Large deviations for optimal local alignment scores of independent sequences
- Steffen Grossmann (University of Frankfurt)
- Benjamin Yakir
The distribution function of the optimal local gapped alignment
score of two
long unrelated DNA sequences of length n is widely believed to be
of the Gumbel type
. Whereas this is well known
for gapless alignment
(Dembo et al., 1994), a rigorous justification of this belief in the
gapped case has only been given in special cases (e.g. Siegmund/Yakir, 2000).
The two parameters K and of course depend on the scoring scheme,
but numerically useable representations are available in these cases.
We look at
in the large
deviations regime, that is where . We give a connection
between this large deviations rate and the growth constant of the
expectation of in the logarithmic regime (Arratia/Waterman,
1994). We also provide a new representation for this limit via a characteristic
equation for moment-generating functions of optimal global
alignment scores. This representation is similar to the one known
from gapless alignment.
Assuming the correctness of the Gumbel form, this gives a new representation
for the parameter .