The cool idea here is that the brain could be borrowing a form of cellular memory from developmental biology to use for what we think of as memory.
Memories on DNA? You mean like the Bene Gesserit? Or Duncan Idaho?
If you haven’t read Dune, you won’t get that. The point is, that once again, science fiction seems to have predicted something that we are only now starting to understand. The human body is a crazy place.