Comparing Multiple Strings Simultaneously
In “Consensus and Profile”, we generalized the notion of Hamming distance to find an average case for a collection of nucleic acids or peptides. However, this method only worked if the polymers had the same length. As we have already noted in “Edit Distance”, homologous strands of DNA have varying lengths because of the effect of mutations inserting and deleting intervals of genetic material; as a result, we need to generalize the notion of alignment to cover multiple strings.
A multiple alignment score is obtained by taking the sum of an alignment score over all possible pairs of augmented strings. The only difference in scoring the alignment of two strings is that two gap symbols may be aligned for a given pair (requiring us to specify a score for matched gap symbols).
Return: A multiple alignment of the strings having maximum score, where we score matched symbols 0 (including matched gap symbols) and all mismatched symbols -1 (thus incorporating a linear gap penalty of 1).
>Rosalind_7 ATATCCG >Rosalind_35 TCCG >Rosalind_23 ATGTACTG >Rosalind_44 ATGTCTG
-18 ATAT-CCG -T---CCG ATGTACTG ATGT-CTG