Twisting and Stretching
Single Molecules
Adding a twist to DNA
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A pair of powerful magnets located above the sample are used to control DNA stretching and supercoiling.


These rare earth magnets (BdFeB) have been designed to produce a very strong magnetic field gradient. As depicted in the accompanying figure, the magnetic field is horizontal whereas the field gradient is vertical. The magnets are aligned with the optical axis of the microscope, and the gap between the magnet pole pieces provides a convenient light path for microscope illumination. The magnets are vertically translated (towards or away from the sample) by a fast translation stage. The magnetic force pulling on the bead displays an exponential dependence on the distance z separating the bead from the magnets: F = F0 exp(-z/z0). Typically z0 is on the order of a fraction of a millimeter, while F0 depends of the bead size. For the MyOne Dynal bead with 1 micron diameter, F0 = 15 pN. The translation stage can vary z by one millimeter in 200 ms, thus changing the force by a factor of 4. Since z0 is much larger than the displacement of the bead (~ 1 μm for 3-kb DNA) when z is maintained constant, the magnetic tweezers naturally function in a constant force regime.

When the magnets are rotated about the vertical axis by a second motor, the magnetic field direction follows this rotation while the field gradient remains constant. Thus the magnet rotation imposes the angular orientation of the bead, which effectively behaves like a small compass needle in a magnetic field, all the while maintaining a constant stretching force. Rotation rates on the order of 10 revolutions per second - compatible with most biomolecular motors - are easily attained. Both the rotation angle and stretching force are controlled by the same software package which tracks the bead position, making it possible to change these control parameters on the fly to rapidly test different reaction conditions.
Magnetic field gradient
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