Loops in canonical RNA pseudoknot structures

Abstract

In this paper we compute the limit distributions of the numbers of hairpin-loops, interior-loops and bulges in k-noncrossing RNA structures. The latter are coarse grained RNA structures allowing for cross-serial interactions, subject to the constraint that there are at most k-1 mutually crossing arcs in the diagram representation of the molecule. We prove central limit theorems by means of studying the corresponding bivariate generating functions. These generating functions are obtained by symbolic inflation of Ik5-shapes.