Developing Pareto front models for the improved description of plant's dynamic root system architecture

利用野生番茄砧木来提高栽培番茄的生产力和环境适应能力。通过将根结构评价为一个网络，可以区分野生番茄在视觉上不同的根形状。在这个网络中，吸收水分和营养的侧根尖需要连接到支持幼苗生长的根基部。这种网络设计考虑了两个相互竞争的目标：最小化网络的构建块（成本）和最小化从根尖到根基的传输时间（速度）。为了提高模型与植物生理的相关性，该模型将被扩展到包括重力的影响，并考虑到主根和侧根之间的解剖差异。为了确定根网络设计背后的基因，我们将使用遗传方法并产生突变植物，这些突变植物将被评估网络效率、植物生产力和恢复力。了解植物结构背后的数学和遗传机制将有助于设计出具有更高生产力和抗逆性的更好的作物，从而有助于提高粮食生产的可持续性。此外，对生物网络及其生长方式的更好理解可以应用于交通网络，使交通系统随着人口增长而自然扩展。本项目将开发解释和优化自然运输网络结构的方法，例如野生番茄植物的根系结构。最初的工作将包括开发一个数值优化算法，用于构造受非线性约束的最小欧几里得斯坦纳树。我们将应用欧几里得斯坦纳树算法来量化番茄根系结构如何优化节约材料成本和确保有效的养分和水分运输之间的权衡，特别是当生长轨迹受到重力和根系解剖差异所施加的差异成本/运输质量的限制时。我们还将研究根结构生长的测量，以使用纯分布式计算对构建最佳斯坦纳树的算法进行逆向工程。我们的目标是利用正向遗传学来确定在非胁迫和盐胁迫条件下发展最佳结构的遗传成分。确定的算法、理想型和遗传机制将作为植物育种和基因工程抗逆性作物的目标。我们期望我们开发的方法可以推广到其他自然和工程系统中发现的交通网络的解释、设计和优化。在未来，我们的工作可以为设计有效扩展的公共交通网络提供见解。该项目由生物科学理事会数学科学部、数学生物学计划和综合有机系统部、植物基因组研究计划（PGRP）共同资助。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Wild tomato root stocks are used to enhance cultivated tomato productivity and environmental resilience. Visually distinct root shapes of wild tomato can be distinguished by evaluating the root architecture as a network in which lateral root tips, which absorb water and nutrients, need to be connected to the root base, which supports shoot growth. This network design considers two competing objectives: minimizing the building blocks of a network (cost) and minimizing the transport time from root tips to root base (speed). To improve the relevance of the model to the physiology of plants, the model will be expanded to include the effects of gravitational forces and account for anatomical differences between the main and lateral roots. To identify the genes underlying root network design, we will use genetic approaches and generate mutant plants that will be evaluated for network efficiency, as well as plant productivity and resilience. Understanding mathematical and genetic mechanisms underlying plant architecture will lead to designing better crops with improved productivity and stress resilience, thereby contributing to increased sustainability of food production. Additionally, an improved understanding of biological networks and how they grow can be applied to transportation networks, allowing transit systems to naturally scale with population growth.This project will develop methods for explaining and optimizing the structure of natural transportation networks, such as the root system architecture of wild tomato plants. Initial work will involve developing a numerical optimization algorithm for constructing minimal Euclidean Steiner trees that are subjected to non-linear constraints. We will apply the Euclidean Steiner tree algorithms towards quantifying how tomato root architectures optimize trade-offs between conserving material costs and ensuring efficient nutrient and water transport, especially when growth trajectories are constrained by gravitational forces and differential cost/transport qualities imposed by the differences in root anatomy. We will also study measurements of root architecture growth to reverse-engineer an algorithm for constructing optimal Steiner trees using purely distributed computation. Our goal is to use forward genetics to identify genetic components underlying the development of optimal architectures under non-stress and salt stress conditions. The identified algorithms, ideotypes and genetic mechanisms will serve as targets for plant breeding and genetically engineering stress-resilient crops. We anticipate that the methods we develop can be generalized towards explaining, designing, and optimizing transportation networks found in other natural and engineered systems. In the future, our work can provide insight into designing public transport networks that scale efficiently.This project is jointly funded by the Division of Mathematical Sciences, Mathematical Biology Program and the Division of Integrative Organismal Systems, Plant Genome Research Program (PGRP) in the Directorate for Biological Sciences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.