Marcel Kucharík1, Ivo L Hofacker2, Peter F Stadler3, Jing Qin4. 1. Institute for Theoretical Chemistry and Research group BCB, Faculty of Computer Science, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria, Center for non-coding RNA in Technology and Health, University of Copenhagen, Grønnegårdsvej 3, 1870 Frederiksberg C, Denmark, Department of Computer Science & IZBI & iDiv & LIFE, Härtelstraße 16-18, D-04107 University of Leipzig, Max Planck Institute for Mathematics in the Sciences and Fraunhofer Institute IZI, Leipzig, Germany, Santa Fe Institute, Santa Fe, NM 87501, USA and Department of Mathematics and Computer Science, University Of Southern Denmark, Odense, Denmark. 2. Institute for Theoretical Chemistry and Research group BCB, Faculty of Computer Science, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria, Center for non-coding RNA in Technology and Health, University of Copenhagen, Grønnegårdsvej 3, 1870 Frederiksberg C, Denmark, Department of Computer Science & IZBI & iDiv & LIFE, Härtelstraße 16-18, D-04107 University of Leipzig, Max Planck Institute for Mathematics in the Sciences and Fraunhofer Institute IZI, Leipzig, Germany, Santa Fe Institute, Santa Fe, NM 87501, USA and Department of Mathematics and Computer Science, University Of Southern Denmark, Odense, DenmarkInstitute for Theoretical Chemistry and Research group BCB, Faculty of Computer Science, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria, Center for non-coding RNA in Technology and Health, University of Copenhagen, Grønnegårdsvej 3, 1870 Frederiksberg C, Denmark, Department of Computer Science & IZBI & iDiv & LIFE, Härtelstraße 16-18, D-04107 University of Leipzig, Max Planck Institute for Mathematics in the Sciences and Fraunhofer Institute IZI, Leipzig, Germany, Santa Fe Institute, Santa Fe, NM 87501, USA and Department of Mathematics and Computer Science, University Of Southern Denmark, Odense, DenmarkInstitute for Theoretical Chemistry and Research group BCB, Faculty of Computer Science, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria, Center for non-coding RNA in Technology and Health, University of Copenhagen, Grønnegårdsvej 3, 1870 Frederiksberg C, Denmark, Department of Computer Science & IZBI & iDiv & LIFE, Härtelstraße 16-18, D-04107 University of Leipzig, Max Planck Institute for Mathematics in the Sciences and Fraunhofer Institute IZI, Leipzig, Germany, Santa Fe Institute, Santa Fe, NM 87501, USA and Department of Mathematics and Computer Science, University Of Southern Denmark, Odense, Denmark. 3. Institute for Theoretical Chemistry and Research group BCB, Faculty of Computer Science, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria, Center for non-coding RNA in Technology and Health, University of Copenhagen, Grønnegårdsvej 3, 1870 Frederiksberg C, Denmark, Department of Computer Science & IZBI & iDiv & LIFE, Härtelstraße 16-18, D-04107 University of Leipzig, Max Planck Institute for Mathematics in the Sciences and Fraunhofer Institute IZI, Leipzig, Germany, Santa Fe Institute, Santa Fe, NM 87501, USA and Department of Mathematics and Computer Science, University Of Southern Denmark, Odense, DenmarkInstitute for Theoretical Chemistry and Research group BCB, Faculty of Computer Science, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria, Center for non-coding RNA in Technology and Health, University of Copenhagen, Grønnegårdsvej 3, 1870 Frederiksberg C, Denmark, Department of Computer Science & IZBI & iDiv & LIFE, Härtelstraße 16-18, D-04107 University of Leipzig, Max Planck Institute for Mathematics in the Sciences and Fraunhofer Institute IZI, Leipzig, Germany, Santa Fe Institute, Santa Fe, NM 87501, USA and Department of Mathematics and Computer Science, University Of Southern Denmark, Odense, DenmarkInstitute for Theoretical Chemistry and Research group BCB, Faculty of Computer Science, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria, Center for non-coding RNA in Technology and Health, University of Copenhagen, Grønnegårdsvej 3, 1870 Frederiksberg C, Denmark, Department of Computer Science & IZBI & iDiv & LIFE, Härtelstraße 16-18, D-04107 University of Leipzig, Max Planck Institute for Mathematics in the Sciences and Fraunhofer Institute IZI, Leipzig, Germany, Santa Fe Institute, Santa Fe, NM 87501, USA and Department of Mathematics and Computer Science, University Of Southern Denmark, Odense, DenmarkInstitute for Theoretical Chemistry and Research group BCB, Faculty of Computer Science, Univer 4. Institute for Theoretical Chemistry and Research group BCB, Faculty of Computer Science, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria, Center for non-coding RNA in Technology and Health, University of Copenhagen, Grønnegårdsvej 3, 1870 Frederiksberg C, Denmark, Department of Computer Science & IZBI & iDiv & LIFE, Härtelstraße 16-18, D-04107 University of Leipzig, Max Planck Institute for Mathematics in the Sciences and Fraunhofer Institute IZI, Leipzig, Germany, Santa Fe Institute, Santa Fe, NM 87501, USA and Department of Mathematics and Computer Science, University Of Southern Denmark, Odense, DenmarkInstitute for Theoretical Chemistry and Research group BCB, Faculty of Computer Science, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria, Center for non-coding RNA in Technology and Health, University of Copenhagen, Grønnegårdsvej 3, 1870 Frederiksberg C, Denmark, Department of Computer Science & IZBI & iDiv & LIFE, Härtelstraße 16-18, D-04107 University of Leipzig, Max Planck Institute for Mathematics in the Sciences and Fraunhofer Institute IZI, Leipzig, Germany, Santa Fe Institute, Santa Fe, NM 87501, USA and Department of Mathematics and Computer Science, University Of Southern Denmark, Odense, Denmark.
Abstract
MOTIVATION: RNA folding is a complicated kinetic process. The minimum free energy structure provides only a static view of the most stable conformational state of the system. It is insufficient to give detailed insights into the dynamic behavior of RNAs. A sufficiently sophisticated analysis of the folding free energy landscape, however, can provide the relevant information. RESULTS: We introduce the Basin Hopping Graph (BHG) as a novel coarse-grained model of folding landscapes. Each vertex of the BHG is a local minimum, which represents the corresponding basin in the landscape. Its edges connect basins when the direct transitions between them are 'energetically favorable'. Edge weights endcode the corresponding saddle heights and thus measure the difficulties of these favorable transitions. BHGs can be approximated accurately and efficiently for RNA molecules well beyond the length range accessible to enumerative algorithms. AVAILABILITY AND IMPLEMENTATION: The algorithms described here are implemented in C++ as standalone programs. Its source code and supplemental material can be freely downloaded from http://www.tbi.univie.ac.at/bhg.html.
MOTIVATION: RNA folding is a complicated kinetic process. The minimum free energy structure provides only a static view of the most stable conformational state of the system. It is insufficient to give detailed insights into the dynamic behavior of RNAs. A sufficiently sophisticated analysis of the folding free energy landscape, however, can provide the relevant information. RESULTS: We introduce the Basin Hopping Graph (BHG) as a novel coarse-grained model of folding landscapes. Each vertex of the BHG is a local minimum, which represents the corresponding basin in the landscape. Its edges connect basins when the direct transitions between them are 'energetically favorable'. Edge weights endcode the corresponding saddle heights and thus measure the difficulties of these favorable transitions. BHGs can be approximated accurately and efficiently for RNA molecules well beyond the length range accessible to enumerative algorithms. AVAILABILITY AND IMPLEMENTATION: The algorithms described here are implemented in C++ as standalone programs. Its source code and supplemental material can be freely downloaded from http://www.tbi.univie.ac.at/bhg.html.
Authors: Ronny Lorenz; Stephan H Bernhart; Christian Höner Zu Siederdissen; Hakim Tafer; Christoph Flamm; Peter F Stadler; Ivo L Hofacker Journal: Algorithms Mol Biol Date: 2011-11-24 Impact factor: 1.405