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 |
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Format: | Artikel |
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. |
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ISSN: | 0092-8240 1522-9602 |
DOI: | 10.1007/s11538-007-9240-y |