Oscillations in a cAMP signalling model for cell aggregation - a geometric analysis

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:483

Article

Miao, Zhouqian¹  Popovic, Nikola^2,3  Szmolyan, Peter¹ 

[1] Tech Univ Wien, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

[2] Univ Edinburgh, Sch Math, James Clerk Maxwell Bldg,Kings Bldg, Edinburgh EH9 3FD, Midlothian, Scotland

[3] Maxwell Inst Math Sci, James Clerk Maxwell Bldg,Kings Bldg, Edinburgh EH9 3FD, Midlothian, Scotland

关键词: cAMP signalling;    Singular perturbation;    Geometric singular perturbation theory;    Blow-up technique;    Relaxation oscillation;    Periodic orbit;   

DOI  :  10.1016/j.jmaa.2019.123577

来源: Elsevier

【 摘 要 】

We study a singularly perturbed model for a cyclic adenosine monophosphate (cAMP) signalling system that controls aggregation of the amoeboid microorganism Dictyostelium discoideum. The model, which is based on a classical model due to Martiel and Goldbeter [16], takes the form of a planar system of ordinary differential equations with two singular perturbation parameters which manifest very differently: while one parameter encodes the separation of scales between the slow and fast variables, the other induces a non-uniformity in the corresponding vector field in the singular limit. We apply geometric singular perturbation theory and the desingularisation technique known as blow-up to construct a family of attracting, periodic (relaxation-type) orbits; in the process, we elucidate the novel singular structure of the model, and we describe in detail the resulting oscillatory dynamics. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free