Origin of the extrinsic noise floor in gene expression
In plain words
Genetically identical cells contain different amounts of each protein. For highly expressed proteins this variation stops shrinking at a floor that random chemistry at a single gene does not explain.
Precise statement
In E. coli, the squared coefficient of variation of protein copy number, $\mathrm{CV}^{2}$, falls as $1/\langle n\rangle$ at low mean copy number $\langle n\rangle$ but saturates at a floor of approximately 0.1 for highly expressed genes (Taniguchi and co-workers, 2010). Identify the cell-to-cell variables responsible (cell size, growth rate, cell-cycle phase, ribosome and polymerase content, partitioning at division) and predict the floor value quantitatively.
What would settle it
Single-cell measurements that track the candidate global variables alongside protein levels and account for the floor value within experimental error.