you can run M0 either with and without constraining omega to be 1.
run the null hypothesis with
fix_omega = 1
omega = 1
then the alternative hypothesis with
Compare twice the log likelihood difference with chi square with df = 1 (significance value 6.63 at 1%). presumably you will reject the null in virtually every dataset.
every functional protein is under purifying selection, so the test will not excite people.
ziheng