The figure shows schematically the experiment of T. Strick, J. Allemand, D. Bensimon, A. Bensimon, and V. Croquette, ``The elasticity of a single supercoiled DNA molecule,'' Science 271 (1996) 1835.
The graphs show a single global fit of our theory to two different experiments. The left figure shows experimental data (courtesy of J.-F. Allemand and V. Croquette, Ecole Normale Superieure Paris); the right figure shows data from the experimental paper above.
The graphs give the relative extension Z/L of a single lambda-DNA molecule under various fixed values of tension, as a function of imposed excess linking number. The tensions used range from 0.1pN (lowest curves) to 8.0pN (top curve on right), while the fractional overtwist ranges from sigma = -.04 to +.04. Dots are experiment, solid lines are our theory (here's our original paper.) Dashed lines show a less accurate theory, for comparison.
The open circles were not used in the fit because the calculation may be expected to lose accuracy here. Nevertheless most of them fit anyway, using parameter values calculated from the solid circles! We used essentially two fitting parameters: the bend stiffness, and twist stiffness of DNA. The first of these is independently known and serves as a check on the theory. The values of other is our main result. We get a value comparable to expectations based on older experiments, but the single-molecule technique offers greater accuracy and freedom from many experimental and theoretical difficulties. Remarkably, the mathematical technique for solving this problem rests on a connection to the quantum-mechanical spinning top!
The data also hint at a new phenomenon found in our analysis, the renormalization of twist stiffness by bend fluctuations.
Phil Nelson