BLAST

This is the Title of the Book, eMatter Edition

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

Amino Acid Similarity

|

57

A random DNA source has an entropy of:

- ( (0.25)(-2) + (0.25)(-2) + (0.25)(-2) + (0.25)(-2) ) = 2 bits

However, a DNA source that emits 90 percent A or T and 10 percent G or C has an

entropy of:

- ( 2(0.45)(-1.15) + 2(0.05)(-4.32) ) = 1.47 bits

In these examples, you’ve been given the frequency distribution as some kind of

truth. But it’s rare to know such things a priori, and the parameters must be esti-

mated from actual data. You may find the following Perl program informative and

entertaining. It calculates the entropy of any file.

# Shannon Entropy Calculator

my %Count; # stores the counts of each symbol

my $total = 0; # total symbols counted

while (<>) { # read lines of input

foreach my $char (split(//, $_)) { # split the line into characters

$Count{$char}++; # add one to this character count

$total++; # add one to total counts

}

}

my $H = 0; # H is the entropy

foreach my $char (keys %Count) { # iterate through characters

my $p = $Count{$char}/$total; # probability of character

$H += $p * log($p); # p * log(p)

}

$H = -$H/log(2); # negate sum, convert base e to base 2

print "H = $H bits\n"; # output

Amino Acid Similarity

Molecular biologists usually think of amino acid similarity in terms of chemical simi-

larity (see Table 2-1). Figure 4-1 depicts a rough