Structural alignment of two RNA sequences with lagrangian relaxation

RNA is generally a single-stranded molecule where the bases form hydrogen bonds within the same molecule leading to structure formation. In comparing different homologous RNA molecules it is usually not sufficient to consider only the primary sequence, but it is important to consider both the sequence and the structure of the molecules. Traditional alignment algorithms can only account for the sequence of bases, but not for the base pairings. Considering the structure leads to significant computational problems because of the dependencies introduced by the base pairings and the presence of pseudoknots. In this paper we address the problem of optimally aligning two given RNA sequences either with or without known structure (allowing for pseudoknots). We phrase the problem as an integer linear program and then solve it using Lagrangian relaxation. In our computational experiments we could align large problem instances - 18S and 23S ribosomal RNA with up to 1500 bases within minutes while preserving pseudoknots.