Figure 1.
Principle of magnetic tweezers (MT) and increase in data throughput via parallelization.
Positioning and rotation of an external magnet pair allows application of a force and torque to DNA-molecules bound to paramagnetic beads. DNA-bead tethers in the flow cell (FC) are visualized using a microscope system, consisting of an LED, a lens (L), an objective (OBJ), a tube lens and a camera. Images of the experiment are JPEG-compressed and saved to a hard drive. After the experiment, the images are analyzed and the xyz-positions of all beads in the field of view are extracted.
Figure 2.
3D modeling of the variation of the force across the field of view and angle of the force vector.
A Magnitude of force, Fmag, acting on paramagnetic beads as function of their position in the field of view (field of view size = 400×400 µm) for a magnet height of 1 mm (symmetry axis of the magnet pair parallel to y-axis). A maximum variation in the force magnitude of 1.2% is found. B Angle between the force vector and the vertical axis, α, for a bead-DNA tether at the edge of the field of view (position in x, posX = 0.2 mm, position in y, posY = 0 mm). α = 27.7° for Zmag = 0 mm and α = 3.4° for Zmag = 1 mm.
Figure 3.
Rotational response of a DNA-bead tether.
A The response of a DNA-bead tether subject to a rotating external magnet pair (frequency of rotation ωmag) that is misaligned with respect to the axis of rotation of the magnet pair and for which the DNA attachment position is eccentric, is a combination of a precessional motion with radius, Rprec and frequency ω = 2ωmag (panel I) and a rotational motion around the DNA attachement point with radius, Ratt and frequency ω = ωmag (panel II). The bi-circular rotation pattern describes a roulette that is a special case of the epitrochoid: the Limaçon (panel III). B Measurement of the rotational response for a DNA-bead tether at different positions in the field of view The * denotes the position of the rotation axis of the magnet. For clarity in presentation, the patterns were scaled up by a factor 37.5 compared to the scale of the field of view. C Ratt and Rprec as function of the distance of the tether position to the center of the magnet. Ratt is independent of the position of the tether in the field of view, as expected. Rprec increases with the distance to the center of the magnet. Red line is prediction based on calculations of the 3D force field (as in Fig. 2).
Figure 4.
Fact characterization of the mechanical properties of a DNA-bead tether. A
Characterization of the DNA length. The lowest bead height in the absence of an applied force is measured and the length is accordingly offset corrected. B Measurement of bead attachment offset from rotational response of the DNA-bead tether (cf. Fig. 3). C Dynamic measurement of the force-extension characteristic of the molecule. The length of the molecule was measured while linearly increasing the magnet height. The applied vertical magnetic force, Fmag,z, is exponentially dependent on the magnet height (see sup Fig. S7). . F0 is a force-calibration factor that was characterized in an independent measurement to account for bead-to-bead variations in magnetic polarizability. D Energy versus extension curve allows extracting values for the persistence length and contour length with high fidelity [4]. Energy versus extension was calculated from the data in panel c using eq. (2).
Figure 5.
Ensemble analysis of DNA mechanics.
A Multiplexed measurements of the persistence length, Lp, versus the contour length, Lc, for DNA molecules with different length (2.2 kb (N = 19), 7.3 kb (N = 16), 11.9 kb (N = 36) and 20.1 kb (N = 9)). The data is compared to predictions from finite-difference modeling in the absence of thermal fluctuations (black line) and in the presence of thermal fluctuations (blue line). B Histogram of extracted force-calibration factor F0/<F0> (N = 120). C Ensemble study of attachment position of the DNA on the bead. The histogram shows the distribution of DNA-bead attachment offsets (N = 45). Red line is the expected distribution (see Fig. S5 and eq. 3).