Near-field-magnetic-tweezer manipulation of single DNA molecules

We have developed an instrument for micromanipulation of single DNA molecules end labeled with $3\text{−}\mu \mathrm{m}$-diameter paramagnetic particles. A small, permanent magnet that can be moved as close as $10\mu \mathrm{m}$ to the particle being manipulated can generate forces in excess of $200\mathrm{pN}$, significantly larger than obtained in other recent “magnetic-tweezer” studies. Our instrument generates these forces in the focal plane of a microscope objective, allowing straightforward real-time observation of molecule extension with a position resolution of approximately $30\mathrm{nm}$. We show how our magnetic manipulation system can be combined with manipulation and force measurement using glass micropipettes to allow rapid switching between measurements in fixed-force and fixed-extension ensembles. We demonstrate the use of our system to study formation of DNA loops by an enzyme which strongly binds two copies of a specific 6-base-pair sequence.

Figure 1

Three glass micropipettes and a submillimeter-size magnet are involved in the experiment: (1) The upper pipette is the movable catching pipette ($2\text{−}\mu \mathrm{m}$ opening diameter) used to catch a bead pair connected by a single DNA. (2) The lower pipette is the force-measuring pipette ($\sim 2\text{−}\mu \mathrm{m}$ opening size) mounted on the microscope stage. It has a long taper so as to have a force constant $\sim 200\mathrm{pN}∕\mu \mathrm{m}$ deflection from its equilibrium position. Calibration is done by the technique in Ref. 13. (3) The left pipette is the loading pipette ($\sim 20\text{−}\mu \mathrm{m}$ opening size) used to inject the prepared DNA sample into the open cell made by plastic ring. Once a single-DNA pair is found, the catching pipette delivers its nonmagnetic end to the force measuring pipette. Fluctuations of the magnetic end can be used to calibrate force; alternately, it can be moved by the catching pipette to do a fixed-extension experiment. (4) The object to the right is the front of the submillimeter-size magnet glued to a glass pipette. It can be moved to any position in the cell.

Figure 2

The deflection of a force-measuring pipette holding a magnetic bead is shown as a function of distance between the bead and the front of the magnet. The force-measuring pipette was calibrated using the technique described in Ref. 13 to have a force constant of $137\mathrm{pN}∕\mu \mathrm{m}$. The deflection was then converted to the force applied on the magnetic bead. The magnet used in this experiment can provide more than $200\mathrm{pN}$ on the magnetic bead at a distance about $15\mu \mathrm{m}$ away.

Figure 3

Using the transverse fluctuations of the paramagnetic bead, the force applied to a single DNA can be measured. A $\mathrm{\lambda }$-DNA bead pair was caught in PBS and its end-to-end distance, $z$, was studied, as a function of the applied force determined by the transverse fluctuation of the magnetic bead. Six lengths were measured at six different forces between $1$ and $6\mathrm{pN}$. We plot $z∕L$ vs $\sqrt{1∕f}$ here. The slope of the linear fit is $-0.14\sqrt{\mathrm{pN}}$, corresponding to $A=52\mathrm{nm}$ for $T=300\mathrm{K}$, via use of the worm-like chain model (see the text).

Figure 4

Calibration of force-measuring pipette using magnetic tweezer and single DNA. For time $<5\mathrm{s}$, magnetic force was $<1\mathrm{pN}$, and deflection of pipette reflects essentially its zero-force position. During times between 5 and $18\mathrm{s}$, magnet is moved; variations in pipette deflection reflect hydrodynamic noise. For time $>18\mathrm{s}$, magnet is at a position close enough to generate a measurable pipette deflection of $0.2\mu \mathrm{m}$; by simultaneously measuring paramagnetic bead fluctuations, we are able to determine that the force being applied is $33\mathrm{pN}$, which allows the pipette bending moment to be determined (see the text for details.)

Figure 5

Time series for opening loops along a $\mathrm{\lambda }$-DNA, formed by the type IIs restriction (cutting) enzyme BspMI, at a force $\sim 4.5\mathrm{pN}$. We used the catching pipette to move the magnetic particle to a constant position $8\mu \mathrm{m}$ away from the nonmagnetic bead, allowing the $16\text{−}\mu \mathrm{m}$ molecule to encounter itself in a solution of $6\text{units}∕\mathrm{ml}$ BspMI in PBS with $100\text{−}\mu \mathrm{m}$ $\mathrm{Ca}{\mathrm{C}}_2$. After incubation for 10 min, we released the magnetic bead, thus placing the molecule under tension of $4.5\mathrm{pN}$ applied by the magnet. A series of jumps in DNA extension was observed, as the loops were opened. The largest jump was $\sim 500\mathrm{nm}$ (note that between times of $215$ and $225\mathrm{s}$ there are three jumps, the largest one about $500\mathrm{nm}$). Upper inset shows the first $70\mathrm{s}$ to show small jumps of $\sim 150$, $\sim 50$, and $30\mathrm{nm}$. A series of experiments of this type allowed us to determine a critical force of $1.75\pm 0.25\mathrm{pN}$ for opening the BspMI loops.