Magnetic tweezer

Such attempts have been made with the radiation pressure of a laser beam [353,349], optical trapping [354], and electrophoresis [355], 

Background noise can lead to a shift and broadening of the potential energy profile. 

In an external magnetic field of field strength B, a superparamagnetic bead with radius i p will have a magnetic moment of 

The selection of the optimum bead size is a compromise. On the one hand, the particles should be as small as possible to minimize force due to Brownian motion. On the other hand, optical video microscopy is used for position tracking and the magnetic force scales with the particle volume (Eq. (3.36)). Typical head diameters are 0.5-5 pm. 

The position of the probe bead is commonly determined by video microscopy and digital image processing. The x- and,y- positions can be determined from fits of the bead image with a resolution of wlO nm [366]. Higher resolution in bead position in all directions can be achieved if the magnetic tweezers are equipped with a laser illumination allowing back-focal plane interferometry [367, 368]. 

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Fig. 5. Magnetic tweezers, (a) Principle of action and formula to determine the force applied to the tethered bead (for details see text), (b) Horizontal version of the instrument used in the laboratories of SHL and JZ.

Fig. 6. Schematic illustration of the stopped-flow magnetic tweezers experiments to follow single chromatin fiber assembly, (a) Flow diagram of how the experiment was performed, (b) A blow-up of the cuvette, with the bead attached to its side note that the DNA tether is not normal to the wall of the cuvette because of the position of the external magnet, i.e., the z direction is out of the plane of the video frame, (c) A schematic explaining the calculation of the distance traveled by the bead across the videoscreen. The X- and y-coordinates of the bead position on each successive video frame are used to calculate the projected traveled distance, (d) The actual shortening of the fiber can be calculated from the projected shortening (travel of bead across screen) and the cosine of the angle theta.

By using two traps, it is possible to maintain a constant force [91]. This is also possible with magnetic tweezers. However, because of the low stiffness of the magnetic trap, the spatial resolution due to thermal flucmations is limited to a few tens of nanometers. 

Molecular probes, such as optical or magnetic tweezers,64-71 micropipets,72 and microfibers,73-74 have been developed to manipulate single molecules and to measure their response to mechanical actions such as stretching, torsion, and compression. A force resolution down to 0.1 pN enabled quantitative measurement of the molecular forces and provided novel information on the basic principles of folding, motion, and interactions of individual molecules. Complementary to the local mechanical probes, actions of external fields were monitored on individual polymer molecules.75 77... 

Optical and magnetic tweezers manipulate a handle in the form of a bead attached to the end of a molecule such as DNA. Optical tweezers and traps exploit the restoring force that can be exerted on a dielectric microbead by the electric-field gradients at the focus of a laser beam. In the case of magnetic tweezers, a magnetic bead is manipulated between magnetic poles. 

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