Northwestern University researchers have found that structural features of the brain are close to a critical point similar to the phase transition observed in species as diverse as humans, mice and fruit flies. This finding suggests that a universal principle may govern the structure of the brain, which could inspire new computational models to mimic the complexity of the brain.
The brain exhibits structural criticality near phase transitions, consistent across specieswhich could lead to the development of new models of the brain.
When a magnet heats up, it reaches a critical point where it loses magnetization, known as “criticality”. This point of high complexity is reached when a physical object undergoes a phase transition.
Recently, researchers from Northwestern University discovered that structural features of the brain reside near a similar critical point—either at or near a structural phase transition. These results are consistent across human, mouse and fruit fly brains, suggesting that the finding may be universal. Although it is not clear which stages brain structure transitions between, these findings could enable new designs for computational models of brain complexity.
Their research was published in Communication physics.
3D reconstruction of selected neurons in a small region of the human cortex dataset. Credit: Harvard University/Google
Brain structure and computational models
“The human brain is one of the most complex systems known, and many properties of the details that govern its structure are not yet understood,” said lead author István Kovács, an assistant professor of physics and astronomy at Northwestern.
“Several other researchers have studied brain criticality in terms of neuronal dynamics. But we look at criticality at a structural level to ultimately understand how it supports the complexity of brain dynamics. That was the missing piece of how we think about the complexity of the brain. Unlike a computer where any software can run on the same hardware, in the brain the dynamics and the hardware are closely related.”
3D reconstruction of selected neurons in a small region of the human cortex dataset. Credit: Harvard University/Google
“The structure of the brain at the cellular level appears to be close to a phase transition,” said first author Helen Ansell, a Tarbutton Fellow at Emory University who was a postdoctoral fellow in Kovács’ lab during the study. “An everyday example of this is when ice melts into water. They are still water molecules, but they are going through the transition from solid to liquid. We’re definitely not saying the brain is about to melt. We actually have no way of knowing which two phases the brain might be transitioning between. Because if it was on either side of the critical point, it wouldn’t be a brain.’
Applications of statistical physics to neuroscience
Although scientists have long studied brain dynamics using functional magnetic resonance imaging (fMRI) and electroencephalograms (EEGs), advances in neuroscience have only recently provided massive data sets for the cellular structure of the brain. These data opened up the possibility for Kovács and his team to use statistical physics techniques to measure the physical structure of neurons.
Snapshot of selected neurons from the human cortex dataset, viewed using the neuroglacer online platform. Credit: Harvard University/Google
Identification of critical components in brain structure
Kovács and Ansell analyzed publicly available data from 3D brain reconstructions of humans, fruit flies and mice. By examining the brain at nanoscale resolution, the researchers found that the samples exhibited characteristic physical properties associated with criticality.
One such property is the well-known fractal-like structure of neurons. This non-trivial fractal dimension is exemplified by a set of observables, called “critical exponents”, that appear as the system approaches a phase transition.
Brain cells are arranged in a fractal-like statistical pattern at different scales. When zoomed in, fractal shapes are “self-similar”, meaning that smaller parts of the pattern resemble the whole pattern. The sizes of the different neuron segments observed are also different, providing another clue. According to Kovács, self-similarity, long-range correlation, and a broad size distribution are signatures of a critical state where properties are neither too organized nor too random. These observations lead to a set of critical exponents that characterize these structural features.
“These are things we see in all critical systems in physics,” Kovács said. “The brain appears to be in a delicate balance between two phases.”
Examples of reconstruction of a single neuron from each propeller, mouse, and human dataset. Credit: Northwestern University
Universal criticality across species
Kovács and Ansell were amazed to find that all the brain samples they studied—from humans, mice, and fruit flies—had consistent critical exponents across organisms, meaning they shared the same quantitative features of criticality. The underlying, compatible structures between organisms suggest that there might be a universal governing principle at play. Their new findings could help explain why the brains of different creatures share some of the same basic principles.
“At first, these structures look quite different — the entire brain of a fly is roughly the size of a small human neuron,” Ansell said. “But then we found new properties that are surprisingly similar.”
“Among the many characteristics that vary greatly between organisms, we relied on suggestions from statistical physics to verify which measures are potentially universal, such as critical exponents.” These are actually consistent across organisms,” said Kovács. “As an even deeper sign of criticality, the obtained critical exponents are not independent—from any three we can calculate the remainder as dictated by statistical physics. This finding paves the way for the formulation of simple physical models to capture the statistical patterns of brain structure. Such models are useful inputs for dynamical models brain and can be inspiring for artificial neural network architectures.
In the future, the researchers plan to apply their techniques to emerging new data sets, including larger parts of the brain and more organisms. Their goal is to find out if universality will still hold.
Reference: “Revealing universal aspects of the brain’s cellular anatomy” by Helen S. Ansell and István A. Kovács, 10 Jun 2024, Communication physics.
DOI: 10.1038/s42005-024-01665-y
Funding: This study was supported in part through computational resources at the Quest High Performance Computing Facility at Northwestern.