Researchers at Northwestern University have discovered that the structural features of the brain are almost at a critical point, similar to a phase transition, observed in various species such as humans, mice and fruit flies. This finding suggests that a universal principle could govern brain structure, which could inspire new computational models to mimic the complexity of the brain.
The brain exhibits structural criticality near phase transitions, consistent across the board kindthat may guide 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 the structural features of the brain are near a similar critical point – at or near a structural phase transition. These results are consistent across the brains of humans, mice and fruit flies, suggesting the finding could be universal. Although it remains unclear between which phases brain structure occurs, these findings may enable new designs for computational models of brain complexity.
Their research was published in Communication physics.
3D reconstruction of selected neurons in a small part of the human cortex dataset. Credit: Harvard University/Google
Brain structure and computer models
“The human brain is one of the most complex systems known, and many properties of the details that determine its structure are not yet understood,” said senior author István Kovács, assistant professor of physics and astronomy at Northwestern.
“Several other researchers have studied brain criticality in terms of neuron dynamics. But we look at criticality at the structural level to ultimately understand how this supports the complexity of brain dynamics. That has been a missing piece in the way we think about the complexity of the brain. Unlike a computer where all software can run on the same hardware, in the brain the dynamics and the hardware are strongly connected.”
3D reconstruction of selected neurons in a small part of the human cortex dataset. Credit: Harvard University/Google
“The structure of the brain at the cellular level appears to be in the vicinity of a phase transition,” said first author Helen Ansell, a Tarbutton Fellow at Emory University and a postdoctoral fellow in Kovács’ laboratory during the study. “An everyday example of this is when ice melts in water. They are still water molecules, but they are undergoing a transition from solid to liquid. We’re certainly not saying that the brain is about to melt. In fact, we have no way of knowing between which two phases the brain might be. Because if it were on either side of the critical point, it wouldn’t be a brain.”
Applying statistical physics to neuroscience
Although researchers have long studied brain dynamics using functional magnetic resonance imaging (fMRI) and electroencephalograms (EEG), advances in neuroscience have only recently produced vast data sets for 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.
Snapshot of selected neurons from the human cortex dataset viewed using the online neuroglacer platform. Credit: Harvard University/Google
Identification of critical exponents in brain structure
Kovács and Ansell analyzed publicly available data from 3D brain reconstructions of humans, fruit flies and mice. By examining the brain nanoscale resolution, the researchers found that the samples showed characteristics of physical properties associated with criticality.
One of those properties 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 arise 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, the fractal shapes are “self-similar,” meaning smaller parts of the sample resemble the entire sample. The sizes of the different neuron segments observed are also diverse, providing another clue. According to Kovács, similarity, long-range correlations, and broad size distributions are all characteristics of a critical state, in which features are neither too organized nor too random. These observations lead to a series of critical exponents that characterize these structural features.
“These are things we see in all critical systems in physics,” Kovács said. “It seems that the brain is in a delicate balance between two phases.”
Examples of a single neuron reconstruction from each of the fruit fly, mouse, and human datasets. Credit: Northwestern University
Universal criticality across species
Kovács and Ansell were surprised to find that all brain samples studied – from humans, mice and fruit flies – have consistent critical exponents for all organisms, meaning they share the same quantitative characteristics of criticality. The underlying compatible structures between organisms indicate that a universal principle of governance may be at play. Their new findings may help explain why brains from different creatures share some of the same fundamental principles.
“Initially, these structures look very different: an entire fly brain is about the size of a small human neuron,” Ansell said. “But then we found emerging properties that are surprisingly similar.”
“Of the many features that are very different between organisms, we relied on the suggestions of statistical physics to check which measurements are potentially universal, such as critical exponents. These are indeed consistent across all organisms,” Kovács said. “As an even deeper sign of criticality, the critical exponents obtained are not independent – for any three we can calculate the rest, as dictated by statistical physics. This finding opens the way to formulating simple physical models to capture statistical patterns of brain structure. Such models are useful input for dynamic brain models and can be inspiring for artificial neural network architectures.”
In the future, the researchers plan to apply their techniques to new data sets, including larger parts of the brain and more organisms. They want to find out whether universality still applies.
Reference: “Revealing Universal Aspects of the Brain’s Cellular Anatomy” by Helen S. Ansell and István A. Kovács, June 10, 2024, Communication physics.
DOI: 10.1038/s42005-024-01665-y
Funding: This study was supported in part by the computing resources of the Quest high-performance computing facility at Northwestern.