Kramer E M
Physics Department, Simon's Rock College, Great Barrington, MA, 01230, USA.
J Theor Biol. 2001 Feb 21;208(4):387-97. doi: 10.1006/jtbi.2000.2220.
A mathematical model is presented to describe the coupling between the concentration of indole-3-acetic acid (IAA) in the cambial region of a tree branch and the radial expansion of the branch during active growth. The main features of the model are (1) the branch cambium is treated as an approximately cylindrical surface of negligible thickness, (2) the rate of radial growth is proportional to the mass of IAA per unit area on the cambial surface, and (3) IAA is transported basipetally through the cambium at a constant speed. We neglect the role of elastic strains in the determination of branch shape, and the effects of IAA synthesis and metabolization in the cambium, so the model is not quantitatively accurate. However, the model does reproduce several important qualitative features of tree growth including the approximate area-preserving property of tree branch junctions and the ability of a branch to maintain its shape despite perturbations due to injury.
提出了一个数学模型，用于描述树枝形成层区域中吲哚 - 3 - 乙酸（IAA）浓度与活跃生长期间树枝径向扩展之间的耦合关系。该模型的主要特点是：（1）将树枝形成层视为厚度可忽略不计的近似圆柱形表面；（2）径向生长速率与形成层表面单位面积上的IAA质量成正比；（3）IAA以恒定速度通过形成层向基部运输。我们忽略了弹性应变在确定树枝形状中的作用以及形成层中IAA合成和代谢的影响，因此该模型在数量上并不精确。然而，该模型确实再现了树木生长的几个重要定性特征，包括树枝连接处近似的面积守恒特性以及树枝在受到损伤引起的扰动时保持其形状的能力。
