6.1.1 Force feedback

The force feedback of the instrument follows a proportional protocol (see Eq. C.2) that corrects the position of the optical trap to keep the force constant. The feedback runs at 4 kHz but the natural bandwidth of the wiggler is about $ \sim 2$ kHz [19]. It means that the electronic controller can give orders faster than the time spent by the wiggler to reposition the optical trap. Strictly speaking, the bandwidth of the wiggler limits the chances to perform unzipping at CF. In addition, the thermal force spectrum of a polystyrene bead surrounded by distilled water in a trap stiffness of $ \sim$75 pN$ \cdot \mu $m$ ^{-1}$ has a corner frequency of about 1 kHz. Our force feedback has a similar bandwidth and it is not capable of canceling out the noise of the thermal forces. Nevertheless, we are not really interested in having the thermal forces constant. Instead, we want to control the force when the opening of base pairs is produced during unzipping, which is a phenomenon that occurs at a time scale of 1 s (=1 Hz). Because of the difference in time scales, the force feedback is useful to perform our experiments.

Figure 6.1 shows the typical measurements in a CF unzipping experiment performed on a 2.2 kbp sequence. These experiments are characterized by the loading rate, which is 0.05 pN$ \cdot $s$ ^{-1}$ in this particular example. The force is the control parameter that increases monotonically while the distance evolves according to the opening of base pairs of the DNA molecule. We compare the new measurements with a previous ones with controlled trap position.

Figure 6.1: Data from a CF pulling experiment. (a) Force vs. time (upper panel) and Distance vs. time (lower panel). The force is increased monotonically at a loading rate of 0.05 pN/s (red curve) until the molecule is fully unzipped (i.e., converted into ssDNA). Then, the loading rate is increased up to 2 pN/s (magenta curve) to pull the released ssDNA. Even at high loading rates, the pulling of ssDNA is reversible. So the loading rate is increased in order to reduce the time spent in the pulling cycle. During the rezipping, the force is decreased at -2 pN/s (cyan curve) and at -0.05 pN/s (blue curve). The distance suddenly increases (decreases) when a group of bases is unzipped (rezipped). Note that the force feedback is not capable of reducing the fluctuations of the thermal noise. The force undergoes some bumps during the opening of base pairs due to the finite bandwidth of the force feedback. (b) Resulting FDC of previous measurement. This is a typical FDC at controlled force that exhibits an appreciable cycle of hysteresis.
\includegraphics[width=\textwidth]{figs/chapter6/CFcycle.eps}

JM Huguet 2014-02-12