Figure 7. Topo VI unlinking single DNA crossings.

(A) Single crossing assay schematic with DNA crossing geometry for positive (left-handed, red) and negative (right-handed, blue) DNA writhe. One 360° clockwise magnet rotation imparts a positive crossing, which is unlinked by topo VI, followed by the generation and subsequent topo VI-dependent unlinking of a negative DNA crossing, formed by a 360° anticlockwise magnet rotation. The crossing angle is defined as the clockwise angle between the top and bottom DNA strands. For positive crossings this is an acute angle (α); for negative crossings the obtuse angle is the supplement (π-α) of the positive angle. For topo VI, achieving the preferred angle (α₀ < 90) requires a smaller thermal fluctuation of positive crossings, therefore there is a higher probability of α₀ being achieved than for negative crossings. (B) Single crossing unlinking data, collected for a braid formed from 3 kb DNA tethers, spaced 624 nm apart, at a force of 1 pN, using 0.9 nM topo VI and 1 mM ATP. Positive crossings (red) were relaxed more rapidly than negative crossings (blue). (C) Distributions of the topo VI-dependent unlinking times for negative (blue bars) and positive (red bars) crossings, of the data shown in B. The data were fitted with single exponentials, P(t) = τ^–1exp(-t/τ), returning characteristic unlinking times of τ_R = 47 ± 7 s for negative crossings, and τ_L = 8 ± 1 s for positive crossings, giving a ratio of τ_L/ τ_R = 0.19 ± 0.04.

Figure 7—figure supplement 1. Braid tether calibration and geometric fit.

(A) The DNA extension of a 3 kb double tether, plotted as a function of magnet rotations and fitted to a geometric function (Neuman et al., 2009). $L=\sqrt{L_0^2-4e^2{sin}^2\left(n\pi \right)}–r+\sqrt{r^2-e^2},\left|n\right|\S amp;lt;0.5$ Where L is the measured DNA extension, L₀ is the maximum DNA extension (dependent on the force applied), e is half the separation distance between the DNA molecules, n is the number of magnet rotations, and r is the radius of the magnetic bead to which the tethers are bound. The first term in the expression describes the extension of a twisted swing, whilst the second two terms are a correction for the spherical bead, see Neuman et al., 2009 for a full description. (B) Geometric parameters of the DNA tethers, attained through the calibration and subsequent geometric fit (seen in Figure 7A), namely the length of the DNA tethers (L) and the separation distance between them ($2e$). Along with the force and number of turns, this information was used in Monte Carlo (MC) and Brownian Dynamics (DB) simulations.