It's been a while since our PLoS Biology paper (2006), but I've found that every so often, I meet someone for whom the following information is relevant, so here it is:
In that paper, we found that transcription occurs in bursts, whereby we mean that the gene itself transitions randomly between an active and inactive state. We found this to be the case when we isolated clones in which each clone had stably inserted a RNA-FISHable transgene into a particular (but unknown) locus. In the paper, we analyzed one of those clones to show that for that one clone, changing the concentration of transactivator resulted in a change in the burst size (i.e., number of mRNA produced during a gene ON event).
What we didn't report is what happened in other clones. I didn't analyze any further clones in great detail, but we did observe something interesting. Just by eye, I noticed that the fraction of ON cells seemed to vary tremendously from clone to clone--some had every other cell ON, some had just 1 in 25 or so ON. But in each ON cell, the degree to which it was ON didn't really seem to vary much. On the other hand, varying the promoter (between 7x and 1x tetO) seemed to change the degree to which a cell was ON. So together, this would argue that in this one specific case, burst frequency is largely determined by the genetic context of the gene, but burst size is governed by transcription factor activity and how the transcription factor binds interacts with the promoter. Anyway, just in case someone finds this minor technical point interesting...