Loops Within Loops: Optimal Distribution Networks and Leaf Vein Architecture

自爱迪生时代以来，人们就知道，要想最佳地分配可替代商品（如电或水），需要由干线、干线和子公司组成的分层系统。从这个意义上讲，大多数生物分布网络都是分层的，它们的元素大小差别很大。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，或蜻蜓翅膀的静脉，都有织物般的纹理。这样的网络不仅包含从源头出发的最直接路线的链接，而且还包含许多交叉支撑连接，即使在元件损坏或暂时阻塞时，它也能继续运行，并且在只有部分生物体需要好的时候，它能最大限度地发挥能力。交叉支撑的连接形成了封闭的环路，它们本身是分层的，所以网络看起来像嵌在大环路中的小环路，不像高速公路、大道、街道和小巷的网络。该项目将发展这种环形分层体系结构的理论，特别强调理解如何在最小成本、抗损坏、抗波动载荷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，从而产生在自然界中观察到的复杂、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，从其架构中读出形成它的特定成本组合。这些方法将应用于一个大型的树叶数据库，试图将它们的建筑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，并通过实验对其性能进行表征。这个项目的新理论和实验数据将阐明我们不仅对植物界的理解，而且对我们自己的维管系统的设计原则的理解。拟议的研究将直接为高中学生、本科生和研究生以及博士后研究人员的教育和推广项目做出贡献。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本计划的优先事项。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中。

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.