How is the inactivation of one of the X chromosomes preserved/propagated when the cell replicates?
Background: In the XX/XY system of sex determination (i.e. mammals and marsupials), in female animals (having twice as many X chromosomes as males) one of the X chromosomes is inactivated (for dosage compensation), forming a "Barr body" in the nucleus. In mammals this inactivation occurs randomly (in each cell independently) at a fairly early stage of development, but the same chromosome-selection is carried through subsequent cell divisions (resulting in the patterned appearance of tortoiseshell and calico cats, where the alternative X chromosomes have phenotypically different alleles).
What is the mechanism by which the Barr body replicates (for cellular division)? In particular, if most other transcription for that DNA is blocked, is there an unusual mechanism for duplicating the DNA? And what mechanism ensures that in both daughter cells, the same version of the X chromosome is inactivated as had been chosen in the parent cell?