Canonical RNA pseudoknot structures

Abstract

In this paper we study $k$-noncrossing, canonical RNA pseudoknot structures with minimum arc-length $\ge 4$. Let ${\mathsf{T}}_{k,\sigma }^{[4]}(n)$ denote the number of these structures. We derive exact enumeration results by computing the generating function ${\mathbf{T}}_{k,\sigma }^{[4]}(z)={\sum }_n{\mathsf{T}}_{k,\sigma }^{[4]}(n)z^n$ and derive the asymptotic formulas ${\mathsf{T}}_{k,3}^{[4]}(n{)}^{}\sim c_k{n}^{-(k-1{)}^2-\frac{k-1}{2}}({\gamma }_{k,3}^{[4]}{)}^{-n}$ for $k=3,...,9$. In particular we have for $k=3$, ${\mathsf{T}}_{3,3}^{[4]}(n{)}^{}\sim c_3{n}^{-5}2.0348^n$. Our results prove that the set of biophysically relevant RNA pseudoknot structures is surprisingly small and suggest a new structure class as target for prediction algorithms.

21 pages,7 figures

References in corpus (2)

• RNA-LEGO: Combinatorial Design of Pseudoknot RNA
• Asymptotic analysis of $k$-noncrossing matchings

Cited by in corpus (1)

• Stacks in canonical RNA pseudoknot structures