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Knotted Loops Identical To Knotted Molecules Fall Flat

Researchers from University of Warsaw developed a knotted loop of metal beads that organizes into a flat horizontal ring when drifting down through a viscous fluid

Long-chain molecules can develop knots that are responsible for the movement of molecules through a liquid medium. Now, a team of Polish and Swiss researchers at the University of Warsaw devised an experiment with loops of small metal beads dropped in a viscous fluid, to understand this behavior. The team mimicked the knotted molecular chains by arranging each loop to wind around itself in a loose knot. The team observed that when the knotted loops fell they settled into horizontally flat configurations irrespective of the pattern of their initial drop. The results demonstrate a connection between topology and hydrodynamics, which can further help to understand the shape evolution of large molecules moving in fluids.

In previous studies with DNA knots, researchers found that the speed of a drifting knotted DNA molecule through a thick gel depends on the complexity of its knot. The team used macroscopic loops as filming the drift for nanoscopic DNA is nearly impossible. The loops resemble small beaded bracelets and were formed with multiple loops that intertwined. This resulted in loose, open knots that resemble a trefoil knot and a figure-eight knot. The loops were dropped one at a time into a tall cylinder filled with silicone oil. The loops evolved from a random jumble of beads into a torus shape when these fell into the oil. The torus shape comprised a flattened loop of intertwined strands that swirled around each other in a cyclic pattern. Furthermore, the team performed numerical simulations and offered theoretical explanation of the flattening and swirling of the loops as a result of bead interactions mediated by the fluid. The findings provide insight about the underlining mechanism of large molecules residing inside a rapidly rotating centrifuge. The research was published in the journal Physical Review Letters on September 18, 2018.