You're reading the file twice in your loop, first in the condition then again before the end of the loop, is this intentional? Also a few other suggestions - your match regex ^R.* can drop the .* as it achieves nothing because it says match 'R' at the beginning of the string, optionally followed by 0 or more of anything, in fact it would be better suited with a simple index. You could also drop the indexing using $i and replace it with the push function e.g

while ( $line = <TR_INFILE> ) {
    if ( index( $line, 'R' ) == 0 ) {
        ## removed /g as it's unnecessary
        $line =~ s/^Results://;
        
        print OUTFILE3 "$line";
        
        ## the ' ' is special, see. perldoc -f split
        my @chunks = split ' ', $line;
        push @trstart, shift @chunks;
        push @trend,   shift @chunks;
        push @period,  shift @chunks;
        push @copy,    shift @chunks;
        push @consize, shift @chunks;
        push @matches, shift @chunks;
        push @indels,  shift @chunks;
        push @score,   shift @chunks;
        push @numa,    shift @chunks;
        push @numc,    shift @chunks;
        push @numg,    shift @chunks;
        push @numt,    shift @chunks;
        push @entropy, shift @chunks;
        $TRID++;
    } elsif ( index($line, 'S') == 0 ) {
        $line =~ s/^Sequence:\s*//;
        push @TR_Accession, $line;
        $SEQID++;
    }   
}
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Some of that code massaging is style but it will also be much faster than your current code as most of the fiddly stuff is now done by perl and it also saves a lot of hard-coding. See. push, index, shift for more info on the functions used above.
HTH

_________
broquaint