image: a,b, Representative velocity and vorticity fields observed in monolayers of eukaryotic MDCK cells (a) and prokaryotic WT P. aeruginosa cells (b). The colour map shows the local vorticity and the zero-vorticity contours are marked with black lines. The vorticity is normalized by its maximum value. The insets show a subset of cells within a single field of view, which have been overlaid with green arrows showing the local velocity. Here we have quantified movement using single-cell tracking (PIV), but we have also verified our results using PTV.
Credit: Benjamin H. Andersen, Francisco M. R. Safara, Valeriia Grudtsyna, Oliver J. Meacock, Simon G. Andersen, William M. Durham, Nuno A. M. Araujo & Amin Doostmohammadi
The study "Evidence of universal conformal invariance in living biological matter", with the participation of Nuno Araújo from the Department of Physics at the Faculty of Sciences of the University of Lisbon, has just been published in the prestigious journal Nature Physics. The study, which focused on analyzing cell models, found universality in their movement—an important discovery that could impact both health and robotics.
The starting point for the research was the question: How do individual cells interact with one another without being aware that they are part of a larger whole? The study focused on biological matter and cellular behavior—bringing together two major disciplines: Physics and Biology. "While in Physics we systematically find the same patterns in different systems, in Biology, there is always a tendency to think that each system is unique," explains Nuno Araújo, professor and researcher at the Department of Physics at the Faculty of Sciences of the University of Lisbon and one of the study’s authors.
Specifically, the research demonstrates that "the collective movement of cells—from systems as diverse as dog kidney cells, human breast cancer cells, or two different types of pathogenic bacteria—exhibits a robust invariance." The concept may seem complex, but Nuno Araújo uses the visual example of broccoli to simplify the discovery: "A broccoli has the shape of a tree, but if we cut off each branch, it also looks like a tree. If I showed you a picture of each piece and asked which one was the largest, you wouldn’t be able to tell. That is scale invariance, and that’s what we discovered here. All these systems share the same scale invariance."
The researchers focused on four types of cells: two prokaryotic and two eukaryotic. Despite being structurally different, they were found to behave similarly in groups. This opens doors to a greater and deeper understanding of the fundamental matter that constitutes life, leading to numerous potential applications. The findings could help improve our understanding of oncological diseases and their progression (including metastasis), but also be valuable for tissue engineering, aiding in the development of artificial organs. Additionally, the study provides insights into how bacterial infections spread—potentially leading to better hospital environment management.
These are just a few examples of its impact: in fact, the discovery could also have applications in other systems, such as robotics. As Nuno Araújo explains, it could help improve robot navigation or even influence the development of video games and artificial intelligence systems.
What does this mean? That a form of universality has been identified—something not typically expected in Biology. "This opens doors for us to use physics techniques to study biological systems, but also for biological systems to be used to study physical phenomena," says Nuno Araújo.
The study involved the Department of Physics and the Center for Theoretical and Computational Physics at the Faculty of Sciences of the University of Lisbon, as well as several academics from universities in Denmark, Switzerland, and the United Kingdom.
Journal
Nature Physics
Method of Research
Experimental study
Article Title
Evidence of universal conformal invariance in living biological matter
Article Publication Date
14-Mar-2025