I, also, am confused about what is supposed to be summed while processing the file (I can't see anything numeric in your sample data). (Update: I also don't understand what you want to do with a 2D array, or why.) However, this code will produce exactly the output you specify from the given input. (Caution: The tabs that are supposed to be in the  __DATA__ section may not survive the posting process. Check and restore them as needed.)

use strict;
use warnings;

<DATA>;  # ignore first input line

while (my $line = <DATA>) {

    $line =~ s{ \t }{; }xmsg;

    # make output ProteinName field min 4 cols wide, right justified.
    $line =~ s{ \A ([^;]*) (?= ;) }{ sprintf '%4s', $1 }xmse;

    print $line;

    }

exit;

__DATA__
ProteinName    MF1    MF2    MF3
GH1    Growth factor activity    Growth hormone receptor binding    Ho
+rmone activity
POMC    G protein-coupled receptor binding    Hormone activity    Sign
+aling receptor binding
THRAP3    ATP binding Source    Nuclear receptor transcription coactiv
+ator activity    Phosphoprotein binding
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Update: I just round-tripped the code posted above and it looks like the tabs in the  __DATA__ section survived intact!