Fig. 1: Torsional response of naked DNA measured by the angular optical trap (AOT).

a Experimental configuration for measuring DNA torsional response on the AOT. A 12.7 kb DNA molecule containing a random sequence was torsionally constrained between a birefringent quartz cylinder and the coverslip surface of a microscope sample chamber. The AOT simultaneously measured and controlled the DNA extension, force, rotation, and torque. b Extension and torque versus turns added to DNA under constant force. Data were averaged from \(N=\)22 biologically independent traces held under 0.5 pN force. In the pre-buckled regime, torque increased linearly as turns were added. The linear fit within the pre-buckled regime (middle red line) yields an effective twist persistence length of 78.9 ± 0.3 nm, consistent with previous measurements within measurement uncertainty³². At the buckling transitions (vertical dashed black lines), DNA underwent phase transitions to form plectonemes. The torque plateaued with further plectoneme extrusion at +7.7 ± 0.2 pN∙nm (mean ± s.d) for the (+) supercoiled DNA and −7.6 ± 0.3 pN∙nm for the (-) supercoiled DNA (horizontal red lines). c Partitioning of twist and writhe. The DNA supercoiling state is defined by the turns added to DNA, or the change in the linking number \(\triangle {Lk}={Lk}-{{Lk}}_{0}\), with \({{Lk}}_{0}\) being the linking number of torsionally relaxed DNA. \(\triangle {Lk}\) is partitioned into a change in twist \(\triangle {Tw}\) (torsion) and a change in writhe \(\triangle {Wr}\): \(\triangle {Lk}=\triangle {Tw}+\triangle {Wr}\). The superhelical density \(\sigma\) is used to characterize the degree of supercoiling: \(\sigma=\frac{{Lk}-{{Lk}}_{0}}{{{Lk}}_{0}}=\frac{\triangle {Lk}}{{{Lk}}_{0}}\). Using the fit parameters from (b), the partitioning of added turns into the twist and writhe was obtained. In the pre-buckling regime, the added turns partition mostly into twist, which increases linearly with turns; the partitioning of twist was calculated from the ratio of the effective twist persistence length, 78.9 nm, and the intrinsic twist persistence length, 109 nm³². Beyond the buckling transition, all added turns partition into writhe, thus maintaining a constant torque. Source data are provided as a Source Data file.