MONOTONIC DYNAMICS OF MRNA DEGRADATION BY TWO PATHWAYS

Jianshe Yu; Xuejie Liu

doi:10.11948/2017097

2017 Volume 7 Issue 4

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Jianshe Yu, Xuejie Liu. MONOTONIC DYNAMICS OF MRNA DEGRADATION BY TWO PATHWAYS[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1598-1612. doi: 10.11948/2017097

Citation:

Jianshe Yu, Xuejie Liu. MONOTONIC DYNAMICS OF MRNA DEGRADATION BY TWO PATHWAYS[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1598-1612. doi: 10.11948/2017097

MONOTONIC DYNAMICS OF MRNA DEGRADATION BY TWO PATHWAYS

Jianshe Yu¹,
Xuejie Liu^1,2

1 Research Center of Applied Mathematics, Guangzhou University, 230 Guangzhou University City Outer Ring Road, 510006 Guangzhou, China;
2 School of Mathematics and Statistics, Shaoguan University, 512005 Shaoguan, China

Fund Project:

Abstract

Abstract

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 5' → 3' and 3' → 5' for short, where there are two degradation rates δ₁, δ₂ on 5' → 3' pathway and the degradation rate on 3' → 5' pathway is δ₃. The advantage of this model is that it captures fundamental biochemical reactions in the gene expression process in eukaryotic cells. 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 κ, but is strictly decreasing in γ, where p,κ and γ are the initial activation frequency, the activation rate, and the inactivation rate, respectively,(2) the newly mean level is strictly decreasing in both δ₂ and δ₃, remarkably, is strictly increasing in δ₁ when δ₂<δ₃ and decreasing when δ₂>δ₃ and,(3) the newly mean level is strictly increasing in time t when p<κ=(κ + γ). These conclusions not only provide a better understanding on gene expression dynamics but also would be helpful to design reasonable gene expression modules.
- Monotonic dynamics /
- mRNA degradation /
- model /
- two pathways
MSC: 92C40;60J20;37H10

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References

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