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The scaling properties of DNA knots of different complexities were studied byatomic force microscope. Following two different protocols DNA knots areadsorbed onto a mica surface in regimes of (i) strong binding, that induces akinetic trapping of the three-dimensional (3D) configuration, and of (ii) weakbinding, that permits (partial) relaxation on the surface. In (i) the gyrationradius of the adsorbed DNA knot scales with the 3D Flory exponent $\nu\approx0.58$ within error. In (ii), we find $\nu\approx 0.66$, a value between the 3Dand 2D ($\nu=3/4$) exponents, indicating an incomplete 2D relaxation or adifferent polymer universality class. Compelling evidence is also presented forthe localization of the knot crossings in 2D.Comment: 4 pages, 3 figure

Fractal Dimension and Localization of DNA Knots