Mathematical analysis of a generalised p53-Mdm2 protein gene expression model

被引：7

作者：

Piotrowska, Monika J. ^{[1
]}

Bartlomiejczyk, Agnieszka ^{[2
]}

Bodnar, Marek ^{[1
]}

机构：

[1] Univ Warsaw, Inst Appl Math & Mech, Fac Math Informat & Mech, Banacha 2, PL-02097 Warsaw, Poland

[2] Gdansk Univ Technol, Fac Tech Phys & Appl Math, G Narutowicza 11-12, PL-80233 Gdansk, Poland

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 328卷

关键词：

Delay differential equations; Stability analysis; Hopf bifurcation; p53; protein; TUMOR-SUPPRESSOR PROTEIN; DNA-DAMAGE RESPONSE; KAPPA-B SYSTEMS; EXPLORING MECHANISMS; FEEDBACK LOOP; P53; PULSES; OSCILLATIONS; DYNAMICS; CELLS; APOPTOSIS;

D O I：

10.1016/j.amc.2018.01.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose the generalisation of the p53-Mdm2 protein gene expression model introduced by Monk (2003). We investigate the stability of a unique positive steady state and formulate conditions which guarantee the occurrence of the Hopf bifurcation. We show that oscillatory behaviour can be caused not only by time lag in protein transcription process, but also can be present in the model without time delay. Moreover, we investigate the stability of new born periodic solutions. Theoretical results are illustrated by numerical simulations and interpreted from the biological point of view. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：26 / 44

页数：19

共 36 条

[1] Generation of oscillations by the p53-Mdm2 feedback loop: A theoretical and experimental study [J].