Knots, a ubiquitous phenomenon found in everything from tangled headphones to the intricate packing of DNA strands within viruses, have long puzzled scientists in the realm of soft-matter physics. The mystery of how an isolated filament can knot itself without external forces or collisions has now been unraveled by a collaborative team of researchers from Rice University, Georgetown University, and the University of Trento in Italy.
Their groundbreaking discovery, recently published in Physical Review Letters, reveals a surprising physical mechanism that allows a single filament, even one that is too short or too stiff to easily wrap around itself, to form a knot while sinking through a fluid under strong gravitational forces. This insight into the physics of polymer dynamics has far-reaching implications, from understanding DNA behavior under confinement to designing advanced soft materials and nanostructures.
Uncovering the Mechanism Behind Fluid Knotting
“It is inherently difficult for a single, isolated filament to knot on its own,” said Sibani Lisa Biswal, corresponding author and chair of Rice’s Department of Chemical and Biomolecular 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.”
Utilizing Brownian dynamics simulations, the researchers demonstrated that as a semiflexible filament descends through a viscous fluid—akin to conditions in ultracentrifugation—long-range hydrodynamic flows can bend and fold the filament onto itself. This process concentrates part of the filament into a compact head while stretching the remainder into a trailing tail, creating a configuration that enables 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 at Rice.
Implications for Biological Systems and Material Science
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 extended periods, stabilized by tension within the filament due to hydrodynamics and friction between segments, allowing the system to achieve 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. “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 or even detrimental, as seen with genomic DNA. Understanding how these 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.”
Future Directions and Technological Innovations
Beyond biology, these findings could inform emerging approaches to nanomaterials fabrication, where controlling knotting could lead to patterned or mechanically reinforced structures. 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.”
Moreover, the 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.
