Making ends meet or just meeting at the ends? Assessing end-to-end distance in folded RNA sequences and other branched structures

Abstract

Researchers have repeatedly found that the ends of an RNA sequence are significantly closer than expected for a random linear chain. However, we prove that the ends of a branched structure are almost certainly close. Our results are obtained via combinatorial branching models of increasing complexity using tools from multivariate analytic combinatorics. We completely characterize parameters tracking end-to-end distance, including means and variances. Then, we compare to existing datasets of known RNA structures, as well as the minimum free-energy structures of randomized shuffles. We find that the shuffled structures resemble our theoretical distributions while the known RNA structures have similar parameter values but are more concentrated.