Mathematical Modeling of Plant Root Hair Initiation: Dynamics of Localized Patches
Mathematical Modeling of Plant Root Hair Initiation: Dynamics of Localized Patches
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DOI：
10.1137/120902264
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发表时间：
2014-01-01
影响因子：
2.1
通讯作者：
Ward, M. J.
中科院分区：
文献类型：
--
作者：
Brena-Medina, V.;Champneys, A. R.;Ward, M. J.
本文对Schnakenberg反应-扩散系统进行了一维数学分析，该系统具有控制活性反应的空间梯度。这个系统以前被认为是拟南芥从根表皮开始产生毛发的一个模型，这是一个关键的细胞水平形态发生问题。这个过程涉及到植物的小g蛋白（rho）的动力学，它们结合在细胞膜上形成一个单一的局部斑块，促进细胞壁软化和随后的毛发生长。数值分岔分析提出了两个关键参数，包括细胞长度和生长素催化剂的总浓度，是不同的。结果显示，从一个边界斑块到一个内部斑块，再到多个斑块，这些斑块的位置由生长素梯度精心控制。利用半强相互作用理论的渐近分析证实了这一结果，得到了斑块位置和强度的封闭表达式。对于生物真实的参数值，数值分岔结果与渐近理论非常吻合。通过基于非局部特征值问题的线性化稳定性分析，深入了解了过渡机制的起始。该结果进一步解释了最近在野生型和突变型毛细胞的模型和生物学数据之间发现的一致性。
A mathematical analysis is undertaken of a Schnakenberg reaction-diffusion system in one dimension with a spatial gradient governing the active reaction. This system has previously been proposed as a model of the initiation of hairs from the root epidermis Arabidopsis, a key cellular-level morphogenesis problem. This process involves the dynamics of the small G-proteins, Rhos of plants, which bind to form a single localized patch on the cell membrane, prompting cell wall softening and subsequent hair growth. A numerical bifurcation analysis is presented as two key parameters, involving the cell length and the overall concentration of the auxin catalyst, are varied. The results show hysteretic transitions from a boundary patch to a single interior patch, and to multiple patches whose locations are carefully controlled by the auxin gradient. The results are confirmed by an asymptotic analysis using semistrong interaction theory, leading to closed form expressions for the patch locations and intensities. A close agreement between the numerical bifurcation results and the asymptotic theory is found for biologically realistic parameter values. Insight into the initiation of transition mechanisms is obtained through a linearized stability analysis based on a nonlocal eigenvalue problem. The results provide further explanation of the recent agreement found between the model and biological data for both wild-type and mutant hair cells.