Prossibly not useable (this has the stench of homework about it) but considering the problem domain BioPerl would be the first thing to check out. Even if it is homework you're supposed to build from scratch you may be able to gain inspiration, but judging by the orphaned method call on a $mySeq instance its use could be expected.

And mentioning because it jumped out at me: ALWAYS CHECK THE RETURN FROM open CALLS. You did your first but you didn't creating some of your output file(s) which means that's inevitably going to silently fail some time and you're then going to be stuck trying to track down what's gone wrong when that happens (and it will; Murphy sez so). Even your trick conditionally opening the last output it might be useful to print an informational diagnostic message to indicate why you're not writing to the file rather than STDOUT.

if( not $succ ) {
  print STDERR qq{Unable to append to '$file', using STDOUT: $!\n};
  $fh = \*STDOUT;
}
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