# Single-molecule experiments

To manipulate single DNA molecules and study their interactions with a variety of proteins (helicases, chromatine remodelling factors, topoisomearses, etc.) we are using magnetic tweezers, a system now commercialised by picotwist. The set-up consists of  super-paramagnetic beads (sold by Dynal) in a fluidic cell that allows for buffer exchange positioned on top of a microscope objective. The streptavidin coated beads are tethered to the bottom glass coverslip (coated with anti-Dig)  by one (or a few) DNA molecules (labelled at their extremities with biotin or Digoxigenin (Dig)). Small magnets positioned above the fluidic cell exert a force on the beads that is uniform (in the field of view) and controlled by the distance of the magnets to the beads (see Fig.1). By rotating the magnets the DNA tethering the beads to the surface can be twisted (if it is not nicked).

Fig.1: Schematics of a magnetic tweezers set-up built on top of an inverted microscope.A small superparamagnetic bead is tethered to a surface by a single DNA molecule that is stretched and twisted by small magnets placed above the sample. The force is set by the distance of the magnets to the sample, while the DNA twist is determined by the number of rotation of the magnets.

Fig.2: Numerical simulations of the fluctuations of a bead tethered by a single DNA molecule and pulled by a pair of magnets positioned above the bead. By moving the magnets up or down you can control the force applied on the bead (and thus its fluctuations: small at large forces and large at small forces).

The 3D position of the bead can be determined by analysing the image of the bead. The X,Y coordinate are determined by the center of the bead. The Z-coordinate is determined by correlating the image of the bead with images(exhibiting diffraction rings of varying size) taken at different focal position of the objective (see Fig.2).

Fig.3: Principle of vertical position determination by comparing the bead image at one position with a library of images of the bead at different focal positions of the objective.

The force $F$ applied on the bead can be estimated via the fluctuations $\lt dx^2 \gt$ of the bead. The bead-DNA system in the magnetic field of the magnets is similar to a pendulum with transverse rigidity $k_x = F/l$ (where $l$ is the DNA length, the distance of the bead to the surface).  From the dissipation-fluctuation theorem the amplitude of the transverse fluctuations are then given by $\lt dx^2 \gt = k_B T / k_x$. From here we derived

$F = k_B T l / \lt dx^2 \gt$

Magnetic tweezers provide a constant force set-up where forces between 0.01pN and 100pN can be easily applied and measured. By monitoring the change in extension of a stretched (and possibly twisted) DNA molecule when interacting with a protein (helicase, polymerase, topoisomerase, etc.) one can monitor its action in real time and characterize its parameters (rate, processivity, step-size, ...).