FIGURE 3. Torque calibration and twist elasticity of DNA.

a, Torque versus twist for 37 runs from 16 molecules (520 nm rotor beads; 45 pN constant tension). Inset, calibration of _crit,+. Angular velocities () of beads with mean diameters of 920 nm (n = 5), 760 nm (n = 6) or 520 nm (n = 16) were measured during the P B transition at 45 pN (filled circles, s.d.). Viscosity-corrected is proportional to r^-3; the best-fit slope (red) gives _crit,+ = 34 2 pN nm. Open circle, extrapolated P B angular velocity for 400 nm beads (n = 3; see Methods). b, Averaged twist elasticity data. Negative torques: average of 39 runs at 15 pN. Positive torques: 37 runs at 45 pN and 27 runs at 15 pN gave very similar traces and were averaged together. Green lines, constant-torque structural transitions. Blue, linear fit to the data points falling within 8 pN nm. Anharmonic models (C() = a - b/N, where N = 14,795 bp) give superior fits to the data over the full range of B-DNA stability. Red, two-parameter anharmonic fit (b/a = 4.5); dashed purple, anharmonic fit constraining b/a = 8.16 to agree with FPA data¹³. Blue and red fits give C(0) = 4.1 10² pN nm²; purple fit gives C(0) = 4.3 10² pN nm². Fits to 45 pN or 15 pN positive torque data alone (not shown) give C(0) = 4.1 10² or 4.3 10² pN nm², respectively. Inset, independent measure of C(0) using the equipartition theorem <² > = k_BTL/C, where L = 5.03 m. Twist fluctuations of five molecules (520 nm rotor beads, 15 pN tension) were tracked at 50 Hz (example shown). Angular variance (red gaussian plot over blue data histogram) gives C(0) = (4.4 0.4) 10² pN nm².