Magnetic tweezers: micromanipulation and force measurement at the molecular level

ABSTRACT Cantilevers and optical tweezers are widely used for micromanipulating cells or biomolecules for measuring their mechanical properties. However, they do not allow easy rotary motion and can sometimes damage the handled material. We present here a system of magnetic tweezers that overcomes those drawbacks while retaining most of the previous dynamometers properties. Electromagnets are coupled to a microscope-based particle tracking system through a digital feedback loop. Magnetic beads are first trapped in a potential well of stiffness 107 N/m. Thus, they can be manipulated in three dimensions at a speed of 10 m/s and rotated along the optical axis at a frequency of 10 Hz. In addition, our apparatus can work as a dynamometer relying on either usual calibration against the viscous drag or complete calibration using Brownian fluctuations. By stretching a DNA molecule between a magnetic particle and a glass surface, we applied and measured vertical forces ranging from 50 fN to 20 pN. Similarly, nearly horizontal forces up to 5 pN were obtained. From those experiments, we conclude that magnetic tweezers represent a low-cost and biocompatible setup that could become a suitable alternative to the other available micromanipulators. LIST OF SYMBOLS Au (NA1) the factor between the force and the cur-rent flowing in the coils (Defined in Eq. 2) (nondimensional) the proportional feedback factor in the digital model (Defined in Eq. 11) Bu (m s1A1) the proportional factor between the velocity of a bead and the associated driving cur-rent (Defined in Eq. 19) (nondimensional) the ratio between the integral and the proportional feedback factors (Defined in Eq. 17) Cu (nondimensional) the correction signal in feedbac