  Frameshift mutations in protein-coding DNA sequences produce a drastic change
in the resulting protein sequence, which prevents classic protein alignment
methods from revealing the proteins' common origin. Moreover, when a large
number of substitutions are additionally involved in the divergence, the
homology detection becomes difficult even at the DNA level. To cope with this
situation, we propose a novel method to infer distant homology relations of two
proteins, that accounts for frameshift and point mutations that may have
affected the coding sequences. We design a dynamic programming alignment
algorithm over memory-efficient graph representations of the complete set of
putative DNA sequences of each protein, with the goal of determining the two
putative DNA sequences which have the best scoring alignment under a powerful
scoring system designed to reflect the most probable evolutionary process. This
allows us to uncover evolutionary information that is not captured by
traditional alignment methods, which is confirmed by biologically significant
examples.
