No, only one daughter cell would get the DNA episo

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No, only one daughter cell would get the DNA episome. Translation of the episome (production of LRM) may wash out over time, as gene therapy does not last forever, at least not in the liver for Hemophilia A.

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Yes, of course. I appreciate that.
In the Interphase stage of Mitosis, the DNA duplicates as well as all the organelle. I guess I was assuming the episome would also duplicate. But I guess the cell "knows" that the episome is not an original part of its self so it does not duplicate it?

Therefore it only ends up in one daughter cell.

I guess the hope then is that by the time the production of LRM washes out, all of the dormant/hibernating HIV would have by then emerged from their reservoirs, finding only a few daughter CD4 cells without LRM which they could infect, are then destroyed by the adaptive immune system which already has memory of the HIV virus.

Maybe a subsequent infusion of the AAV vector will be required every 3 years or so, or maybe measurements of LRM receptor occupancy need to be made and when below say 75%, it needs to be reinfused?