$k$-noncrossing RNA structures with arc-length $\ge 3$

Abstract

In this paper we enumerate $k$-noncrossing RNA pseudoknot structures with given minimum arc- and stack-length. That is, we study the numbers of RNA pseudoknot structures with arc-length $\ge 3$, stack-length $\ge \sigma$ and in which there are at most $k-1$ mutually crossing bonds, denoted by ${\mathsf{T}}_{k,\sigma }^{[3]}(n)$. In particular we prove that the numbers of 3, 4 and 5-noncrossing RNA structures with arc-length $\ge 3$ and stack-length $\ge 2$ satisfy ${\mathsf{T}}_{3,2}^{[3]}(n{)}^{}\sim K_3{n}^{-5}2.5723^n$, ${\mathsf{T}}_{4,2}^{[3]}(n)\sim K_4{n}^{-21/2}3.0306^n$, and ${\mathsf{T}}_{5,2}^{[3]}(n)\sim K_5{n}^{-18}3.4092^n$, respectively, where $K_3,K_4,K_5$ are constants. Our results are of importance for prediction algorithms for RNA pseudoknot structures.

17 pages, 4 figures

References in corpus (1)

• RNA-LEGO: Combinatorial Design of Pseudoknot RNA