The 5'-3' distance of RNA secondary structures

TL;DR

This paper computes the exact and limit distributions of 5'-3' distances in RNA secondary structures, revealing that these distances are generally small and differ from those in minimum free energy structures, with implications for understanding RNA folding.

Contribution

It provides the first exact distribution calculations for 5'-3' distances in RNA secondary structures for any finite length, and compares these with limit distributions and energy-based structures.

Findings

Exact distribution matches limit distribution for n=30

Distances are smaller than in minimum free energy structures

Distances are largely independent of sequence length

Abstract

Recently Yoffe {\it et al.} observed that the average distances between $5'-3'$ ends of RNA molecules are very small and largely independent of sequence length. This observation is based on numerical computations as well as theoretical arguments maximizing certain entropy functionals. In this paper we compute the exact distribution of $5'-3'$ distances of RNA secondary structures for any finite $n$. We furthermore compute the limit distribution and show that already for $n=30$ the exact distribution and the limit distribution are very close. Our results show that the distances of random RNA secondary structures are distinctively lower than those of minimum free energy structures of random RNA sequences.