Open AccessPattern dynamics of the reaction-diffusion immune system
Author(s) -
Qianqian Zheng,
Jianwei Shen,
Zhijie Wang
Publication year - 2018
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0190176
Subject(s) - reaction–diffusion system , pattern formation , turing , stability (learning theory) , computer science , biological system , mechanism (biology) , diffusion , dynamical systems theory , statistical physics , dynamics (music) , system dynamics , complex dynamics , artificial intelligence , mathematics , biology , physics , machine learning , mathematical analysis , genetics , quantum mechanics , acoustics , programming language , thermodynamics
In this paper, we will investigate the effect of diffusion, which is ubiquitous in nature, on the immune system using a reaction-diffusion model in order to understand the dynamical behavior of complex patterns and control the dynamics of different patterns. Through control theory and linear stability analysis of local equilibrium, we obtain the optimal condition under which the system loses stability and a Turing pattern occurs. By combining mathematical analysis and numerical simulation, we show the possible patterns and how these patterns evolve. In addition, we establish a bridge between the complex patterns and the biological mechanism using the results from a previous study in Nature Cell Biology. The results in this paper can help us better understand the biological significance of the immune system.