Combinatorics of RNA Structures with Pseudoknots

In this paper, we derive the generating function of RNA structures with pseudoknots. We enumerate all k -noncrossing RNA pseudoknot structures categorized by their maximal sets of mutually intersecting arcs. In addition, we enumerate pseudoknot structures over circular RNA. For 3-noncrossing RNA str...

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Veröffentlicht in:Bulletin of mathematical biology 2008, Vol.70 (1), p.45-67
Hauptverfasser: Jin, Emma Y., Qin, Jing, Reidys, Christian M.
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Sprache:eng
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Zusammenfassung:In this paper, we derive the generating function of RNA structures with pseudoknots. We enumerate all k -noncrossing RNA pseudoknot structures categorized by their maximal sets of mutually intersecting arcs. In addition, we enumerate pseudoknot structures over circular RNA. For 3-noncrossing RNA structures and RNA secondary structures we present a novel 4-term recursion formula and a 2-term recursion, respectively. Furthermore, we enumerate for arbitrary k all k -noncrossing, restricted RNA structures i.e.  k -noncrossing RNA structures without 2-arcs i.e. arcs of the form ( i , i +2), for 1≤ i ≤ n −2.
ISSN:0092-8240
1522-9602
DOI:10.1007/s11538-007-9240-y