BLAST

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Copyright © 2012 O’Reilly & Associates, Inc. All rights reserved.

Basic BLAST Statistics

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101

#

return nToB($l*$raw_score – log($k));

}

The Expect of an HSP

Now calculate the Expect for the HSP shown in Figure 7-1, recalling that

. Again, a simple Perl function is useful:

sub rawScoreToExpect {

my $raw_score = shift;

my $k = shift;

my $l = shift; # lambda in nats

my $m = shift; # effective length of query

my $n = shift; # effective length of database

#

return $k*$m*$n*exp(-1*$l*$raw_score);

}

Using this function, the values of k and λ, given in Table 7-1, combined with the val-

ues m´ (222) and n´ (7648142) that you calculated in your discussion of effective

lengths, gives an Expect of 8e

-13

for the alignment shown in Figure 7-1.

You can also calculate the Expect of an alignment with a normalized score, S´

(Figure 7-1). The Karlin-Altschul equation is formulated for the raw

score, S, not the normalized score S´. To calculate an Expect using a normalized

score S´ whose units are nats, use the equation . Note that k doesn’t

appear in this equation; it has already been accounted for when deriving the normal-

ized (nat) score (e.g., ).

To calculate the Expect of an HSP from its bit score (Figure 7-1) use the Perl func-

tion shown next. The formula is similar to that used to calculate an Expect from a

nat score. However, the base of the exponent is 2 rather ...