Extrinsic Noise Suppression in Micro RNA Mediated Incoherent Feedforward Loops

MicroRNA mediated incoherent feed forward loops (IFFLs) are recurrent network motifs in mammalian cells and have been a topic of study for their noise rejection and buffering properties. Previous work showed that IFFLs can adapt to varying promoter activity and are less prone to noise than similar circuits without the feed forward loop. Furthermore, it has been shown that microRNAs are better at rejecting extrinsic noise than intrinsic noise. This work studies the biological mechanisms that lead to extrinsic noise rejection for microRNA mediated feed forward network motifs. Specifically, we compare the effects of microRNA-induced mRNA degradation and translational inhibition on extrinsic noise rejection, and identify the parameter regimes where noise is most efficiently rejected. In the case of static extrinsic noise, we find that translational inhibition can expand the regime of extrinsic noise rejection. We then analyze rejection of dynamic extrinsic noise in the case of a single-gene feed forward loop (sgFFL), a special case of the IFFL motif where the microRNA and target mRNA are co-expressed. For this special case, we demonstrate that depending on the time-scale of fluctuations in the extrinsic variable compared to the mRN $A$ and microRNA decay rates, the feed forward loop can both buffer or amplify fluctuations in gene product copy numbers.