Why do DNA loops forming different knot types sediment at different speeds? Researchers from SIB, UNIL and EPFL joined forces with Polish colleagues to answer this question. To their surprise, what they observed closely resembled another, fascinating physics phenomenon, namely the way smoke rings behave in the air. This would certainly have pleased Lord Kelvin, who was among the first scientists to study their behavior. The results, published in the prestigious journal Physical Review Letters, could improve our understanding of the shape and function of biomolecules.

Box 1. Lord Kelvin’s dream

In 1867, British physicist Sir William Thomson, known today as Lord Kelvin, became fascinated by the experiments of one of his peers, Peter Guthrie Tait, on smoke rings. He was particularly impressed by their self-sustained stability and vortex-like movement. If smoke rings were formed as knotted, they could never become unknotted, he suggested. Although attempts by Kelvin and his collaborators to produce knotted smoke rings were unsuccessful, their seminal work led to some important applications, from particle physics to superconductors.

smoke rings tait vortexTait Lecture 1878. Device designed to produce ‘ideal’ smoke rings: when tapped on the back of the box filled with thick smoke, vortex rings shot out from a hole in the front.

Tell me your knot type, and I will tell how you were formed

Biological processes such as DNA transcription – the first step of gene expression – can result in the formation of various types of transient DNA knots, which are conditioned by the 3D arrangement of the DNA molecules. By studying the types of formed knots, biologists can thus infer important details about the overall architecture of chromosomal DNA.

Determining DNA knot types often relies on a method called analytical centrifugation, where sedimenting molecules with different spatial arrangements segregate from each other. But so far, the relationship between knot types and their dynamics has remained elusive.

In order to gain a better understanding of this relationship, a joint project was set up, involving Giovanni Dietler’s group at EPFL and Andrzej Stasiak, Group Leader at SIB and UNIL. How did they proceed? “We designed flexible knots made of steel beaded chains in order to mimic knotted macromolecules,” explains Stasiak.

The strange behavior of sinking knotted loops

“What we observed when these knotted chains where sinking into the viscous liquid was quite remarkable,” he adds. “It appeared to us that they were behaving very much like Lord Kelvin’s smoke rings did in the air!” (see Box 1).
Indeed, after an initial rearrangement on a single horizontal plane, the steel chains twirled and rotated while sinking, in a very stable fashion (see video below), not unlike the vortices of smoke rings studied by the famous British physicist.

Experimental setup: flexible beaded chains sedimenting in oil. 

A general hydrodynamic model

To describe the phenomenon in a more general context, the team – now including fluid dynamics groups from the Polish Academy of Science and the University of Warsaw, performed numerical simulations that took into account the hydrodynamic interactions between the sedimenting knotted elastic chains, and the surrounding liquid at micro scale.

smoke rings trefModel of knotted chains used for the numeric simulations.

“Our simulations recapitulated the experimental observations and supported the proposal that knotted vortices can form long-lasting regular structures translating in fluids, making one of Kelvin’s numerous dreams come true,” concludes Stasiak.

These findings could lead to improved interpretations of ultracentrifugation data, which are widely used for the quantitative and topology analysis of knotted DNA.


Gruziel M, Thyagarajan K, Dietler G, Stasiak A, Ekiel-Jezewska M L, Szymczak P. Periodic motion of sedimenting flexible knots. Physical Review Letters 2018.
Full text available at: https://arxiv.org/abs/1808.05818