Figure 1

Anchored alignment and parallel computation of sub-alignments for pair-wise sequence comparison. (a) Un-constrained alignment: an optimal chain of fragments f₁, f₂, f₃ is identified in the comparison matrix spanned by input sequences S₁ and S₂. (b) Anchored alignment: an anchor point (A₁, A₂) is defined prior to the alignment procedure, and an optimal chain of fragments is searched under the constraints imposed by this anchor. That is, residues to the left of A₁ can be aligned only to residues to the left of A₂ and vice versa, so the alignment search space is reduced by a factor of 2. If anchor point (A₁, A₂) is consistent with the optimal un-constrained alignment as shown in (a), the constraints imposed by this anchor point do not affect the resulting alignment, so exactly the same fragment chain f₁, f₂, f₃ is obtained. (c) In the parallel aligment procedure, sequence S₁ and S₂ are split into sub-sequences , and , , respectively, where the anchor point (A₁, A₂) defines the exact cutting-position. Alignments of and and of and are calculated independently, and concatenated to obtain an output alignment of S₁ and S₂. In (c), the obtimal sub-alignments involve fragments and which are sub-fragments of f₂ contained in the un-constrained alignment. In this case, the resulting final alignment of sequences S₁ and S₂ is therefore the same as the un-constrained one in example (a). Note, however, that the scoring function w for fragments is not additive and we may have, for example, . Therefore, even if anchor point (A₁, A₂) is consistent with the optimal un-constrained alignment, there is no guarantee that concatenating optimal sub-alignments yields the same alignment as the un-constrained alignment of the input sequences S₁ and S₂. The algorithm may end up with a situation as shown in example (d) where the parallel alignment procedure leads to a different output alignment.