Direct Measurement of the Confining Forces Imposed on a Single Molecule in a Concentrated Solution of Circular Polymers

Abstract

We measure the forces confining the displacement of a single DNA molecule embedded within a concentrated solution of long relaxed circular DNA molecules (115 kbp at 1 mg/mL) using optical tweezers. We compare these measurements with our previous measurements of forces imposed by entangled linear DNA molecules of the same length and concentration. A tube-like confining field and three relaxation modes were observed, but the tube radius was 25% smaller (=0.6 µm) and the longest relaxation time ∼3 times shorter (=11 s) than with linear molecules, consistent with recent theoretical predictions by Iyer, Lele, and Juvekar. For displacements greater than the tube radius, the confining force imposed by circular polymers was substantially lower and shorter range than that measured with linear polymers.

DNA as a Model for Probing Polymer Entanglements: Circular Polymers and Non-Classical Dynamics

“…Similar experiments carried out for entangled ring DNA of the same length and concentration showed that the tube radius a C was ~25% smaller than that for linear DNA ( a C ≅ 0.75 a L ≅ 0.6 µm), and the confinement field was weaker, displaying a subharmonic dependence on displacement [ 84 ]. The measured tube radius was close to predictions based on the pom–pom ring (PPR) model that applies the pom–pom model concept of lattice-tree polymer configurations, originally developed for branched polymers, to entangled rings [ 49 ].…”

Analysis of the Adequacy of the Representation of Entanglement Effects by Chain Loops

“…It is considered that chain uncrossability is better demonstrated by experiments with ring polymers since only they are capable of forming mathematically rigourous topological ''knots'' with neighbouring chains that permanently prevent chain crossing. [34] However, direct measurement of confining forces in concentrated solutions of linear and circular polymers demonstrate that the confining force imposed by circular polymers was substantially lower and of shorter range than that measured with linear polymers. [34] Based on these results, it was concluded that circular chains are less effective than linear chains at producing restrictive entanglements.…”

“…[34] However, direct measurement of confining forces in concentrated solutions of linear and circular polymers demonstrate that the confining force imposed by circular polymers was substantially lower and of shorter range than that measured with linear polymers. [34] Based on these results, it was concluded that circular chains are less effective than linear chains at producing restrictive entanglements. Still another demonstration that the looping picture and binary contacts between polymer chains cannot explain the elastic properties of polymer melts was obtained with experiments performed with entangled, non-concatenated, ring polystyrenes.…”

Effect of molecular architecture on ring polymer dynamics in semidilute linear polymer solutions

“…Here, it is important to note that c * is defined under equilibrium conditions when the linear polymers are unstretched by flow. Moreover, ring polymers generally exhibit a markedly different molecular weight dependence of the center-of-mass diffusion coefficient compared to linear polymers in background solutions of concentrated linear polymers or melts 19,20 . Nevertheless, it is possible to use single ring polymers as tracer polymers or probes to study entangled linear chain dynamics through small angle neutron scattering (SANS) or neutron spin echo (NSE) spectroscopy 21,22 , essentially by taking advantage of the slow diffusion of rings in ring-linear blends.…”