The following picture shows an inverted repeat sequence in a response element. Response element sequences for glucocorticoids, estrogen, and thyroid hormone show that they all contain inverse repeats. Why do these inverted repeats exist in so many response sequences? In other words, what advantage do they pose to the function of the response element?
Starting with prokaryotic (i.e., bacterial) transcription factors--which were the first to be characterized in depth, this type of pattern was noted. Even for the "classic" Type II Restriction Endonucleases used for molecular cloning have palindromic recognition sequences. In all three cases the answer is that the sequence-specific DNA binding protein binds as a dimer, and so each monomer is recognizing a "half-site" (one of the inverted sequences).