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Combinatorial Insights into RNA Secondary Structure

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Discrete and Topological Models in Molecular Biology

Part of the book series: Natural Computing Series ((NCS))

Abstract

The interaction of discrete mathematics with molecular biology advances our understanding of important sequence/structure/function relationships. By their nature, biological sequences are often abstracted to combinatorial objects namely strings over finite alphabets and their representation as graphs or formal languages. As described in this chapter, results based on these mathematical abstractions have been used to count, compare, classify, and otherwise analyze RNA secondary structures. In this way, they provide important insights into the base pairing of RNA sequences, thereby advancing our understanding of RNA folding.

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Notes

  1. 1.

    On March 5, 2013, the PDB [7] contained 82,105 protein and 2,510 nucleic acid structures. Concurrently, the Rfam database [12] listed 60 families of RNA molecules with at least one member having a three-dimensional structure available in the PDB. Of those, five-sixths had an average length below 250 nucleotides. The only families with an average length exceeding 400 nucleotides were three ribosomal RNA ones (archaeal, bacterial, and eukaryotic). It is worth noting that a high-resolution structure of the E. coli ribosome was first published only in 2005 [82].

  2. 2.

    Nearly all of these are for the special cases of small internal loops, denoted by the number of single-stranded bases on each side as 1 × 1, 2 × 1/1 × 2, and 2 × 2. The same special cases are included in the Turner04 parameters. It is worth noting that the number of parameters for formal-language models can also be quite large, depending on the grammar.

  3. 3.

    The degree of a loop here is the total number of base pairs in the loop.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

    Christine Heitsch

  2. Department of Mathematical Sciences, Clemson University, Clemson, SC, 29634-0975, USA

    Svetlana Poznanović

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    Nataša Jonoska

  2. Dept. Mathematics & Statistics, University of South Florida, Tampa, Florida, USA

    Masahico Saito

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Heitsch, C., Poznanović, S. (2014). Combinatorial Insights into RNA Secondary Structure. In: Jonoska, N., Saito, M. (eds) Discrete and Topological Models in Molecular Biology. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40193-0_7

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