Abstract
We introduce a new algebraic representation of RNA secondary structures as a composition of hairpins, considered as basic loops. Starting from it, we define an abstract algebraic representation and we propose a novel methodology to classify RNA structures based on two topological invariants, the genus and the crossing number. It takes advantage of the abstract representation to easily obtain two intersection graphs: one of the RNA molecule and another one of the relative shape. The edges cardinality of the former corresponds to the number of interactions among hairpins, whereas the edges cardinality of the latter is the crossing number of the shape associated to the molecule. The aforementioned crossing number together with the genus permits to define a more precise energy function than the standard one which is based on the genus only. Our methodology is validated over a subset of RNA structures extracted from Pseudobase++ database, and we classify them according to the two topological invariants.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Adams, P.L., Stahley, M.R., Gill, M.L., Kosen, A.B., Wang, J., Strobel, S.A.: Crystal structure of a group I intron splicing intermediate. RNA 10(12), 1867–1887 (2004)
Bellaousov, S., Mathews, D.H.: Probknot: fast prediction of RNA secondary structure including pseudoknots. RNA 16(10), 1870–1880 (2010)
Berman, H., Henrick, K., Nakamura, H.: Announcing the worldwide protein data bank. Nature Struct. Mol. Biol. 10(12), 980–980 (2003)
Bon, M., Vernizzi, G., Orland, H., Zee, A.: Topological classification of RNA structures. J. Mol. Biol. 379(4), 900–911 (2008)
Elliott, D., Ladomery, M.: Molecular Biology of RNA. Oxford University Press, Oxford (2017)
Harrison, M.A.: Introduction to Formal Language Theory. Addison-Wesley Longman Publishing Co., Inc., Boston (1978)
Huang, F.W., Reidys, C.M.: Topological language for RNA. Math. Biosci. 282, 109–120 (2016)
Lyngsø, R.B., Pedersen, C.N.: RNA pseudoknot prediction in energy-based models. J. Comput. Biol. 7(3–4), 409–427 (2000)
Mans, R.M., Pleij, C.W., Bosch, L.: tRNA-like structures. structure, function and evolutionary significance. Eur. J. Biochem. 201(1), 303–324 (1991)
McKee, T.A., McMorris, F.R.: Topics in Intersection Graph Theory. SIAM, Philadelphia (1999)
Metzler, D., Nebel, M.E.: Predicting RNA secondary structures with pseudoknots by MCMC sampling. J. Math. Biol. 56(1), 161–181 (2008)
Munkres, J.R.: Analysis on Manifolds. Westview Press, USA (1997)
Rastogi, T., Beattie, T.L., Olive, J.E., Collins, R.A.: A long-range pseudoknot is required for activity of the Neurospora VS ribozyme. EMBO J. 15(11), 2820 (1996)
Reidys, C.M., Huang, F.W., Andersen, J.E., Penner, R.C., Stadler, P.F., Nebel, M.E.: Topology and prediction of RNA pseudoknots. Bioinformatics 27(8), 1076–1085 (2011)
Seki, H., Matsumura, T., Fujii, M., Kasami, T.: On multiple context-free grammars. Theoret. Comput. Sci. 88(2), 191–229 (1991)
Taufer, M., Licon, A., Araiza, R., Mireles, D., Van Batenburg, F., Gultyaev, A.P., Leung, M.Y.: Pseudobase++: an extension of PseudoBase for easy searching, formatting and visualization of pseudoknots. Nucleic Acids Res. 37(suppl. 1), D127–D135 (2008)
Theimer, C.A., Blois, C.A., Feigon, J.: Structure of the human telomerase RNA pseudoknot reveals conserved tertiary interactions essential for function. Mol. Cell 17(5), 671–682 (2005)
Vernizzi, G., Orland, H., Zee, A.: Classification and predictions of RNA pseudoknots based on topological invariants. Phys. Rev. E 94(4), 042410 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Quadrini, M., Culmone, R., Merelli, E. (2017). Topological Classification of RNA Structures via Intersection Graph. In: Martín-Vide, C., Neruda, R., Vega-Rodríguez, M. (eds) Theory and Practice of Natural Computing. TPNC 2017. Lecture Notes in Computer Science(), vol 10687. Springer, Cham. https://doi.org/10.1007/978-3-319-71069-3_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-71069-3_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-71068-6
Online ISBN: 978-3-319-71069-3
eBook Packages: Computer ScienceComputer Science (R0)