Figure 1. Schematic view of the apparatus used to twist and stretch single DNA molecules. DNA molecules were first prepared with biotin attached to one end and digoxigenin (dig) bound to the other. These end-labelled DNA molecules are incubated with streptavidin-coated magnetic beads and then flowed into a square glass capillary coated with an antibody to dig (antidig). The DNA molecules bind specifically to the bead via biotin/streptavidin coupling and to the glass via dig/antidig coupling. The capillary is placed above an inverted microscope and magnets are placed above the capillary. By moving the magnets nearer we increase the stretching force on the bead and thus on the molecule. With rotation of the magnets the molecule is twisted at constant force. A frame grabber installed in a PC allows tracking of the Brownian fluctuations <x² of the bead. The determination of <x² and of the molecule's extension l leads to a measure of the stretching force: F=k_BTl/<x².

Figure 2. A continuous polymer chain can be simulated by a chain of freely rotating segments of size b and orientation vector t_i. The direction of the stretching force F defines the z axis. _i and _i are the angles between respectively t_i and t_i–1 and t_i the z axis.

Figure 3. Force versus relative extension curves of single DNA molecules. The data points correspond to several experiments performed over a wide range of forces. The force was measured using the Brownian fluctuation technique (Strick et al., 1996). The solid curve is a best fit to the WLC model for forces smaller than 5 pN. The dashed curve is the result of the FJC model with the same persistence length (it is clearly a worse description of the behaviour of DNA under stress than the WLC model). At high forces, the molecule first elongates slightly, as would any material in its elastic regime. Above 70 pN, the length abruptly increases, corresponding to the appearance of a new structure termed S-DNA.

Figure 4. (a) Schematic view of the buckling transition for a twisted rubber tube (dotted line) or a DNA molecule (solid line). Below a critical number of turns n_c,b the rubber tube's torque increases linearly as it stores twisting energy. When n_c,b turns have been added, the system abruptly exchanges twisting energy for bending energy and plectonemes begin to form. The plectonemes grow linearly with subsequent twisting and the torque remains constant thereafter. In the case of DNA the same picture holds, except that thermal fluctuation round off the transition that takes place at n_c,b. (b) Results from the rod-like chain model corresponding to a stretching force of F=0.33 pN. The x axis represents the supercoiling variable =2n_T/l₀ 95, and the y axis is in arbitrary units. The magenta curve represents the torque acting on the DNA: as described above, it increases linearly until _c,b ~1 ( ~ 0.01) and remains essentially constant thereafter. The green curve represents the ratio of writhe to twist: note that the writhe is never zero and increases rapidly as > 1. Finally, the red line measures the fraction of plectonemes in DNA: stable supercoiled structures appear only after the torsional buckling transition has been passed.

Figure 5. Relative extension of a DNA molecule versus the degree of supercoiling = 2n _T/l_o – 95 for various stretching forces. For the three curves obtained at low force, the behaviour is symmetric under –. The shortening corresponds to the formation of plectonemes upon writhing. For these low forces, the comparison between the experimental data (points) and the RLC model with C/k_BT=86 nm (full-line) is very good. When the force is increased above 0.5 pN, the curve becomes asymmetric: supercoils still form for positive coiling, while local denaturation absorbs the torsional stress for negative . At forces larger than 3 pN, no plectonemes are observed: the torsional stress is absorbed not by writhe but in local structural changes of the molecule.