Loops Within Loops: Optimal Distribution Networks and Leaf Vein Architecture

自爱迪生时代以来，人们就知道，最佳分配可替代的商品，如电力或水，需要由干线，干线和子公司组成的分层系统。从这个意义上说，大多数生物分布网络都是分层的，它们的组成部分大小相差很大。而且，许多生物分布网络，如树叶的静脉，大脑皮层表面的小动脉，或翅膀的静脉，都有类似织物的纹理。这样的网络不仅包含从源头出发的最直接路径，而且还包含许多交叉支撑连接，使其即使在元素被损坏或暂时堵塞时也能继续发挥作用，并在只有部分有机体需要商品时最大限度地提高容量。交叉支撑的连接形成了封闭的回路，它们本身是分层的，所以网络看起来像是嵌套在更大回路中的小回路，与高速公路、大道、街道和小巷的网络没有什么不同。该项目将开发这种循环分层架构的理论，特别强调理解如何在最小成本，抗损坏，抗波动负载和最大可接受梯度的不同和经常相互冲突的要求之间进行权衡，从而产生复杂，美丽和微妙的独特模式。PI将开发数学方法，给出这种模式的自然范例，从其架构中读出塑造它的特定成本组合。这些方法将应用于大型树叶数据库，试图将它们的架构差异与环境和生理联系起来。最后，将生成这些网络的人工版本，并通过实验表征其性能。这个项目的新理论和实验数据将阐明我们的理解，不仅是植物王国，而且是我们自己的血管系统的设计原则。拟议的研究将直接有助于高中生，本科生和研究生以及博士后研究人员的教育和推广计划。这些活动将通过洛克菲勒大学正在进行的项目进行协调。促进少数民族本科生和研究生参与研究环境将是该计划的优先事项。该项目的成果将被纳入生物学学生的网络理论和高级建模的新研究生课程。

It has been known since the time of Edison that optimally distributing fungible goods, such as electricity or water, requires hierarchical systems consisting of trunks, mains and subsidiaries. Most biological distribution networks are hierarchical in this sense, and their elements come in vastly different sizes. But also, many biological distribution networks, such as the veins of a leaf, the arterioles in the surface of the cerebral cortex, or the veins of a dragonfly wing, have a fabric-like texture. Such networks do not only contain the links with the most direct route from the source, but also many cross-bracing connections, that permit it to continue functioning even when elements are damaged or temporarily clogged, and to maximize capacity when only part of the organism is demanding the good. The cross-bracing connections form closed loops, and they themselves are hierarchical, so the networks look like little loops nested within larger loops, not unlike networks of highways, avenues, streets and alleys. This project will develop the theory of such loopy hierarchical architectures, with a particular emphasis to understanding how the tradeoffs between the different and often conflicting requirements of minimal cost, resistance to damage, resistance to fluctuating loads, and maximum acceptable gradients result in the complex, beautiful and subtly distinct patterns observed in nature. The PI will develop mathematical ways, given a natural exemplar of such patterns, to read off from its the architecture the particular combination of costs that shaped it. These methods will be applied to a large database of leaves, to try to correlate their architectural differences with their environment and physiology. Finally, artificial versions of these networks will be generated and their performance characterized experimentally. New theory and experimental data from this project will illuminate our understanding, not only of the plant kingdom, but also of design principles for our own vascular systems. The proposed research will contribute directly to education and outreach programs for high school students, undergraduate and graduate students, and postdoctoral researchers. These activities will be coordinated through ongoing programs at Rockefeller University. Promoting the involvement of minority undergraduate and graduate students in research environments will be a priority of this program. Results from the project will be incorporated into novel graduate courses on network theory and advanced modeling for biology students.