  Assessing the significance of alignment scores of optimally aligned DNA or
amino acid sequences can be achieved via the knowledge of the score
distribution of random sequences. But this requires obtaining the distribution
in the biologically relevant high-scoring region, where the probabilities are
exponentially small. For gapless local alignments of infinitely long sequences
this distribution is known analytically to follow a Gumbel distribution.
Distributions for gapped local alignments and global alignments of finite
lengths can only be obtained numerically. To obtain result for the
small-probability region, specific statistical mechanics-based rare-event
algorithms can be applied. In previous studies, this was achieved for pairwise
alignments. They showed that, contrary to results from previous simple sampling
studies, strong deviations from the Gumbel distribution occur in case of finite
sequence lengths. Here we extend the studies to the for practical applications
in Molecular Biology much more relevant case of multiple sequence alignments
with gaps. We study the distributions of scores over a large range of the
support, reaching probabilities as small as 10^-160, for global and local
(sum-of-pair scores) multiple alignments. We find that even after suitable
rescaling, eliminating the sequence-length dependence, the distributions for
multiple alignment differ from the pairwise alignment case. Furthermore, we
also show that the previously discussed Gaussian correction to the Gumbel
distribution needs to be refined, also for the case of pairwise alignments.
