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| Natural physical networks are continuous, three-dimensional objects, like the small mathematical model displayed here. Researchers have found that physical networks in living systems follow rules borrowed from string theory, a theoretical physics framework. Illustration Credit: Xiangyi Meng/RPI |
For more than a century, scientists have wondered why physical structures like blood vessels, neurons, tree branches, and other biological networks look the way they do. The prevailing theory held that nature simply builds these systems as efficiently as possible, minimizing the amount of material needed. But in the past, when researchers tested these networks against traditional mathematical optimization theories, the predictions consistently fell short.
The problem, it turns out, was that scientists were thinking in one dimension when they should have been thinking in three. "We were treating these structures like wire diagrams," Rensselaer Polytechnic Institute (RPI) physicist Xiangyi Meng, Ph.D., explains. "But they're not thin wires, they're three-dimensional physical objects with surfaces that must connect smoothly."
This month, Meng and colleagues published a paper in the journal Nature showing that physical networks in living systems follow rules borrowed from an unlikely source: string theory, the exotic branch of physics that attempts to explain the fundamental structure of the universe.
The work represents the first time string theory — a framework developed to unify quantum mechanics and gravity — has successfully described real biological structures. While string theory remains unverified as a description of fundamental physics, its mathematical machinery proves unexpectedly practical for understanding how life organizes itself in three-dimensional space.
“There seems to be a universal rule governing the formation of biological networks,” Meng said. “This optimization rule is purely geometric. It does not care about types of materials or tasks, and it turns out to be quite universal and applicable to many different datasets.”
In the 1980s, physicists wrestling with the mathematics of vibrating strings in higher dimensions developed sophisticated tools to calculate "minimal surfaces" — the smoothest, most efficient way to connect objects in space. These same equations, Meng and his colleagues discovered, almost perfectly describe how biological networks minimize their material costs.
Traditional mathematical models, for instance, predict biological networks that rely heavily on bifurcations, or two-way splits. But as anyone who’s looked at the branch structure of a tree could tell you, three-way, four-way and other types of junctions are quite common in nature.
String theory’s surface minimization principles, by contrast, allow for these higher-order splits. They also predict "orthogonal sprouts,” essentially thinner, dead-end buds that commonly appear in natural structures like plants and neurons. In the human brain, for instance, 98 percent of these perpendicular sprouts terminate in synapses — the connection points between neurons. The sprouts essentially allow neurons to reach out and connect with neighbors using the least amount of biological material. Similarly, plant roots and fungal threads sprout perpendicularly to explore soil more efficiently for water and nutrients.
The researchers tested their theory against high-resolution 3D scans of six different types of networks: human and fruit fly neurons, human blood vessels, tropical trees, corals, and the plant Arabidopsis, a type of cress commonly studied by biologists. In every case, the branching patterns matched the predictions of surface minimization better than older theories based on simple wiring minimization.
This doesn't mean that every detail of these networks is explained by physics alone. Biological systems face many competing pressures, and the researchers found that real-world networks can be up to 25 percent longer than the absolute minimum predicted by the theory. But the consistency of branching patterns across such diverse life forms suggests that nature has converged on mathematical principles that hold across the tree of life.
"These results demonstrate and provide a fascinating example how the abstract toolbox of theoretical physics can also bring us closer to solving real-world problems, such as exploring and better understanding the connectivity patterns in the brain and vascular networks,” said Gyorgy Korniss, Ph.D., head of RPI’s Department of Physics, Applied Physics and Astronomy.
The findings may eventually help engineers design better artificial networks, from 3D-printed tissues with working blood vessels to more efficient transportation systems. But perhaps the deeper lesson is about nature's economy: evolution often adheres to the same mathematical principles that physicists find when studying the universe itself.
Published in journal: Nature
Title: Surface optimization governs the local design of physical networks
Authors: Xiangyi Meng, Benjamin Piazza, Csaba Both, Baruch Barzel, and Albert-László Barabási
Source/Credit: Rensselaer Polytechnic Institute
Reference Number: phy010726_01
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