Background: RNA molecules form thermodynamic ensembles, but interpretation often requires a single representative structure. Existing base-pair centroid estimators assess agreement at the level of individual base pairs and do not directly target nesting depth along the sequence. Methods: We introduce Mountain Centroid, which minimizes expected squared mountain-profile distance, and derive dynamic programming algorithms with and without RNA pairing constraints. We also combine the Mountain Centroid objective with the base-pair centroid gain. Results: Across 21,254 RNAStrAlign sequences, Mountain Centroid had lower median normalized mean squared mountain distance (NMSMD) than minimum-free-energy (MFE) and base-pair centroid ({gamma} = 1) structures, whereas its median base-pair F1 was lower. Imposing RNA pairing constraints improved base-pair F1 for 59.35% of sequences and reduced it for 3.58%. At an illustrative weight, the combined objective had median base-pair F1 similar to MFE while retaining lower median NMSMD than MFE and all tested {gamma}-centroid settings. Conclusions: Mountain Centroid represents an RNA structural ensemble with a single secondary structure that reflects how nesting depth varies across nucleotide positions. Combining mountain-profile and individual-base-pair criteria allows their relative contributions to be varied.
Otagaki, T., Asai, K., Sato, K.
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