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Typically, when performing gene-knockout, the experimenters select one gene to remove/replace-with-junk and then see if the prokaryote can still undergo fission. If it continues to reproduce then the gene is labeled as non-essential; if the organism cannot reproduce then the gene is labeled as essential; and some-times (if the organism can reproduce but only for a certain number of generations) the gene is labeled as quasi-essential.

Typically, if gene X is essential, and you knock-out both gene X and some other gene Y then the organism still dies; this is an example of monotonic behavior. However, this doesn't always have to be the case, it could be that gene X is essential only in the presence of gene Y (for instance if the two proteins produced are in a delicate feedback loop). Is there examples when knocking out gene X makes the organism nonviable, but knocking out gene X and Y maintains viability? In the most extreme case, is there an example where both gene X and Y are essential, but if both are knocked-out then the organism is still viable? I am primarily interested in simple prokaryotes (an answer for Mycoplasma genitalium or Escherichia coli would be best) but more complicated organisms are preferred over no answer.