Abrupt Buckling Transition Observed during the Plectoneme Formation of Individual DNA Molecules

The response of single DNA molecules to externally applied forces and torques was directly measured using an angular optical trap. Upon overwinding, DNA buckled abruptly as revealed by a sharp extension drop followed by a torque plateau. When the DNA was held at the buckling transition, its extension hopped rapidly between two distinct states. Furthermore, the initial plectonemic loop absorbed approximately twice as much extension as was absorbed into the plectoneme upon each additional turn. The observed extension change after buckling and the postbuckling torque support a recent DNA elasticity model.

Figure 1

Experimental configuration. A DNA molecule was tethered to a nanofabricated birefringent quartz cylinder (extraordinary axis ${\chi }_e$) held in an angular optical trap. Both ends of the DNA were torsionally constrained via its multiple tags: at one end via biotin-streptavidin and at the other end via digoxigenin (dig) and antidig. Force on the cylinder was applied in the axial direction and held constant by feeding back on a piezoelectric stage which displaced the coverslip. The DNA molecule was subsequently overwound by rotation of the linear polarization of the trapping laser.

Figure 2

Examples of torque and extension versus turn number. DNA molecules of 2.2 kbp in length were overwound under a constant force. Data were collected at 2 kHz and averaged with a sliding window of 1.5 s for torque and 0.05 s for extension. The torque signal had more Brownian noise relative to signal and was subjected to more filtering. As a result, higher frequency features in the torque signal, especially those near the buckling transition, might have been obscured. DNA buckling, locations indicated by dashed lines, was dependent on the applied force. (a) Torque versus number of turns. (b) The corresponding extension versus number of turns.

Figure 3

Extension change at the buckling transition. (a) The extension change versus force. The extension change for the initial plectoneme loop (red symbols) was well fit by a power law of $F^{-0.5}$ (solid red) and was much larger than the extension change per turn for subsequent plectoneme growth (blue symbols). Three different DNA templates (2.2 kbp •, $N=119$; 4.2 kbp ◊, $N=35$; another 2.2 kbp ★, $N=4$) all exhibited the same trend. The two dashed lines show predictions by a simple model and a fit to the Marko model, respectively. Error bars are standard errors of the means. (b) A 2.2 kbp molecule was held at constant tension (2 pN) and overwound extremely slowly ($0.04\mathrm{\text{turn}}/\mathrm{s}$) through its buckling transition. Data were taken at 2 kHz, low pass filtered to 400 Hz (solid dots), and then median filtered to 20 Hz (red curve). An extension histogram of the median-filtered data is shown on the right and was well fit by the sum of two Gaussians (black curve). The DNA was observed to rapidly fluctuate between two distinct states, separated by 79 nm, corresponding to pre- and postformation of the first plectonemic loop.

Figure 4

Direct measurements of torque. (a) Torque prior to the buckling. Torque-turn relations prior to buckling were pooled from data for both the 2.2 kbp DNA (121 traces) and 4.2 kbp DNA (65 traces). Individual traces are shown as gray lines and resulted in a gray region when plotted together. Each solid curve indicates the average of all traces of a given length DNA. Torsional modulus for each DNA length (see text for values) was obtained by the slope of a linear fit to the average curve. (b) Torque after buckling. The torque after buckling at each force was pooled from data from the three DNA templates (blue symbols: 2.2 kbp •, $N=119$; 4.2 kbp ◊, $N=35$; another 2.2 kbp ★, $N=4$). The two dashed lines show predictions by the simple model and a fit to the Marko model, respectively.