4.1 Detection of intermediate states

As described in the previous chapter, the quasistatic unzipping of DNA at controlled position is performed by moving the center of the optical trap at a very low speed ($ \sim$10 nm/s). Along these experiments, the dsDNA is progressively converted into ssDNA through a succession of intermediate states corresponding to the successive opening of the CURs. In these intermediate states, the DNA molecule is partially open. The molecule remains in this state if the distance between the two beads is not modified. If this distance is being increased, we can measure the FDC. The experimentally measured FDC shows a sawtooth-like pattern that alternates force rips and gentle slopes (see Fig. 4.1a). Slopes correspond to the elastic response of the molecule while the force rips correspond to the opening of groups of base-pairs. These openings are called CURs (see Fig. 4.1b).

The number of open base-pairs of a CUR is variable: It ranges from 5-10 base-pairs up to 80-100 and it depends on the sequence of the DNA molecule and the specific region that is being unzipped. The size of a CUR can be inferred from the difference of slopes that precede and follow a given force rip. However, the slopes can be hardly isolated because the experimental FDC exhibits noise (see Fig. 4.1b). The force fluctuations of the elements of the system (bead, handles) might be confused with the different forces at which the two intermediate states of the DNA duplex coexist. A classification by hand of the experimental points might lead to a biased interpretation of slopes and rips due to the human intervention. In order to avoid this, we adopt a Bayesian approach.

A Bayesian approach consists in using the probability inferred from the experimental data to accept or reject a hypothesis. In our particular case, the experimental data is first classified into intermediate states. Then, the most stable of them are identified as metastable states. Finally, the regions between each pair of consecutive metastable states are identified as CURs. Once this is achieved, the unzipping of DNA can be studied in terms of a new statistical object: the CUR size distribution.

Next section describes how to extract the experimental metastable states according to the Bayesian inference.

Figure 4.1: Intermediate states in experimental data. (a) Unzipping of a 2.2 kbp sequence. The raw experimental data is depicted in red and filtered data at 1 Hz bandwidth, in green. The yellow (blue) curve shows the elastic response of the system when all (no) base pairs are open. (b) Zoomed region. Same color code as in panel a. From left to right, the blue curves correspond to the elastic response of intermediate states with 0,19,70,123,142 open base pairs. Except for the force fluctuations, the slopes of the experimental data lie on the partial elastic responses of the system. Note that the number of open base pairs of the system is no longer clear for distances larger than 450 nm, where the force fluctuations are as large as the difference in force between the slopes of the coexisting intermediate states. Filtering data with a low-pass filter could be a solution. However, the force rips are smoothed and the hopping transitions are averaged out.

JM Huguet 2014-02-12