Dynamics of DNA Knots during Chain Relaxation

Abstract

We perform single-molecule experiments and simulations to study the swelling of complex knots in linearly extended DNA molecules. We induce self-entanglement of DNA molecules in a microfluidic T-junction using an electrohydrodynamic instability and then stretch the molecules using divergent electric fields. After the chain is fully extended, the knot appears as a region of excess fluorescent brightness, and we shut off the field and observe the knot swelling over time. We find (1) the knot topologies created by the instability are more complex than what is expected from equilibrium simulations of knot formation, (2) the knot swells at a time scale comparable to the end-to-end relaxation of the chain, which indicates that the swelling is dictated by the chain’s global dynamics, and (3) knots are long-lived when the DNA is in the coiled state. These findings demonstrate the rich physics involved in the relaxation of knotted polymers which has not been examined heretofore.

Knots modify the coil–stretch transition in linear DNA polymers

“…While the length scale of the knot is too small to be resolved by fluorescence microscopy, we can use intensity as a measure of the contour length stored within the knot. 20 We use as a measure of fractional knot size the integrated intensity of the knotted region divided by the integrated intensity of the molecule, where the knotted region is defined as a 9-pixel (1.6 mm) window centered around the brightest pixel of the knot. While this is not a direct measure of the knot contour, we find it the most systematic way of characterizing knot sizes for the purposes of this work, as discussed in the ESI.…”

“…Qualitatively, we can rationalize the faster relaxation of knotted molecules by considering the free contour length of the molecule. Previous studies involving knots in T4 DNA molecules induced by an electrohydrodynamic collapse have estimated the knot contour in tight knots to be between 1 mm and 5 mm, 19,20 which corresponds to between 1% and 6% of the contour length. Stored contour in the knot results in the molecule having less free chain contour for relaxation, and smaller molecules relax at a faster rate.…”

“…10 Most experiments to date have involved linear DNA molecules, 15 although there is recent interest in circular DNA molecules, 16,17 as well as other complex topologies, including molecules with branches 18 and knots. 19,20 Theoretically, it has been proven that the knotting probability of a chain approaches unity as the chain length tends to infinity, hence knots are inevitably present in long polymer chains. 21 The probability of knot formation in DNA has been studied both computationally [22][23][24] and experimentally 25,26 on length scales of relevance.…”

“…44 Previous work from our group investigated the swelling of knots in DNA molecules during chain relaxation and showed that the knot growth time scale is governed by the global chain relaxation time scale. 20 Knotted DNA molecules subjected to elongational fields were shown to exhibit nucleation-type behavior of the coilstretch transition and to stretch at a much slower rate compared to unknotted molecules. 19 Experimentally, the dynamics of knotted polymers is a rich area for exploration.…”

Hydrodynamic inflation of ring polymers under shear

“…Knots are naturally found on long DNA strands [29][30][31] and proteins [32][33][34] while at the same time they can also be artificially [35,36] or synthetically manufactured [37] . The influence of such knots * maximilian.liebetreu@univie.ac.at † christos.likos@univie.ac.at in equilibrium and relaxation properties in the bulk [38][39][40][41][42][43][44][45][46] , under confinement [47][48][49][50][51][52][53][54][55][56] and under tension [57][58][59][60][61][62][63][64] has been thoroughly investigated. Recently, the sedimentation behavior of flexible, non-Brownian knots has been added to the host of counterintuitive phenomena [65] .…”