  RNA molecules follow a succession of enzyme-mediated processing steps from
transcription until maturation. The participating enzymes, for example the
spliceosome for mRNAs and Drosha and Dicer for microRNAs, are also produced in
the cell and their copy-numbers fluctuate over time. Enzyme copy-number changes
affect the processing rate of the substrate molecules; high enzyme numbers
increase the processing probability, low enzyme numbers decrease it. We study
different RNA processing cascades where enzyme copy-numbers are either fixed or
fluctuate. We find that for fixed enzyme-copy numbers the substrates at
steady-state are Poisson-distributed, and the whole RNA cascade dynamics can be
understood as a single birth-death process of the mature RNA product. 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 numerically that
when enzyme copy-numbers fluctuate, the strength of RNA fluctuations increases
linearly with the RNA transcription rate. This linear effect becomes stronger
as the speed of enzyme dynamics decreases relative to the speed of RNA
dynamics. Interestingly, we find that under certain conditions, the RNA cascade
can reduce the strength of fluctuations in the expression level of the mature
RNA product. Finally, by investigating the effects of processing polymorphisms
we show that it is possible for the effects of transcriptional polymorphisms to
be enhanced, reduced, or even reversed. Our results provide a framework to
understand the dynamics of RNA processing.
