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Physics: Publication in Nature Communications
Physicists from Heinrich Heine University Düsseldorf (HHU) have, in collaboration with colleagues from Darmstadt and Dresden, examined the movement in clusters of active, self-propelled, flexible polymer chains. In the process, they identified new physical laws, with which they also can describe living clusters of worms and tentacles. In the journal Nature Communications, they describe that the active movement of living individuals causes novel internal entanglements to arise, which can stiffen such a dynamic cluster to the extent that it practically becomes a solid.
Earthworms often form a cluster, from which they can barely free themselves. A similarly active, writhing structure forms when the tentacles of lion’s mane jellyfish become entangled. Robotic grippers utilise this principle by using multiple synthetic flexible arms to grip and move objects. And such interlinked self-propelled filaments can also be found at the smaller micrometre scale, for example in a biological cell.
The chains or tentacles are also known as polymer chains. Where they are only subject to thermal noise, the structure and dynamics of such tangles are described by conventional polymer physics. The theoretical description is based on a tube model: A polymer chain moves randomly back and forth within a convoluted tube formed by its neighbours.
Professor Dr Hartmut Löwen from the Institute for Theoretical Physics II at HHU: “Using this model, physicists can predict how quickly a chain can extricate itself from a cluster. The time needed is determined via a so-called scaling law with a universal exponent and is closely correlated to the length of the chain, i.e.: how much longer does it take until a chain has freed itself when it is twice as long.” Pierre-Gilles de Gennes was awarded the Nobel Prize in Physics in 1991 for this polymer modelling.
However, it was not known how the model changes when the polymers are active, for example when they are made up of randomly writhing chains of living worms. This central question from the research field of “active soft matter” has long remained unanswered. Researchers from HHU, the Technical University of Darmstadt and Dresden University of Technology have, in collaboration with the Max Planck Institute for the Physics of Complex Systems in Dresden, now uncovered these dynamics with the help of large-scale computer simulations. They were able to show that the scaling laws change fundamentally: The associated exponent changes significantly compared with the passive case of randomly externally initiated chains.
In the process, the researchers not only determined the new exponent, but also created a new tube model in which the new phenomena can be classified and clearly understood. With the model, they established that the rigidity of this living polymer mass increases significantly as internal grip forces cause a living system to entangle and block itself.
Lead author Dr Davide Breoni, who gained his doctorate under the supervision of Professor Löwen and now conducts research in Trento, Italy: “Preparing these clusters for various polymer sizes in our computer model was painstaking work. However, we were then able to numerically extract the underlying scaling laws for various polymer lengths.”
Dr Suvendu Mandel, who worked as a postdoc at HHU and now works in Darmstadt, continues: “The new laws revolutionise polymer physics. They show that it is very easy for living systems to become collectively entangled, increasing their rigidity overall. Intuitively, one would expect the opposite – that their active movement enables them to untangle themselves more quickly.”
Professor Löwen indicates a practical benefit of these findings: “They could enable the development of new ‘smart materials’, which become more rigid at the push of a button, i.e. which can drastically alter their viscoelastic properties.”
Davide Breoni, Christina Kurzthaler, Benno Liebchen, Hartmut Löwen, Suvendu Mandal. Giant Activity-Induced Stress Plateau in Entangled Polymer Solutions. Nature Communications 16, 5305 (2025).
DOI: 10.1038/s41467-025-60210-9
Cluster of 200 Californian blackworms (Lumbriculus variegatus). Length scale: 3mm.
Copyright: Image from: Patil et al., Science 380, 392-398 (2023)
Computer simulation snapshot of entangled active flexible polymer filaments. Different colours indic ...
Copyright: HHU/Davide Breoni
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Cluster of 200 Californian blackworms (Lumbriculus variegatus). Length scale: 3mm.
Copyright: Image from: Patil et al., Science 380, 392-398 (2023)
Computer simulation snapshot of entangled active flexible polymer filaments. Different colours indic ...
Copyright: HHU/Davide Breoni
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