The role of time delays in P53 gene regulatory network stimulated by growth factor

1.
Department of Mathematics, Yunnan Normal University, Kunming, 650500, China
2.
Department of Dynamics and Control, Beihang University, Beijing 100191, China

Received: 20 February 2020 Accepted: 21 May 2020 Published: 25 May 2020

Abstract
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In this paper, a delayed mathematical model for the P53-Mdm2 network is developed. The P53-Mdm2 network we study is triggered by growth factor instead of DNA damage and the amount of DNA damage is regarded as zero. We study the influences of time delays, growth factor and other important chemical reaction rates on the dynamic behaviors in the system. It is shown that the time delay is a critical factor and its length determines the period, amplitude and stability of the P53 oscillation. Furthermore, as for some important chemical reaction rates, we also obtain some interesting results through numerical simulation. Especially, S (growth factor), k₃ (rate constant for Mdm2_p dephosphorylation), k₁₀ (basal expression of PTEN) and k₁₄ (Rate constant for PTEN-induced Akt dephosphorylation) could undermine the dynamic behavior of the system in different degree. These findings are expected to understand the mechanisms of action of several carcinogenic and tumor suppressor factors in humans under normal conditions.
- growth factor,
- P53-Mdm2 network,
- time delays,
- Hopf bifurcation,
- oscillation
Citation: Changyong Dai, Haihong Liu, Fang Yan. The role of time delays in P53 gene regulatory network stimulated by growth factor[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 3794-3835. doi: 10.3934/mbe.2020213

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Abstract

In this paper, a delayed mathematical model for the P53-Mdm2 network is developed. The P53-Mdm2 network we study is triggered by growth factor instead of DNA damage and the amount of DNA damage is regarded as zero. We study the influences of time delays, growth factor and other important chemical reaction rates on the dynamic behaviors in the system. It is shown that the time delay is a critical factor and its length determines the period, amplitude and stability of the P53 oscillation. Furthermore, as for some important chemical reaction rates, we also obtain some interesting results through numerical simulation. Especially, S (growth factor), k₃ (rate constant for Mdm2_p dephosphorylation), k₁₀ (basal expression of PTEN) and k₁₄ (Rate constant for PTEN-induced Akt dephosphorylation) could undermine the dynamic behavior of the system in different degree. These findings are expected to understand the mechanisms of action of several carcinogenic and tumor suppressor factors in humans under normal conditions.

References

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