Optical tweezers based assays (not to scale). (a) Interaction assay. A low concentration of polystyrene or silica beads (green spheres) sparsely coated with kinesin molecules (yellow) are diffusing in solution. One bead is captured by the optical trap formed near the focus of an infrared laser (pink). The assay consists of bringing the trapped bead to the microtubule (brown tube) attached to the surface of the trapping chamber. The force and displacement generated by the individual kinesin molecule as it walks along the microtubule are determined from the displacement of the bead in the optical trap^{11, 20, 57}. (b) Tethered assay. An RNA polymerase molecule (purple) is attached to an optically trapped bead (green sphere), and the free end of the DNA template (red and blue) is attached to the surface of the trapping chamber. As the DNA is transcribed, the bead is pulled along the DNA by the polymerase. By moving the stage to compensate for this motion, thereby keeping the bead at the same position in the optical trap, long transcriptional records can be obtained at a constant force⁶³. (c) Dumbbell assay. This assay is similar to the tethered assay but the free end of the DNA is attached to a second bead, which is held in a second, independent, optical trap. The force on the bead is kept constant by moving one of the traps^{13, 62, 64}.

Magnetic tweezers. (a) Cartoon depicting the layout of a magnetic tweezers based on permanent magnets (not to scale). A superparamagnetic bead (green) is attached to the surface of the trapping chamber by a single molecule of DNA (red and blue). A pair of small permanent magnets (red and blue) above the trapping chamber produces a magnetic field gradient (dashed lines) along the axial direction, which results in a force on the bead directed up toward the magnets. The force is controlled by moving the magnets in the axial direction (black straight arrow). Rotation of the magnets (black circular arrow) produces rotation of the magnetic bead (red circular arrow) with a one-to-one correspondence. A microscope objective (grey) images the bead onto a CCD camera (not shown) for real time position tracking. (b) Schematic representation of an electromagnetic tweezers pole configuration permitting full three-dimensional control (adapted from reference⁸⁴) (not to scale). Thin (~180 μm) pole pieces (brown and grey) are laser machined from magnetic foil. Two sets of three pole pieces are symmetrically arranged in two axial planes, which provide full three-dimensional control over the position of the bead (green sphere). The pole pieces are sandwiched between electromagnetic coils in an assembly that mounts on an inverted microscope (not shown). (c) DNA topology measured with magnetic tweezers (not to scale). The extension as a function of rotation for a 1 μm superparamagnetic bead (green) tethered to the surface by a 3 kb molecule of DNA (red and blue) under 0.4 pN of pulling force. As the DNA is over- or under-wound (supercoiled) there is a slight decrease in extension near zero turns, which is due to the accumulation of twist in the DNA molecule. At ±4 turns the DNA buckles, forming a plectoneme loop. Each subsequent turn increases the plectoneme by another loop, leading to a linear decrease in extension from 4 to 12 turns (left and right cartoons). Removal of the plectonemes by the activity of a topoisomerase can be directly observed in real time by monitoring the extension of a supercoiled DNA molecule.

(a). Cartoon of the atomic force microscope (not to scale). The AFM consists of a cantilever with a sharp tip (yellow) held above a piezo scanning stage (grey). Deflection of the AFM cantilever is measured from the displacement of a low power laser (red beam) reflected off the cantilever on a position sensitive device (PSD) (blue disc). A typical AFM pulling experiment is displayed in which a poly-protein molecule (purple) is attached to the sample surface (copper) and the AFM cantilever tip. The piezo stage is retracted along the axial direction, increasing the separation between the cantilever and the sample surface. The force on the molecule is provided by the cantilever defection, and the extension of the molecule is equal to the separation between the AFM tip and the sample surface. (b) MFP stretching curve displays the force-induced unfolding of individual domain repeats of a hypothetical tetramer protein. Thin solid lines are the WLC fits to the data with a persistence length P_L of ~ 0.8 nm and the contour length increment ΔL_C of 15 nm.

Influence of probe size, stiffness and measurement bandwidth on spatial resolution. The power spectrum (Eq. 3) of the fluctuations of a probe particle attached to a spring undergoing Brownian motion. The noise power amplitude expressed as nm²·Hz⁻¹ is plotted as a function of frequency on a double logarithmic scale. The power spectrum for a one micron particle with a roll-off frequency of 2 kHz is shown in red. The power spectrum for the same particle with half the drag coefficient is shown in blue, and the power spectrum for a two-fold increase in stiffness is shown in green. Both of these changes increase the roll-off frequency while simultaneously decreasing the low frequency amplitude of the power spectrum. However, the area under the curve, and hence the position noise, is reduced only by increasing the stiffness (Eq. 1). The decrease in low frequency amplitude is compensated by the extended roll-off frequency when the drag is halved (blue trace), consequently the noise is equivalent for the red and blue curves. This is no longer the case if the signals are filtered. The reduction in noise achieved by filtering is illustrated by the shaded grey region that corresponds to a frequency bandwidth of 100 Hz. By limiting the measurement bandwidth to 100 Hz, the noise is reduced to the area under the curves in the shaded region, and there is a large difference in noise among the red, blue and green curves (see Eq. 4).