Making Ends Meet or Just Meeting at the Ends? Assessing End-to-End Distance in Folded RNA Sequences and Other Branched Structures.

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. The helices on the exterior loop of a structure draw the ends of the sequence together, and we find evidence that these helices are more stable than expected when compared to their counterparts in uniformly random branched structures.