MAGNETIC TWEEZERS
KRITHIKA MOHAN 20081048
Credit: TU Delft/Tremani Magnetic Tweezers
Fundamental role of force in biological systems.
Important single molecule manipulation technique to measure forces (pN) and displacements (nm).
Why single molecule techniques? Advantages of single-molecule techniques over conventional ensemble measurements - Direct measurement, no population averaging. - Capture rare/transient phenomena. - Measure dynamics under equilibrium conditions. Magnetic Tweezers – Physical concept
A magnetic particle in an external magnetic field experiences a force proportional to the gradient of the square of the magnetic field. Energy of a particle in a magnetic field B: U = - m(B) . B, where m is magnetic moment of the particle
Force, F = - grad(U) = grad(m(B) . B)
For small external fields: m(B) ∞ B F ∞ grad (B2).
For large external fields : F = grad (msat . B), where msat = saturation value of magnetic moment. Technique
Basic magnetic tweezers consist of a pair of permanent magnets placed above the sample holder of an inverted microscope outfitted with a CCD camera.
Experiment preparation: Typically, a DNA/ RNA/ Protein molecule is first anchored to a surface with one end and with the other to a probe, through which force is applied.
The probe is usually a trapped micron-sized superparamagnetic bead, the displacement of which allows measurement of the force. For anchoring the molecule, the substrate and the probe are prepared in a specific way. Substrate and Probe
Magnetic Tweezers
General Considerations: Molecule attachment – specific end- binding, support infinite loads, inert surface. Measurement concerns – ability to measure accurate position of probe. Technical details
1. Superparamagnetic beads – size of the order of µm, thermal ordering of magnetic domains on external magnetic field B.
2. Permanent magnet – Strongest Nedymium magnets, collocated with a 1mm gap, 3D is not possible in this setup, constant force experiments.
3. Magnetic interactions – Measure displacement of sensor tethered to a fixed surface by polymer using equivalence to an inverted pendulum. Neuman KC, Nagy A. Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy. Nat Methods. 2008;5:491–505. Force measurement - Magnetic Pendulum
Magnetic tweezers calibration in flow fields using Brownian motion.
Brownian motion – DNA Bead system is subject to Brownian fluctuations.
Using equipartition theorem, each degree of 2 2 freedom goes as x or v , with an energy of kbT/2
2 ½ k
2 Therefore, F = kbT l /
4. Electromagnets – Force and rotation can be controlled by changing the current rather than moving the magnets.
But, iron pole pieces to increase magnetic field, generation of heat Two sets of three pole pieces are Figure: Schematic representation of an symmetrically arranged in two axial electromagnetic tweezers pole planes, which provide full three- configuration permitting full three- dimensional control over the dimensional control. Thin (180 µm) position of the bead. The pole pole pieces (brown and gray) are pieces are sandwiched between laser machined from magnetic foil. electromagnetic coils in an assembly that mounts on an inverted microscope. Neuman KC, Nagy A. Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy. Nat Methods. 2008;5:491–505. Manipulation of single molecule with MT
DNA condensation and de-condensation involves the molecular conformation of supercoil – twisted and compacted state.
A magnetic field is used to torsionally constrain the DNA molecules enabling us to investigate the structure and topology of supercoiled DNA.
P.K. Purohit; Plectoneme formation in twisted fluctuating rods; Journal of the Mechanics and Physics of Solid, vol. 56, issue 5: 1715-1729, 2007 DNA Topology
DNA Supercoiling can be characterized by three quantities: a) Twist – Number of times the two strands of DNA twist around each other in a helical structure. b) Writhe – Number of crossings of the molecule axis over itself, when the molecule shape is projected onto a plane. c) Linking number – Twist + Writhe; topologically invariant in a constrained DNA molecule.
Degree of supercoiling = Lk – Lk0/Lk0 Twist DNA under an applied force F
Rotating the bead attached to a torsionally constrained DNA changes its linking number Lk. Starting from a torsionally relaxed molecule, change in linking number is equivalent to increasing twist, writhe unchanged. Here, torque ∞ number of turns (n).
After certain n = nb, DNA undergoes buckling transition and loops are formed to ‘store additional mechanical energy’. T.R. Strick, M-N. Dessimges, N.H Dekker, J-F. Allemand, D. Bensimon, V. Croquette; Stretching of macromolecules and proteins; Reports on Progress in Physics 66: 1-45, 2003 Buckling instability at F = 1 pN
We identify two regions:
- n < nb – DNA extension is unchanged
- n > nb - DNA extension decreases regularly.
T.R. Strick, J.-F. Allemand, D. Bensimon, V. Croquette; Bahavior of Supercoiled DNA; Biophysical Journal, 74: 2016-2028, 1998 Inducing plectonemes
Low forces – Plectonemes are induced independent whether overwinding or unwinding DNA
High forces – Overwinding or unwinding the molecule induces different behaviours due to the chiral nature of DNA.
Even higher forces (>5pN), no more plectonemes, new structure. Torsion free DNA.
D. Salerno, et al. Magnetic tweezers measurements of the nanomechanical properties of DNA in the presence of drugs; Nucleic Acids Reserach, vol.38, no.20: 7089-7099, 2010