Scientists find evidence of universal conformal invariance in diverse cellular movement

In a new Nature Physics study, researchers have provided evidence of universal conformal invariance in living biological cells. They show that a universal feature in the collective behavior emerges in groups of living cells.

The researchers studied four cellular systems to find evidence of universal conformal invariance. Despite being separated by billions of years of evolution, the researchers found that all four systems generated vortex-like flow patterns with identical statistical properties.

Phys.org spoke to one of the study’s co-authors, Dr. Amin Doostmohammadi, an Associate Professor at the University of Copenhagen.

“When you stir a cup of water, you see whirlpools form and disappear. Something similar happens when bacteria or human cells move collectively; they form swirling patterns, too,” he explained.

“What was astonishing to us was to find that these vastly different cell types all display a hidden symmetry known as conformal invariance in their swirling patterns. This means that their collective motion follows the same statistical patterns, even when you zoom in or out, stretch, or reshape them.”

Collective behaviors and CFT

Collective movement emerges due to the specific properties of the individual constituents. This includes their interaction, movement, and response to stimuli.

The resultant emergent properties vary from system to system, making it challenging to study universal principles governing collective movement—if they are present.

In previous studies, researchers have been able to identify universal behaviors near critical regimes in inanimate systems like metal or alloy materials.

These universal behaviors are described by conformal field theory (CFT), a powerful mathematical framework. CFT can be applied to scale-invariant and angle-preserving systems, which are often seen at critical points (like phase changes).

“Understanding how living matter organizes itself is one of the biggest unsolved puzzles in science. Our inspiration came from a bold question: Could there be universal laws, akin to those in physics, that govern how cells self-organize?” said Dr. Doostmohammadi.

Analyzing four different living systems

The researchers examined the cells of wild-type Pseudomonas aeruginosa bacteria, a mutant strain of the same bacteria, Madin-Darby canine kidney cells, and aggressive human breast cancer cells.

The four systems represent a wide range of cell types (eukaryotes and prokaryotes) with different movement mechanisms and cellular properties.

For each system, the researchers created monolayers of cells and tracked their movement using high-resolution imaging. The resulting velocity fields were then analyzed to calculate the vorticity, which represents the local rotation at a point.

For the zero vorticity regions—which represent the boundary where the system’s rotational behavior changes—they performed mathematical analyses. These included measuring the fractal dimension, testing if the contours follow Schramm-Loewner evolution (SLE), and calculating winding angles.

“SLE is a theory typically used in physics to describe percolation, magnetism, and even aspects of quantum gravity,” said Dr. Doostmohammadi.

In SLE, conformally invariant curves are characterized by a single parameter κ, which identifies specific universality classes exhibiting similar emergent behaviors.

The researchers also developed a simple computational model to recapitulate the same patterns seen in the four systems, suggesting these universal properties emerge naturally from collective dynamics regardless of cellular details.

Percolation universality class

The researchers found that the parameter κ was measured to be six for all four systems. This belongs to the percolation universality class—the same class that describes the movement of particles or fluids through a porous medium, like water flowing through a porous rock.

“This discovery suggests that, at a fundamental level, living matter organizes itself according to universal laws—laws that apply across the tree of life, from bacteria to human cells with very different biology and very different morphologies,” noted Dr. Doostmohammadi.

This finding of universal conformal invariance bridges biology with concepts of theoretical mathematics and physics.

This universality is even more remarkable considering that these biological systems operate far from equilibrium, constantly consuming energy to maintain their movement—unlike the equilibrium states where such universal behaviors are typically observed in physics and mathematics.

Looking to the future, Dr. Doostmohammadi points out that this work can help improve our understanding of cancer progression, wound healing, and tissue development. Additionally, it could inspire new methodologies in synthetic biology and regenerative medicine.

Not only that, but these biological systems can now serve as experimental platforms to test predictions from CFT that have primarily been limited to theoretical and numerical simulations.

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