Force measurements

As shown in the last section it should be possible to measure the force-extension curve of a DNA carpet, provided that the drift of the experimental setup is small enough.

It turned out that performing a force measurement is in practice not an easy task.

For example it often happens that within the gap formed by the cantilever and the fiber a dust particle is located, although all liquids used were filtered with 200 nm pore size filters. The fragility of the cantilevers and of the fibers made a successful sample preparation a rare event. The very low yield of successful experiments might be caused additionally from the fact that it is not possible to cover the fiber with DNA within the sample cell but one has to do the DNA grafting outside the sample cell and then introduce the sample into the cell. The introduction of DNA into the sample cell is done in the following way. A freshly gold-covered fiber (length around 2 cm) is carefully placed into an Eppendorf tube with a thiol and biotin functionalized DNA sample (typically concentration was ≈ 3^ng_µl ). After an incubation time of 2h the fiber is carefully taken out and introduced into the cone. At the top of the fiber the buffer solution formed a small droplet protecting the DNA at the surface. The cone with the fiber fits very tightly into the sample cell and then the sample cell was filled with TBE buffer (pH 8.6). The whole procedure was performed in a flow box to avoid decontamination of the sample with dust. To verify that the DNA grafted at the front side of the fiber sustain this treatment we tried to visualize the DNA with fluorescence microscopy. Therefore the fiber is mounted face-down in the microscope

-20 -15 -10 -5 0 5 10 15 20 25 30

Displacement cantilever z c [m]

Displacement piezo z_p [ m]

Displacement Piezo z_p[ m]

Signal Quadrant Diode [V]

Monitor Voltage Piezo [V]

Force [m]

Gap Cantilever/Fiber z [ m]

Figure 4.14: Blank measurement with the steps of the raw data conversion to a force extension curve. Measuring time about 10 minutes. a) Raw data. The data have to be read from right to left. Black curve: Initially the cantilever and fiber are in contact. The initial monitor voltage of the piezo is about 9 V and the signal of the quadrant diode is set to zero. The fiber is then retracted with the piezo and one sees how the cantilever follows the movement of the fiber. When the fiber does not touch any more the fiber is in a stable equilibrium position. red line: the piezo makes the same movement backwards. b) The monitor voltage of the piezo is then scaled into the displacement z_p of the piezo. And the resolution of the quadrant diode is determined from the slope of the incremental part of the curve. c) For convenience the whole curve is mirrored at the touching point of the fiber and the cantilever and the displacement of the cantilever z_c is scaled in units of µ m. The zero of the cantilever deflection z_c is set to the equilibrium position of the cantilever. d) The distance between the cantilever and the bottom surface is then easily evaluated by determining∆z =z_p−z_c. Finally by multiplying z_c with the known spring constant of the cantilever k_c ≈ 1^N_m the force extension curve is obtained. black line: fiber retracts from cantilever. red line: approaches the cantilever. Note that the touching point of the cantilever and the fiber is known only with an accuracy of about2µm.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Figure 4.15: Force-distance curves of a DNA carpet of λ-DNA with l₀ = 16µ m. a) The fiber is initially in contact with the cantilever and then retracted (red curve).

After an extension of 1.6l₀ the fiber approaches again the cantilever at a very close distance it seem as if an soft repulsive force acts causing a rounding of the curve (black curve). b) the same as a). c),b) The fiber is initially not in contact with the cantilever and then approaches the cantilever (black line). After the fiber and the cantilever are in contact the fiber is retracted again.

and introduced into a droplet of buffer solution. Although gold/thiol attachment of DNA works very reliable as described in Chap.2, it was never possible to visualize a whole carpet of DNA but only some isolated molecules. Probably the low grafting densities were caused by strong shear flows during the handling of the fiber.¹³

All these practical difficulties in addition with incalculable stability problems as de-scribed in Sec.4.2.3 limited the numbers of promising measurements that can be done within a certain time. We have never detected a force when we tried to bring the cantilever into the vicinity of the bottom surface without touching it and then re-tracting the fiber to a distance smaller than ∼ 1µm. However when the cantilever was brought in contact with the fiber which was then retracted once a force appeared.

The force-distance curves for this case is shown in Fig.4.15. The curves are obtained by evaluating the raw data as described in the previous section. In the first two graphs Fig.4.15(a) and Fig.4.15(b) the cantilever was touched by the fiber which then was retracted. At the beginning a strong attractive force shows up. This is maybe caused by the fact that the cantilever touched the fiber and thus the whole contour of the DNA adheres unspecifically at the surface. The work necessary to pull off the whole contour could be responsible for the attractive force. After an extension of the DNA to about 0.4L0 (L0 denotes the contour length of the DNA) the ”adhesion force” dropped back to zero. However at an extension of about 0.8l₀ the force again increases strongly as one would expect from the WLC model. At a distances of the full contour length l₀ of the DNA the force drops rapidly as if the molecules would have been broken. The fact that the breakage occurs at the contour length ofλ-DNA strongly indicates that DNA is responsible for the measured force. After an extension of 1.6l₀ the fiber approaches again the cantilever. For small distances a round off of the curve is visible what could come from squeezing of the DNA carpet.

The same measurement is shown in Fig.4.15.c and Fig.4.15.d but the fiber started at a distance at 1.2l₀ from the cantilever. Again by approaching the fiber and the can-tilever a rounding off of the force curve is visible, and when the fiber retracts from the cantilever a force behavior qualitatively the same as described above is observed. If one assumes that breakage occurs where the plateau of the B-S transition for a single DNA should start, one can deduce from the breakage force a estimate of the numbers of molecules involved into to force extension curve. Since the B-S transition occurs at a force of 65pN and the breakage occurs at 1.6µN around 2.6×10⁴ molecules

13Remember that the washing procedure can remove the grafted DNA from a surface and one has to do this very carefully with a sufficient big droplet of buffer solution.

0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 4.16: Fit to the WLC Model with a persistent length of 53nm from the fit one gets the number of molecules. (a) Number of molecules 1.07·10⁴ b) Number of molecules 2.2·10⁴

contributed to the measured force. This number is consistent with the number of molecules grafted to the front side of the fiber at a grafting density of about 0.1 molecules perµm², which would be around 4·10⁴ molecules in total. However, as one cannot expect that all molecules are grafted on both sides this is an upper limit of molecules one can measure. The part of the force-distance curve between 0.5l₀ and 0.9l₀ were fitted to the interpolation formula of the WLC force versus extension:

F =k Fig.4.16(a) and 2.2×10⁴ for Fig.4.16(b) respectively. Both numbers are consistent with the number of molecules grafted on the front side of the fiber. It should be em-phasized that the measurement was not reproducible because of the reasons described above.