Optimal Alignment of Multiple Sequence Alignments

An essential tool in biology is the alignment of multiple sequences. Biologists use multiple sequence alignments for tasks such as predicting protein structure and function, reconstructing phylogenetic trees, and finding motifs. Constructing high-quality multiple alignments is computationally hard, both in theory and in practice, and is typically done using heuristic methods. The majority of state-of-the-art multiple alignment programs employ a form and polish strategy, where in the construction phase, an initial multiple alignment is formed by progressively merging smaller alignments, starting with single sequences. Then in a local-search phase, the resulting alignment is polished by repeatedly splitting it into smaller alignments and re-merging. This merging of alignments, the basic computational problem in the construction and local-search phases of the best multiple alignment heuristics, is called the Aligning Alignments Problem. Under the sum-of-pairs objective for scoring multiple alignments, this problem may seem to be a simple extension of two-sequence alignment. It is proven here, however, that with affine gap costs (which are recognized as necessary to get biologically-informative alignments) the problem is NP-complete when gaps are counted exactly. Interestingly, this form of multiple alignment is polynomial-time solvable when we relax the exact count, showing that exact gap counts themselves are inherently hard in multiple sequence alignment. Unlike general multiple alignment however, we show that Aligning Alignments with affine gap costs and exact counts is tractable in practice, by demonstrating an effective algorithm and a fast implementation. Our software AlignAlign is both time- and space-efficient on biological data. Computational experiments on biological data show instances derived from standard benchmark suites can be optimally aligned with surprising efficiency, and experiments on simulated data show the time and space both scale well