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Background  As a highly efficient and specific gene regulation technology, RNAi has broad application fields and good prospects. The effect of RNAi enhances as the dosage of siRNA increases, while an exorbitant siRNA dosage will inhibit the RNAi effect. So it is crucial to formulate a dose-effect model to describe the degradation effects of the target mRNA at different siRNA dosages.    Results  In this work, a simple RNA interference model with hill kinetic function (Giulia Cuccato et al. (2011)) is extended. Firstly, by introducing both the degradation time delay  τ  1  of mRNA caused by siRNA and the transportation time delay  τ  2  of mRNA from the nucleus to the cytoplasm during protein translation, one acquires a novel delay differential equations (DDEs) model with physiology lags. Secondly, qualitative analyses are executed to identify regions of stability of the positive equilibrium and to determine the corresponding parameter scales. Next, the approximate period of the limit cycle at Hopf bifurcation points is computed. Furthermore we analyze the parameter sensitivity of the limit cycle. Finally, we propose an optimal strategy to select siRNA dosage which arouses significant silencing efficiency.    Conclusions  Our researches indicate that when the dosage of siRNA is large, oscillating periods are identical for disparate number of siRNA target sites even if it greatly impacts the critical siRNA dosage which is the switch of oscillating behavior. Furthermore, parametric sensitivity analyses of limit cycle disclose that both of degradation lag and maximum degradation rate of mRNA due to RNAi are principal elements on determining periodic oscillation. Our explorations will provide evidence for gene regulation and RNAi.

Periodicity and dosage optimization of an RNAi model in eukaryotes cells