Modeling RNA interference in mammalian cells

Background: RNA interference (RNAi) is a regulatory cellular process that controls post-postranscriptional gene silencing. During RNAi double-doubletranded RNA (dsRNA) induces sequence-sequencepecific degradation of homologous mRNA via the generation of smaller dsRNA oligomers of length between 21-23nt (siRNAs). siRNAs are then loaded onto the RNA-Induced Silencing multiprotein Complex (RISC), which uses the siRNA antisense strand to specifically recognize mRNA species which exhibit a complementary sequence. Once the siRNA loaded-RISC binds the target mRNA, the mRNA is cleaved and degraded, and the siRNA loaded-RISC can degrade additional mRNA molecules. Despite the widespread use of siRNAs for gene silencing, and the importance of dosage for its efficiency and to avoid off target effects, none of the numerous mathematical models proposed in literature was validated to quantitatively capture the effects of RNAi on the target mRNA degradation for different concentrations of siRNAs. Here, we address this pressing open problem performing in vitro experiments of RNAi in mammalian cells and testing and comparing different mathematical models fitting experimental data to in-inilico generated data. We performed in vitro experiments in human and hamster cell lines constitutively expressing respectively EGFP protein or tTA protein, measuring both mRNA levels, by quantitative Real-Time PCR, and protein levels, by FACS analysis, for a large range of concentrations of siRNA oligomers. Results: We tested and validated four different mathematical models of RNA interference by quantitatively fitting models' parameters to best capture the in vitro experimental data. We show that a simple Hill kinetic model is the most efficient way to model RNA interference. Our experimental and modeling findings clearly show that the RNAi-mediated degradation of mRNA is subject to saturation effects. Conclusions: Our model has a simple mathematical form, amenable to analytical investigations and a small set of parameters with an intuitive physical meaning, that makes it a unique and reliable mathematical tool. The findings here presented will be a useful instrument for better understanding RNAi biology and as modelling tool in Systems and Synthetic Biology.