Scientists from Rensselaer Polytechnic Institute (RPI) have used mathematical concepts from string theory, a theoretical description of the mechanics of the entire universe, to upend over a century of assumptions about how living systems, such as tree roots and neurons, build their telltale branching networks.
Although the application of string theory to characterize biological systems was successful, the research team behind the study said their effort does not necessarily support the theory itself. However, the researchers noted that their work demonstrates how the abstract toolbox of theoretical physics can be applied to real-world problems, such as surface optimization.
The RPI team said their findings may also help engineers build better artificial networks, including 3D-printed tissues with working blood vessels or hyper-efficient transportation systems.
String Theory to the Rescue?
In an email to The Debrief, the study’s lead author, RPI’s Xiangyi Meng, explained that the team set out to explore the growth and structure of biological systems involving diverse materials, such as blood vessels and plants. However, the researcher explained, despite their obvious differences, these types of biological systems “all tend to follow the same surface optimization formula.”
According to the RPI team’s published study, understanding how nature maximizes efficiency when designing such systems has inspired decades of research into wiring economy. As a result, scientists have several testable predictions about the expected function and architecture of natural branching networks.
In the new study, the team explored the branching geometry underlying several such networks to test the accuracy of long-standing predictions regarding wiring minimization. Although previous efforts have tackled the same issue, the researchers said their latest effort revealed that predicting the true costs of a physical network, such as a tree branch or a brain connectome, requires accounting for the system’s “full three-dimensional geometry.”
Unfortunately, the team said this realization led to a largely intractable optimization problem. According to the study, the tools previously used to search for a solution were also coming up short. Curious if an alternative approach could solve the problem, the team turned to the physics toolkit of string theory.
“We are borrowing the sophisticated mathematical toolkit developed by string theorists and applying it to a biological context,” Meng told The Debrief.
Toolkit Results in “Excellent Agreement” with Real World Networks
According to the team’s study, when current surface-optimization theories are used to account for the full three-dimensional structure of networks, such as neurons, blood vessels, trees, corals, and roots, they fall short. Instead, they found that many biological networks do not follow the classical “minimize material” rules, as many biological systems often do.
For example, the study authors note that traditional approaches cannot explain why nature uses multiway junctions and short perpendicular “sprouts” in these design architectures. However, when the team performed an exact mapping of surface minimization onto high-dimensional Feynman diagrams used in string theory, their data showed that “with increasing link thickness, a locally tree-like network undergoes a transition into configurations that can no longer be explained by length minimization.”
The application of string theory also allowed the RPI team to predict the existence of stable orthogonal sprouts, “which are not only prevalent in real networks but also play a key functional role” in biological systems, including improving synapse formation in the brain and nutrient access in plants and fungi. When the team broadened their use of the string theory toolkit, they found that the approach outperformed traditional network-minimization theories across six biological systems, ranging from blood vessels and human neurons to fruit fly neurons and plant roots.
“Specifically, surface minimization predicts the emergence of trifurcations and branching angles in excellent agreement with the local tree organization of physical networks across a wide range of application domains,” they explained.
Using Theoretical Physics to Formulate the Architecture of Biological Systems
When asked what aspect of the research was most surprising, Meng pointed to the study’s mathematical revelations.
“I find it surprising and insightful that biological discoveries often adhere to the same mathematical principles that physicists find when studying fundamental concepts,” the researcher explained.
When discussing the implications of their work, Meng told The Debrief that their study “does not weigh in on whether string theory describes the fundamental fabric of the universe.”
“We must be cautious,” Meng told The Debrief. “Our approach does not suggest the brain is ‘quantum.’ Indeed, it utilizes mathematical tools from string theory that are applied here in the absence of any quantum fluctuations.”
Instead, the researcher said that their work simply borrowed the string theory toolkit and applied it to a biological context “in the absence of any quantum fluctuations.”
“The significance of this work lies in the bridge we build,” Meng told The Debrief. “It’s the first time the string-theoretical framework has been used to formulate the architecture of biological systems.”
Although the RPI team cautioned that their study was “fundamental” in nature and that they are still awaiting practical applications, they did note some areas that may benefit from the findings.
“We believe our findings hold potential for understanding neuron dynamics and computational complexity, as well as uncovering the mechanisms behind certain neuronal disorders,” Meng told The Debrief. “Another potential application is using this mathematical framework for network material design—such as artificial blood vessels or 3D-printable metamaterials.”
The study “Surface optimization governs the local design of physical networks” was published in Nature.
Christopher Plain is a Science Fiction and Fantasy novelist and Head Science Writer at The Debrief. Follow and connect with him on X, learn about his books at plainfiction.com, or email him directly at christopher@thedebrief.org.