If you want to populate $1, you have to use parentheses:

$readingframe =~ /(MHGR)/;
$protein = $1;
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or you can assign it directly:

($protein) = $readingframe =~ /(MHGR)/;
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In your case, though, you can just output MHGR, as there is nothing dynamic in your regular expression.

See also Regexp Quote Like Operators, perlretut, perlre.