I endorse all the excellent improvements made by GrandFather.
Some further minor tweaks follow.
For removing whitespace, you could change from:
$seq =~ s/\s//g;
$seq =~ s/\s+//g;
That should be a touch more efficient and is more idiomatic -- see also perlfaq4
"How do I strip blank space from the beginning/end of a string?".
An alternative for counting the number of bases is to change from:
my $A = () = $seq =~ /A/ig;
my $A = $seq =~ tr/aA//;
Counting characters with tr
seems a bit odd
but is normally fastest and is idiomatic Perl -- see Quote and Quote-like Operators
Finally, to see what actually matches in the regex, and so help you debug it,
note that you could expand it a bit like this:
my @matches = $seq =~ /[AG]TG.*?T[AG][AG]/ig;
print "Here are the matched parts of the string:\n";
print " '$_'\n" for @matches;
my $GENE = @matches;