From 2007.igem.org

Biologists always use symmetric LacI-family operators, e.g. AATTGTGAAC GTTCACAATT (O44) and AATTGTAAGC GCTTACAATT (O22). Please notice that they are all 20bp long and each right 10bp-long strand’s complementary strand is reversed symmetric with its left 10bp-long strand. For short we call this kinds of symmetrical operators as Oxx, for example, O44, O22, etc. Then you must have already understood what O24 means-- Yes, it means the asymmetric operator AATTGTAAGC GTTCACAATT (O24), which has the left 10bp-long strand of O22 and the right 10bp-long one of O44. Again for example, O42 means AATTGTGAAC GCTTACAATT (O42), and so on. We also give these asymmetric operators another name: Hybrid Operators.

Biologists always use symmetric operators like O22 because they are the most suitable ones to be bound by their own specific repressor(s). If we call the highly specific repressor protein which can bind well on O44 as R4 and the one on O22 as R2, well then it is clearly that asymmetric O24 can be bind by both R2 and R4, but they are all not very suitable because R4 is specific for O44 instead of O22 and vice versa. Luckily these LacI-family Repressors are also symmetric, they each is combined by two self-same monomers, so one side of R2 can bind on O24’s left-half strand while the other side would not bring any remarkable effect on the right. To bind on half strand could still show repression, but distinctly it could not be strong. Now we can say that hybrid operator O24 is a “weaker” operator to R2 or R4 for their weaker binding than R2+O22 or R4+O44.

There is another kind of “weaker” operators, for example, AATTGTGAAC GCTCATAATT (O46). The symmetric prototype AATTATGAGC GCTCATAATT (O66) is an interesting operator, because all the known LacI-family repressors would not show detectable repression on it.[参考文献] It is obvious that O46 is a “weaker” operator only to R4 (than R4+O44), but not a valid operator to other repressors that are not specific for O44. On the other hand, O24 is a “weaker” operator to both R4 and R2.