BLAST, BLAT and FASTA - Algorithms in Bioinformatics

Bioinformatics I, WS’09-10, S. Henz (script by D. Huson) November 26, 2009 51
The number of random HSPs (s, t) with σ(s, t) ≥ S can be described by a Poisson distribution with
parameter v = Kmne −λS . The number of HSPs with score ≥ S that we expect to see due to chance
is then the parameter v, also called the E-value:
E(S) =Kmne −λS
The parameters K and λ depend on the background probabilities of the symbols and on the employed
scoring matrix. We define λ as the unique value for y that satisfies the equation
a,b∈Σ
papbe S(a,b)y =1
K and λ are scaling-factors for the search space and for the scoring scheme, respectively.
Hence the probability of finding exactly x HSPs with a score ≥ S is given by
−E Ex
P(X = x) =e
x!
The probability of finding at least one HSP “by chance” is
where E is the E-value for S.
P(S) = 1 − P(X = 0) = 1 − e −E ,
Thus we see that the probability distribution of the scores follows an extreme value distribution.
BLAST reports E-values rather than ”P-values” as it is easier to interpret the difference between
E-values than to interpret the difference between P-values.
The raw scores S are of little use without detailed knowledge of the scoring system used, that is, of
the statistical parameters K and λ.
Therefore we introduced a normalized raw score called bit score S ′ that is defined as
E-values and bit scores are related by
(exercise!)
4.6 Gapped BLAST
S ′ =
λS − ln K
.
ln 2
E = mn2 −S′
A new version of BLAST called BLAST 2.0 2 allows gaps in the extension phase.
4.7 The BLAST family
• BLASTN: compares a DNA query sequence to a DNA sequence database
2 S. F. Altschul, T. L. Madden, A.A. Schäffer, J. Zhang, Z. Zhang, W. Miller, and D. J. Lipman: Gapped BLAST and
PSI-BLAST: a new generation of protein database search programs. Nucleic Acids Res. 25(17):3389-402 (1997).