RNA molecules may experience independent selection pressures on their sequence and secondary)structure. Structural features then may be preserved without maintaining their exact position along the sequence. In such cases, corresponding base pairs are no longer formed by homologous bases, leading to the incongruent evolutionary conservation of sequence and structure. In order to model this phenomenon, we introduce bi-alignments as a superposition of two alignments: one modeling sequence homology; the other, structural homology. We show that under natural assumptions on the scoring functions, bi-alignments form a special case of 4-way alignments, in which the incongruencies are measured as indels in the pairwise alignment of the two alignment copies. A preliminary survey of the Rfam database suggests that incongruent evolution of RNAs is not a very rare phenomenon.

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