FIG. 8.

Rebuckling transition for various defect sizes. (a) Schematic of the three possible states at the rebuckling transition: the critically-big defect-pinned plectoneme domain (℘₁₀, green solid lines), one mobile plectoneme domain (℘₀₁, red dot-dashed lines), and two-domain plectoneme containing one defect-pinned and one mobile domains (℘₁₁, cyan dotted lines). (b) Total probability of the three states at the rebuckling point (ΔLk=28 under f = 2 pN and 0.5 M Na⁺, see Fig. 6) as a function of the defect size ε. For small defects (0 < ε < 0.1), the post-buckling state is the mobile domain (℘₀₁) and not the defect-pinned domain (℘₁₀) (see Fig. 7). As a result, rebuckling is not observed for small defects and the ℘₀₁ state continues to increase in size after buckling, same as the case for a defect-free DNA (Fig. 2). For intermediate defects (0.1 < ε < 0.25), the defect is large enough to bias nucleation of the defect-pinned domain (℘₁₀) at the buckling transition (Fig. 7); however, at the rebuckling point, one mobile domain (℘₀₁) is more stable than the two-domain state (℘₁₁). For large defects (ε > 0.25), the defect-pinned domain (℘₁₀) is highly stable, resulting in nucleation of a new mobile domain at the rebuckling point; this makes the two domain state (℘₁₁) favored after the rebuckling transition. Note the higher probability of ℘₁₀ for larger defects, which is due to a shift of the rebuckling transition to higher linking numbers for larger defect sizes (Fig. 10). (c) Probability density of extension for ε = 0.25 at the rebuckling point. The bimodal extension profile is due to the finite nucleation energy associated with a teardrop loop of a mobile domain. The state populating the lower-extension mode of the distribution depends on the size of the defect, such that large and intermediate defects favor ℘₁₁ and ℘₀₁ states, respectively. Small defects show a unimodal extension profile after buckling transition, and do not exhibit rebuckling.