The chemical dynamics of organ positioning in conifer development

虽然数学一直被用来描述植物的模式（例如，在侧面器官排列中观察到的斐波那契数，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模式植物拟南芥中激素生长素（局部生长的主要决定因素）的空间分布。***我们的工作重点是针叶树形态发生中发育模式和生长的独特动态方面。拟南芥有两个子叶（“种子叶”），呈平面排列；针叶树有不同的数量（通常从2到12），它们在圆顶几何形状上形成一个螺旋。因此针叶树子叶可以具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）。我们使用反应扩散（RD）模型来表征三维表面上的浓度模式，该模式与局部生长相结合，代表了针叶树轮定位的对称性破坏机制。我们研究了图案对实验观察到的圆顶扁平的几何依赖性，并扩展了早期的理论思想，即圆顶几何形状上的螺旋结构分两个阶段形成——第一阶段定位轮，第二阶段将轮细分为子叶。在实验中，我们发现云杉有两个这样的阶段，它们被生长素运输的中断所分离。***我们现在计划将独特的“向上梯度”极性生长素运输（PAT）动力学（在拟南芥中发现）纳入我们的3D模型。这解决了针叶树的几何形状和局部生长（不包含在任何拟南芥模型中），也将产生一个新的，连续的PAT公式（先前的模型是基于细胞和离散的）。有限元计算和数学分析将用于寻找RD和PAT（在生长域）在针叶树子叶形成中的相对贡献（包括对特定反应非线性的依赖）。生长素分布的新三维实验数据将改进模型动力学。***对领域的好处：推进植物科学中的新数学技术；培养跨学科的科学家；利用最近在拟南芥中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、定量生物学方面的专业知识，以获得对针叶树发展的定量理解和控制，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).*****************