String-theory concept boosts understanding of biological networks
Many biological networks – including blood vessels and plant roots – are not organized to minimize total length, as long assumed. Instead, their geometry follows a principle of surface minimization, following a rule that is also prevalent in string theory. That is the conclusion of physicists in the US, who have created a unifying framework that explains structural features long seen in real networks but poorly captured by traditional mathematical models.
Biological transport and communication networks have fascinated scientists for decades. Neurons branch to form synapses, blood vessels split to supply tissues, and plant roots spread through soil. Since the mid-20th century, many researchers believed that evolution favours networks that minimize total length or volume.
“There is a longstanding hypothesis, going back to Cecil Murray from the 1940s, that many biological networks are optimized for their length and volume,” Albert-László Barabási of Northeastern University explains. “That is, biological networks, like the brain and the vascular systems, are built to achieve their goals with the minimal material needs.” Until recently, however, it had been difficult to characterize the complicated nature of biological networks.
Now, advances in imaging have given Barabási and colleagues a detailed 3D picture of real physical networks, from individual neurons to entire vascular systems. With these new data in hand, the researchers found that previous theories are unable to describe real networks in quantitative terms.
From graphs to surfaces
To remedy this, the team defined the problem in terms of physical networks, systems whose nodes and links have finite thickness and occupy space. Rather than treating them as abstract graphs made of idealized edges, the team models them as geometrical objects embedded in 3D space.
To do this, the researchers turned to an unexpected mathematical tool. “Our work relies on the framework of covariant closed string field theory, developed by Barton Zwiebach and others in the 1980s,” says team member Xiangyi Meng at Rensselaer Polytechnic Institute. This framework provides a correspondence between network-like graphs and smooth surfaces.
Unlike string theory, their approach is entirely classical. “These surfaces, obtained in the absence of quantum fluctuations, are precisely the minimal surfaces we seek,” Meng says. No quantum mechanics, supersymmetry, or exotic string-theory ingredients are required. “Those aspects were introduced mainly to make string theory quantum and thus do not apply to our current context.”
Using this framework, the team analysed a wide range of biological systems. “We studied human and fruit fly neurons, blood vessels, trees, corals, and plants like Arabidopsis,” says Meng. Across all these cases, a consistent pattern emerged: the geometry of the networks is better predicted by minimizing surface area rather than total length.
Complex junctions
One of the most striking outcomes of the surface-minimization framework is its ability to explain structural features that previous models cannot. Traditional length-based theories typically predict simple Y-shaped bifurcations, where one branch splits into two. Real networks, however, often display far richer geometries.
“While traditional models are limited to simple bifurcations, our framework predicts the existence of higher-order junctions and ‘orthogonal sprouts’,” explains Meng.
These include three- or four-way splits and perpendicular, dead-end offshoots. Under a surface-based principle, such features arise naturally and allow neurons to form synapses using less membrane material overall and enable plant roots to probe their environment more effectively.
Ginestra Bianconi of the UK’s Queen Mary University of London says that the key result of the new study is the demonstration that “physical networks such as the brain or vascular networks are not wired according to a principle of minimization of edge length, but rather that their geometry follows a principle of surface minimization.”
Bianconi, who was not involved in the study, also highlights the interdisciplinary leap of invoking ideas from string theory, “This is a beautiful demonstration of how basic research works”.
Interdisciplinary leap
The team emphasizes that their work is not immediately technological. “This is fundamental research, but we know that such research may one day lead to practical applications,” Barabási says. In the near term, he expects the strongest impact in neuroscience and vascular biology, where understanding wiring and morphology is essential.
Bianconi agrees that important questions remain. “The next step would be to understand whether this new principle can help us understand brain function or have an impact on our understanding of brain diseases,” she says. Surface optimization could, for example, offer new ways to interpret structural changes observed in neurological disorders.
Looking further ahead, the framework may influence the design of engineered systems. “Physical networks are also relevant for new materials systems, like metamaterials, who are also aiming to achieve functions at minimal cost,” Barabási notes. Meng points to network materials as a particularly promising area, where surface-based optimization could inspire new architectures with tailored mechanical or transport properties.
The research is described in Nature.
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