Intrinsic noise in post-transcriptional gene regulation by small non-coding RNA

Small non-coding RNA (sRNA) plays very important role in the post transcriptional regulation in various organisms. In complex regulatory networks, highly significant relative fluctuations in RNAs copy numbers can not be neglected due to very small copy number of individual RNA molecules. Here we consider two simple regulation schemes, where one is single target gene regulated by a sRNA and the other is two target mRNAs (mRNAR and mRNAT) regulated by one sRNA. The Fano factor (a measure of the relative size of the internal fluctuations) formulae of RNA molecules in the post transcriptional regulation are theoretically derived by using of the Langevin theory. For single target gene regulated by a sRNA, it is shown that the intrinsic noise of both mRNA and sRNA approaches the bare Poissonian limit in the regimen of both target RNA silencing and surviving. However, the strong anti-correlation between the fluctuations of two components result in a large intrinsic fluctuations in the level of RNA molecules in the regimen of crossover. For two target mRNAs regulated by one sRNA, in the regimen of crossover, it is found that, with the increasing of transcription rate of target mRNAT, the maximal intrinsic fluctuation of RNA molecules is shifted from sRNA to target mRNAR, and then to target mRNAT. The intrinsic noise intensity of target mRNAR is determined by both the transcriptional rate of itself and that of sRNA, and independent of the transcriptional rate of the other target mRNAT.