Figure 4. Topo VI activity on braided DNA substrates.

(A) Calibration curve for a DNA braid formed from two 5 kb DNA duplexes tethered to a single magnetic bead. DNA extension is plotted as a function of magnet turns. Negative magnet-turn values represent the right-handed rotation of the magnets producing negative writhe, and positive magnet-turn values represent the generation of positive writhe via left-handed magnet rotation. (Note: this is the reverse scenario of forming a plectoneme, see Figure 1A). The first positive or negative 360° turn results in a sharp decrease in DNA extension as a single crossing is input. This is followed by a gradual decrease in extension with rotation, representing the formation of a DNA braid. At a critical number of turns, the braid buckles upon itself to form a supercoiled braid, which is evident in the graph as a switch to a steeper gradient. (B) An example of raw magnetic tweezers data, showing topo VI relaxation activity on a DNA braid with positive chirality. Data collected at a force of 0.5 pN, at 21 °C, using 0.1 nM topo VI and 1 mM ATP. Scale bar (black) represents ΔLk of 12, which corresponds to a change in DNA extension of 200 nm. A total of 10 DNA crossings are relaxed by topo VI in ~20 s (blue dashed line), measured as the time between the imposition and complete relaxation of the braids. Data collected at 200 Hz (grey dots) and plotted with a 1 second Savitzky–Golay smoothing filter (black line) and the T-test fit in red (Seol et al., 2016). Additional examples of braid relaxation data and the T-test fits are provided in Figure 4—figure supplement 1. (C) The average rate of topo VI braid unlinking activity (± SEM), of both positive (N tethers across all data points = 92) and negative (N tethers across all data points = 55) braids, measured as the number of strand-passage events/min and plotted as a function of topo VI concentration (0.05–0.9 nM). Data were fitted to a Michaelis-Menten-like function ($V_0=\frac{V_{max}\left[E\right]}{K_{d,app}+\left[E\right]}$). (D) The processive burst rate of topo VI (± SEM) on both positive (N burst events across all data points = 206) and negative (N burst events across all data points = 104) braids, measured as the average number of events min^–1 in a burst, and plotted as a function of topo VI concentration. A burst is defined as rapid topo VI activity corresponding to the passage of two or more consecutive T-segments in which individual strand-passage events cannot be discerned by the step-finder. Any single strand-passage events detected were omitted from the average. The horizontal dashed lines represent the average processive burst rate (± SEM) across all concentrations of topo VI assayed. (E) The average burst size of topo VI (± SEM) on both positive (N burst events across all data points = 217) and negative (N burst events across all data points = 132) braids, measured as the average number of strand-passage events per burst, plotted as a function of topo VI concentration. Single passage events were included in the average burst size. The horizontal dashed lines represent the average processive burst size (± SEM) across all concentrations of topo VI assayed. (F) The dwell times between processive bursts of topo VI activity on both positive (N dwell times across all data points = 156) and negative (N dwell times across all data points = 119) braids, plotted as a function of topo VI concentration. A dwell time is defined as a period of time in which the DNA extension remains constant, reflecting lack of topo VI-dependent braid unlinking activity. In C-F, data was collected at a force of 0.5 pN, at 21 °C, using 1 mM ATP, with topo VI activity on positive DNA braids in red, and in blue for negative DNA braids. Raw data were analysed in IgorPro 7 (WaveMentrics) using a T-test-based method, first described in Seol et al., 2016. Figure 4—figure supplement 2 provides a comparison between the analysis of the experimental braid relaxation data and the analysis of simulated purely distributive braid relaxation data. Figure 4—figure supplement 3 provides examples of the t-test based fitting of the simulated data sets.

Figure 4—figure supplement 1. Additional examples of T-test fits to braid relaxation data.

Extension versus time data for topo VI relaxing braided DNA (red lines) and the T-test based fit to the data (black lines). The sign of the braiding and the concentration of topo VI are indicated on each graph. For panels A-G, the applied force was 0.5 PN. The applied force for panels H and I are indicated on the graphs. Although the extension change per braided link varies slightly among different braids (15–50 nm) the most common extension change per link was ~40 nm.

Figure 4—figure supplement 2. Comparison of the experimental braid relaxation data with a purely distributive relaxation model via simulations.

To test the possibility that the braid relaxation data are consistent with purely distributive relaxation by topo VI, we performed simulations of distributive braid relaxation with average rates corresponding to the average measured braid relaxation rates (the number of crossings relaxed divided by the total time to relax the crossing including all pauses) at different topo VI concentrations (Figure 4C) and performed T-test fitting of the simulated extension versus time data with identical T-test parameters used for the experimental data (see Figure 4—figure supplement 3 for examples of T-test fits to simulated data). One hundred simulations of the distributive relaxation of braids containing 12 links were performed for each of six different average relaxation rates and the statistics of the simulated relaxation data were obtained from the T-test fits. (A) The average burst-size (linking number difference) for positive (red filled circles) and negative (blue filled circles) braids and simulated braid relaxation data (open circles) plotted as a function of the average braid relaxation rate with error bars corresponding to the standard error of the mean. The average step-size for the simulated perfectly distributive relaxation slightly exceeds one due to individual steps that are missed in the t-test analysis. (B) The average processive burst probability for positive (red filled circles) and negative (blue filled circles) braids and simulated braid relaxation data plotted as a function of the average braid relaxation rate. Fitted steps larger than 150% of the extension change for a single linking number were scored as a processive burst and the probability was obtained by dividing this number by the total number of fitted steps. (C) The average pause time between steps for positive (red filled circles) and negative (blue filled circles) braids and simulated braid relaxation data plotted as a function of the average braid relaxation rate with error bars corresponding to the standard error of the mean.

Figure 4—figure supplement 3. Examples of T-test based fits to simulated braid relaxation data.

Simulated DNA extension versus time for distributive relaxation (grey line) along with the T-test fit (black line) and the simulated extension in the absence of noise (green dashed line) at average relaxation rates of: (A) 8 Lk/min. (B) 12 Lk/min, and (C) 20 Lk/min. Each simulated trace consists of a series of 12, 40 nm increases in DNA extension that occur at exponentially distributed time intervals with a mean time corresponding to the average relaxation rate. Gaussian noise with a standard deviation of 60 nm, estimated from experimental trajectories at 0.5 pN (Figure 4, Figure 4—figure supplement 1), was added to the simulated trajectories. T-test fitting of the trajectories was performed with the same parameters as those used for the experimental data: Initial data down-sampled 10-fold to 20 Hz, T-test comparison window size of 40 points, T-test significance level (alpha parameter) of 10^–7, minimum step size of 20 nm (half the extension associated with a single relaxation event, 40 nm).