Figure 4.

Three-state kinetics of topoisomerase IA gate dynamics. (a) Three-state kinetic model. (b) Example of a single kinetic cycle of topo III from cleavage to transient opening and closing of the gate, followed by religation. Black line is smoothed data, red line is the HMM fit from vbFRET. (c) Force dependent kinetic analysis of k_cleavage (blue), k_ligation (orange), k_open (green), and k_close (red), n_tethers = 8 for topo III, n_tethers = 7 for topo I. Values were calculated from exponential fits of the lifetimes of each state (Supplementary Fig. 3–4). Error bars represent standard deviations of the fit coefficients. For k_cleavage, k_ligation, and k_open, lines represent average values_. k_close values were fit with k = k₀exp(−FΔx/k_BT). The fit returned Δx and k₀ values of 1.10 ± 0.04 nm and 1.8 ± 0.3 s⁻¹ respectively, for topo III and 2.2 ± 0.1 nm and 1642 ± 549 s⁻¹ for topo I. (d) Magnesium concentration dependence of ligation and cleavage rates for topo III at 8 pN force (n_tethers = 3, 8, 3, and 2 for 1, 3, 5, and 10 mM Mg²⁺, respectively) and topo I at 12 pN force (n_tethers = 6, 4, 3, 5, and 2 for and 0, 0.1, 0.3, 0.5 and 3 mM Mg²⁺). The topo III magnesium-dependent ligation rate was fit with a sigmoid with a K_m of 8.3 ± 1.2 mM Mg²⁺ and a V_max of 17 ± 5 s⁻¹.