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Monotonic dynamics of mrna degradation by two pathways
Keywords:Monotonic dynamics; mRNA degradation; model; Two pathways.
      mRNA degradation plays an important role in gene regulation. However, a defect in mRNA decay is expected to result in an increase in mRNA levels. In this paper, we will first establish a model of mRNA regulation by two pathways denoted by 3′ → 5′ and 5′ → 3′ for short, where there are two decaying rates 1, 2 on 5′ → 3′ pathway and the decaying rate on 3′ → 5′ pathway is 3. The advantage of this model is that it captures fundamental biochemical reactions in the gene expression process in eukaryotic cells. And then we obtain several basic principles on the monotonicity of the mean level of newly accumulated mRNAs. It is proved that(1) the newly mean level is strictly increasing in p and , but is strictly decreasing in , here p;  and are the initial activation frequency, the activation rate and the inactivation rate, respectively;(2) the newly mean level is strictly decreasing in both 2 and 3, remarkably, is strictly increasing in 1 when 2 < 3 and decreasing when 2 > 3 and (3) the newly mean level is strictly increasing in time t when p < =( + ).These conclusions not only provide a better understanding on gene expression dynamics but also would be helpful to design reasonable gene expression modules.