CD8 Tregs also exist. See publication for example:
Hye-Jung Kim, Bert Verbinnen, Xiaolei Tang, Linrong Lu & Harvey Cantor. 2010. Inhibition of of follicular T-helper cells by CD8+ regulatory cells is essential for self tolerance. Nature 467:328.
I have seen the paper you mentioned before. And I am so sorry that I didn't describe clearly about my question. My point is why CD8+ T cells don't express Foxp3? Now we have a model about how nTreg develop in thymus, it says Foxp3 expresses after CD4 single positive T cell formation so we can't see any CD8+Foxp3+ T cells. But recently someone has published his data and said that in small intestine there are a group of T cells who character as CD4+CD8+FOXP3+ and they have the function of protecting small intestine from inflammation. So it is so interest that during which time foxp3 expresses and why when nTreg cells develop they delete CD8+FOXP3+ T cells?
This is a good question. Maybe it needs someone to answer this question. Our group is also doing some work about Treg development. Maybe the distribution of Foxp3+ subset cells are different. There are something different in different environment? I'm just wondering.