Single-molecule techniques to control DNA topology (not to scale). a, magnetic tweezers consist of two magnets (red and blue) held above a microscope flow cell in which a magnetic bead (blue) is tethered to the surface (light blue) by a single DNA molecule (red and blue). The magnets impose an upward force on the beads, which depends on the vertical position of the magnets (black arrow). Rotating the magnets (black curved arrow) rotates the bead (red curved arrow), thereby changing the linking number of the DNA. b, optical rotation uses a focused laser (pink) to apply force on a quartz cylinder (blue) that is tethered to the surface of the flow cell by a molecule of DNA. The optical axis of the cylinder (blue arrow) experiences a torque that tends to align it with the polarization direction of the laser (pink arrow), which is focused by a microscope objective below the flow cell. c, rotor bead tracking uses a reporter bead (green) attached near a specific nick in the DNA molecule (red star). A magnetic bead (blue) at the distal end of the DNA allows torque and tension to be applied.