Knots are everywhere — from tangled headphones to DNA strands packed inside viruses — but how an isolated filament can knot itself without collisions or external agitation has remained a longstanding puzzle in soft-matter physics.
Now, a team of researchers at Rice University, Georgetown University and the University of Trento in Italy has uncovered a surprising physical mechanism that explains how a single filament, even one too short or too stiff to easily wrap around itself, can form a knot while sinking through a fluid under strong gravitational forces. The discovery, published in Physical Review Letters , provides new insight into the physics of polymer dynamics, with implications ranging from understanding how DNA behaves under confinement to designing next-generation soft materials and nanostructures.
"It is inherently difficult for a single, isolated filament to knot on its own," said Sibani Lisa Biswal , corresponding author, chair of Rice's Department of Chemical and Biomolecular Engineering and the William M. McCardell Professor in Chemical Engineering. "What's remarkable about this study is that it shows a surprisingly simple and elegant mechanism that allows a filament to form a knot purely because of stochastic forces as it sediments through a fluid under strong gravitational forces."
Using Brownian dynamics simulations, the researchers demonstrated that as a semiflexible filament falls through a viscous fluid — similar to conditions in ultracentrifugation — long-range hydrodynamic flows can bend and fold the filament onto itself. Those flows concentrate part of the filament into a compact head while stretching the remainder into a trailing tail, creating a configuration that allows loops to cross and lock into stable knots.
"We found that these knots don't just appear, but rather they evolve through a dynamic hierarchy, tightening and reorganizing into more stable topologies, almost like an annealing process," said Fred MacKintosh , co-corresponding author and the J.S. Abercrombie Professor of Chemical and Biomolecular Engineering and professor of chemistry and physics and astronomy at Rice. "This mechanism offers a new perspective on how complex structures can self-assemble under flow and force."
The simulations revealed that stronger gravitational fields increase both the likelihood and stability of knot formation and that more flexible filaments more easily form a wide range of knot types. At high field strengths, the knots persist for long periods, stabilized by tension within the filament due to hydrodynamics and friction between segments — allowing the system to reach intricate and long-lived configurations.
"I was surprised when I first observed the stable-knotted configurations in our simulations," said Lucas H.P. Cunha, first author and former Rice doctoral student who is currently a postdoctoral fellow at Georgetown University. "Deciphering the mechanisms behind this phenomenon proved to be an exciting journey, revealing strong evidence of the key role played by hydrodynamics on small scales."
The knotting of polymers plays a critical role in biological systems. Proteins and other macromolecules can form knots that influence their behavior and function inside cells. In some cases, they are beneficial. In others, they are neutral, and in some cases, like genomic DNA, they can be detrimental. Understanding how those knots form and stabilize provides a new foundation for interpreting processes such as genome packaging, electrophoresis and nanopore transport.
"This study deepens our understanding of how forces and flows shape polymer behavior," Biswal said. "It opens the door to designing new materials whose mechanical properties are programmed by their topology and not just their composition."
Beyond biology, these findings could inform emerging approaches to nanomaterials fabrication, where controlling knotting could lead to patterned or mechanically reinforced structures, and it may also offer insight into improving large-scale separation and characterization tools used in laboratories and industry.
"Field-driven knotting may someday provide a scalable alternative to what researchers currently call 'knot factories,'" MacKintosh said. "By learning how to harness this natural process, we can imagine new technologies that leverage hydrodynamics and self-assembly instead of manual or chemical manipulation."
This is not the only advantage: "In general, knots appear in very long polymers and require even longer polymers to become tight and stable," said Luca Tubiana, co-author and associate professor at the University of Trento. "Our study suggests an experimentally achievable way to obtain long-lived, tight, complex knots in very short polymers, opening the possibility to better connect knot theoretical and polymer theory predictions with experimental observations."
This research was supported by the National Science Foundation Divisions of Materials Research, Center for Theoretical Biological Physics and Directorate for Technology, Innovation and Partnerships.
