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Recent research published in Nature Physics highlights a significant discovery regarding the behavior of living biological cells. The study reveals that a fundamental characteristic known as universal conformal invariance can be observed in the collective dynamics of these cells, regardless of their evolutionary backgrounds.
The research team investigated four distinct cellular systems, encompassing a variety of cell types, and documented the emergence of vortex-like flow patterns. Despite their divergence over billions of years of evolution, these systems exhibited strikingly similar statistical properties in their behavior.
Dr. Amin Doostmohammadi, an Associate Professor at the University of Copenhagen and co-author of the study, elaborated on the findings by likening the movement of cells to whirlpools forming in a stirred cup of water. “Just as whirlpools come and go in water, collective movements in bacteria and human cells give rise to similar swirling patterns,” he remarked. Dr. Doostmohammadi noted the surprising aspect of their findings: the presence of conformal invariance in the cellular patterns. This indicates that the group motion maintains consistent statistical properties even when scaled or transformed.
Understanding Collective Behaviors through CFT
The phenomenon of collective movement is influenced by various attributes of individual cells, including their interactions, movements, and responses to environmental stimuli. The emergent properties of these interactions can differ substantially, complicating the identification of universal principles governing collective behavior.
Previous research has successfully identified universal behaviors in non-biological systems, particularly near critical points in materials such as metals and alloys. These behaviors can be framed within the context of conformal field theory (CFT), a mathematical construct applicable to systems that are scale-invariant and maintain angle-preservation. Such systems often reveal universal characteristics at critical transitions, like those occurring during phase changes.
“The organization of living matter presents one of science’s greatest enigmas,” Dr. Doostmohammadi stated. “Our investigation was driven by the question of whether there might be universal laws, similar to those in physics, that dictate how cells organize themselves.”
Exploring Diverse Cellular Systems
The research analyzed different cellular systems, including both wild-type and mutant strains of Pseudomonas aeruginosa bacteria, Madin-Darby canine kidney cells, and aggressive human breast cancer cells. These selected systems offered a broad spectrum of cell types, integrating both eukaryotic and prokaryotic organisms with various movement mechanisms.
The researchers meticulously constructed monolayers of cells and tracked their movements using advanced imaging techniques, allowing for high-resolution observation. This led to the calculation of velocity fields, which were subsequently analyzed to assess vorticity, indicating local rotation within the systems.
For regions of zero vorticity, signifying transitions in rotational behaviors, the team employed mathematical analyses, such as measuring fractal dimensions and evaluating contour properties through Schramm-Loewner evolution (SLE) methodologies. Dr. Doostmohammadi explained that SLE is commonly utilized in physics to explore concepts related to percolation and magnetism.
The parameter κ, central to SLE, was found to be consistent across the four systems, computed to be six. This value aligns with the percolation universality class, a framework used to describe the dynamics of particles and fluids navigating through porous materials, showcasing profound implications for understanding collective cellular behaviors.
Implications and Future Directions
The revelations of universal conformal invariance suggest that living organisms, despite their diverse biological structures and functions, adhere to universal governing principles. This finding is particularly noteworthy as it bridges biological phenomena with advanced theoretical concepts from mathematics and physics.
Furthermore, the implications of this research extend beyond theoretical musings; they may pave the way for advancements in understanding cancer progression, wound healing, and tissue development. Dr. Doostmohammadi emphasized the potential for this knowledge to inspire new approaches in synthetic biology and regenerative medicine. Furthermore, biological systems could be utilized as experimental platforms to test the predictions made by CFT, which have predominantly existed within theoretical frameworks.
More information: Benjamin H. Andersen et al, Evidence of universal conformal invariance in living biological matter, Nature Physics (2025). DOI: 10.1038/s41567-025-02791-2.
Source
phys.org