Some thoughts on simple transcription models.
Best case: noise is Poisson — limited only by the arrival of a single rate limiting component. This allows for only linear control: doubling activator doubles arrival rate of transcription machinery.
Adding opening and closing we have two general regimes: long lived promoter open state, which minimizes the contribution of promoter switching noise, but reduces the temporal control of the gene. Fast switching allows for much more precise temporal control, but inevitably introduces noise. If activation is also rapid, then fast switching and Poisson noise can be achieved. There may however be fundamental constraints between the maximum re-initiation rate achievable and the maximum promoter opening rate achievable.
The probability of getting n% active.
Consider a gene whose target expression levels require that 70% (n%) of cells be transcribing the gene at any given time. In order to assure spatial uniformity, it is necessary that which 70% are transcribing changes constantly. This is best achieved through a rapid promoter closing rate coupled to a rapid activation rate, [with an efficiency such that only 70% of inactive cells are activated at any instant].
Consider this process governed by a single regulatory unit, that is to say, a single enhancer. The number of cells activated during the appropriate time window (which is set by the promoter closing rate) is at best Poisson with mean N = n*N_tot cells, where n is the active fraction. If there are 100 responding cells and 70% should be active at any time, then n = .7 and N = 70. This process will have a variance of 70, and thus a standard deviation of root 70, or ~8. The probability of observing more than 80 cells active is given by the 1-cdf of the poisson at 80. This is equivelantly the upper incomplete gamma function(80,floor(70)). Similarly, the probability of observing less than 60 cells active is given by the lower incomplete gamma function at 60, which are 12 and 11% respectively.
Now consider two independent enhancer regulating this same gene. Still Poisson, same mean rate. Standard deviation can reduce by sqrt(2) as previously discussed.