Oscillatory behavior of p53-Mdm2 system driven by transcriptional and translational time delays
作者机构：Department of MathematicsYunnan Norrmal University No.768Juxian StreetChenggong District KunmingP.R.China School of Mathermatics and Information Technology Yuci Norrmal UniversityNo.134Fenghuang Road Yuxi CityYunnan ProvinceP.R.China
出 版 物：《International Journal of Biomathematics》 (生物数学学报（英文版）)
年 卷 期：2020年第13卷第5期
页 面：63-95页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：The authors express gratitude to the anony imnous referee for his/her helpful Sug-gestions and the partial supports of the National Natural Science Foundations of China(Grants Nos.11762022,11562021 and 11572278) the youth academic and technical leaders of Yunnan Province(No.2019HB015)
主 题：Time delays stability Hopf bifurcation p53-Mdm2 pathway
摘 要：Biological experiments clarify that p53-Mdm2 module is the core of tumor network and p53 oscillation plays an important role in determining the tumor cell *** this paper,we investigate the effect of time delay on the oscillatory behavior induced by Hopf bifurcation in p53-Mdm2 ***,the stability of the unique positive equilibriurm point and the existence of Hopf bifurcation are investigated by using the time delay as the bifurcation parameter and by applying the bifurcation ***,the explicit criteria determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are developed based on the normal form theory and the center manifold *** addition,the combination of numerical simulation results and theoretical calculation results indicates that time delays in p53-Mdm2 system are critical for p53 *** results may help us to better understand the biological functions of p53 pathway and provide clues for treatment of cancer.
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