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Type II topoisomerases are essential enzymes that regulate DNA topology through a strand-passage mechanism. Some type II topoisomerases relax supercoils, unknot and decatenate DNA to below thermodynamic equilibrium. Several models of this non-equilibrium topology simplification phenomenon have been proposed. The kinetic proofreading (KPR) model postulates that strand passage requires a DNA-bound topoisomerase to collide twice in rapid succession with a second DNA segment, implying a quadratic relationship between DNA collision frequency and relaxation rate. To test this model, we used a single-molecule assay to measure the unlinking rate as a function of DNA collision frequency for Escherichia coli topoisomerase IV (topo IV) that displays efficient non-equilibrium topology simplification activity, and for E. coli topoisomerase III (topo III), a type IA topoisomerase that unlinks and unknots DNA to equilibrium levels. Contrary to the predictions of the KPR model, topo IV and topo III unlinking rates were linearly related to the DNA collision frequency. Furthermore, topo III exhibited decatenation activity comparable with that of topo IV, supporting proposed roles for topo III in DNA segregation. This study enables us to rule out the KPR model for non-equilibrium topology simplification. More generally, we establish an experimental approach to systematically control DNA collision frequency.
DNA topoisomerases are ubiquitous enzymes with essential roles in regulating DNA topology in all domains of life (1–5). They are categorized into two classes, type I and II, based on the number of DNA strands cleaved and dependence on adenosine triphosphate (ATP) hydrolysis (1). Type I topoisomerases introduce a transient nick in one strand of duplex DNA and either pass the intact single-stranded segment of DNA through the nick (type IA) or allow controlled rotation around the phosphate bond in the intact single strand (type IB). Type I topoisomerases relax supercoiled DNA towards thermodynamic equilibrium, as they do not use ATP. Type II topoisomerases (topo II), which are further subdivided into type IIA (eukaryotic, prokaryotic and viral) and IIB (archaeal, some higher plants and a few bacteria) based on structural, biochemical and evolutionary differences, introduce a transient double-strand break in one segment of duplex DNA (the gate or G-segment) through which a second segment of duplex DNA (the transfer or T-segment) is passed (6,7). Through this ATP-dependent reaction, type II topoisomerases can relax DNA supercoils, as well as generate and remove links and knots in or between closed DNA molecules. Among the type IIA topoisomerases, DNA gyrase displays the unique ability to negatively supercoil DNA and is the only type IIA topoisomerase that uses the energy of ATP hydrolysis to perform work on the DNA (1,4,8–10). The remainder of the type IIA enzymes catalyse, on average, energetically favourable topological reactions, i.e. relaxing supercoiled DNA. However, Rybenkov et al. (11) demonstrated that type IIA topoisomerases, with the exception of gyrase, simplify DNA topology to steady-state concentrations of unlinked and unknotted molecules that are lower than those found at thermodynamic equilibrium and generate topoisomer distributions of relaxed DNA that have smaller variances than the equilibrium distribution. As topo IIA enzymatic activity is coupled to the energy release of ATP hydrolysis, no thermodynamic principles are violated; however, the mechanism by which topo IIA acting at the local scale can sense the global topology of the DNA substrate remains speculative. Proposed models of non-equilibrium topology simplification posit different mechanisms of topological discrimination, i.e. how the topoisomerase distinguishes DNA crossings in linked, knotted and supercoiled DNA from those occurring randomly in or between DNA molecules (8,12). Two of the models currently under debate, the G-segment DNA-bending model and the hooked-juxtaposition model, assume that local geometry sensing by the topo IIA enzyme influences T-segment capture and transfer (12–18). In the G-segment–bending model, the degree of G-segment bending imposed by topo IIA dictates the degree of non-equilibrium topology simplification (12,16,19,20). However, a recent study found that the degree of G-segment bending by several topo IIAs was similar and uncorrelated with their non-equilibrium unlinking activity. This finding is inconsistent with predictions of the G-segment–bending model and suggests that DNA bending alone is insufficient to account for non-equilibrium topology simplification (21). The hooked-juxtaposition model posits that topo IIA preferentially unlinks juxtaposed DNA segments that are sharply bent towards one another (13,14,22–24). Simulations suggest that the specific unlinking of hooked juxtapositions can account for much, but not all, of the observed degree of topological simplification (22); however, the model has not yet been experimentally tested. In contrast to these geometric selection models, the kinetic proofreading (KPR) model, based on KPR mechanisms proposed by Hopfield and Ninio (25,26), posits that topo IIA uses ‘kinetic selection’ of the T-segment (17–19). In this model, G-segment–bound topo IIA undergoes a transition to an ‘activated’ state on the first collision with a T-segment (Figure 1B). Coupling this activated state transition with the energy of ATP binding makes it irreversible. Strand passage occurs only if a second T-segment collision occurs before decay of the activated state. Non-equilibrium topology simplification results because strand passage depends on the product of the initial, activating strand collision frequency and the second, productive strand collision frequency (Figure 1B). Under the assumption that these frequencies are comparable, the unlinking rate would scale with the square of the collision frequency. This non-linear relationship between unlinking rate and strand collision frequency results in non-equilibrium simplification, as the equilibrium simplification reaction would depend linearly on the collision frequency. As a concrete example, consider the steady-state inter-conversion of linked and unlinked circular DNA molecules. At equilibrium, the concentrations of linked and unlinked DNA would be proportional to the ratio of strand collision frequencies of unlinked and linked circles. Under the KPR model, the concentrations of the two species would be proportional to the square of the DNA collision frequencies for the unlinked and linked molecules. The quadratic dependence on the collision frequency arises because, in order for strand passage to take place, two collisions must occur in rapid succession, the probability of which scales as the square of the collision rate. Thus, the central tenet of the KPR model is that the strand transfer rate scales quadratically with the DNA strand-collision frequency.
Simulations of the KPR model suggest that the kinetic amplification may not be sufficient to achieve experimentally observed levels of non-equilibrium topology simplification for DNA knots unless combined with aspects of the DNA G-segment–bending model or some other complementary non-equilibrium simplification mechanism (16,27). Furthermore, the KPR model seems difficult to rationalize with accepted models of strand passage in which ATP binding triggers N-gate closure that traps the T-segment and favours its passage through the cleaved G-segment (7,28–31). This model, based on a combination of structural and biochemical evidence, seems to be at odds with the central tenet of the KPR model that postulates T-segment release and recapture after the binding of at least one ATP (8,10). Despite this apparent contradiction, there is sufficient uncertainty in the kinetics of binding two ATP molecules and the subsequent kinetics of N-clamp closure that the KPR model, which is a kinetic model, cannot be entirely ruled out based on existing data. Therefore, the hypothesis that topo IIA requires a double collision between the G-segment–bound topoisomerase and a T-segment for strand passage remains a potential, but unverified, mechanism that would result in non-equilibrium topology simplification. Although ensemble approaches allow geometric features of DNA-topoisomerases complexes to be indirectly measured and, therefore, used to test the validity of models based on DNA bending, testing the KPR model experimentally is challenging, as it requires a means of assessing and varying the collision frequency between DNA strands, referred to hereafter as collision frequency.
Here, we tested the KPR model by investigating the relationship between DNA collision frequency and DNA unlinking rate using a novel strategy based on the micromanipulation of a single-DNA crossing. We measured the unlinking rates of Escherichia coli topo IV, a type IIA topoisomerase that displays efficient non-equilibrium topology simplification, using a single-molecule DNA unlinking assay in which the relative collision frequency could be controlled (Figure 1A). Combining these measurements with collision frequencies obtained from Monte Carlo (MC) simulations permitted a sensitive measure of the relationship between collision frequency and unlinking rate. Because this comparison relies on the assumption that the collision frequency obtained from MC simulations is proportional to the actual collision frequency, we measured the unlinking rate as a function of computed collision frequency for E. coli topo III, a type IA topoisomerase that unlinks and unknots DNA to equilibrium levels (11). Topo III is an efficient decatenase that is thought to play important roles in chromosome segregation and the resolution of linked DNA intermediates without using ATP (32–35). Topo III uses a strand-passage mechanism common to all type IA topos (1,4,36,37), but it can uniquely pass duplex DNA through a single-stranded nick or gap (1), thereby permitting reversible linking and knotting reactions with gapped DNA substrates. In the context of the KPR model, topo III is expected to display a linear relationship between unlinking rate and collision frequency because it uses an ATP-independent mechanism based on a single collision of two DNA segments (Figure 1B).
Contrary to the predictions of the KPR model, we found that the unlinking rates of both topo IV and topo III were linearly related to the collision frequency. Moreover, the unlinking rates of the two enzymes measured with comparable double tether geometries were linearly related over the range of DNA collision frequencies investigated. We conclude from these results that non-equilibrium topology simplification activity does not arise in whole or in part from a KPR mechanism, thus ruling out the KPR model. However, our results reveal that topo III, unlike E. coli topoisomerase IA (topo I), is an efficient DNA decatenase, on par with topo IV, lending support to its putative roles in chromosome segregation and unlinking in vivo (33).
Linear 5-kb dsDNA labelled with a single biotin or digoxigenin at each 5′-end was prepared by polymerase chain reaction (PCR) using pET28b (EMD Science) as a template with a biotin-labelled forward primer and digoxigenin-labelled reverse primer (Eurofins MWG Operon). The PCR product was purified with a QIAquick PCR purification kit (Qiagen).
Linear 5-kb dsDNA with a 37-nt gap (2258–2294) with a single biotin or digoxigenin at each 5′-end was prepared similarly to the topo IV DNA substrate except that the PCR template was pKZ1. pKZ1 was made by ligating a 44-bp dsDNA segment containing two BbvCI sites separated by 37 nt into pET28b at the BamHI site. The 5-kb PCR product was digested with Nt.BbvCI (New England Biolabs) to create two nicks at positions 2258 and 2294, near the middle of the DNA template. After digestion, the 37-nt oligomer was removed by heating the DNA to 80°C for 20 min and cooling down gradually to 4°C in the presence of excess complementary 37-nt oligomer. The 4-kb multi-nicked DNA molecules were prepared by PCR of pFC94 (38) from position 5422–9520 with a biotin-labelled forward primer and digoxigenin-labelled reverse primer (Eurofins MWG Operon) and were nicked with four nicking enzymes: Nb.BsmI, Nt.AIwI, Nb.BtsI and Nt.BtsNBI (New England Biolabs), generating 14 nicks located over the middle third of the DNA.
E. coli topoisomerase I was purchased from New England Biolabs.
The pET-15btopB plasmid encoding K12 E. coli topoisomerase III was provided by J. Keck (University of Wisconsin Madison). A tobacco etch virus (TEV) protease cleavage site with an additional two glycine residue spacer was inserted upstream of the topB gene using the QuikChange II XL mutagenesis kit (Stratagene), and the sequence of the resulting plasmid (pET-15btopB+TEV) was verified. Rosetta (DE3) pLysS Competent Cells (EMD4Bioscience) transformed with pET-15btopB+TEV were grown at 37°C in Luria-Bertani broth containing 50 μg/ml of carbenicillin and 34 μg/ml of chloramphenicol. The expressed protein was induced with 1 mM isopropyl β-d-thiogalactopyranoside. After induction at 37°C for 20 h, cells were harvested by centrifugation. The collected cells were suspended in buffer A [50 mM Tris–HCl, pH 7.5, 300 mM NaCl and 10% (v/v) glycerol] and emulsified using a high pressure cell homogenizer (Avestin). The cell lysate was then centrifuged at 40 krpm at 4°C for 1 h in a Ti45 rotor (Beckman). The supernatant was loaded onto a HisTrap-FF 5 ml Ni-Nitrilotriacetic acid (NTA) column (GE). His-tagged protein was eluted with buffer B [50 mM Tris–HCl, pH 7.5, 0.5 M imidazole, 0.3 M NaCl, 10 mM β-mercaptoethanol and 10% (v/v) glycerol]. The eluted proteins were concentrated and buffer-exchanged with buffer A using an Amicon Ultra-15 centrifugal filter unit with Ultracel-30 membrane (Millipore). The his tag was removed from the protein by digestion with 0.5 U/μg of Pro-TEV (Promega) for 6 h. The protein digestion mixture was run twice through an Ni-NTA column (Qiagen) to remove Pro-TEV and uncleaved protein. The size and purity of cleaved topo III were evaluated by sodium dodecyl sulphate–polyacrylamide gel electrophoresis (Invitrogen).
To prepare double-DNA tethers for DNA unlinking experiments, 1 µl of 0.15 nM singly biotin- and digoxigenin-labelled 5-kb dsDNA was incubated with 1 µl of magnetic beads [1% (w/v), MyOne, Invitrogen] in 200 µl of wash buffer [WB: 1× phosphate-buffered saline, 0.3% (w/v) bovine serum albumin (BSA) and 0.04% Tween-20) at room temperature (22°C) overnight at a 3:1 DNA to bead ratio. The sample cell was incubated with 30 µl of 10 µg/ml of anti-digoxigenin in 1× phosphate-buffered saline for 1 h at room temperature followed by a wash with 200 µl of WB. The DNA-bead mixture was incubated in the anti–digoxigenin-coated sample cell for 30 min before washing with 400 µl of WB. The magnetic tweezers instrumentation has been previously described (40–42). During the experiment, double-DNA tethered beads were identified by rotating the magnet assembly. In contrast to a bead tethered by a single DNA, the DNA extension of a double-DNA tethered bead decreases symmetrically for negative and positive turns (Figure 2A) independent of the tension on the DNA (43). Topo IV activity buffer [25 mM Tris–HCl, pH 7.5, 100 mM potassium glutamate, 10 mM magnesium chloride, 1 mM dithiothreitol, 0.3% (w/v) BSA and 0.04% (v/v) Tween-20] containing 2 nM topo IV and 1 mM ATP was introduced once 20 double-tethered beads were found, and their tethering geometries (spacing between DNA molecules and verification of parallel tether geometry—see later in the text) were characterized. Topo IV DNA unlinking rates were measured for bead rotations of −0.6 to −1 turn (Figure 3A), which imposes left-handed DNA crossings as found in positive writhe. Topo III unlinking measurements were similar except that 5-kb DNA molecules containing a 37-nt gap near their centres were used as substrates, as topo III requires a single-stranded region for strand passage. Unlinking measurements were performed with 5 nM topo III in topo III activity buffer [40 mM HEPES, pH 8.0 adjusted with KOH, 1 mM magnesium acetate, pH 7, 0.3% (w/v) BSA and 0.04% (v/v) Tween-20]. Data traces were analysed using a custom step-finding algorithm to identify the waiting time, Twait (the time interval between rotating the bead to generate the DNA link and it being unlinked by topoisomerase). The Twait values (100–200 events for each rotation) were binned, and the histogram was fitted with a single exponential to obtain the strand-passage rate. Topo I (New England Biolabs) unlinking measurements were performed using the same substrate used for topo III experiments with ~130 or 325 nM of topo I in topo I activity buffer [50 mM potassium acetate, pH 7.9, 10 mM magnesium acetate, 1 mM dithiothreitol, 0.3% (w/v) BSA and 0.04% (v/v) Tween-20].
The geometry of the two DNA strands tethering the bead to the surface was determined by measuring the extension, Z(n), as a function of the number of turns (n). The region from −0.5 to 0.5 turns was fit with Equation (1) to obtain the distance between two DNA molecules (2e) and the DNA extension at n = 0 (Z0) (Figure 2A):
where Rb is the bead radius (0.5 μm) (44). Tethered beads were selected for unlinking measurements if the DNA extension at zero rotation (Z0) was within 10% of the predicted extension at the applied force. This selection criterion eliminated tether geometries that were not parallel, as trapezoidal tether geometry would result in a decreased DNA extension at zero rotation, and eliminated beads tethered by more than two DNA molecules.
The experimentally determined tether geometry (2e, n, DNA length and applied force, F) was used to calculate the number of collisions between two DNA segments using a custom-written MC simulation routine for double-tethered beads, as previously described (44,45). Briefly, the simulation program models the two DNA molecules as discrete worm-like chains consisting of 10-nm rigid segments of fixed length. For each braid geometry, 106 simulation steps were calculated and were sampled once every 103 steps to obtain uncorrelated configurations. At each sample step, the collision frequency, was calculated from the total number of collisions over the previous 103 MC steps. Collisions were considered to have occurred when two segments on the two DNA molecules were closer than a cut-off distance of 12 nm. Thus, for 106 steps, 103 collision frequencies were generated for each tether geometry. The values for each condition were binned, plotted as a histogram and fitted with a Gaussian distribution to obtain the mean as shown in Figure 2B.
To test the KPR model of non-equilibrium topology simplification, we developed a single-molecule DNA unlinking assay (Figure 2A) that permitted measurement of the unlinking rate as a function of strand collision frequency. The KPR model predicts a quadratic relationship between unlinking rate and collision frequency. The unlinking assay is a variation on similar unlinking assays (44–46) in which a magnetic bead is tethered by two rotationally unconstrained 5-kb DNA molecules. Rotating the bead wraps the two DNA strands around one another, which reduces the height of the bead. The action of a single topoisomerase on this substrate resulted in a sudden increase in the height, indicating the unlinking of the DNA strands. After a brief delay, the bead was automatically rotated to create a new substrate for the enzyme (Figure 1). The experiment consists of imposing a series of partial rotations (−1 ≤ n ≤ −0.6, corresponding to positive writhe) on the bead and measuring the rate at which the corresponding crossings are unlinked by topo IV. The frequency of DNA strand collisions is expected to increase in proportion to the degree of linking, i.e. the magnitude of the bead rotation, which has been verified by MC simulations (Figure 2B and C). Therefore, by measuring the unlinking rate as a function of imposed bead rotation and estimating the strand collision frequency from MC simulations of the experimental configuration, the relationship between strand collision frequency and unlinking rate can be determined.
In practice, once a double-tethered magnetic bead was identified, the DNA crossing geometry was characterized to obtain the spacing between the DNA tethers, 2e (Figure 2A). Based on the tether geometry and the applied force, the inter-strand collision frequency as a function of bead rotation was obtained from MC simulations (Figure 2B and C). The unlinking rate was measured as a function of bead rotation from −0.6 to −1 turn in the presence of 2 nM topo IV (above the Kd of ~0.2 nM measured under similar conditions) (47) and saturating (1 mM) ATP. Under these conditions, T-segment capture is expected to be rate limiting for strand passage; thus, the unlinking rate will be determined by the DNA collision frequency. The observed increase in unlinking rate with rotation (Figure 3B) is consistent with this assumption. The time interval between rotating the bead and the unlinking reaction was obtained from the extension traces (Figure 1), and the distributions of unlinking times were fit with single-exponential functions to obtain the mean unlinking rate for each rotation (Figure 3). To compare unlinking rates as a function of bead rotation measured with different double-tether geometries and to account for other possible differences among nominally identical measurement conditions, unlinking rates for each tether were normalized to the unlinking rate at n = 1 turn (Figure 4A).
The normalized unlinking rates, , increased as a function of bead rotation at both 1 and 2 pN of applied force on the bead (Figure 4A). To investigate the relationship between the unlinking rates and collision frequencies, we plotted (n) as a function of the normalized collision frequencies at the same bead rotation, (n) (Figure 4B). The values were calculated in a similar manner to that used to obtain : the collision frequency at each rotation was normalized by the collision frequency at n = 1 turn for each double-tether geometry. The normalized unlinking rates seemed to be linearly related to the normalized collision frequencies (Figure 4B). Fitting versus with a power function, returned a power close to 1: P = 1.10 ± 0.03 (±SD) with a reduced chi-square, . Fitting with P = 2 resulted in a 2-fold increase in reduced chi-square, Fitting to a line (P = 1) returned a slope of 0.87 ± 0.01 (±SD) and a linear correlation coefficient of 0.75. Overall, the fits suggest a linear relationship between the normalized rates and collision frequencies in contrast to the quadratic relationship predicted by the KPR model.
Although we found a linear relationship between the normalized unlinking rates of topo IV and the predicted collision frequencies, it is possible that the collision frequencies obtained from MC simulations were not good estimates of the relative collision frequencies. To verify the MC simulation results, we measured the unlinking rates of topo III as a function of bead rotation and compared the normalized rates with the normalized computed collision frequencies.
The unlinking rates of topo III (10 nM) as a function of bead rotation were measured using the same protocol and conditions used for topo IV except that the 5-kb DNA tethers contained a 37-nt single-stranded gapped region near the middle of each DNA molecule, as intact 5-kb DNA molecules and multi-nicked 4-kb DNA molecules were not decatenated by topo III. These observations confirmed that a single-stranded region of DNA is essential for topo III decatenation in addition to relaxation, similar to topo I (35,36). However, we found that E. coli topo IA was incapable of decatenation. Despite rapidly relaxing negative supercoils, topo IA did not unlink crossings of a double-DNA tether at a ~30-fold higher concentration (325 nM) than that of topo III, for which efficient unlinking of the same tether was observed (Supplementary Figures S2 and S3). The average unlinking rate at one turn for topo III (5.9 ± 0.7 s−1 mean ± standard error) was comparable with that for topo IV (5.1 ± 0.5 s−1), indicating that topo III is an efficient decatenase on par with topo IV. The normalized rates for topo III ( were plotted as a function of , calculated in the same manner as for topo IV (Figure 5A) and fitted with a linear function. As expected, the topo III unlinking rate was linearly related to, and strongly correlated with, the collision frequency. The fit returned a slope = 1.00 ± 0.01 (±SD), , and a linear correlation coefficient = 0.76.
Comparing the unlinking rates of topo III and topo IV as a function of bead rotation, i.e. DNA collision frequency for similar bead geometries, provides an independent test of the KPR model that does not depend on the results of the MC simulations. As the unlinking rate of topo III is reasonably expected to be linearly related to the strand collision frequency, the normalized topo III unlinking rate reflects the relative strand collision frequency. Therefore, plotting the normalized relaxation rates of topo IV as a function of the normalized relaxation rates of topo III at the same bead rotation for comparable tether geometries (difference in 2e ≤ 0.2 µm) and applied force provides a simulation-independent comparison between unlinking rate and strand collision frequency (Figure 5B). Fitting versus to a line returned a slope of 0.97 ± 0.02 with and a linear correlation coefficient of 0.78. Fitting the data with a power function, , returned A = 0.99 ± 0.04 and P = 1.02 ± 0.05 with . Fixing P = 2, i.e. a quadratic fit, increased to 17.9. This direct comparison confirmed that the strand-passage reaction of topo IV and topo III depends linearly on the DNA collision frequency.
In this study, we showed that the unlinking rate of topo IV increases linearly rather than quadratically with increasing collision frequencies between two DNA segments. The linear relationship between the topo III unlinking rate and collision frequency confirmed the validity of the combined experimental and computational approach while providing a simulation-independent test of the KPR model. Overall, our study indicates that a single collision with T-segment DNA is likely sufficient for strand passage by topo IV, suggesting that non-equilibrium topology simplification cannot be explained within the framework of the KPR model (17,18). This conclusion is further supported by the fact that Drosophila topo II (48) showed a similar linear relationship when compared with topo III under similar geometric conditions (Supplementary Figure S1). Although theoretical and computational studies have shown that the KPR model could not fully explain the measured non-equilibrium topology simplification (12), our work experimentally demonstrates that topo IV does not require a double collision with a T-segment DNA for strand passage. This result likely applies to other topo IIA enzymes, as they share a common two-gate mechanism for a strand passage through well-conserved core domains (4,49,50), and topo IV exhibits the most dramatic non-equilibrium topology simplification activity among the type IIA topoisomerases for which this activity has been characterized (11).
Since the remarkable discovery by Rybenkov et al. (11) that type IIA topoisomerases can simplify DNA topology to below equilibrium levels, several mechanisms of non-equilibrium topology simplification have been proposed, and their merits have been debated, largely through simulations. Recently, experimental tests of some non-equilibrium models have been performed. For example, direct measurements of the bend angles imposed on G-segment DNA by three type IIA topoisomerases suggest that the bend-angle model can account for some but not all of the non-equilibrium simplification activity (21). Stuchinskaya et al. (27) made a number of measurements of non-equilibrium topology simplification activity, some of which ruled out a ‘translocation’ model originally proposed by Rybenkov et al. to explain the non-equilibrium activity. In this model, type II topos use the energy of ATP hydrolysis to translocate along the DNA, thereby localizing links to smaller loops that are more readily removed. Contrary to the premise of this model, the presence of high affinity DNA-binding proteins acting as translocation ‘roadblocks’ did not alter the degree of non-equilibrium topology simplification. A ‘three-segment’ binding model that postulates the binding of two separate potential T-segments, one of which is passed through the G-segment, provides a mechanism of non-equilibrium simplification, but it is also associated with a shift of the centre of the steady-state topoisomer distribution that has not been observed in multiple independent studies (21,27). The remaining models that have not been directly tested are the KPR model and the hooked-juxtaposition model. The hooked-juxtaposition model shares elements of the bend-angle model, but rather than the enzyme imposing a bend on the G-segment, the model postulates that the enzyme preferentially unlinks T- and G-segments that are bent towards each other. We focused our attention on the KPR model, in which the strand-passage rate scales non-linearly, likely quadratically, with the strand collision frequency.
The experimental challenge was to devise a method of reproducibly controlling the strand collision frequency and measuring the unlinking rate. To address this challenge, we modified a single-molecule DNA ‘braiding’ assay, in which two strands of DNA attached to a magnetic bead can be wrapped around one another by rotating the bead in a magnetic tweezers instrument. We reasoned that rotating the bead by less than one full turn would impose on average a partial link between the two DNA strands, and that the relative frequency of strand collisions that a topoisomerase could act on would increase with increasing bead rotation. MC simulations of the DNA configurations based on the geometry of the double tether measured in situ confirm that the relative probability of strand collisions, which is proportional to the frequency of strand collisions under reasonable equilibrium assumptions, increases linearly with increasing bead rotation (Figure 3). Unlinking measurements with topo III confirm the increase in collision frequency with increasing bead rotation and provide a test of the assumptions implicit in comparing the results of MC simulations that provide the probability of strand collision with experimental measurement of unlinking rate. As the conclusions of the current study rely heavily on this reasonable but untested hypothesis, the topo III results were an important verification of the approach and serve as a validation of the method, which may be generally useful to probe protein-mediated DNA synapse formation. In addition, the unlinking measurements of topo III provide explicit experimental evidence, indicating that topo III is an efficient decatenase, comparable with topo IV, provided the linked DNA includes a single-stranded gapped region, lending support to its putative roles in chromosome segregation and unlinking in vivo (33). In comparison with topo III, we found that topo I failed to unlink crossed DNA molecules when tested with the same substrate, confirming that topo I and topo III likely play different roles in in vivo (Supplementary Figure S3).
The combination of the partial linking assay and MC simulations of DNA conformations permitted a sensitive test of the non-linear relationship between strand collision frequency and unlinking rate that is the central feature of the KPR model. Ruling out the kinetic selection embodied in this model raises the question as to how topo IIA enzymes achieve non-equilibrium topology simplification. As has been pointed out by Vologodskii and others, local DNA conformations and the corresponding probability of topological conversions by a topoisomerase likely result in different degrees of non-equilibrium topology simplification by different topo IIA enzymes (11,13–17,19). As proposed models have been experimentally tested and shown to be either inconsistent or insufficient to fully account for the degree of topological simplification, we posit that either local DNA bending coupled with an as yet undetermined mechanism or a selection based on an existing local conformation such as ‘hookedness’ hold the greatest promise to explain this phenomenon (13,14). MC simulations of the DNA tethers used in this study suggest that local DNA bending and hookedness did not vary significantly under our experimental conditions; thus, we were unable to test the effects of local geometry with the current measurements. We anticipate that similar approaches may be applicable to evaluate the effect of local bending and hookedness on DNA unlinking activity, and that these approaches will help elucidate the mechanistic basis for non-equilibrium topology simplification and, more generally, the process of strand capture and passage that is central to the activity of type II topoisomerases.
Supplementary Data are available at NAR Online: Supplementary Figures 1–3 and Supplementary References [48,51].
Intramural Research Program of the National Heart, Lung, and Blood Institute, National Institutes of Health (in part); Young Investigator Award from the Human Frontiers Science Program (to K.C.N.) (in part). Funding for open access charge: The Intramural Research Program of the National Heart, Lung, and Blood Institute, National Institutes of Health.
Conflict of interest statement. None declared.
The authors thank James Keck for providing the topo III expression construct, Richard Neuman and Tamara Litwin for editing the manuscript, Krishan Zaveri for assistance with the gapped template construction, Alfonso Mondragón for useful discussions and David Bensimon and Vincent Croquette for supporting and encouraging this work in its initial phase.