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#!/usr/bin/perl -w
use strict;
...
    print Dumper \@AA; # See what's really in that array. Note the bac
+kslash.

    ...

foreach $AA(@AA) 
{
...
             # ^^
             # incorrect syntax
}

# Sum the proteins' molecular weights.
my $sum;  # no need to declare $sum until here.
...
    print "AA: $AA Weight: $MWs{ $AA }\n";
    $sum += $MWs{ $AA };
}