Researchers at Northwestern University have found that structural features of the brain are near a critical point similar to a phase transition seen in species as diverse as humans, mice and fruit flies. This finding suggests that a universal principle may govern the brain’s structure, which may inspire new computational models to emulate the brain’s complexity.
The brain exhibits structural criticality near phase transitions consistent throughout kindspotentially guiding the development of new brain models.
When a magnet is heated, 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 have found that structural features of the brain lie near a similar critical point—either at or near a structural phase transition. These results were consistent across the brains of humans, mice and fruit flies, suggesting that the finding may be universal. Although it remains unclear which phases the brain’s structure passes between, these findings could enable new designs for computational models of the brain’s complexity.
Their research was published in Physics of communications.
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 governing its structure are still not understood,” said senior author István Kovacs, an assistant professor of physics and astronomy at Northwestern.
“Several other researchers have investigated the criticality of the brain in terms of neuronal dynamics. But we look at criticality at a structural level to ultimately understand how it underlies the complexity of brain dynamics. This is a 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 tightly coupled.
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 Kovacs’ lab during the study. “An everyday example of this is when ice melts into water. These are still water molecules, but they are going from a solid to a liquid state. We’re certainly not saying the brain is close to melting. We actually have no way of knowing which two phases the brain can go between. Because if it was on either side of the critical point, it wouldn’t be a brain.
Applying statistical physics to the neurosciences
Although researchers have long studied brain dynamics using functional magnetic resonance imaging (fMRI) and electroencephalograms (EEG), advances in neuroscience have only recently provided massive data sets on the cellular structure of the brain. These data opened up opportunities for Kovacs and his team to apply statistical physics techniques to measure the physical structure of neurons.
Snapshot of selected neurons from the human cortex dataset viewed using the neuroglancer online platform. Credit: Harvard University/Google
Identifying critical indicators in brain structure
Kovacs and Ansel analyzed publicly available data from 3D brain reconstructions of humans, fruit flies and mice. By examining the brain in nanoscale resolution, the researchers found that the samples demonstrated distinctive physical properties associated with criticality.
One such property is the well-known fractal structure of neurons. This nontrivial fractal dimension is an example of a set of observables called “critical exponents” that appear when the system is close to a phase transition.
Brain cells are arranged in a fractal statistical pattern at different scales. When magnified, fractal shapes are “self-similar”, meaning that smaller parts of the sample resemble the whole sample. The sizes of the different observed neuronal segments are also different, providing another clue. According to Kovacs, self-similarity, long-range correlations, and wide size distributions are signs of a critical state where features 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,” Kovacs said. “The brain appears to be in a delicate balance between two phases.”
Examples of single neuron reconstruction from each data set for fruit fly, mouse, and human. Credit: Northwestern University
Universal criticality across species
Kovacs and Ansel 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 characteristics of criticality. The underlying, compatible structures between organisms suggest that a universal governing principle may be at play. Their new findings could potentially help explain why the brains of different creatures share some of the same fundamental principles.
“At first, these structures look quite different — the entire brain of a fly is about the size of a small human neuron,” Ansel said. “But then we found emerging properties that are surprisingly similar.”
“Among the many features that are very different across organisms, we relied on the suggestions of statistical physics to test which measures are potentially universal, such as critical metrics. Indeed, they are consistent across organisms,” Kovacs said. “As an even deeper sign of criticality, the resulting critical metrics are not independent—from any three we can calculate the others, as statistical physics dictates. This discovery opens the way to formulating simple physical models to capture statistical patterns of brain structure. Such patterns are useful inputs for dynamic brain models and can be inspirational for artificial neural network architectures.
Moving forward, the researchers plan to apply their techniques to emerging new data sets, including larger brain regions and more organisms. They aim to discover whether universality will still apply.
Reference: “Unraveling universal aspects of the brain’s cellular anatomy” by Helen S. Ansel and István A. Kovacs, 10 Jun 2024, Physics of communications.
DOI: 10.1038/s42005-024-01665-y
Funding: This study was supported in part through the computational resources of the Quest High Performance Computing Facility at Northwestern.
