Before revision:  Further, we show analytically and verify numerically that when enzyme copy-numbers fluctuate  the strength of substrate fluctuations increases linearly with the RNA transcription rate.
After revision:  In this case, solely fluctuations in the timing of RNA processing lead to variation in the number of RNA molecules. However, we show analytically and verify numerically that when enzyme copy-numbers fluctuate the strength of substrate fluctuations increases linearly with the RNA transcription rate.