The chemical dynamics of organ positioning in conifer development

虽然长期以来，数学一直被用来描述植物的模式(例如，在侧向器官排列中观察到的斐波纳契数，如松果)，但最近分子成像的发展促使生物学中越来越多的人认识到，植物发育的许多方面本质上是定量的(如器官间距、植物形状和结构)，需要数学理论来解释潜在的分子机制。许多新的定量和数学工作都是关于激素生长素(局部生长的主要决定因素)在模式植物拟南芥中的空间分布。 我们的工作集中在针叶树形态发生中发育模式和生长的独特动力学方面。拟南芥有两个子叶(种子叶)，形成平面排列；针叶树有可变的数目(通常从2到12个)，在圆顶的几何形状上形成轮生。因此，针叶树子叶可以有更复杂的空间模式(即生长催化剂模式的高阶模式；更复杂的模式选择以产生轮生形态发生)。我们使用反应-扩散(RD)模型来表征三维表面的浓度图案，它与局部生长相结合，代表了定位针叶树轮生的对称破坏机制。我们研究了图案的几何依赖于实验观察到的穹顶展平，以及扩展了早期的理论观点，即在穹顶几何形状上形成螺纹结构分两个阶段-第一阶段定位螺纹，第二阶段将螺纹细分为子叶。在实验上，我们在云杉中发现了两个这样的阶段，这两个阶段可以通过中断生长素的运输来分离。 我们现在计划将独特的“向上梯度”的生长素极地运输(PAT)动力学(在拟南芥中发现)纳入我们的3D模型中。这解决了针叶树的几何形状和局部生长(没有包含在任何拟南芥模型中)，还将产生新的、连续的PAT公式(先前的模型是基于细胞的和离散的)。有限元计算和数学分析将被用来找出在针叶树子叶形成中RD和PAT(在生长区域上)的相对贡献(包括对特定反应非线性的依赖)。模型动力学将通过生长素分布的新的3D实验数据进行改进。 对实地的好处：推进植物科学中的新数学技术；培训跨学科科学家；利用最近在拟南芥方面的大分子和建模工作来了解针叶树。对加拿大的好处：支持加拿大在数学和数量生物学方面的专业知识，以获得对针叶树发展的定量了解和控制，针叶树对该国的生态和经济具有核心价值(林业占GDP的200亿美元，近80%的森林树种是针叶树)。

While math has long been used to describe plant patterns (e.g. the Fibonacci numbers observed in lateral organ arrangements, such as in pine cones), recent developments in molecular imaging have spurred a growing recognition in biology that many aspects of plant development are inherently quantitative (such as organ spacing, plant shape and architecture) and require mathematical theory to explain the underlying molecular mechanisms. Much of the new quantitative and mathematical work has been on the spatial distribution of the hormone auxin (a primary determinant of local growth) in the model plant Arabidopsis. Our work focuses on the unique dynamical aspects of developmental patterning and growth in conifer morphogenesis. Arabidopsis has two cotyledons (‘seed leaves’), which form in a planar arrangement; conifers have a variable number (frequently from 2 to 12), which form in a whorl on a domed geometry. Conifer cotyledons can therefore have much more complex spatial patterning (i.e. higher-order modes for growth catalyst patterns; more complex pattern selection to produce whorled morphogenesis). We have used reaction-diffusion (RD) models to characterize concentration patterning on surfaces in 3D which, coupled to local growth, represent the symmetry-breaking mechanism positioning the conifer whorls. We have studied the geometric dependence of patterning on experimentally-observed dome flattening, as well as expanding earlier theoretical ideas that whorled structures on domed geometries form in two stages - a 1st stage to position the whorl, a 2nd stage to subdivide the whorl into cotyledons. Experimentally, we have found two such stages in spruce, and that they are separable by disruption of auxin transport. We now plan to incorporate the unique ‘up-the-gradient’ polar auxin transport (PAT) dynamics (discovered in Arabidopsis) into our 3D model. This addresses conifer geometry and local growth (which are not contained in any of the Arabidopsis models), and will also produce a new, continuous formulation of PAT (prior models are cell-based and discrete). Finite-element computations and mathematical analysis will be used to find the relative contributions of RD and PAT (on a growing domain) in conifer cotyledon formation (including dependence on particular reaction nonlinearities). Model dynamics will be refined by new 3D experimental data on auxin distributions. Benefits to field: advancing new mathematical techniques in plant science; training interdisciplinary scientists; leveraging recent large molecular and modelling efforts in Arabidopsis to understand conifers. Benefits to Canada: supporting Canadian expertise in mathematical, quantitative biology to gain quantitative understanding and control of the development of conifers, which are of central value to the country’s ecology and economy (forestry is $20B of GDP, nearly 80% of forest tree species are conifers).