{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T08:54:51Z","timestamp":1774169691772,"version":"3.50.1"},"reference-count":58,"publisher":"Oxford University Press (OUP)","issue":"8","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011,4,15]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Motivation: Several dynamic programming algorithms for predicting RNA structures with pseudoknots have been proposed that differ dramatically from one another in the classes of structures considered.<\/jats:p>\n               <jats:p>Results: Here, we use the natural topological classification of RNA structures in terms of irreducible components that are embeddable in the surfaces of fixed genus. We add to the conventional secondary structures four building blocks of genus one in order to construct certain structures of arbitrarily high genus. A corresponding unambiguous multiple context-free grammar provides an efficient dynamic programming approach for energy minimization, partition function and stochastic sampling. It admits a topology-dependent parametrization of pseudoknot penalties that increases the sensitivity and positive predictive value of predicted base pairs by 10\u201320% compared with earlier approaches. More general models based on building blocks of higher genus are also discussed.<\/jats:p>\n               <jats:p>Availability: The source code of gfold is freely available at http:\/\/www.combinatorics.cn\/cbpc\/gfold.tar.gz.<\/jats:p>\n               <jats:p>Contact: \u00a0duck@santafe.edu<\/jats:p>\n               <jats:p>Supplementary information: \u00a0Supplementary data are available at Bioinformatics online.<\/jats:p>","DOI":"10.1093\/bioinformatics\/btr090","type":"journal-article","created":{"date-parts":[[2011,2,19]],"date-time":"2011-02-19T01:17:51Z","timestamp":1298078271000},"page":"1076-1085","source":"Crossref","is-referenced-by-count":81,"title":["Topology and prediction of RNA pseudoknots"],"prefix":"10.1093","volume":"27","author":[{"given":"Christian M.","family":"Reidys","sequence":"first","affiliation":[{"name":"1 Department of Mathematics, Center for Combinatorics, Key Laboratory of Pure Mathematics and Combinatorics - TianJin key Laboratory of Combinatorics, 2Department of Biology, College of Life Science, Nankai University Tianjin 300071, P.R. China, 3Department of Mathematics, Center for Quantum Geometry of Moduli Spaces, Aarhus University, DK-8000 \u00c5rhus C, Denmark, 4Department of Mathematics and Physics, California Institute of Technology, Pasadena, CA 91125, USA, 5Bioinformatics Group, Department of Computer Science, and Interdisciplinary Center for Bioinformatics, University of Leipzig, H\u00e4rtelstrasse 16-18, D-04107 Leipzig, 6Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 7RNomics Group, Fraunhofer IZI, Perlickstrasse 1, D-04103 Leipzig, Germany, 8Institut fur Theoretical Chemistry, University of Vienna, W\u00e4hringerstrasse 17, A-1090 Vienna, Austria, 9Center for non-coding RNA in Technology and Health, University of Copenhagen, Gr\u00f8nneg\u00e5rdsvej 3, DK-1870 Frederiksberg, Denmark, 10The Santa"},{"name":"1 Department of Mathematics, Center for Combinatorics, Key Laboratory of Pure Mathematics and Combinatorics - TianJin key Laboratory of Combinatorics, 2Department of Biology, College of Life Science, Nankai University Tianjin 300071, P.R. China, 3Department of Mathematics, Center for Quantum Geometry of Moduli Spaces, Aarhus University, DK-8000 \u00c5rhus C, Denmark, 4Department of Mathematics and Physics, California Institute of Technology, Pasadena, CA 91125, USA, 5Bioinformatics Group, Department of Computer Science, and Interdisciplinary Center for Bioinformatics, University of Leipzig, H\u00e4rtelstrasse 16-18, D-04107 Leipzig, 6Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 7RNomics Group, Fraunhofer IZI, Perlickstrasse 1, D-04103 Leipzig, Germany, 8Institut fur Theoretical Chemistry, University of Vienna, W\u00e4hringerstrasse 17, A-1090 Vienna, Austria, 9Center for non-coding RNA in Technology and Health, University of Copenhagen, Gr\u00f8nneg\u00e5rdsvej 3, DK-1870 Frederiksberg, Denmark, 10The Santa"}]},{"given":"Fenix W. D.","family":"Huang","sequence":"additional","affiliation":[{"name":"1 Department of Mathematics, Center for Combinatorics, Key Laboratory of Pure Mathematics and Combinatorics - TianJin key Laboratory of Combinatorics, 2Department of Biology, College of Life Science, Nankai University Tianjin 300071, P.R. China, 3Department of Mathematics, Center for Quantum Geometry of Moduli Spaces, Aarhus University, DK-8000 \u00c5rhus C, Denmark, 4Department of Mathematics and Physics, California Institute of Technology, Pasadena, CA 91125, USA, 5Bioinformatics Group, Department of Computer Science, and Interdisciplinary Center for Bioinformatics, University of Leipzig, H\u00e4rtelstrasse 16-18, D-04107 Leipzig, 6Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 7RNomics Group, Fraunhofer IZI, Perlickstrasse 1, D-04103 Leipzig, Germany, 8Institut fur Theoretical Chemistry, University of Vienna, W\u00e4hringerstrasse 17, A-1090 Vienna, Austria, 9Center for non-coding RNA in Technology and Health, University of Copenhagen, Gr\u00f8nneg\u00e5rdsvej 3, DK-1870 Frederiksberg, Denmark, 10The Santa"}]},{"given":"J\u00f8rgen E.","family":"Andersen","sequence":"additional","affiliation":[{"name":"1 Department of Mathematics, Center for Combinatorics, Key Laboratory of Pure Mathematics and Combinatorics - TianJin key Laboratory of Combinatorics, 2Department of Biology, College of Life Science, Nankai University Tianjin 300071, P.R. China, 3Department of Mathematics, Center for Quantum Geometry of Moduli Spaces, Aarhus University, DK-8000 \u00c5rhus C, Denmark, 4Department of Mathematics and Physics, California Institute of Technology, Pasadena, CA 91125, USA, 5Bioinformatics Group, Department of Computer Science, and Interdisciplinary Center for Bioinformatics, University of Leipzig, H\u00e4rtelstrasse 16-18, D-04107 Leipzig, 6Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 7RNomics Group, Fraunhofer IZI, Perlickstrasse 1, D-04103 Leipzig, Germany, 8Institut fur Theoretical Chemistry, University of Vienna, W\u00e4hringerstrasse 17, A-1090 Vienna, Austria, 9Center for non-coding RNA in Technology and Health, University of Copenhagen, Gr\u00f8nneg\u00e5rdsvej 3, DK-1870 Frederiksberg, Denmark, 10The Santa"}]},{"given":"Robert C.","family":"Penner","sequence":"additional","affiliation":[{"name":"1 Department of Mathematics, Center for Combinatorics, Key Laboratory of Pure Mathematics and Combinatorics - TianJin key Laboratory of Combinatorics, 2Department of Biology, College of Life Science, Nankai University Tianjin 300071, P.R. 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China, 3Department of Mathematics, Center for Quantum Geometry of Moduli Spaces, Aarhus University, DK-8000 \u00c5rhus C, Denmark, 4Department of Mathematics and Physics, California Institute of Technology, Pasadena, CA 91125, USA, 5Bioinformatics Group, Department of Computer Science, and Interdisciplinary Center for Bioinformatics, University of Leipzig, H\u00e4rtelstrasse 16-18, D-04107 Leipzig, 6Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 7RNomics Group, Fraunhofer IZI, Perlickstrasse 1, D-04103 Leipzig, Germany, 8Institut fur Theoretical Chemistry, University of Vienna, W\u00e4hringerstrasse 17, A-1090 Vienna, Austria, 9Center for non-coding RNA in Technology and Health, University of Copenhagen, Gr\u00f8nneg\u00e5rdsvej 3, DK-1870 Frederiksberg, Denmark, 10The Santa"}]}],"member":"286","published-online":{"date-parts":[[2011,2,17]]},"reference":[{"key":"2023061311372997100_B1","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/S0166-218X(00)00186-4","article-title":"Dynamic programming algorithms for RNA secondary structure prediction with pseudoknots","volume":"104","author":"Akutsu","year":"2000","journal-title":"Discr. 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