Journal of Combinatorics

Volume 14 (2023)

Number 4

On a barrier height problem for RNA branching

Pages: 485 – 506



Christine Heitsch (School of Mathematics, Georgia Institute of Technology, Atlanta, Ga., U.S.A.)

Chi N. Y. Huynh (Analysis Group, Inc., U.S.A.)

Greg Johnston (Rubrik, Inc., U.S.A.)


The branching of an RNA molecule is an important structural characteristic yet difficult to predict correctly, especially for longer sequences. Using plane trees as a combinatorial model for RNA folding, we consider the thermodynamic cost, known as the barrier height, of transitioning between branching configurations. Using branching skew as a coarse energy approximation, we characterize various types of paths in the discrete configuration landscape. In particular, we give sufficient conditions for a path to have both minimal length and minimal branching skew. The proofs offer some biological insights, notably the potential importance of both hairpin stability and domain architecture to higher resolution RNA barrier height analyses.


RNA secondary structure, barrier height, plane tree

2010 Mathematics Subject Classification

Primary 92D20. Secondary 05A18, 05C05.

Christine Heitsch was partially supported by a BWF CASI, NSF DMS-1815044, and NIH R01-GM126554.

This work was supported by the Burroughs Wellcome Fund (2005 CASI to CH), National Science Foundation (DMS-1815044 to CH), and National Institutes of Health (R01-GM126554 to CH).

Received 22 November 2021

Published 14 April 2023