Mathematics Department, British Columbia Institute of Technology, Burnaby, B.C., Canada.
Biology Department, University of Victoria, Victoria, B.C., Canada.
Ann Bot. 2018 Mar 5;121(3):525-534. doi: 10.1093/aob/mcx185.
Conifer embryos, unlike those of monocots or dicots, have variable numbers of cotyledons, even within the same species. Cotyledons form in a single whorl on a dome-shaped embryo. The closely spaced cotyledons are not found outside this ring, indicating a radial control on where they can form. Polar transport of the hormone auxin affects outgrowth of distinct cotyledons, but not the radial aspect of the whorl or the within-whorl spacing between cotyledons. A quantitative model of plant growth regulator patterning is needed to understand the dynamics of this complex morphogenetic process.
A two-stage reaction-diffusion model is developed for the spatial patterning of growth regulators on the embryo surface, with a radial pattern (P1) constraining the shorter-wavelength cotyledon pattern (P2) to a whorl. These patterns drive three-dimensional (3-D) morphogenesis by catalysing local surface growth.
Growth driven by P2 generates single whorls across the experimentally observed range of two to 11 cotyledons, as well as the circularly symmetric response to auxin transport interference. These computations are the first corroboration of earlier theoretical proposals for hierarchical control of whorl formation. The model generates the linear relationship between cotyledon number and embryo diameter observed experimentally. This accounts for normal integer cotyledon number selection, as well as the less common cotyledon fusings and splittings observed experimentally. Flattening of the embryo during development may affect the upward outgrowth angle of the cotyledons.
Cotyledon morphogenesis is more complex geometrically in conifers than in angiosperms, involving 2-D patterning which deforms a surface in three dimensions. This work develops a quantitative framework for understanding the growth and patterning dynamics involved in conifer cotyledon development, and applies more generally to the morphogenesis of whorls with many primordia.
与单子叶植物或双子叶植物不同,针叶植物的胚具有可变数量的子叶,甚至在同一物种内也是如此。子叶在一个穹顶形胚上形成一个单独的轮。密集排列的子叶不在这个环之外发现,表明它们可以形成的位置受到径向控制。激素生长素的极性运输影响不同子叶的生长,但不影响轮的径向方面或子叶之间的轮内间距。需要一种植物生长调节剂模式的定量模型来理解这个复杂形态发生过程的动态。
为了在胚胎表面上生长调节剂的空间模式,开发了一个两阶段的反应扩散模型,一个径向模式(P1)将较短波长的子叶模式(P2)约束在一个轮上。这些模式通过催化局部表面生长来驱动三维(3-D)形态发生。
由 P2 驱动的生长在实验观察到的两个到十一个子叶的范围内生成单个轮,以及对生长素运输干扰的圆形对称响应。这些计算是对轮形成的层次控制的早期理论建议的首次验证。该模型生成了实验观察到的子叶数量与胚胎直径之间的线性关系。这解释了正常整数子叶数量的选择,以及实验中观察到的较少常见的子叶融合和分裂。在发育过程中胚胎的扁平化可能会影响子叶的向上生长角度。
与被子植物相比,针叶植物的子叶形态发生在几何上更为复杂,涉及到 2-D 模式,它在三维空间中变形表面。这项工作为理解针叶植物子叶发育中涉及的生长和模式动态提供了一个定量框架,并更普遍地适用于具有许多原基的轮的形态发生。