A reaction diffusion model for understanding phyllotactic formation
A reaction diffusion model for understanding phyllotactic formation
复制标题
用于理解叶序形成的反应扩散模型
DOI：
10.1007/s13160-015-0202-8
复制
发表时间：
2016
影响因子：
0.9
通讯作者：
M. Mimura and H. Ninomiya
中科院分区：
文献类型：
--
作者：
Y. Tanaka;M. Mimura and H. Ninomiya
众所周知，植物的叶序格局与黄金分割率有关。实际上，许多数学模型使用的理论抑制效应被提出来重现这些叶序格局。1996年，Douady和Couder引入了一个利用磁排斥的模型，并成功地在数值上再现了叶序图案。另一方面，最近在生物学实验中揭示，植物激素生长素作为激活剂调节叶序形成（Reinhardt et al.，自然426：255-260，2003年）。因此，生长素对植物根尖的抑制作用与生长素的作用有着密切的关系，本文提出了一个反应扩散模型，该模型考虑了生长素在植物根尖中的行为。奇异极限分析表明了Douady和Couder模型与本文模型之间的关系。给出了抑制效应对应的势函数和分岔图。
Phyllotactic patterns in plants are well known to be related to the golden ratio. Actually, many mathematical models using the theoretical inhibitory effect were proposed to reproduce these phyllotactic patterns. In 1996, Douady and Couder introduced a model using magnetic repulsion and succeeded in reproducing phyllotactic patterns numerically. On the other hand, it was recently revealed in biological experiments that a plant hormone, auxin, regulates the phyllotactic formation as an activator (Reinhardt et al., Nature 426:255–260, 2003). Then, there arises a natural question as tohow the inhibitory effect can be related to the auxin.In this paper, a reaction diffusion model is proposed by taking account of auxin behavior in plant tips. The relationship between Douady and Couder’s model and our model is shown by singular limit analysis. It also provides us with the potential function corresponding to the inhibitory effect, and the bifurcation diagram.