High-force magnetic tweezers with hysteresis-free force feedback

ABSTRACT Magnetic tweezers based on solenoids with iron alloy cores are widely used to apply large forces (~100 nN) onto micron-sized (~5 μ m) superparamagnetic particles for mechanical manipulation or microrheological measurements at the cellular and molecular level. The precision of magnetic tweezers, however, is limited by the magnetic hysteresis of the core material, especially for time-varying force protocols. Here, we eliminate magnetic hysteresis by a feedback control of the magnetic induction, which we measure with a Hall sensor mounted to the distal end of the solenoid core. We find that the generated force depends on the induction according to a power-law relationship, and on the bead-tip distance according to a stretched exponential relationship. Together, both relationships allow for an accurate force calibration and precise force feedback with only 3 calibration parameters. We apply our method to measure the force-dependence of the viscoelastic and plastic properties of fibroblasts using a protocol with stepwise increasing and decreasing forces. We find that soft cells show an increasing stiffness but decreasing plasticity at higher forces, indicating a pronounced stress stiffening of the cytoskeleton. By contrast, stiff cells show no stress stiffening but an increasing plasticity at higher forces. These findings indicate profound differences between soft and stiff cells regarding their protection mechanisms against external mechanical stress. In summary, our method increases the precision, simplifies the handling and extends the applicability of magnetic tweezers. SIGNIFICANCE Magnetic tweezers are widely used, versatile tools to investigate the mechanical behavior of cells or to measure the strength of receptor-ligand bonds. A limitation of existing high-force magnetic tweezer setups, however, is caused by the magnetic hysteresis of the tweezer core material. This magnetic hysteresis requires that the tweezer core must be de-magnetized (de-Gaussed) prior to each measurement, and that flexible force protocols with decreasing forces are not possible. We describe how these limitations can be overcome with a force feedback though direct magnetic field measurement. We demonstrate the applicability of our setup by investigating the visco-elastic and plastic deformations of fibroblasts to forces of different amplitudes.