Researchers at Northwestern University have discovered that structural features of the brain are nearing a critical point similar to a phase transition, observed in species as diverse as humans, mice and fruit flies. This discovery suggests that a universal principle may guide the structure of the brain, which may inspire new computational models to mimic the complexity of the brain.
The brain exhibits structural criticality near phase transitions, consistent throughout speciespotentially 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 is undergoing 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 are consistent across the brains of humans, mice and fruit flies, suggesting that the finding may be universal. While it remains unclear which stages the brain structure is going through, these findings may enable new designs for computational models of brain 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 of the detailed properties that govern its structure are not yet understood,” said senior author István Kovács, an assistant professor of physics and astronomy at Northwestern.
“Several other researchers have studied the criticality of the brain in terms of neuronal dynamics. But we are looking at the critique at the structural level in order to ultimately understand how it underpins the complexity of brain dynamics. This has been 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 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 researcher 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 from solid to liquid. We’re certainly not saying the brain is about to melt. In fact, we have no way of knowing which two stages the brain may go through. For if it were on either side of the critical point, it would not be a brain.”
Application of statistical physics in neuroscience
Although researchers have long studied brain dynamics using functional magnetic resonance imaging (fMRI) and electroencephalograms (EEG), advances in neuroscience have only recently provided massive datasets on the cellular structure of the brain. These data opened up opportunities for Kovács and his team to apply statistical physics techniques to measure the physical structure of neurons.
Photo of selected neurons from the human cortex dataset, viewed using the neuroglancer online platform. Credit: Harvard University/Google
Identification of Critical Exponents in Brain Structure
Kovács and Ansell analyzed publicly available data from 3D brain reconstructions from humans, fruit flies and mice. Examining the brain in nanoscale resolution, the researchers found that the samples exhibited distinctive physical properties associated with crit.
One such property is the well-known, fractal-like structure of neurons. This non-trivial fractal dimension is an example of a set of observables, called “critical exponents”, that appear when a system is close to a phase transition.
Brain cells are arranged in a fractal-like statistical pattern at different scales. When zoomed in, fractal shapes are “similar,” meaning that the smallest parts of the sample resemble the entire sample. The sizes of the different segments of the observed neurons are also different, which provides another clue. According to Kovács, self-similarity, long-range correlations, and broad size distributions are all signatures of a critical state, where features are neither highly organized nor highly random. These observations lead to a set of critical exponents characterizing these structural features.
“These are things we see in all critical systems in physics,” Kovács said. “It appears that the brain is in a delicate balance between the two phases.”
Examples of single neuron reconstructions from each of the fruit fly, mouse, and human datasets. Credit: Northwestern University
Universal criticality across species
Kovács and Ansell were amazed to find that all brain samples studied—from humans, mice, and fruit flies—have critical exponents consistent across organisms, meaning they share the same quantitative characteristics of criticality. Basic, compatible structures among organisms hint that a universal governing principle may be at play. Their new findings could potentially help explain why brains from different creatures share some of the same basic principles.
“At first, these structures look quite different—an entire fly brain is about the size of a small human neuron,” Ansell said. “But then we found properties under development that are surprisingly similar.”
“Among the many characteristics that are very different between organisms, we relied on suggestions from statistical physics to check which measures are potentially universal, such as critical exponents. Indeed, they are stable across organisms,” Kovács said. “As an even deeper sign of criticality, the criticality exponents obtained are not independent—from any three, we can calculate the rest, as dictated from statistical physics. This discovery paves the way for the formulation of simple physical models to capture statistical patterns of brain structure. Such patterns are useful inputs for dynamic brain models and can be inspiring for artificial neural network architectures.”
Moving forward, the researchers plan to apply their techniques to new emerging datasets, including larger brain sections and more organisms. They aim to find out whether universality will continue to apply.
Reference: “Uncovering universal aspects of the brain’s cellular anatomy” by Helen S. Ansell and István A. Kovács, 10 Jun 2024, Physics of communications.
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.