Summary: A groundbreaking study by physicists and neuroscientists shows that connections between neurons arise from universal network principles, not just biological features.
By analyzing different model organisms, the researchers discovered a consistent distribution of heavy-tailed neuronal connections driven by Hebbian dynamics. This shows that neuronal connectivity depends on the overall organization of the network.
This discovery, which transcends biology, can also be applied to non-biological networks such as social interactions and offer insights into the fundamental nature of networks.
Important facts:
- The study analyzed neuronal connectivity in a variety of organisms, including fruit flies, nematodes, and mice. It found a universal pattern of “heavy tails.”
- The researchers developed a model based on Hebbian dynamics, which successfully reflected the observed neuronal connectivity between species.
- The results suggest that neural connections are governed by universal network principles, which may also apply to various networks outside the brain.
Source: University of Chicago
A new study by physicists and neuroscientists from the University of Chicago, Harvard and Yale explains how connections between neurons are established through general principles of networking and self-organization, rather than by an individual’s biological characteristics.
The research, published in Nature Physics on January 17, 2024, accurately describes neural connectivity in several model organisms and can also be applied to non-biological networks such as social interactions.
“When you build simple models to explain biological data, you hope you get a good approximation that fits some scenarios, but not all,” said Stephanie Palmer, PhD, associate professor of physical biology and organismal anatomy at the University of Chicago and senior author on the paper.
“When you go into the details you don’t expect it to work that well, but when we did it here, we explained things in a very satisfying way.”
Understanding how neurons connect.
Neurons form a complex network of connections between synapses to communicate and interact with each other. Although the large number of connections may seem random, neural networks are usually dominated by a small number of connections that are stronger than the majority.
This “heavy-tailed” distribution of connections (named for its graph shape) forms the backbone of the circuits that allow organisms to think, learn, communicate, and move. Despite the importance of these strong connections, scientists were unsure whether this heavy-tailed structural pattern arose from biological processes specific to different organisms or from fundamental principles of network organization.
To answer these questions, Palmer and Christopher Lin, PhD, assistant professors of physics at Yale University, and Caroline Holmes, PhD, a postdoctoral researcher at Harvard University, analyzed connectomes, or maps of neural connections. The connectome data came from several classic animal models, including fruit flies, nematodes, sea worms, and the mouse retina.
To understand how neurons form connections with each other, they developed a model based on Hebbian dynamics, a term coined by Canadian psychologist Donald Heb in 1949 that essentially says, “neurons that fire together.” This means that the more neurons that fire together, the stronger their connection becomes.
Overall, the researchers found that these Hebbian dynamics produced the strong, heavy-tailed connections observed in a variety of organisms. The results suggest that this type of organization derives from general network principles rather than anything specific to the biology of fruit flies, mice, or insects.
The model also offered an unexpected explanation for another network phenomenon: clustering. This phenomenon describes the tendency of cells to connect to each other through shared connections.
A good example of clustering occurs in social situations. If a friend introduces a third person, the two are more likely to become friends than if they had met separately.

“Everyone agrees that these mechanisms are going to be fundamental to neuroscience,” Holmes said. “But what we’re seeing here is that, if you analyze the data carefully and quantitatively, you can make out different effects on clustering and distribution, and then you see them across all these organisms.”
Accounting for randomness
As Palmer points out, biology doesn’t always offer a clear and concise explanation, and there’s still randomness and noise in brain circuits. Neurons sometimes disconnect and reconnect: weak connections are cut off, allowing stronger connections to form elsewhere.
This randomness allows us to validate the kind of Hebbian organization the researchers found in this data. Without this organization, strong connections would grow and dominate the network.
The researchers modified their model to account for randomness, improving its accuracy.
“Without this noise, the model would fail,” Lin said. “It wouldn’t have produced anything that worked, which surprised us. It shows that you have to balance the Hebbian snowball effect with randomness to make it look like a real brain.”
Because these rules arise from general network principles, the team hopes to extend this work beyond the brain.
“Another interesting aspect of this work is how the science has evolved,” Palmer said. “The team has a huge diversity of expertise, from theoretical physics and big data analysis to biochemical and evolutionary networks. We focused on the brain, but we can now address other types of networks in future work.”
Funding: This research, titled “Heavy-tailed neuronal connectivity arises from Hebbian self-organization,” received substantial support from multiple funding sources. Primary funding was provided by the National Science Foundation through its backing of the Center for Physics of Biological Function (grant PHY-1734030). In addition, a Graduate Research Fellowship awarded to CMH contributed to the advancement of this work. These resources enabled critical aspects of the research, including data analysis, theoretical modeling, and collaborative development.
About this neuroscience research news
Author: Matt Wood
Source: University of Chicago
Contact: Matt Wood – University of Chicago
Image: The image is credited to StackZone Neuro
Original Research: The findings will appear in Nature Physics
Further support came from a Postdoctoral Fellowship granted to CWL by the James S. McDonnell Foundation, reflecting the foundation’s commitment to advancing understanding in complex systems and neuroscience. The project was also funded by the National Institutes of Health through its Brain Research through Advancing Innovative Neurotechnologies (BRAIN) Initiative under grant R01EB026943. Together, these contributions facilitated the interdisciplinary efforts necessary for the study’s exploration of neuronal connectivity and Hebbian mechanisms.

