Multiple comparisons

In the discussion of the previous section, we have assumed that the sequences or structures would be compared in a pairwise manner. However, such pairwise comparisons of several related proteins may not be self consistent, ie the following transitivity rule can be broken: If residue $a$ from protein $A$ is equivalent to residue $b$ in protein $B$ which in turn is equivalent to residue $c$ in protein $C$ then the residue $a$ from protein $A$ must also be equivalent to residue $c$ from protein $C$. This property is not always attained in the set of usual pairwise comparisons relating a group of similar proteins. For this reason we proceed by simultaneously aligning all proteins. This is achieved by aligning the second sequence with the first one, the third sequence with the alignment of the first two, etc. A more general tree-like growth of the multiple alignment is not yet implemented.

If the number of all proteins is $N$, $N-1$ alignments must be made to obtain the final multiple comparison. It is noted that once an equivalence or gap is introduced it is not changed in later stages.