Final answer:
The false statement about eukaryotic activator proteins is that they stimulate transcriptional initiation by opening up the double helix. Eukaryotic RNA Polymerase II lacks helicase activity and relies on TFIIH for unwinding DNA.
Step-by-step explanation:
The statement about eukaryotic activator proteins that is false is: A. They stimulate transcriptional initiation by opening up the double helix. Unlike prokaryotic RNA polymerase, eukaryotic RNA Polymerase II does not have inherent helicase activity. Instead, it relies on the multi-subunit TFIIH protein, which contains subunits with helicase activity, to assist in unwinding the DNA helix. Activator proteins facilitate transcription by recruiting coactivators and proteins that can modify chromatin structure, promoting the assembly of transcription initiation complexes, and aiding in the assembly of general transcription factors and RNA polymerase at the promoter.