Topological Classification of RNA Structures via Intersection Graph

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.

[1]  Christian N. S. Pedersen,et al.  RNA Pseudoknot Prediction in Energy-Based Models , 2000, J. Comput. Biol..

[2]  C. Pleij,et al.  tRNA-like structures. Structure, function and evolutionary significance. , 1991, European journal of biochemistry.

[3]  Michela Taufer,et al.  PseudoBase++: an extension of PseudoBase for easy searching, formatting and visualization of pseudoknots , 2008, Nucleic Acids Res..

[4]  M. Marias.  Analysis on Manifolds , 2005 .

[5]  Henri Orland,et al.  Classification and predictions of RNA pseudoknots based on topological invariants. , 2016, Physical review. E.

[6]  F. McMorris,et al.  Topics in Intersection Graph Theory , 1987 .

[7]  M. Ladomery,et al.  Molecular biology of RNA , 1988, Journal of Cellular Biochemistry.

[8]  Christian M. Reidys,et al.  Topology and prediction of RNA pseudoknots , 2011, Bioinform..

[9]  Michael A. Arbib,et al.  An Introduction to Formal Language Theory , 1988, Texts and Monographs in Computer Science.

[10]  C. A. Theimer,et al.  Structure of the human telomerase RNA pseudoknot reveals conserved tertiary interactions essential for function. , 2005, Molecular cell.

[11]  Daniel Götzmann.  Multiple Context-Free Grammars , 2007 .

[12]  Christian M. Reidys,et al.  Topological language for RNA , 2016, Mathematical biosciences.

[13]  A. Zee,et al.  Topological classification of RNA structures. , 2006, Journal of molecular biology.

[14]  C. Pleij,et al.  tRNA‐like structures , 1991 .

[15]  Dirk Metzler,et al.  Predicting RNA secondary structures with pseudoknots by MCMC sampling , 2007, Journal of mathematical biology.

[16]  Haruki Nakamura,et al.  Announcing the worldwide Protein Data Bank , 2003, Nature Structural Biology.

[17]  T L Beattie,et al.  A long‐range pseudoknot is required for activity of the Neurospora VS ribozyme. , 1996, The EMBO journal.

[18]  Scott A Strobel,et al.  Crystal structure of a group I intron splicing intermediate. , 2004, RNA.

[19]  D. Mathews,et al.  ProbKnot: fast prediction of RNA secondary structure including pseudoknots. , 2010, RNA.