Long-Lived Self-Entanglements in Ring Polymers

Abstract

The entanglement of ring polymers remains mysterious in many aspects. In this Letter, we use electric fields to induce self-entanglements in circular DNA molecules, which serve as a minimal system for studying chain entanglements. We show that self-threadings give rise to entanglements in ring polymers and can slow down polymer dynamics significantly. We find that strongly entangled circular molecules remain kinetically arrested in a compact state for very long times, thereby providing experimental evidence for the severe topological constraints imposed by threadings.

Self-entanglement of a tumbled circular chain

“…8 may not represent the only ways in which the given self-entanglements can form on circular chains, the possible mechanisms shed light on what gives rise to circular entanglements. In our recent experimental study on self-entangled circular DNA [27], we postulated that the self-entangled states were induced by self-threadings, but were unable to confirm this by direct visualization of individual molecules given the length scales involved. The possibility that circular molecules can self-entangle by forming double-folded knots was deemed negligible due to the energetically unfavorable configuration of having two halves of the chain align together [48].…”

“…The results of this study highlight the advantages of implementing macroscale systems to probe microscale systems. Previous single-molecule DNA experiments performed by our group [27] concluded that circular molecules can selfentangle and remain in an entangled state for long time scales, but due to the resolution limit of the optical system, the nature of the self-entangled states could only be inferred from relaxation dynamics. With a macroscale system of granular chains, we are able to directly visualize the chain conformation and examine the self-entanglements on circular chains.…”

“…8(a) self-entanglements-(3 1 , 0 1 , 1) and (4 1 , 0 1 , 1)-involves twisting of the chain and passing of a double-folded segment through another double-folded segment on the same chain. The configuration in which a double-folded segment opens up and penetrates another double-folded segment on the same chain is known as self-threading, and threadings have been reported to slow down ring polymer dynamics both computationally [45][46][47] and experimentally [27]. It is interesting to observe the disparity in occurrences of (3 1 , 0 1 , 1) and (4 1 , 0 1 , 1) despite the degree of similarity in entanglement pathways, with the only difference being a loop threaded under or over through another loop.…”

“…Most experimental studies on entangled polymers to date have focused on linear chains, although there is growing interest in more complex topologies, such as circular chains [24][25][26]. Recently, our group performed single-molecule experiments to compress and induce self-entanglements in circular DNA with electric fields, with self-entanglements serving as a minimal system for studying chain entanglements [27]. Since the conformations of the compressed circular molecules were not resolvable by fluorescence microscopy, we probed the nature of the compressed states by studying FIG.…”

Topological Tuning of DNA Mobility in Entangled Solutions of Supercoiled Plasmids

“…Entangled solutions of DNA plasmids are not only interesting because of potential applications in bio and nanotechnology but also because they are a proxy to study fundamental questions on the physics of ring polymers [9,25,26]. To characterise the effect of DNA supercoiling in entangled solutions, here we perform large scale Molecular Dynamics simulations of entangled DNA plasmids ( Fig.…”