Sequence Comparison.pdf

60 3 Pairwise Sequence Alignment
tells whether the pair is in all optimal alignments (namely, the pair is in all optimal
alignments if and only if its associated value is non-zero). These computations
are performed using dynamic-programming methods that require only space proportional
to the sum of the two sequence lengths. It has also been shown on how to
efficiently handle the case where alignments are constrained so that each position,
say position i, of the first sequence can be aligned only to positions on a certain
range of the second sequence.
To deliver an optimal alignment, Hirschberg’s approach applies forward and
backward passes in the first nondegenerate rectangle along the optimal path being
generated. Within a subproblem (i.e., rectangle) the scores of paths can be taken
relative to the “start node” at the rectangle’s upper left and the “end node” at the
rightmost cell of the last row. This means that a subproblem is completely specified
by giving the coordinates of those two nodes. In contrast, methods for the robustness
measurement must maintain more information about each pending subproblem.
Fortunately, it can be done in linear space by observing that the total number of the
boundary entries of all pending subproblems of Hirschberg’s approach is bounded
by O(m + n) (see Figure 3.21).
3.8 Bibliographic Notes and Further Reading
Sequence alignment is one of the most fundamental components of bioinformatics.
For more references and applications, see the books by Sankoff and Kruskal [175],
Waterman [197], Gusfield [85], Durbin et al. [61], Pevzner [165], Jones and
Pevzner [98], and Deonier et al. [58], or recent survey papers by Batzoglou [23]
and Notredame [154].
3.1
We compile a list of pairwise alignment tools in Table C.1 of Appendix C.
3.2
It is very easy to visualize in a dot-matrix representation certain sequence similarities
such as insertions, deletions, repeats, or inverted repeats.
3.3
The global alignment method was proposed by Needleman and Wunsch [151].
Such a dynamic-programming method was independently discovered by Wagner
and Fischer [194] and workers in other fields. For a survey of the history, see the
book by Sankoff and Kruskal [175].
3.4