Thin-foil magnetic force system for high-numerical-aperture microscopy

Forces play a key role in a wide range of biological phenomena from single-protein conformational dynamics to transcription and cell division, to name a few. The majority of existing microbiological force application methods can be divided into two categories: those that can apply relatively high forces through the use of a physical connection to a probe and those that apply smaller forces with a detached probe. Existing magnetic manipulators utilizing high fields and high field gradients have been able to reduce this gap in maximum applicable force, but the size of such devices has limited their use in applications where high force and high-numerical-aperture (NA) microscopy must be combined. We have developed a magnetic manipulation system that is capable of applying forces in excess of $700\mathrm{pN}$ on a $1\mathrm{\mu }\mathrm{m}$ paramagnetic particle and $13\mathrm{nN}$ on a $4.5\mathrm{\mu }\mathrm{m}$ paramagnetic particle, forces over the full $4\pi \mathrm{sr}$ , and a bandwidth in excess of $3\mathrm{kHz}$ while remaining compatible with a commercially available high-NA microscope objective. Our system design separates the pole tips from the flux coils so that the magnetic-field geometry at the sample is determined by removable thin-foil pole plates, allowing easy change from experiment to experiment. In addition, we have combined the magnetic manipulator with a feedback-enhanced, high-resolution $\left(2.4\mathrm{nm}\right)$ , high-bandwidth $\left(10\mathrm{kHz}\right)$ , long-range ($100\mathrm{\mu }\mathrm{m}$ xyz range) laser tracking system. We demonstrate the usefulness of this system in a study of the role of forces in higher-order chromosome structure and function.