological structures containing single-stranded RNA (ssRNA) free of strong base pairing interactions can be created either by configuring RNA-DNA hybrid four-way junctions or by template-directed synthesis with a single-stranded DNA (ssDNA) topological structure. By using a constructed ssRNA knot as a highly sensitive topological probe, we find that Escherichia coli DNA topoisomerase I has low RNA topoisomerase activity and that the R173A point mutation abolishes the unknotting activity for ssRNA, but not for ssDNA. Furthermore, we discover the topological inhibition of reverse transcription (RT) and obtain different RT-PCR patterns for an ssRNA knot and circle of the same sequence.
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17
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Tian W, Lei X, Kauffman LH, Liang J. A Knot Polynomial Invariant for Analysis of Topology of RNA Stems and Protein Disulfide Bonds. COMPUTATIONAL AND MATHEMATICAL BIOPHYSICS 2017; 5:21-30. [PMID: 29201869 DOI: 10.1515/mlbmb-2017-0002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Knot polynomials have been used to detect and classify knots in biomolecules. Computation of knot polynomials in DNA and protein molecules have revealed the existence of knotted structures, and provided important insight into their topological structures. However, conventional knot polynomials are not well suited to study RNA molecules, as RNA structures are determined by stem regions which are not taken into account in conventional knot polynomials. In this study, we develop a new class of knot polynomials specifically designed to study RNA molecules, which considers stem regions. We demonstrate that our knot polynomials have direct structural relation with RNA molecules, and can be used to classify the topology of RNA secondary structures. Furthermore, we point out that these knot polynomials can be used to model the topological effects of disulfide bonds in protein molecules.
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Affiliation(s)
- Wei Tian
- Department of Bioengineering, University of Illinois at Chicago, Chicago, IL, 60606, USA
| | - Xue Lei
- Department of Bioengineering, University of Illinois at Chicago, Chicago, IL, 60606, USA
| | - Louis H Kauffman
- Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, 60606, USA
| | - Jie Liang
- Department of Bioengineering, University of Illinois at Chicago, Chicago, IL, 60606, USA
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18
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Abstract
Physical entanglement, and particularly knots arise spontaneously in equilibrated polymers that are sufficiently long and densely packed. Biopolymers are no exceptions: knots have long been known to occur in proteins as well as in encapsidated viral DNA. The rapidly growing number of RNA structures has recently made it possible to investigate the incidence of physical knots in this type of biomolecule, too. Strikingly, no knots have been found to date in the known RNA structures. In this Point of View Article we discuss the absence of knots in currently available RNAs and consider the reasons why knots in RNA have not yet been found, despite the expectation that they should exist in Nature. We conclude by singling out a number of RNA sequences that, based on the properties of their predicted secondary structures, are good candidates for knotted RNAs.
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Affiliation(s)
| | | | - Niles Lehman
- c Department of Chemistry , Portland State University , Portland OR , 97207 USA
| | - Henri Orland
- d Institut de Physique Théorique, Commissariat à l'énergie atomique CEA, IPhT CNRS, UMR3681 , F-91191 Gif-sur-Yvette France.,e Beijing Computational Science Research Center , Haidian District Beijing , 100084 , China
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19
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Jackson SE, Suma A, Micheletti C. How to fold intricately: using theory and experiments to unravel the properties of knotted proteins. Curr Opin Struct Biol 2016; 42:6-14. [PMID: 27794211 DOI: 10.1016/j.sbi.2016.10.002] [Citation(s) in RCA: 56] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2016] [Revised: 09/06/2016] [Accepted: 10/03/2016] [Indexed: 11/15/2022]
Abstract
Over the years, advances in experimental and computational methods have helped us to understand the role of thermodynamic, kinetic and active (chaperone-aided) effects in coordinating the folding steps required to achieving a knotted native state. Here, we review such developments by paying particular attention to the complementarity of experimental and computational studies. Key open issues that could be tackled with either or both approaches are finally pointed out.
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Affiliation(s)
- Sophie E Jackson
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom.
| | - Antonio Suma
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy.
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20
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Chwastyk M, Cieplak M. Multiple folding pathways of proteins with shallow knots and co-translational folding. J Chem Phys 2016; 143:045101. [PMID: 26233164 DOI: 10.1063/1.4927153] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study the folding process in the shallowly knotted protein MJ0366 within two variants of a structure-based model. We observe that the resulting topological pathways are much richer than identified in previous studies. In addition to the single knot-loop events, we find novel, and dominant, two-loop mechanisms. We demonstrate that folding takes place in a range of temperatures and the conditions of most successful folding are at temperatures which are higher than those required for the fastest folding. We also demonstrate that nascent conditions are more favorable to knotting than off-ribosome folding.
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Affiliation(s)
- Mateusz Chwastyk
- Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
| | - Marek Cieplak
- Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
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21
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Lim NCH, Jackson SE. Molecular knots in biology and chemistry. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:354101. [PMID: 26291690 DOI: 10.1088/0953-8984/27/35/354101] [Citation(s) in RCA: 99] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Knots and entanglements are ubiquitous. Beyond their aesthetic appeal, these fascinating topological entities can be either useful or cumbersome. In recent decades, the importance and prevalence of molecular knots have been increasingly recognised by scientists from different disciplines. In this review, we provide an overview on the various molecular knots found in naturally occurring biological systems (DNA, RNA and proteins), and those created by synthetic chemists. We discuss the current knowledge in these fields, including recent developments in experimental and, in some cases, computational studies which are beginning to shed light into the complex interplay between the structure, formation and properties of these topologically intricate molecules.
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Affiliation(s)
- Nicole C H Lim
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK. Faculty of Sciences, Universiti Brunei Darussalam, Gadong BE 1410, Brunei Darussalam
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22
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Faísca PF. Knotted proteins: A tangled tale of Structural Biology. Comput Struct Biotechnol J 2015; 13:459-68. [PMID: 26380658 PMCID: PMC4556803 DOI: 10.1016/j.csbj.2015.08.003] [Citation(s) in RCA: 58] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2015] [Revised: 07/31/2015] [Accepted: 08/07/2015] [Indexed: 01/19/2023] Open
Abstract
Knotted proteins have their native structures arranged in the form of an open knot. In the last ten years researchers have been making significant efforts to reveal their folding mechanism and understand which functional advantage(s) knots convey to their carriers. Molecular simulations have been playing a fundamental role in this endeavor, and early computational predictions about the knotting mechanism have just been confirmed in wet lab experiments. Here we review a collection of simulation results that allow outlining the current status of the field of knotted proteins, and discuss directions for future research.
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23
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Najafi S, Potestio R. Two Adhesive Sites Can Enhance the Knotting Probability of DNA. PLoS One 2015; 10:e0132132. [PMID: 26136125 PMCID: PMC4489926 DOI: 10.1371/journal.pone.0132132] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2015] [Accepted: 06/10/2015] [Indexed: 01/05/2023] Open
Abstract
Self-entanglement, or knotting, is entropically favored in long polymers. Relatively short polymers such as proteins can knot as well, but in this case the entanglement is mainly driven by fine-tuned, sequence-specific interactions. The relation between the sequence of a long polymer and its topological state is here investigated by means of a coarse-grained model of DNA. We demonstrate that the introduction of two adhesive regions along the sequence of a self-avoiding chain substantially increases the probability of forming a knot.
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Affiliation(s)
- Saeed Najafi
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Raffaello Potestio
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
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