Optimal sequence alignment using affine gap costs

When comparing two biological sequences, it is often desirable for a gap to be assigned a cost not directly proportional to its length. If affine gap costs are employed, in other words if opening a gap costsv and each null in the gap costsu, the algorithm of Gotoh (1982,J. molec. Biol. 162, 705) finds the minimum cost of aligning two sequences in orderMN steps. Gotoh's algorithm attempts to find only one from among possibly many optimal (minimum-cost) alignments, but does not always succeed. This paper provides an example for which this part of Gotoh's algorithm fails and describes an algorithm that finds all and only the optimal alignments. This modification of Gotoh's algorithm still requires orderMN steps. A more precise form of path graph than previously used is needed to represent accurately all optimal alignments for affine gap costs.