Mathematical approach to nonlocal interactions using a reaction-diffusion system
Mathematical approach to nonlocal interactions using a reaction-diffusion system
复制标题
使用反应扩散系统的非局域相互作用的数学方法
DOI：
10.1111/dgd.12354
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
and H. Ninomiya
中科院分区：
文献类型：
--
作者：
Y. Tanaka;H. Yamamoto;and H. Ninomiya
近年来，由于分子事件和信号网络等微观信息的整合，在发育过程中引入了空间远程相互作用。它们通常被称为非局部相互作用。如果非局部相互作用的轮廓是由实验确定的，我们可以很容易地研究在没有详细微观事件的情况下如何通过数值模拟产生模式。因此，非局部相互作用是理解复杂生物系统的有用工具。然而，由于信息的集成，非局部相互作用往往不方便观察特定的机制。因此，我们提出了一种新的方法，可以将非局部相互作用转化为具有辅助未知变量的反应-扩散系统。在这篇综述中，通过介绍与非局部相互作用相关的生物学和数学研究，我们将利用反应-扩散系统提出对非局部相互作用的启发式理解。
In recent years, spatial long range interactions during developmental processes have been introduced as a result of the integration of microscopic information, such as molecular events and signaling networks. They are often called nonlocal interactions. If the profile of a nonlocal interaction is determined by experiments, we can easily investigate how patterns generate by numerical simulations without detailed microscopic events. Thus, nonlocal interactions are useful tools to understand complex biosystems. However, nonlocal interactions are often inconvenient for observing specific mechanisms because of the integration of information. Accordingly, we proposed a new method that could convert nonlocal interactions into a reaction‐diffusion system with auxiliary unknown variables. In this review, by introducing biological and mathematical studies related to nonlocal interactions, we will present the heuristic understanding of nonlocal interactions using a reaction‐diffusion system.