Fractal dimension and localization of DNA knots.

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 radius of gyration of the adsorbed DNA knot scales with the 3D Flory exponent nu approximately 0.60 within error. In (ii), we find nu approximately 0.66, a value between the 3D and 2D (nu=3/4) exponents. Evidence is also presented for the localization of knot crossings in 2D under weak adsorption conditions.