Characterization of a single-molecule DNA braiding system. (

*A*) Two nicked DNA molecules (solid black lines) are oriented between one bead on a rotating micropipette and another bead held in an optical trap. As braiding density, |σ

_{br}|, increases, the length of the braid,

*Z*, diminishes gradually until a critical braiding density is reached, |σ

_{br}^{crit}|, at which point the braid buckles, forms a second-order plectonemic superhelix, and shortens much more dramatically with each introduced turn. (

*B*) Shortening of braids as a function of braid density. Braid length for σ

_{br} < σ

_{br}^{crit} can be approximated by a geometric model,

, where

*Z*_{n} is the extension of a braid with

*n* turns,

*Z*_{o} is the maximal extension of the braid,

*d* is the distance between points of attachment of the two DNA ends on each bead, and

*r* is the effective radius of the braid. Braid extensions are shown over a range of σ

_{br} and tensions. ○, Experimental data; solid lines represent the fit to the model. (

*C*) For |σ

_{br}| > |σ

_{br}^{crit}|, the braid compaction no longer obeys the simple model because of the buckling of the DNA braid into a plectonemic superhelix (second-order). The compaction of the braid in this regime is ≈35 nm for each additional turn. (

*D*) Monte Carlo simulations of DNA braids. Braids of two individual 3.5-kb DNA molecules (blue and yellow) with a σ

_{br} = 0.05, held under 1 pN or 0.2 pN of force, are shown.

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