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Publication# Scaling properties of DNA knots studied by atomic force microscopy

Abstract

The main subject of the present thesis is the experimental study of the scaling properties of DNA knots of different complexities by tapping mode atomic force microscopy (AFM) in air. Homo- or heterogeneous mixture of DNA knot types were deposited onto mica in regimes of (i) strong adsorption, which induces a kinetic trapping of the molecules, and of (ii) weak adsorption, which permits relaxation on the surface. The contour of each knotted molecule was analyzed by a box counting algorithm, giving the number of boxes containing a part of the molecule, N(L), as a function of the box size, L, allowing to recover the relation N(L) ≈ L-df, where df is the fractal dimension and ν = 1/df is the scaling exponent. This relationship is complicated by the presence of a persistence length of DNA (about 50 nm) which introduces a crossover from a rigid rod behavior to a self-avoiding walk behavior. In (i) the radius of gyration of the adsorbed DNA knot scales with the 3D Flory exponent ν ≈ 0.58 within error. In (ii), the value ν ≈ 0.66, intermediate between the 3D and 2D (ν = 3/4) exponents, was found, indicating an incomplete 2D relaxation or a different polymer universality class. A different analysis, where the fractal dimension was determined by a customized box counting algorithm giving the knot mass as a function of the box size, yielded compatible results. In the case of weak binding conditions, AFM images show evidence of the localization of knot crossings, which is an effect theoretically predicted for knotted polymers confined in two dimensions (flat knots). Part of this thesis is dedicated to a fascinating application of AFM: the imaging of biomolecules in an aqueous buffer. In particular, images of plasmids adsorbed to mica strong enough to be visualized and loosely enough to see them moving in consecutive scans will be shown. The possibility of imaging under buffer molecules loosely anchored to the substrate opens the way to the investigation of biological processes near physiological conditions. The first step of the study of homologous recombination will be presented. We will also show images concerning our study of the activity of topoisomerase I on supercoiled plasmids. Clusters of DNA molecules and proteins were found when imaging in presence of magnesium, in agreement with recent findings by AFM in air. The research on topoisomerases and their interactions with inhibitors or poisons is a hot topic, being these enzymes targets of anti-cancer drugs. Our study paves the way to the investigation of the activity of topoisomerase II, the enzyme which removes knots from DNA. Finally, the principles of static and dynamic light scattering, and the results of dynamic light scattering on latex beads of known size will be presented. Particular emphasis will be given to the discussion of the contribution of light scattering techniques for future experiments on the study of the static and dynamic properties of DNA knotted molecules in solution. These experiments would contribute to shed light on the possible dependence of the gyration radius of knotted polymers on the knot type, and would allow testing theoretical predictions about their relaxation time.

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Related concepts (34)

Related publications (32)

Knot theory

In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, . Two mathematical knots are equivalent if one can be transformed into the other via a deformation of upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing it through itself.

Knot (mathematics)

In mathematics, a knot is an embedding of the circle S^1 into three-dimensional Euclidean space, R3 (also known as E3). Often two knots are considered equivalent if they are ambient isotopic, that is, if there exists a continuous deformation of R3 which takes one knot to the other. A crucial difference between the standard mathematical and conventional notions of a knot is that mathematical knots are closed — there are no ends to tie or untie on a mathematical knot.

Knot

A knot is an intentional complication in cordage which may be practical or decorative, or both. Practical knots are classified by function, including hitches, bends, loop knots, and splices: a hitch fastens a rope to another object; a bend fastens two ends of a rope to each another; a loop knot is any knot creating a loop; and splice denotes any multi-strand knot, including bends and loops. A knot may also refer, in the strictest sense, to a stopper or knob at the end of a rope to keep that end from slipping through a grommet or eye.

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