RNA pseudoknot structures with arc-length ≥3 and stack-length ≥σ

Authors:
Emma Y. Jin;Christian M. Reidys
Affiliations:
Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, PR China;Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, PR China
Venue:
Discrete Applied Mathematics
Year:
2010

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Abstract

In this paper, we enumerate k-noncrossing RNA pseudoknot structures with a given minimum arc- and stack-length. That is, we study the numbers of RNA pseudoknot structures with arc-length =3, stack-length =@s and in which there are at most k-1 mutually crossing bonds, denoted by T"k","@s^[^3^](n). We prove that the numbers ofk-noncrossing RNA structures with arc-length =3 and stack-length =2 satisfy T"k","2^[^3^](n)^~C"kn^-^(^k^-^1^)^^^2^-^k^-^1^2(@c"k","2^[^3^])^-^n. In the case k=3,4,5, we derive T"3","2^[^3^](n)^~C"3n^-^52.5721^n, T"4","2^[^3^](n)~C"4n^-^2^1^23.0306^n, and T"5","2^[^3^](n)~C"5n^-^1^83.4092^n, respectively, where C"3,C"4,C"5 are constants. Our results are of importance for prediction algorithms for RNA pseudoknot structures.