Fractal Dimension and Localization of DNA Knots

Abstract

The scaling properties of DNA knots of different complexities were studied by atomic force microscope. Following two different protocols DNA knots are adsorbed onto a mica surface in regimes of (i) strong binding, that induces a kinetic trapping of the three-dimensional (3D) configuration, and of (ii) weak binding, that permits (partial) relaxation on the surface. In (i) the gyration radius of the adsorbed DNA knot scales with the 3D Flory exponent $\nu \approx 0.58$ within error. In (ii), we find $\nu \approx 0.66$, a value between the 3D and 2D ($\nu =3/4$) exponents, indicating an incomplete 2D relaxation or a different polymer universality class. Compelling evidence is also presented for the localization of the knot crossings in 2D.

arXiv comment4 pages, 3 figures

References in corpus (6)

• Critical exponents for random knots
• Scaling exponents and probability distributions of DNA end-to-end distance
• What is the length of a knot in a polymer?
• Equilibrium shapes of flat knots
• Pulling Knotted Polymers
• Tight and loose shapes in flat entangled dense polymers

Cited by in corpus (24)

• Polymers with spatial or topological constraints: theoretical and computational results
• Topological jamming of spontaneously knotted polyelectrolyte chains driven through a nanopore
• Metastable tight knots in a worm-like polymer
• Numerical study of linear and circular model DNA chains confined in a slit: metric and topological properties
• Conformation of Circular DNA in 2 Dimensions
• Influence of Rigidity and Knot Complexity on the Knotting of Confined Polymers
• Multiscale entanglement in ring polymers under spherical confinement
• Sequence-specific size, structure, and stability of tight protein knots
• Effect of bending rigidity on the knotting of a polymer under tension
• Excluded volume effects on semiflexible ring polymers
• Universality in the diffusion of knots
• Conformational properties of complex polymers: rosette versus star-like structures
• The circular Kardar-Parisi-Zhang equation as an inflating, self-avoiding ring polymer
• Knot localization in adsorbing polymer rings
• Ring polymers in confined geometries
• Characteristics of shape and knotting in ideal rings
• Structural crossover of polymers in disordered media
• Osmotic pressure of compressed lattice knots
• Fluctuations of ring polymers
• Knotting probabilities after a local strand passage in unknotted self-avoiding polygons
• Aggregation of amphiphilic polymers in the presence of adhesive small colloidal particles
• Free Energy of a Knotted Polymer Confined to Narrow Cylindrical and Conical Channels
• Fluctuation force exerted by a planar self-avoiding polymer
• Scaling properties of diblock copolymers: dynamic simulations study