Knots are a ubiquitous phenomenon, found everywhere from tangled headphones to the intricate twists of DNA strands within viruses. Yet, the mystery of how an isolated filament can knot itself without external interference has puzzled scientists for decades. Now, researchers from Rice University, Georgetown University, and the University of Trento in Italy have uncovered a surprising mechanism that explains this phenomenon. Their findings, published in Physical Review Letters, shed new light on polymer dynamics and could have far-reaching implications in fields ranging from biology to material science.
The team discovered how a single filament, even one too short or stiff to easily wrap around itself, can form a knot as it sinks through a fluid under strong gravitational forces. “It is inherently difficult for a single, isolated filament to knot on its own,” said Sibani Lisa Biswal, the 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.”
Unraveling the Knotting Mechanism
Using Brownian dynamics simulations, the researchers demonstrated that as a semiflexible filament falls through a viscous fluid, 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 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 professor at Rice. “This mechanism offers a new perspective on how complex structures can self-assemble under flow and force.”
Implications for Biological Systems and Material Science
The study’s findings have significant implications for understanding the behavior of polymers in biological systems. Proteins and other macromolecules can form knots that influence their function inside cells. In some cases, these knots are beneficial, while in others, such as genomic DNA, they can be detrimental. Understanding how these knots form and stabilize provides a new foundation for interpreting processes such as genome packaging and nanopore transport.
“This study deepens our understanding of how forces and flows shape polymer behavior,” Biswal noted. “It opens the door to designing new materials whose mechanical properties are programmed by their topology.”
Beyond biology, the findings could inform new approaches to nanomaterials fabrication, where controlling knotting could lead to patterned or mechanically reinforced structures. It may also offer insights into improving large-scale separation and characterization tools used in laboratories and industry.
A New Frontier in Knot Theory
“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.”
Moreover, the study suggests that long-lived, tight, complex knots can be achieved in very short polymers, bridging the gap between knot theoretical predictions and experimental observations. “Our study suggests an experimentally achievable way to obtain long-lived, tight, complex knots in very short polymers,” said Luca Tubiana, co-author and associate professor at the University of Trento.
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.
The discovery of this knotting mechanism not only advances our understanding of polymer dynamics but also opens new avenues for innovation in material science and biotechnology. As researchers continue to explore the implications of these findings, the potential for new applications and technologies seems boundless.
