NSF Award
1058899
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. <br/><br/>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. <br/><br/>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.
