Fig. 5. Supercoiling induces buckling in short plasmids and reduces the threadable area.

(A) The anisotropy shape descriptor (an, see text) for short plasmids M = 100 ≃ 730 bp displays a sharp buckling transition between an open and roughly symmetric state for σ = 0 and a collapsed and anisotropic one for σ > 0. In inset, two examples of conformations are shown. (B) For longer plasmids (M ≥ 200 ≃ 1.5 kbp), supercoiling shifts the anisotropy to larger values, indicating a smoother transition to more prolate conformations. (C) Scaling of the average minimal surface size 〈Σ〉 as a function of plasmid length (solid line shows the linear scaling). In inset, two examples of surfaces for M = 100 ≃ 730 bp are shown. (D) The size of the minimal surface area monotonically decreases with supercoiling (with the exception of short M ≤ 200 ≃ 1.5 kbp plasmids). The solid and dashed lines scale as 1/σ and e^−σ/0.035, respectively, and are drawn as a guide to the eye. R = relaxed. The unit of length is σ_b = 2.5 nm. The error bars, typically smaller than the symbol size, represent the error of the mean area.