Just as a scientific issue this seems very odd to me and not at all
what statisticians usually mean by missing data. Surely if you want to
determine "which treatments introduce similar gene expressionpatterns" then two treatments that both produce no effect on the
expression of the same gene should be counted as more similar to each
other? If you've measured an expression change to be near 0 then
that's a known measured value that happens to be near 0 -- not an
unknown value that could be arbitrarily large or small and you have no
idea which. (Obviously I don't know any of the details about your
setting, but in particular I worry that your reasoning sounds similar
to common misconceptions about what "significant" actually means. "Not
significantly different from zero" might well be "significantly
different from 1000".)