## Main

The double-helical structure of genomic DNA results in supercoiling and topological entanglements during fundamental processes, such as transcription and DNA replication. The excessive torsional buildup, as well as DNA catenanes and knots, can impede these processes, and topoisomerases are essential for resolving such topological challenges.

Type IIA topoisomerases (topo IIs) constitute one topoisomerase family essential for cell viability. Most eukaryotes, such as Saccharomyces cerevisiae, express a single topo II isoform, whereas vertebrates have two: topo IIα and topo IIβ1. Yeast topo II is indispensable in chromosome segregation2 and facilitates the transcription of long genes3. Human topo II isoforms are more specialized in cellular functionality, with topo IIα participating primarily in DNA replication and chromosome segregation and topo IIβ playing a crucial role in transcription regulation1.

All eukaryotic topo IIs are homodimers and share significant homology in sequence and structure4,5,6. These enzymes also share a similar ATP-dependent strand passage mechanism1 (Fig. 1a). During a catalytic cycle, topo II binds to a primary segment of DNA (the gate-segment, or G-segment) and then captures a second DNA duplex (the transport-segment, or T-segment). Upon binding to ATP, one dimer interface (termed the N-gate) closes around the T-segment, leading topo II to create a transient break in the G-segment DNA by the formation of a covalent enzyme–DNA link. Next, the region binding the cleaved G-segment (the DNA-gate) separates, allowing the T-segment to pass through the transiently opened DNA-gate. After passage, the G-segment is resealed, and the T-segment is expelled by the temporary opening of a C-terminal dimerization interface (the C-gate), allowing the enzyme to restart its catalytic cycle7,8.

In a typical catalytic cycle, the DNA break formed by topo II is transient. However, if topo II fails to religate this cleaved intermediate, permanent double-stranded breaks (DSBs) can accumulate, threaten genome stability and ultimately induce cell death9,10. This vulnerability has been exploited in developing effective small molecule therapeutics that target topo II to kill proliferating cancerous cells. A potent group of anti-cancer drugs, commonly referred to as ‘topoisomerase poisons’, directly prevents DNA religation by stabilizing the cleavage complex11,12. If the cleaved complex persists, it can be converted into a DSB, eliciting cell death13,14.

Etoposide is a topo II poison with broad clinical use as a chemotherapeutic agent15,16. Although a molecular picture of how etoposide binds to the topo II–DNA cleavage complex to stabilize break formation is known6,12, whether and how etoposide can also interfere with enzyme dynamics has remained unclear. It has been hypothesized that an etoposide-mediated DNA cleavage complex presents a physical obstacle against the progression of other DNA-based processes, such as transcription and DNA replication, and attempts to overcome such barriers result in DNA breaks13. However, direct physical evidence that the cleavage complex represents a highly stable barrier has been lacking.

In the present work, we investigated the physical and dynamic impact of etoposide on yeast topo II, human topo IIα and human topo IIβ. We examined the mobility of bound topo II sliding on DNA, the force required to disrupt topo II binding at a DNA crossover and the force required to expose the DNA break in a cleavage complex. We also investigated how etoposide alters these physical properties and the relaxation of DNA supercoiling by topo II.

## Results

### Direct detection of topo II-induced DNA loop formation

To investigate the strength of the interaction between topo II and DNA, we employed a single-molecule DNA stretching assay using an optical trap (also referred to as optical tweezers) to examine budding yeast topo II, human topo IIα and human topo IIβ (Extended Data Fig. 1). In a stretching assay, a double-stranded DNA (dsDNA) molecule (Fig. 1b and Extended Data Fig. 1a) was anchored between the surface of a sample chamber microscope coverslip and an optically trapped microsphere. The DNA was then stretched as the coverslip was moved away from the optical trap at a constant velocity17 (Methods).

In the presence of topo II (Fig. 1c), as a DNA molecule was stretched, the force began to rise above the naked DNA force baseline18,19, suggesting DNA tether shortening due to topo II interactions with the DNA. Previous studies using magnetic tweezers (MT) also reported that Drosophila topo II and topo IV shorten DNA extension20,21.

As stretching continued, clear force peaks were detected in a topo II concentration-dependent manner. At each force peak, the force rise was followed by a sudden force drop with a concurrent increase in DNA length, indicating disruption of topo II–DNA interactions and subsequent release of DNA captured by topo II. Force peaks recurred throughout stretching until the DNA reached its full extension. When etoposide was introduced with topo II but without ATP, these force features did not change substantially (Fig. 1d). Interestingly, when ATP was also present, the force peaks became much more pronounced, and the DNA tether broke more frequently during stretching (Fig. 1e and Extended Data Fig. 2a,b). These behaviors demonstrate that the action of etoposide is linked to the ATPase cycle of topo II.

An initial shortening of the DNA tether in the stretching traces suggested that topo II induces DNA compaction (Fig. 1c–e, insets, and Methods). For all three topo II isoforms, we found that DNA extension (measured at 0.5 pN) decreased as topo II concentration increased (Fig. 2a,b). Based on the topo II concentration required to compact the DNA to the same extent, yeast topo II compacted DNA most effectively, whereas human topo IIβ compacted DNA least effectively. The presence of etoposide enhanced DNA compaction, particularly for yeast topo II and human topo IIβ.

Each force peak in a force–extension curve corresponds to a sudden release of DNA initially captured by topo II (step 1 of Fig. 2c). Topo II could capture DNA via a DNA loop, likely by binding to a DNA crossover formed from both the G-segment and the T-segment22,23, and the applied tension in the DNA may disrupt topo II binding at this crossover, releasing the DNA captured in the loop. Because topo II-mediated DNA loop formation was detected even at a very low topo II concentration (Extended Data Fig. 2c,d), it is possible that a single topo II can capture such a loop.

We characterized the amount of DNA release (referred to as DNA loop size) in each force disruption event (Extended Data Fig. 2a,b). The distribution of the loop size is broad, showing a peak at ~100 base pairs (bp) and a long tail in the distribution (Fig. 2d). Monte Carlo (MC) simulations (Methods and Extended Data Fig. 3) indicate that this distribution may be a combination of two populations: a long-loop population (several hundreds of base pairs in size) that can be described by a simple DNA loop formation model (green curve in Fig. 2d)24,25 and a short-loop population (~100 bp in size) that requires a sharp DNA bend within the DNA loop (blue curve in Fig. 2d).

The short-loop (<200 bp) population could arise from the binding of another topo II molecule within the loop or possible bending or wrapping activity manifested by topo II itself26. Alternatively, this population may also result from ‘stick-and-slip’ of topo II interactions with the T-strand as the size of a single loop is reduced under pulling, resulting in clustered, smaller DNA lengthening events in some traces (Extended Data Fig. 4a). The mean loop size for each trace reduces with higher enzyme concentrations (Extended Data Fig. 4b), consistent with multi-topo II binding contributing to the short-loop population.

The presence of etoposide with topo II and ATP did not substantially change the loop size distribution (Fig. 2d) but increased the number of loops trapped per trace for all three types of topo isoforms (Extended Data Fig. 4c). Notably, the presence of etoposide increased the loop rupture force (Figs. 1e and 2e and Extended Data Fig. 4d). The mean loop rupture force was about 16 pN for the three topo II isoforms in the absence of etoposide and increased to about 28 pN in the presence of etoposide and ATP, demonstrating that etoposide enhances topo II-mediated DNA loop stabilization.

### Direct detection of topo II-mediated DNA breaks

The hallmark of etoposide’s action on topo II is the stabilization of a cleavage complex11,12. Methods for detecting the cleavage complex typically rely on treating topo II–DNA reactions with strong detergents to denature the protein and expose the DSB11,27. With those approaches, capturing an accurate snapshot of the cleavage complex population is difficult without altering the dynamics of gate opening and closing of topo II28.

The stretching method described here is highly sensitive to DNA breaks and provides a direct detection approach. We observed that, in the absence of topo II, DNA tethers could withstand a very high force, with a mean breakage force of about 92 pN (Fig. 2f). The presence of topo II and ATP without etoposide slightly decreased the mean to about 89 pN. The addition of etoposide reduced this mean DNA breakage force for all three topo II isoforms to about 58 pN (Figs. 1e and 2f), consistent with etoposide increasing the frequency of topo II-mediated DNA tether breakage.

We interpret the increase seen for topo II-mediated tether breakage to result from enzyme dimer separation under tension applied to the DNA (step 2 in Fig. 2c). When topo II forms a cleavage complex, each topo II monomer becomes covalently linked to one end of a cleaved DNA segment12,29,30. As the two DNA segments are pulled away from each other under tension, the two monomers could separate, resulting in tether breakage.

To more accurately investigate topo II-mediated DNA tether breakage, we used a constant-force stretching experiment where each DNA tether was rapidly stretched to 60 pN and then held at this force via the force-clamp mode of the optical trap (Fig. 3a,b and Methods). In this method, increased levels of tether breakage result in a net reduction in the lifetime of the DNA tether withstanding this force. For these experiments, we used a very low topo II concentration to reduce the frequency of DNA loop formation (Extended Data Fig. 2c,d). We then plotted the fraction of the remaining tethers as a function of time by pooling measurements from multiple DNA tethers. Each plot was fit by a double exponential function (Fig. 3c). For simplicity, we used the half-life from the fit (t1/2) to characterize the tether lifetime.

As shown in Fig. 3d, for DNA alone, the tether half-life was 270 seconds. The tether lifetime under this condition was likely limited by DNA end anchor detachment from the anti-digoxigenin-coated surface or the streptavidin-coated bead. The presence of topo II decreased the tether half-life to about 100 seconds for all three topo II isoforms tested, likely due to transient topo II-mediated DNA breaks that occurred during a normal catalytic cycle, demonstrating an exceptional level of sensitivity for the method.

When etoposide was also present, the tether half-life was reduced more than 100-fold (to ≤1.0 seconds) compared to that of either the naked DNA or topo II. Control experiments using a DNA nicking enzyme suggest that DNA breakage observed with topo II in the presence of etoposide derives from dsDNA breaks and not single-stranded DNA (ssDNA) nicks (Extended Data Fig. 5). A control experiment using a lower concentration of etoposide, which favors ssDNA breaks31, showed much-reduced DNA loop stabilization (Extended Data Fig. 4d), indicating that full DNA breakage is coupled with loop trapping.

Altogether, the approaches developed here provide the first direct measurement of the overall stability of the topo II dimer in the absence or presence of etoposide by mechanical separation. Our data from both the constant-velocity stretching and constant-force stretching suggest that etoposide binding destabilizes the DNA–topo II complex overall.

### ATP hydrolysis is required for etoposide-induced dynamics

The topo II catalytic reaction requires chemomechanical coordination between different domains of the enzyme and its ATP hydrolysis cycle. Previous studies found that ATP binding allows topo II to capture a T-segment, whereas ATP hydrolysis (at least for yeast topo II) biases DNA-gate opening for the subsequent transfer of the T-segment through the DNA-gate5,22. To further examine the role of ATP on the action of etoposide, we systematically examined topo II-mediated loop capture and topo II-mediated DNA breaks in the absence of either ATP binding or ATP hydrolysis.

We found that, for topo II-mediated DNA loop capture, etoposide did not strengthen the loop rupture force without ATP and only slightly strengthened the loop rupture force with the non-hydrolyzable ATP analog AMP-PNP (Fig. 4a). Thus, topo II can still capture DNA loops without ATP, but hydrolyzable ATP is required for the tightened loop capture in the presence of etoposide. Because ATP hydrolysis is known to promote strand passage32, these findings suggest that etoposide leads to trapping of the T-segment between the DNA-gate and a closed C-gate after strand passage (Fig. 2c). For topo II-mediated DSBs, etoposide only slightly increased DNA breakage without ATP or with AMP-PNP (Fig. 4a). Thus, etoposide can significantly enhance topo II-mediated DSB formation in the presence of hydrolyzable ATP (Fig. 4b).

By comparison, we found that ICRF-187, a topo II catalytic inhibitor that stabilizes the dimer interface of the two ATPase domains near the N-gate33, only moderately increased the DNA loop rupture force and did not enhance the appearance of topo II-mediated DNA breaks (Fig. 4a). When etoposide was present together with ICRF-187, the DNA loop rupture force was similar to that with etoposide only, but the topo II-mediated DNA tether breakage force was higher under constant-velocity stretching, and the tether half-life was longer under constant-force stretching, compared with those of the etoposide-only condition. These findings are consistent with ICRF inhibitors reducing the ATP hydrolysis rate of topo II34,35, which may, in turn, reduce the frequency of etoposide-induced DSBs.

The ability of etoposide to promote the trapping of DNA loops and stabilize DSBs only in the presence of hydrolyzable ATP is notable (Fig. 4b). These observations provide evidence that a DNA-gate that has entered into a cleavage-competent state with a G-segment can be stabilized by etoposide to secure the DNA break; entry into this state also stabilizes closure of the C-gate, providing a mechanism to prevent subunit dissociation while the target DNA remains cleaved4,36. Our findings further indicate that etoposide-induced stabilization of the C-gate, when formed under normal ATP cycling conditions, can lead to a topological lock of both the G-segment and the T-segment.

### Etoposide converts topo II into a stronger roadblock

It has been suggested that a topo II molecule trapped on DNA by the action of a poison such as etoposide could become a roadblock to motor protein progression and disrupt DNA processing37,38. To better understand the physical nature of a topo II barrier, we measured the difficulty of removing a bound topo II by mechanically unzipping DNA through the bound enzyme using the DNA unzipping mapper technique39,40 (Fig. 5a and Extended Data Fig. 1b).

We found that topo II bound to DNA at random locations along the DNA sequence (Extended Data Fig. 6a,b) and displayed diverse force features (Fig. 5b). Although some traces showed binding at a single region, other traces indicated binding at multiple regions (Fig. 5b and Extended Data Fig. 6c,d), possibly corresponding to the formation of a DNA loop or binding of more than one topo II molecule. Many traces clearly showed an extended interaction region, where the force was elevated from the underlying naked DNA baseline while still following the baseline profile (Fig. 5b, insets), suggesting that topo II can slide along the DNA under the influence of a progressing unzipping fork.

When etoposide was present, topo II unzipping force signatures became more dramatic. A large fraction of bound traces (>80%) showed a sharp high-force rise before tether breakage, consistent with the unzipping fork encountering a tightly bound cleavage complex (Fig. 5b). Most of the remaining traces showed some sliding behavior where the force rose gradually over some distance, which was typically followed by tether breakage (Fig. 5b). This response is consistent for what would be expected if topo II were bound to two segments in a DNA loop and the unzipping fork encountered the T-segment first (Extended Data Fig. 7). In this case, unzipping might slide topo II along the T-segment until this strand is released, after which the cleavage complex is encountered. Control experiments confirmed that the tether breakage detected in the assay was not due to DNA end anchor detachment or topo II-mediated DNA breaks in the DNA adaptor arms (Extended Data Fig. 6e).

The interaction range, defined as the region of DNA with a force rise above the DNA baseline by at least 2 pN before tether breakage, reflects the sliding distance of topo II along DNA (Fig. 5c). In the absence of etoposide, the mean distance was 380–490 bp for the three topo II isoforms, of the same order of magnitude of the DNA loop size, suggesting that DNA loop formation likely contributes to topo II mobility on DNA. The presence of etoposide greatly reduced the mean distance to 120–140 bp. Therefore, etoposide restricts topo II’s ability to slide along DNA. The mean maximum force detected in the topoisomerase-bound traces (Fig. 5d), which served as a measure of the obstacle to unzipping, increased substantially from about 20 pN without etoposide to about 39 pN with etoposide, above the naked DNA baseline (15 pN). This indicates that etoposide converts a bound topo II into a much strong barrier for unwinding. In addition, etoposide increased the probability of a tether breakage from about 38% to about 92% (Fig. 5e). Thus, the presence of etoposide greatly increases both the resistance of topo II to removal and the susceptibility of the DNA tether to breakage.

Because the unzipping fork mimics motor progress through a bound protein, these results suggest that a motor protein can slide a bound topo II in the absence of etoposide (Fig. 5f). However, the presence of etoposide and ATP converts topo II into a strong roadblock that resists removal by a motor protein, and the eventual removal of topo II leads to a DSB.

### Etoposide induces prolonged pausing of topo II

Although etoposide is known to interfere with topoisomerase supercoiling relaxation, the dynamics of this interference have yet to be fully elucidated. To probe how etoposide interferes with topo II relaxation of DNA supercoils, we directly monitored topo II enzymatic activity using an MT supercoiling assay20,41 (Fig. 6a).

In the absence of etoposide, the topo II isoforms relaxed DNA with minimal pausing (Fig. 6b and Extended Data Fig. 8a–c). However, in the presence of etoposide, processive DNA relaxation was abruptly interrupted by long pauses, giving rise to a ‘burst-and-pause’ behavior (Fig. 6b and Extended Data Fig. 8a–c). Detailed analysis of turns relaxed by topo II between pauses showed that pausing occurred predominantly at integer multiples of 2 turns (Extended Data Fig. 8a–c), a value that matches the expected change in the supercoiling state after each catalytic cycle20,42.

Our data show that etoposide does not uniformly slow down actively relaxing topo II action during the process of topo II relaxation of supercoiled DNA. Instead, etoposide allows topo II to proceed for multiple enzymatic cycles with minimal interference but then sporadically jams topo II for a prolonged duration. For all three topo II isoforms, the overall rate of relaxation (including the pauses) decreased with an increase in etoposide concentration (Fig. 6c), and the extent of rate reduction is in reasonable agreement with that of a previous bulk study32. Intriguingly, the relaxation rate between pauses was essentially independent of etoposide concentration (Fig. 6c and Extended Data Fig. 8d). However, the pausing frequency was highly dependent on etoposide concentration and increased roughly linearly with an increase in etoposide concentration (Fig. 6c and Extended Data Fig. 8e). To ensure that these observations reflected the behavior of single topo II molecules, we incubated topo II at a very low concentration with the DNA substrate before removing any free topo II before measurements (Extended Data Fig. 9). Supercoiling relaxation assays under these conditions yielded a nearly identical relationship of the pausing frequency to etoposide concentration as shown in Fig. 6c.

The observed behaviors also reveal a supercoiling chirality dependence that is isoform specific to the topoisomerases being examined. Whereas human topo IIα shows a mean rate of relaxation about twice as fast on (+) supercoiled DNA than on (−), human topo IIβ and yeast topo II showed minimal chirality dependence (Fig. 6c). The chirality dependence of human topo IIα results from a combination of a faster pause-free relaxation rate and a lower pause frequency on (+) supercoiled DNA (Fig. 6c). In contrast, topo IIβ showed no detectable chirality dependence. Indeed, previous biochemical studies also found that human topo IIα prefers (+) supercoiled DNA, whereas human topo IIβ has no such preference26,43,44. The presence of etoposide did not substantially alter the chirality preference.

The observed prolonged pausing indicates that topo II was trapped in a stable state in the presence of etoposide. To determine if this state corresponds to a configuration of a stable topo II-mediated DNA loop, we measured DNA length under tension first before topo II introduction and then after topo II relaxation for 600 seconds (Fig. 6d). We found a pronounced reduction in the DNA extension after topo II relaxation in the presence of etoposide, both on (+) and (−) supercoiled DNA (Fig. 6d). This reduction is consistent with trapping supercoiled loops by topo II in the presence of etoposide. Control experiments without etoposide showed minimal detectable loop trapping (Fig. 6d). The loop size distributions are broad, with a mean of around 1,000 bp.

Thus, etoposide not only induces prolonged pausing of topo II supercoiling relaxation but also induces topo II to trap supercoiled DNA loops. Thus, the observed pausing is likely due to topo II’s inability to escape from a stably trapped DNA looping state. These findings also show that etoposide promotes the trapping of not only topologically relaxed DNA loops but also supercoiled DNA loops.

## Discussion

In the present work, we investigated the action of the topo II poison etoposide on the molecular mechanisms and dynamics of three topo II homologs (Extended Data Fig. 10) using three single-molecule mechanical manipulation techniques (DNA stretching, unzipping and twisting). We found that, even in the absence of etoposide, topo II can compact DNA by forming DNA loops (Figs. 1c and 2b,d,e), likely as part of its normal catalytic cycle. This compaction does not require ATP (Fig. 4a), suggesting that it is formed by the N-gate transiently capturing a T-segment, an interaction that was reported previously for yeast topo II22. The degree of DNA compaction is topo II isoform specific, with yeast topo II and human topo IIα being more effective than human topo IIβ at trapping a DNA loop. The C-terminal domain of human topo IIα has been suggested as a DNA binding element, but not human topo IIβ26, possibly facilitating DNA loop capture.

We observed that etoposide enhances topo II entrapment of DNA loops for all three isoforms only in the presence of hydrolyzable ATP (Fig. 4a), indicating that the drug stabilizes a state where the T-segment is likely trapped between the DNA-gate and a closed C-gate after strand passage upon ATP hydrolysis. Thus, the single-molecule data have captured a new and important consequence of etoposide binding that has hitherto been overlooked in the field. The degree of compaction is dependent on the concentrations of topo II and etoposide (Fig. 2 and Extended Data Fig. 4d). Given that the topo II concentrations used in this work (0.5–10 pM) are orders of magnitude smaller than those occurring in vivo (on the order of 1 μM)45,46, such compaction may have significant implications for how topo II restructures DNA in vivo. A topo II molecule bound to etoposide could lock two distant DNA segments from the same chromosome or from two different chromosomes, significantly altering chromosome structure and topology.

We directly reveal a DNA break of a topo II cleavage complex by mechanical separation of a topo II dimer interface (Figs. 2f, 3 and 4a). Our finding that etoposide enhances topo II-mediated DSB formation only in the presence of hydrolyzable ATP (Fig. 4a) supports the proposed asynchronization of ATP hydrolysis of the two bound nucleotides32, in which only one ATP is hydrolyzed to allow T-segment transport. When etoposide is present, we posit that the inability to religate the G-segment DNA after T-segment passage interferes with the hydrolysis of the second bound nucleotide, effectively jamming the enzyme.

Stably bound topo II has been proposed to interfere with transcription activity in vivo38. Etoposide could enhance the generation of a DSB by different types of mechanical forces that could either separate a topo II dimer or slide topo II along DNA (Extended Data Fig. 7). Our studies show that DNA-bound topo II is mobile in the absence of etoposide, but it resists relocation and removal in the presence of etoposide (Fig. 5). Topo II’s persistent interactions with DNA are likely facilitated by its binding to two segments of a loop, thereby reducing DNA dissociation. We found that etoposide greatly enhances the probability of forming a topo II-mediated DSB during DNA unzipping, but complete tether breakage (which corresponds to the full separation of the two DNA strands within the enzyme) requires significant force. This result suggests that, although topo II is covalently linked only to the 5′ strand of the cleaved DNA end, the enzyme still tightly clamps the 3′ strand, resisting DNA duplex separation and protein sliding by motor proteins.

Although it has been shown that etoposide significantly slows down topo II during multiple turnover strand passage events on catenated DNA substrates, such as kinetoplast DNA32, the molecular basis for this effect has not previously been fully understood. We found that etoposide interferes with the catalytic activity of topo II by introducing prolonged pausing during processive relaxation of supercoiled DNA in a ‘burst-and-pause’ fashion and that the effect of the drug can be more pronounced for some enzyme isoforms depending on the chirality of the DNA substrate (Fig. 6c). We also found that topo II traps supercoiled DNA loops in the presence of etoposide (Fig. 6d), suggesting that the paused state might be due to the inability of topo II to escape from the loop-trapped state during DNA supercoiling relaxation.

The work described here provides a detailed dissection of the molecular mechanisms by which the topo II poison etoposide corrupts the action of topo II on supercoiled and non-supercoiled DNA templates. It reveals that dynamic interactions of yeast topo II, human topo IIα and human topo IIβ with DNA are remarkably similar, all having a similar ability to resist dimer separation under DNA stretching and to resist sliding along DNA under DNA unzipping. However, they show significant differences in DNA compaction and supercoiling relaxation chirality. These complex behaviors are coming to light via highly sensitive single-molecule assays. We anticipate that the techniques used here will be beneficial in the study of a broad range of topo catalytic inhibitors and poisons, serving as sensitive screening tools that can provide insights into defining drug mechanisms and enzyme isoform specificity.

## Methods

### Protein purification and DNA template construction

Expression and purification of yeast topo II, human topo IIα and human topo IIβ were the same as previously described47. In brief, cultures were grown in selection media; protein expression was induced; cells were harvested by centrifugation; and resulting pellets were flash-frozen. Pellets were lysed, and lysate was loaded onto a series of purification selection columns, resulting in a purified protein free of tags. The protein purity was assessed via SDS–PAGE, and selected fractions were filter concentrated and flash-frozen for storage.

The torsionally constrained DNA construct used for stretching and twisting experiments contained a 12,688-bp DNA segment (~50% GC content), flanked by a ~500-bp multi-labeled tethering adaptor at each end (Extended Data Fig. 1a). The 12.7-kb DNA was amplified from lambda DNA (New England Biolabs (NEB), N3011S) using the primers CTACCCGAGTGCGTGACAT and CCAGTCTCGTGAAGCGGTA with Phusion DNA polymerase (NEB, M0530S). The construct was then purified via PureLink spin-column purification kit (Invitrogen, K310002) and subsequently cleaved with AvaI (NEB, R0152S) and BssSI-v2 (NEB, R0680S) to produce unique DNA overhangs. The final DNA construct was obtained by ligating ~500-bp multi-labeled adaptors to each end of the end-cleaved 12.7-kb DNA with T4 Ligase (NEB, M0202S). These multi-labeled adaptors were amplified from the plasmid pNFRTC (or pMDW111) and labeled via polymerase chain reaction (PCR) with either 24% of dATP replaced by biotin-14-dATP (Invitrogen, 19524-016) or 24% of dTTP replaced by digoxigenin-11-dUTP (Roche, 11093088910). The DNA primers for the biotin-labeled adaptor are CAGTCACGAGGTTGTAAAACG and ACGCCAAGCTTCCACATC, and the DNA primers for the digoxygenin-labeled adaptor are GGGTAACGCTCGGGTTTTCC and ACGCCAAGCTTCCACATC. To create the DNA overhangs, the resulting PCR products were digested with BssSI-v2 (NEB, R0680S) for the biotin adaptor or AvaI (NEB, R0152S) for the digoxygenin adaptor. Ligation products were gel purified to obtain a homogenous DNA sample.

The unzipping experiments used a 4-kb unzipping DNA segment (~50% GC content) ligated to a pair of DNA Y-arms40 with a total length of 2 kb (Extended Data Fig. 1b). The 4-kb DNA unzipping trunk was amplified from lambda DNA (NEB, N3011S) using the DNA primers CCCGCAGCTACTGGATTAAACAAGCC and GTAGCACCAAAGGAAACCATCACCCA with Phusion DNA polymerase (NEB, M0530S). The PCR product was digested with AlwNI (NEB, R0514S), gel purified and ligated to the 2-kb DNA Y-arms40 using T4 Ligase (NEB, M0202S).

### Single-molecule sample chamber preparation

The hydrophobic nitrocellulose-coated grease microfluidic sample chamber was prepared following our previous report41. Before the experiment, a sample chamber was incubated with 20 ng µl−1 of anti-digoxygenin (Roche, 11333089001) for 30 minutes at room temperature. For MT experiments, fiducial marker beads (Dynabeads MyOne Streptavidin T1, 65601) coated with 500-bp biotin and digoxygenin-labeled DNA41 were bound to the surface of the chamber. The surface was then passivated by flushing the chamber with 25 mg ml−1 of β-casein (Sigma-Aldrich, C6905) and incubating for 1 hour at room temperature.

For OT DNA stretching experiments and MT DNA twisting experiments, 1.5 pM of the 12.7-kb DNA in DNA dilution buffer (10 mM Tris-Cl pH 7.8, 50 mM NaCl, 1 mM EDTA and 1.5 mg ml−1 of β-casein) was incubated in the sample chamber for 15 minutes at room temperature. Streptavidin-coated 500-nm polystyrene beads (OT experiments) or 1-μm superparamagnetic beads (Dynabeads MyOne Streptavidin T1, 65601; MT experiments) were then introduced into the chamber. For the OT unzipping experiments, 6 pM of the DNA Y-arms ligated to the unzipping trunk template was incubated in the sample chamber, followed by an incubation of the streptavidin-coated 500-nm polystyrene beads.

Unless stated otherwise, topo II was diluted to 10× the working concentration right before the experiment using topo dilution buffer (30 mM Tris pH 7.8, 500 mM KCl, 10% glycerol (v/v), 0.5 mM TCEP and 0.1 mg ml−1 of β-casein). All experiments were carried out in topo reaction buffer (10 mM Tris-HCl pH 7.8, 50 mM NaCl, 50 mM KCl, 3 mM MgCl2, 0.1 mM EDTA, 1 mM DTT, 0.5 mM TCEP, 1 mM ATP (Roche, 11140965001) and 1.5 mg ml−1 of β-casein) in a soundproof room at a temperature of 23 °C. For the stretching experiments with no ATP, we modified the buffer to contain 2 mM MgCl2 to maintain a similar free MgCl2 concentration as in the topo reaction buffer.

### DNA stretching assay

DNA stretching experiments used a single-beam OT setup17 under one of two modes: constant velocity or constant force. In a sample chamber with anchored 12.7-kb DNA tethers, topo II was diluted to the desired concentration in the topo reaction buffer with or without 100 µM etoposide, introduced into the sample chamber and incubated for 10 minutes at room temperature. Subsequently, the sample chamber was sealed with high vacuum grease (Dow Corning, 1597419). Prior bulk biochemical studies show that etoposide binding has an equilibrium-binding constant of ~5 μM11,48. Thus, 100 μM etoposide should allow a near-saturating occupancy condition.

On the OT setup, for each tether, the bead was trapped, and the tether’s anchoring position was determined by stretching the tether up to 0.5 pN along both positive and negative directions, first along the x axis and then along the y axis. These low-force data were used to determine the degree of DNA compaction. Subsequently, the tether was allowed to relax before being stretched to high forces by moving the coverslip along the x axis. In the constant-velocity mode, the coverslip was moved at a fixed speed of 200 nm s−1. In the constant-force mode, the laser power was fixed, and the coverslip was moved at 8,000 nm s−1 to abruptly increase the tension to 60 pN. Subsequently, the coverslip’s position was modulated to maintain a constant force of 60 pN on the DNA.

In the absence of topo II, a fraction of tethers broke below or at the DNA overstretch transition (~65 pN), indicating that they were likely not torsionally constrained to surfaces. The remaining tethers reached a much higher force without displaying any force features of the overstretch transition, consistent with being torsionally constrained. Some tethers did not break before escaping from the optical trap after reaching the maximum trapping force (about 110 pN at the laser power used). If this occurred, the tether breakage force was indicated by the escape force, which provides a conservative estimate of the breakage force for that trace.

For stretching experiments with etoposide (Sigma-Aldrich, E1383) and AMP-PNP (Roche, 10102547001), we modified the above procedure because AMP-PNP can prevent topo II binding to DNA without free ends49. We diluted topo II in an ATP-free buffer (10 mM Tris-HCl pH 7.8, 50 mM NaCl, 50 mM KCl, 2 mM MgCl2, 0.1 mM EDTA, 1 mM DTT, 0.5 mM TCEP and 1.5 mg ml−1 of β-casein), introduced it into the sample chamber and incubated at room temperature for 30 minutes to allow equilibration of topo II binding to DNA. We then flushed the chamber with a buffer that contained AMP-PNP and etoposide (10 mM Tris-HCl pH 7.8, 50 mM NaCl, 50 mM KCl, 3 mM MgCl2, 0.1 mM EDTA, 1 mM DTT, 0.5 mM TCEP, 1 mM AMP-PNP, 1.5 mg ml−1 of β-casein and 100 μM etoposide) and performed the stretching experiments as described above.

To generate DNA tethers with different numbers of nicks, the surface-anchored DNA was incubated with various Nt.BsmAI (NEB, R0121S) concentrations (0.1, 1, 2, 5 and 30 U ml−1) diluted in the nicking buffer (10 mM Tris-Cl pH 7.8, 10 mM NaCl, 0.5 mM MgCl2, 0.5 mM TCEP and 1.5 mg ml−1 of β-casein). After 15 minutes of nicking, the nickase was removed by flushing the flow chamber with DNA dilution buffer, and the topo reaction buffer was introduced for the stretching experiment. A constant-velocity or constant-force experiment was conducted as described above.

Data were acquired at 10 kHz and decimated by averaging to 1 kHz. Raw data were converted into force and DNA extension as previously described50. For DNA loop disruption peak detection, the data were low-pass filtered with a sliding window of 25 ms.

The OT measurements yielded force versus time F(t) and the corresponding extension versus time x(t). To convert these data to DNA contour length Lo(t), we used the modified Marko–Siggia model19, which states that the force on the DNA depends on the normalized extension $$F\left( {\frac{x}{{L_o}}} \right)$$, as long as the persistence length and stretch modulus are determined. Therefore, once force F(t) and extension x(t) are measured for any timepoint t, the corresponding DNA contour length Lo(t) is also determined. The DNA contour length Lo(t) can then be converted to the number of base pairs (0.338 nm per bp). This strategy was initially developed to determine RNA polymerase position on the DNA during transcription stalling under an external force51 and later used to determine the DNA release from a nucleosome during mechanical disruption17.

### DNA unzipping assay

The DNA unzipping experiments used an OT setup. After the DNA unzipping template was tethered to the surface in a sample chamber, topo II was introduced and incubated for 10 minutes at room temperature. Subsequently, the chamber was sealed with high vacuum grease. For each DNA tether, the tether was stretched and subsequently unzipped by moving the coverslip along the x axis under a constant velocity of 400 nm s−1. For the control experiment with a DNA hairpin, a hairpin with the sequence 5′-/Phos/GCTATTTTTTTAGCTAG was ligated directly to the Y-arms before tethering the DNA to the surface. Subsequent unzipping experiments with the DNA hairpin template were done in the same way as for the 4-kb DNA unzipping trunk template.

Data were acquired at 10 kHz and decimated by averaging to 1 kHz. Raw data were converted into force, DNA extension and the number of base pairs unzipped as previously described50. For sequence alignment, the number of base pairs unzipped data was low-pass filtered with a sliding window of 25 ms.

To convert the measured force and extension data, we used a strategy similar to that described above for dsDNA, except that we simultaneously considered the elastic properties of both ssDNA and dsDNA under tension52,53.

### DNA twisting assay

The DNA twisting experiments used a custom-built MT setup41. The magnetic field was generated with two 0.25-inch cube neodymium magnets (K&J Magnetics, B444) arranged with their dipoles oriented in opposing directions, parallel to the optical axis of the microscope with a separation gap of 0.5 mm. Magnetic bead images were collected by a Nikon objective lens (Plan Apo ×20, 0.75 NA) on a 2.3-megapixel camera (Basler, acA1920-155um) at a frame rate of 10 Hz and an exposure time of 0.15 ms. The bead positions were tracked in three dimensions using an algorithm implemented in LabVIEW based on Omar Saleh’s source code54.

For the DNA twisting experiments, each multi-tagged 12.7-kb DNA molecule was torsionally anchored between a coverslip and a magnetic bead and held at 0.22 ± 0.03 pN (mean ± s.d.). This low force value was chosen to minimize the potential impact of the applied force on topo II speed44. Initially, the magnet was rotated around the zero-turns state to establish the ‘initial hat curve’ for each tether. Then, topo II was introduced into the sample chamber. Then, DNA was (+) or (−) supercoiled by rotating the magnets for 40 turns, and, subsequently, data were recorded for 900 seconds. Subsequent relaxation by topo II was reflected as an increase in the DNA extension. Afterwards, unbound topo II and ATP were removed by topo flushing buffer (10 mM Tris-HCl pH 7.8, 50 mM NaCl, 50 mM KCl, 2 mM MgCl2, 0.1 mM EDTA, 1 mM DTT, 0.5 mM TCEP and 1.5 mg ml−1 of β-casein). A ‘final hat curve’ for each tether was acquired for comparison as for the ‘initial hat curve’. Finally, the tether was wound to the surface to obtain a height offset for absolute length measurement. For the supercoil loop-trapping experiment, after 600 seconds of topo II relaxation, we quickly rotated the magnets at 10 turns per second around the current magnet position to capture a quick-winding hat curve of the tether to check for tether height reduction.

For the pre-binding experiments (Extended Data Fig. 9), after the ‘initial hat curve’ of the 12.7-kb DNA molecule was characterized and the tether was relaxed to a torsional free state under 0.2 pN tension, 0.5 pM yeast topo II was introduced into the sample chamber and incubated for 3 minutes. Then, the chamber was flushed twice with a copious amount of topo reaction buffer (10 chamber volumes for each flush), and −40 turns for (−) supercoiling experiments and +40 turns for (+) supercoiling experiments were quickly added, and the tether’s extension was recorded for 900 seconds. Afterwards, topo activity was stopped by topo flushing buffer; a ‘final hat curve’ was recorded; and the tether was finally wound to the surface.

### Computer simulation of DNA looping

The DNA loop size distribution from topo II binding reflects the probability of juxtaposing non-adjacent DNA regions along the same DNA molecule under no tension to form a DNA loop. We calculated looping probability, or the Jacobson–Stockmayer J-factor for DNA looping, assuming the DNA ends are at a 2-nm end-to-end distance in close contact and that they are free to adopt any orientation relative to each other. We considered two scenarios: a single topo II captures a naturally occurring DNA crossing via the formation of a loop, or a bound topo II bends the DNA significantly and facilitates the formation of a small loop whose ends are captured by a second topo II.

For the first scenario, the J-factor was obtained using a semi-analytical approximation from Douarche and Cocco55 with a 2-nm end-to-end distance and a 45-nm persistence length. For the second scenario, we constructed a coarse-grained model (Extended Data Fig. 3) of topo-bound DNA and used computer simulation to obtain the looping probability24. Looping of <200-bp dsDNA is energetically unfavorable due to the inherent DNA bending stiffness. The sharp DNA bend introduced by a bound topo II facilitates the formation of small DNA loops as it lowers the energy barrier of DNA bending. To calculate the looping probability of topo-bound DNA, we computed the J-factor of looping at the end-to-end distance of 2 nm and bending angle α as a function of total DNA loop size. In this approach, a biased potential $$U = \frac{1}{2}k\left( {r - r_0} \right)^2$$ is added to the total bending energy of the DNA chain to increase the statistics of looping events for the small end-to-end distance r near r0. The spring constant k was chosen as $$\frac{{1.682}}{{25}} \times \exp ( - 0.008664 \ast L) \times (55 - 0.2 \ast \alpha )$$ (pN.nm/bp2) where L is the total DNA contour length in base pairs and α is the bending angle in degrees. A pool of DNA trajectories is generated and equilibrated at room temperature using a standard MC procedure24. For each simulation, 105 initial MC steps were used to equilibrate the system but then discarded, and the data were collected from the subsequent 1.5 × 106 MC steps. A typical MC step involves a pivot rotation of the subchain within the original chain around a random axis that passes through a random vertex of the non-bent DNA with an angle randomly distributed in [−50°,50°]. After obtaining a set of the probability density function of the end-to-end distance, $$P_{biased}(r)$$, for different U(r), the unbiased $$P^0\left( r \right)$$ can be obtained using the weighted histogram analysis method24,56. The J-factor is then computed as $$J\left( r \right) = P^0\left( r \right)/(4\pi r^2)$$ and converted into nanomolar units using the Avogadro constant.

### Statistical analysis

All data were obtained from at least two sample chambers. Statistical details, including the number of traces and s.d. or s.e.m. values, can be found in the manuscript text, Methods subsections, figure captions and Source Data file. Additional details of data analysis are described below.

#### DNA loop disruption peak detection

For filtered stretching data, the disruption force peaks were identified using a MATLAB code called ‘peakfinder.m’, which can be found at https://www.mathworks.com/matlabcentral/fileexchange/25500-peakfinder-x0-sel-thresh-extrema-includeendpoints-interpolate. Only force peaks above 1 pN were selected. To avoid the irrelevant contribution from DNA overstretching, we set an upper threshold for the peak force at 60 pN.

#### DNA alignment algorithm

To improve precision and accuracy of unzipping data, we used custom software written in MATLAB40 to perform a cross-correlation optimization to align each ‘experimental force versus the number of base pairs unzipped’ curve with the corresponding theoretical curve using regions immediately preceding and after the protein disruption57.

#### Pause detection algorithm

To detect pauses in supercoiling relaxation by topo II, we employed an improved pause detection algorithm based on dwell-time analysis40,58. The extension data were low-pass filtered using a non-linear 2nd-order Savitzky–Golay filter with a time constant of 30 seconds. A multi-piece fit to the ‘initial hat curve’ converted extension to the turn state from which the number of helical turns relaxed over time was deduced. The number of turns relaxed was binned to 0.2-turn intervals, and the dwell-time at each bin was computed. Subsequently, clusters of adjacent bins with notable dwell-time (>2 seconds per bin) were identified, and each cluster was assigned as a single pausing state. The pausing regions were mapped back to the time domain by assigning data points within 0.4 turns around the identified pausing levels. Finally, the pausing turn state and pause duration at each state were refined by averaging all data points that belong to the same state.

The pause-free rate was calculated for the ‘bursting’ region before the first pause. After identifying the activity burst before the first pause, the raw data were filtered by a sliding window with a time constant of 5 seconds, and the instantaneous rate was obtained by performing a linear fit to the number of helical turns relaxed over time. The pause-free rate during the first bursting event of each trace was obtained by binning the instantaneous rate into the 0.5-turn bin and taking the median of the binned data.

Pause frequency was measured from the number of helical turns relaxed before entering the first pause. For traces without detected pause, the maximum number of turns relaxed before entering the pre-buckling region of the 12.7-kb DNA twisting under 0.22 pN (~30 turns) was assigned. A cumulative histogram of the relaxed turn numbers was constructed and fitted using a single exponential function to obtain the pause frequency.

### Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.