Knots, ubiquitous in everyday life from tangled headphones to the intricate structure of DNA, have long puzzled scientists, particularly how an isolated filament can knot itself without external interference. Now, a groundbreaking study by researchers from Rice University, Georgetown University, and the University of Trento has revealed a surprising mechanism that explains this phenomenon. Published in Physical Review Letters, the study provides a new perspective on polymer dynamics, with potential applications ranging from DNA behavior analysis to the development of advanced soft materials and nanostructures.
The research team discovered that a single filament, even one too short or stiff to easily wrap around itself, can form a knot while sinking 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 under strong gravitational forces.”
Exploring the Physics of Knot Formation
Utilizing Brownian dynamics simulations, the researchers demonstrated that as a semiflexible filament descends through a viscous fluid, similar to conditions in ultracentrifugation, long-range hydrodynamic flows can bend and fold the filament onto itself. These flows concentrate part of the filament into a compact head while stretching the remainder into a trailing tail, creating a configuration that facilitates the formation of 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 Biology and Material Science
The implications of this discovery extend beyond theoretical physics. In biological systems, the knotting of polymers such as proteins and macromolecules plays a critical role, influencing their behavior and function within cells. Understanding how these knots form and stabilize could provide new insights into processes like 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 and not just their composition.”
Potential Applications in Nanotechnology
Beyond biological implications, the findings could revolutionize approaches to nanomaterials fabrication. Controlling knotting could lead to the creation of patterned or mechanically reinforced structures, offering potential advancements in large-scale separation and characterization tools used in both laboratories and industry.
“Field-driven knotting may someday provide a scalable alternative to what researchers currently call ‘knot factories,'” MacKintosh suggested. “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.”
Future Directions and Research Support
According to Luca Tubiana, co-author and associate professor at the University of Trento, “In general, knots appear in very long polymers and require even longer polymers to become tight and stable. 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. As scientists continue to explore the implications of this discovery, the potential for new technological advancements and deeper understanding of polymer dynamics remains vast.
