Franken-Teeth
As we age, what if we could grow new teeth? British researchers claim to have done just that–well sort of, with help from mouse cells.
What they did was to combine cells from adult gum tissue with mouse cells. The mouse cells were embryonic tooth mesenchyme. “Mesenchyme” are undifferentiated cells from the mesoderm, one of three tissue types of the early embryo. Mesenchyme normally differentiates into bone and circulatory tissues.
In this case, researcher Paul Sharpe and colleagues at King’s College used mouse embryonic mesenchyme to “induce” growth of human teeth from human tissue. As Sharpe concludes: ‘Epithelial cells derived from adult human gum tissue are capable of responding to tooth inducing signals from embryonic tooth mesenchyme in an appropriate way to contribute to tooth crown and root formation and give rise to relevant differentiated cell types, following in vitro culture.”
So how do they know the teeth are “human”? Presumably they tested the molecular composition of the dentine and enamel, for human tissue markers. However, the mouse embryonic tissues were necessary to “induce” teeth formation. This is a problem mainly because there would be immune rejection of the mouse component, and because mouse tissues might harbor hidden viruses.
However, earlier reports show ways of converting adult human cells into seemingly embryonic cells. (Babies from dandruff, remember.) So who knows, our third set of teeth may be on the way.
Ultraphyte 
I was hoping that by now we’d be able to kill all the bacteria in our mouths that cause tooth decay? Then we wouldn’t need a third set.
No way; the bacteria have a long-evolved ecosystem.
I just really like the phrase “tooth inducing signals.”
The researchers can test for particular molecules such as cell-surface proteins that are specific to human cells, encoded by our genes. If the tissues have these proteins (typically tested by antibody reactions) then they must be “human.” However, I’m not sure they can prove the “teeth” material comes entirely from human cells.