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 = F
0 exp(-z/z
0). Typically
z
0 is on the order of a fraction of a millimeter, while
F
0 depends of the bead size. For the MyOne Dynal bead
with 1 micron diameter, F
0 = 15 pN. The translation
stage can vary z by one millimeter in 200 ms, thus changing the force
by a factor of 4. Since z
0 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.