Magnetic tweezers method to measure single molecule torque

1. A system for determining torque applied to a filament, comprising:

a substrate having a first binding point suitable for attachment of a first end of a filament;

a magnet arranged in a relationship opposed to the substrate;

a magnetic probe having a magnetic moment, an azimuthal orientation, and a second binding point suitable for attachment of a second end of the filament, positioned between the substrate and the magnet; and

a translation stage disposed proximate to the substrate and the magnet;

an imaging device proximate to the substrate, magnet, and magnetic probe;

wherein the imaging device is adapted to determine the azimuthal orientation of the magnetic probe, and

wherein the second binding point of the magnetic probe is offset from the magnetic moment.

2. The system of claim 1 , wherein the translation stage is attached to the substrate.

3. The system of claim 1 , wherein the translation stage is attached to the magnet.

4. The system of claim 1 , wherein the magnetic moment of the magnetic probe is approximately parallel to an orientation axis passing through the first binding point and the second binding point.

5. The system of claim 1 , wherein the translation stage has two axes of motion.

6. The system of claim 1 ,

wherein the magnet is a single permanent magnet.

7. The system of claim 6 ,

wherein the single permanent magnet is affixed to a z-stage translatable in a direction approximately parallel to an orientation axis passing through the first binding point and the second binding point.

8. The system of claim 1 ,

wherein the magnet is an electromagnet.

9. The system of claim 8 , wherein a magnetic field of the electromagnet is variable.

10. The system of claim 1 ,

wherein the magnetic probe comprises a magnetic bead and a lever,

wherein the magnetic moment of the magnetic probe passes through the magnetic bead, and

wherein the lever comprises the second binding point.

11. The system of claim 1 ,

wherein the magnetic probe comprises a superparamagnetic material.

12. The system of claim 1 , wherein the filament is a macromolecule.

13. A method for determining the torque applied to a filament, comprising:

affixing a first end of the filament to a substrate;

affixing a second end of the filament to a magnetic probe having an azimuthal orientation;

applying an external magnetic field having a magnetic axis to move the magnetic probe and elongate the filament along an orientation axis passing through the first end and the second end of the filament;

moving the first end of the filament relative to the magnetic axis of the external magnetic field to change the azimuthal orientation of the magnetic probe and impose twist on the filament;

obtaining images of the magnetic probe at a plurality of successive times;

using the images to determine the azimuthal orientation of the magnetic probe at the successive times;

obtaining a probability distribution of azimuthal orientations from the azimuthal orientations at the successive times; and

determining the torque on the filament from the probability distribution of azimuthal orientations.

14. The method of claim 13 , wherein the filament is a polynucleotide.

15. The method of claim 13 , wherein the first end of the filament is moved relative to the magnetic axis by translating the substrate.

16. The method of claim 15 , wherein the substrate is translated in a curve having a winding number about the magnetic probe.

17. The method of claim 16 , wherein the winding number is at least one.

18. The method of claim 16 , further comprising determining the torque on the filament as a function of the azimuthal orientation and/or the winding number.

19. The method of claim 16 , further comprising varying the external magnetic field to vary an elongation force along the orientation axis of the filament.

20. The method of claim 19 , further comprising determining the torque as a function of the elongation force and the azimuthal orientation and/or the winding number.

21. The method of claim 13 , wherein the first end of the filament is moved relative to the magnetic axis by translating the external magnetic field.