Asymmetric Removal of Supercoils Suggests how Topoisomerase II Simplifies DNA Topology

Keeping intracellular DNA untangled: A new role for condensin?

The DNA-passage activity of topoisomerase II accidentally produces DNA knots and interlinks within and between chromatin fibers. Fortunately, these unwanted DNA entanglements are actively removed by some mechanism. Here we present an outline on DNA knot formation and discuss recent studies that have investigated how intracellular DNA knots are removed. First, although topoisomerase II is able to minimize DNA entanglements in vitro to below equilibrium values, it is unclear whether such capacity performs equally in vivo in chromatinized DNA. Second, DNA supercoiling could bias topoisomerase II to untangle the DNA. However, experimental evidence indicates that transcriptional supercoiling of intracellular DNA boosts knot formation. Last, cohesin and condensin could tighten DNA entanglements via DNA loop extrusion (LE) and force their dissolution by topoisomerase II. Recent observations indicate that condensin activity promotes the removal of DNA knots during interphase and mitosis. This activity might facilitate the spatial organization and dynamics of chromatin.

Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology

Grid diagrams with their relatively simple mathematical formalism provide a convenient way to generate and model projections of various knots. It has been an open question whether these 2D diagrams can be used to model a complex 3D process such as the topoisomerase-mediated preferential unknotting of DNA molecules. We model here topoisomerase-mediated passages of double-stranded DNA segments through each other using the formalism of grid diagrams. We show that this grid diagram-based modeling approach captures the essence of the preferential unknotting mechanism, based on topoisomerase selectivity of hooked DNA juxtapositions as the sites of intersegmental passages. We show that the grid diagram-based approach provides an important, new, and computationally convenient framework for investigating entanglement in biopolymers.

Kinetic pathways of topology simplification by Type-II topoisomerases in knotted supercoiled DNA

The topological state of covalently closed, double-stranded DNA is defined by the knot type $K$ and the linking-number difference $\Delta Lk$ relative to unknotted relaxed DNA. DNA topoisomerases are essential enzymes that control the topology of DNA in all cells. In particular, type-II topoisomerases change both $K$ and $\Delta Lk$ by a duplex-strand-passage mechanism and have been shown to simplify the topology of DNA to levels below thermal equilibrium at the expense of ATP hydrolysis. It remains a key question how small enzymes are able to preferentially select strand passages that result in topology simplification in much larger DNA molecules. Using numerical simulations, we consider the non-equilibrium dynamics of transitions between topological states $(K,\Delta Lk)$ in DNA induced by type-II topoisomerases. For a biological process that delivers DNA molecules in a given topological state $(K,\Delta Lk)$ at a constant rate we fully characterize the pathways of topology simplification by type-II topoisomerases in terms of stationary probability distributions and probability currents on the network of topological states $(K,\Delta Lk)$. In particular, we observe that type-II topoisomerase activity is significantly enhanced in DNA molecules that maintain a supercoiled state with constant torsional tension. This is relevant for bacterial cells in which torsional tension is maintained by enzyme-dependent homeostatic mechanisms such as DNA-gyrase activity.

DNA knots occur in intracellular chromatin

In vivo DNA molecules are narrowly folded within chromatin fibers and self-interacting chromatin domains. Therefore, intra-molecular DNA entanglements (knots) might occur via DNA strand passage activity of topoisomerase II. Here, we assessed the presence of such DNA knots in a variety of yeast circular minichromosomes. We found that small steady state fractions of DNA knots are common in intracellular chromatin. These knots occur irrespective of DNA replication and cell proliferation, though their abundance is reduced during DNA transcription. We found also that in vivo DNA knotting probability does not scale proportionately with chromatin length: it reaches a value of ∼0.025 in domains of ∼20 nucleosomes but tends to level off in longer chromatin fibers. These figures suggest that, while high flexibility of nucleosomal fibers and clustering of nearby nucleosomes facilitate DNA knotting locally, some mechanism minimizes the scaling of DNA knot formation throughout intracellular chromatin. We postulate that regulation of topoisomerase II activity and the fractal architecture of chromatin might be crucial to prevent a potentially massive and harmful self-entanglement of DNA molecules in vivo.

Disentangling DNA molecules

The widespread circular form of DNA molecules inside cells creates very serious topological problems during replication. Due to the helical structure of the double helix the parental strands of circular DNA form a link of very high order, and yet they have to be unlinked before the cell division. DNA topoisomerases, the enzymes that catalyze passing of one DNA segment through another, solve this problem in principle. However, it is very difficult to remove all entanglements between the replicated DNA molecules due to huge length of DNA comparing to the cell size. One strategy that nature uses to overcome this problem is to create the topoisomerases that can dramatically reduce the fraction of linked circular DNA molecules relative to the corresponding fraction at thermodynamic equilibrium. This striking property of the enzymes means that the enzymes that interact with DNA only locally can access their topology, a global property of circular DNA molecules. This review considers the experimental studies of the phenomenon and analyzes the theoretical models that have been suggested in attempts to explain it. We describe here how various models of enzyme action can be investigated computationally. There is no doubt at the moment that we understand basic principles governing enzyme action. Still, there are essential quantitative discrepancies between the experimental data and the theoretical predictions. We consider how these discrepancies can be overcome.

Consistent rationalization of type-2 topoisomerases' unknotting, decatenating, supercoil-relaxing actions and their scaling relation

How type-2 topoisomerases discern global topology from local properties of DNA is not known precisely but the hypothesis that the enzymes selectively pass double-helix strands at hook-like juxtapositions is promising. Building upon an investigation of unknotting and decatenating using an improved wormlike DNA model, here we focus primarily on the enzymes' action in narrowing the distribution of linking number (Lk) in supercoiled DNA. Consistent with experiments, with selective passage at a hooked juxtaposition, the simulated narrowing factor RLk diminishes with decreasing DNA circle size but approaches an asymptotic RLk ≈ 1.7-1.8 for circle size ≳3.5 kb. For the larger DNA circles, we found that (RLk - 1) ≈ 0.42log10RK ≈ 0.68log10RL and thus RK ≈ (RL)(1.6) holds for the computed RLk and knot and catenane reduction factors RK and RL attained by selective passage at different juxtaposition geometries. Remarkably, this general scaling relation is essentially identical to that observed experimentally for several type-2 topoisomerases from a variety of organisms, indicating that the different disentangling powers of the topoisomerases likely arise from variations in the hooked geometries they select. Taken together, our results suggest strongly that type-2 topoisomerases recognize not only the curvature of the G-segment but also that of the T-segment.

Direct Evidence for the Formation of Precatenanes during DNA Replication

The dynamics of DNA topology during replication are still poorly understood. Bacterial plasmids are negatively supercoiled. This underwinding facilitates strand separation of the DNA duplex during replication. Leading the replisome, a DNA helicase separates the parental strands that are to be used as templates. This strand separation causes overwinding of the duplex ahead. If this overwinding persists, it would eventually impede fork progression. In bacteria, DNA gyrase and topoisomerase IV act ahead of the fork to keep DNA underwound. However, the processivity of the DNA helicase might overcome DNA gyrase and topoisomerase IV. It was proposed that the overwinding that builds up ahead of the fork could force it to swivel and diffuse this positive supercoiling behind the fork where topoisomerase IV would also act to maintain replicating the DNA underwound. Putative intertwining of sister duplexes in the replicated region are called precatenanes. Fork swiveling and the formation of precatenanes, however, are still questioned. Here, we used classical genetics and high resolution two-dimensional agarose gel electrophoresis to examine the torsional tension of replication intermediates of three bacterial plasmids with the fork stalled at different sites before termination. The results obtained indicated that precatenanes do form as replication progresses before termination.

Topoisomerase II minimizes DNA entanglements by proofreading DNA topology after DNA strand passage

By transporting one DNA double helix (T-segment) through a double-strand break in another (G-segment), topoisomerase II reduces fractions of DNA catenanes, knots and supercoils to below equilibrium values. How DNA segments are selected to simplify the equilibrium DNA topology is enigmatic, and the biological relevance of this activity is unclear. Here we examined the transit of the T-segment across the three gates of topoisomerase II (entry N-gate, DNA-gate and exit C-gate). Our experimental results uncovered that DNA transport probability is determined not only during the capture of a T-segment at the N-gate. When a captured T-segment has crossed the DNA-gate, it can backtrack to the N-gate instead of exiting by the C-gate. When such backtracking is precluded by locking the N-gate or by removing the C-gate, topoisomerase II no longer simplifies equilibrium DNA topology. Therefore, we conclude that the C-gate enables a post-DNA passage proofreading mechanism, which challenges the release of passed T-segments to either complete or cancel DNA transport. This proofreading activity not only clarifies how type-IIA topoisomerases simplify the equilibrium topology of DNA in free solution, but it may explain also why these enzymes are able to solve the topological constraints of intracellular DNA without randomly entangling adjacent chromosomal regions.

The benefit of DNA supercoiling during replication

DNA topology changes dynamically during DNA replication. Supercoiling, precatenation, catenation and knotting interplay throughout the process that is finely regulated by DNA topoisomerases. In the present article, we provide an overview of theoretical and experimental approaches to understand the interplay between various manifestations of topological constraints acting on replicating DNA molecules. Data discussed reveal that DNA entanglements (supercoils and catenanes) play an active role in preventing the formation of deleterious knots.

New biologically motivated knot table

The knot nomenclature in common use, summarized in Rolfsen's knot table [Rolfsen (1990) Knots and Links, American Mathematical Society], was not originally designed to distinguish between mirror images. This ambiguity is particularly inconvenient when studying knotted biopolymers such as DNA and proteins, since their chirality is often significant. In the present article, we propose a biologically meaningful knot table where a representative of a chiral pair is chosen on the basis of its mean writhe. There is numerical evidence that the sign of the mean writhe is invariant for each knot in a chiral pair. We review numerical evidence where, for each knot type K, the mean writhe is taken over a large ensemble of randomly chosen realizations of K. It has also been proposed that a chiral pair can be distinguished by assessing the writhe of a minimal or ideal conformation of the knot. In all cases examined to date, the two methods produce the same results.

Comparison of DNA decatenation by Escherichia coli topoisomerase IV and topoisomerase III: implications for non-equilibrium topology simplification

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.

Local sensing of global DNA topology: from crossover geometry to type II topoisomerase processivity

Type II topoisomerases are ubiquitous enzymes that control the topology and higher order structures of DNA. Type IIA enzymes have the remarkable property to sense locally the global DNA topology. Although many theoretical models have been proposed, the molecular mechanism of chiral discrimination is still unclear. While experimental studies have established that topoisomerases IIA discriminate topology on the basis of crossover geometry, a recent single-molecule experiment has shown that the enzyme has a different processivity on supercoiled DNA of opposite sign. Understanding how cross-over geometry influences enzyme processivity is, therefore, the key to elucidate the mechanism of chiral discrimination. Analysing this question from the DNA side reveals first, that the different stability of chiral DNA cross-overs provides a way to locally sense the global DNA topology. Second, it shows that these enzymes have evolved to recognize the G- and T-segments stably assembled into a right-handed cross-over. Third, it demonstrates how binding right-handed cross-overs across their large angle imposes a different topological link between the topoIIA rings and the plectonemes of opposite sign thus directly affecting the enzyme freedom of motion and processivity. In bridging geometry and kinetic data, this study brings a simple solution for type IIA topoisomerase chiral discrimination.

Direct measurement of DNA bending by type IIA topoisomerases: implications for non-equilibrium topology simplification

Type IIA topoisomerases modify DNA topology by passing one segment of duplex DNA (transfer or T-segment) through a transient double-strand break in a second segment of DNA (gate or G-segment) in an ATP-dependent reaction. Type IIA topoisomerases decatenate, unknot and relax supercoiled DNA to levels below equilibrium, resulting in global topology simplification. The mechanism underlying this non-equilibrium topology simplification remains speculative. The bend angle model postulates that non-equilibrium topology simplification scales with the bend angle imposed on the G-segment DNA by the binding of a type IIA topoisomerase. To test this bend angle model, we used atomic force microscopy and single-molecule Förster resonance energy transfer to measure the extent of bending imposed on DNA by three type IIA topoisomerases that span the range of topology simplification activity. We found that Escherichia coli topoisomerase IV, yeast topoisomerase II and human topoisomerase IIα each bend DNA to a similar degree. These data suggest that DNA bending is not the sole determinant of non-equilibrium topology simplification. Rather, they suggest a fundamental and conserved role for DNA bending in the enzymatic cycle of type IIA topoisomerases.

Action at hooked or twisted-hooked DNA juxtapositions rationalizes unlinking preference of type-2 topoisomerases

The mathematical basis of the hypothesis that type-2 topoisomerases recognize and act at specific DNA juxtapositions has been investigated by coarse-grained lattice polymer models, showing that selective segment passages at hooked juxtapositions can result in dramatic reductions in catenane and knot populations. The lattice modeling approach is here extended to account for the narrowing of variance of linking number (Lk) of DNA circles by type-2 topoisomerases. In general, the steady-state variance of Lk resulting from selective segment passages at a specific juxtaposition geometry j is inversely proportional to the average linking number, Lk(j), of circles with the given juxtaposition. Based on this formulation, we demonstrate that selective segment passages at hooked juxtapositions reduce the variance of Lk. The dependence of this effect on model DNA circle size is remarkably similar to that observed experimentally for type-2 topoisomerases, which appear to be less capable in narrowing Lk variance for small DNA circles than for larger DNA circles. This behavior is rationalized by a substantial cancellation of writhe in small circles with hook-like juxtapositions. During our simulations, we uncovered a twisted variation of the hooked juxtaposition that has an even more dramatic effect on Lk variance narrowing than the hooked juxtaposition. For an extended set of juxtapositions, we detected a significant correlation between the Lk narrowing potential and the logarithmic decatenating and unknotting potentials for a given juxtaposition, a trend reminiscent of scaling relations observed with experimental measurements on type-2 topoisomerases from a variety of organisms. The consistent agreement between theory and experiment argues for type-2 topoisomerase action at hooked or twisted-hooked DNA juxtapositions.

DNA supercoiling and its role in DNA decatenation and unknotting

Chromosomal and plasmid DNA molecules in bacterial cells are maintained under torsional tension and are therefore supercoiled. With the exception of extreme thermophiles, supercoiling has a negative sign, which means that the torsional tension diminishes the DNA helicity and facilitates strand separation. In consequence, negative supercoiling aids such processes as DNA replication or transcription that require global- or local-strand separation. In extreme thermophiles, DNA is positively supercoiled which protects it from thermal denaturation. While the role of DNA supercoiling connected to the control of DNA stability, is thoroughly researched and subject of many reviews, a less known role of DNA supercoiling emerges and consists of aiding DNA topoisomerases in DNA decatenation and unknotting. Although DNA catenanes are natural intermediates in the process of DNA replication of circular DNA molecules, it is necessary that they become very efficiently decatenated, as otherwise the segregation of freshly replicated DNA molecules would be blocked. DNA knots arise as by-products of topoisomerase-mediated intramolecular passages that are needed to facilitate general DNA metabolism, including DNA replication, transcription or recombination. The formed knots are, however, very harmful for cells if not removed efficiently. Here, we overview the role of DNA supercoiling in DNA unknotting and decatenation.

Local site preference rationalizes disentangling by DNA topoisomerases

To rationalize the disentangling action of type II topoisomerases, an improved wormlike DNA model was used to delineate the degree of unknotting and decatenating achievable by selective segment passage at specific juxtaposition geometries and to determine how these activities were affected by DNA circle size and solution ionic strength. We found that segment passage at hooked geometries can reduce knot populations as dramatically as seen in experiments. Selective segment passage also provided theoretical underpinning for an intriguing empirical scaling relation between unknotting and decatenating potentials.

Helical chirality: a link between local interactions and global topology in DNA

DNA supercoiling plays a major role in many cellular functions. The global DNA conformation is however intimately linked to local DNA-DNA interactions influencing both the physical properties and the biological functions of the supercoiled molecule. Juxtaposition of DNA double helices in ubiquitous crossover arrangements participates in multiple functions such as recombination, gene regulation and DNA packaging. However, little is currently known about how the structure and stability of direct DNA-DNA interactions influence the topological state of DNA. Here, a crystallographic analysis shows that due to the intrinsic helical chirality of DNA, crossovers of opposite handedness exhibit markedly different geometries. While right-handed crossovers are self-fitted by sequence-specific groove-backbone interaction and bridging Mg(2+) sites, left-handed crossovers are juxtaposed by groove-groove interaction. Our previous calculations have shown that the different geometries result in differential stabilisation in solution, in the presence of divalent cations. The present study reveals that the various topological states of the cell are associated with different inter-segmental interactions. While the unstable left-handed crossovers are exclusively formed in negatively supercoiled DNA, stable right-handed crossovers constitute the local signature of an unusual topological state in the cell, such as the positively supercoiled or relaxed DNA. These findings not only provide a simple mechanism for locally sensing the DNA topology but also lead to the prediction that, due to their different tertiary intra-molecular interactions, supercoiled molecules of opposite signs must display markedly different physical properties. Sticky inter-segmental interactions in positively supercoiled or relaxed DNA are expected to greatly slow down the slithering dynamics of DNA. We therefore suggest that the intrinsic helical chirality of DNA may have oriented the early evolutionary choices for DNA topology.

Simulation of DNA catenanes

DNA catenanes are important objects in biology, foremost as they appear during replication of circular DNA molecules. In this review we analyze how conformational properties of DNA catenanes can be studied by computer simulation. We consider classification of catenanes, their topological invariants and the methods of calculation of these invariants. We briefly analyze the DNA model and the simulation procedure used to sample the equilibrium conformational ensemble of catenanes with a particular topology. We consider how to avoid direct simulation of many DNA molecules when we need to account for the linking-unlinking process. The simulation methods and their comparisons with experiments are illustrated by some examples. We also describe an approach that allows simulating the steady state fraction of DNA catenanes created by type II topoisomerases.

Interplay of DNA supercoiling and catenation during the segregation of sister duplexes

The discrete regulation of supercoiling, catenation and knotting by DNA topoisomerases is well documented both in vivo and in vitro, but the interplay between them is still poorly understood. Here we studied DNA catenanes of bacterial plasmids arising as a result of DNA replication in Escherichia coli cells whose topoisomerase IV activity was inhibited. We combined high-resolution two-dimensional agarose gel electrophoresis with numerical simulations in order to better understand the relationship between the negative supercoiling of DNA generated by DNA gyrase and the DNA interlinking resulting from replication of circular DNA molecules. We showed that in those replication intermediates formed in vivo, catenation and negative supercoiling compete with each other. In interlinked molecules with high catenation numbers negative supercoiling is greatly limited. However, when interlinking decreases, as required for the segregation of newly replicated sister duplexes, their negative supercoiling increases. This observation indicates that negative supercoiling plays an active role during progressive decatenation of newly replicated DNA molecules in vivo.

Theoretical models of DNA topology simplification by type IIA DNA topoisomerases

It was discovered 12 years ago that type IIA topoisomerases can simplify DNA topology--the steady-state fractions of knots and links created by the enzymes are many times lower than the corresponding equilibrium fractions. Though this property of the enzymes made clear biological sense, it was not clear how small enzymes could selectively change the topology of very large DNA molecules, since topology is a global property and cannot be determined by a local DNA-protein interaction. A few models, suggested to explain the phenomenon, are analyzed in this review. We also consider experimental data that both support and contravene these models.

Mechanisms of chiral discrimination by topoisomerase IV

Topoisomerase IV (Topo IV), an essential ATP-dependent bacterial type II topoisomerase, transports one segment of DNA through a transient double-strand break in a second segment of DNA. In vivo, Topo IV unlinks catenated chromosomes before cell division and relaxes positive supercoils generated during DNA replication. In vitro, Topo IV relaxes positive supercoils at least 20-fold faster than negative supercoils. The mechanisms underlying this chiral discrimination by Topo IV and other type II topoisomerases remain speculative. We used magnetic tweezers to measure the relaxation rates of single and multiple DNA crossings by Topo IV. These measurements allowed us to determine unambiguously the relative importance of DNA crossing geometry and enzymatic processivity in chiral discrimination by Topo IV. Our results indicate that Topo IV binds and passes DNA strands juxtaposed in a nearly perpendicular orientation and that relaxation of negative supercoiled DNA is perfectly distributive. Together, these results suggest that chiral discrimination arises primarily from dramatic differences in the processivity of relaxing positive and negative supercoiled DNA: Topo IV is highly processive on positively supercoiled DNA, whereas it is perfectly distributive on negatively supercoiled DNA. These results provide fresh insight into topoisomerase mechanisms and lead to a model that reconciles contradictory aspects of previous findings while providing a framework to interpret future results.

The why and how of DNA unlinking

The nucleotide sequence of DNA is the repository of hereditary information. Yet, it is now clear that the DNA itself plays an active role in regulating the ability of the cell to extract its information. Basic biological processes, including control of gene transcription, faithful DNA replication and segregation, maintenance of the genome and cellular differentiation are subject to the conformational and topological properties of DNA in addition to the regulation imparted by the sequence itself. How do these DNA features manifest such striking effects and how does the cell regulate them? In this review, we describe how misregulation of DNA topology can lead to cellular dysfunction. We then address how cells prevent these topological problems. We close with a discussion on recent theoretical advances indicating that the topological problems, themselves, can provide the cues necessary for their resolution by type-2 topoisomerases.

How do type II topoisomerases use ATP hydrolysis to simplify DNA topology beyond equilibrium? Investigating the relaxation reaction of nonsupercoiling type II topoisomerases

DNA topoisomerases control the topology of DNA (e.g., the level of supercoiling) in all cells. Type IIA topoisomerases are ATP-dependent enzymes that have been shown to simplify the topology of their DNA substrates to a level beyond that expected at equilibrium (i.e., more relaxed than the product of relaxation by ATP-independent enzymes, such as type I topoisomerases, or a lower-than-equilibrium level of catenation). The mechanism of this effect is currently unknown, although several models have been suggested. We have analyzed the DNA relaxation reactions of type II topoisomerases to further explore this phenomenon. We find that all type IIA topoisomerases tested exhibit the effect to a similar degree and that it is not dependent on the supercoil-sensing C-terminal domains of the enzymes. As recently reported, the type IIB topoisomerase, topoisomerase VI (which is only distantly related to type IIA enzymes), does not exhibit topology simplification. We find that topology simplification is not significantly dependent on circle size in the range approximately 2-9 kbp and is not altered by reducing the free energy available from ATP hydrolysis by varying the ADP:ATP ratio. A direct test of one model (DNA tracking; i.e., sliding of a protein clamp along DNA to trap supercoils) suggests that this is unlikely to be the explanation for the effect. We conclude that geometric selection of DNA segments by the enzymes is likely to be a primary source of the effect, but that it is possible that other kinetic factors contribute. We also speculate whether topology simplification might simply be an evolutionary relic, with no adaptive significance.

Topoisomerase II: a fitted mechanism for the chromatin landscape

The mechanism by which type-2A topoisomerases transport one DNA duplex through a transient double-strand break produced in another exhibits fascinating traits. One of them is the fine coupling between inter-domainal movements and ATP usage; another is their preference to transport DNA in particular directions. These capabilities have been inferred from in vitro studies but we ignore their significance inside the cell, where DNA configurations markedly differ from those of DNA in free solution. The eukaryotic type-2A enzyme, topoisomerase II, is the second most abundant chromatin protein after histones and its biological roles include the decatenation of newly replicated DNA and the relaxation of polymerase-driven supercoils. Yet, topoisomerase II is also implicated in other cellular processes such as chromatin folding and gene expression, in which the topological transformations catalysed by the enzyme are uncertain. Here, some capabilities of topoisomerase II that might be relevant to infer the enzyme performance in the context of chromatin architecture are discussed. Some aspects addressed are the importance of the DNA rejoining step to ensure genome stability, the regulation of the enzyme activity and of its putative structural role, and the selectively of DNA transport in the chromatin milieu.

DNA topoisomerases: harnessing and constraining energy to govern chromosome topology

DNA topoisomerases are a diverse set of essential enzymes responsible for maintaining chromosomes in an appropriate topological state. Although they vary considerably in structure and mechanism, the partnership between topoisomerases and DNA has engendered commonalities in how these enzymes engage nucleic acid substrates and control DNA strand manipulations. All topoisomerases can harness the free energy stored in supercoiled DNA to drive their reactions; some further use the energy of ATP to alter the topology of DNA away from an enzyme-free equilibrium ground state. In the cell, topoisomerases regulate DNA supercoiling and unlink tangled nucleic acid strands to actively maintain chromosomes in a topological state commensurate with particular replicative and transcriptional needs. To carry out these reactions, topoisomerases rely on dynamic macromolecular contacts that alternate between associated and dissociated states throughout the catalytic cycle. In this review, we describe how structural and biochemical studies have furthered our understanding of DNA topoisomerases, with an emphasis on how these complex molecular machines use interfacial interactions to harness and constrain the energy required to manage DNA topology.

3D visualization software to analyze topological outcomes of topoisomerase reactions

The action of various DNA topoisomerases frequently results in characteristic changes in DNA topology. Important information for understanding mechanistic details of action of these topoisomerases can be provided by investigating the knot types resulting from topoisomerase action on circular DNA forming a particular knot type. Depending on the topological bias of a given topoisomerase reaction, one observes different subsets of knotted products. To establish the character of topological bias, one needs to be aware of all possible topological outcomes of intersegmental passages occurring within a given knot type. However, it is not trivial to systematically enumerate topological outcomes of strand passage from a given knot type. We present here a 3D visualization software (TopoICE-X in KnotPlot) that incorporates topological analysis methods in order to visualize, for example, knots that can be obtained from a given knot by one intersegmental passage. The software has several other options for the topological analysis of mechanisms of action of various topoisomerases.

Structural basis for gate-DNA recognition and bending by type IIA topoisomerases

Type II topoisomerases disentangle DNA to facilitate chromosome segregation, and represent a major class of therapeutic targets. Although these enzymes have been studied extensively, a molecular understanding of DNA binding has been lacking. Here we present the structure of a complex between the DNA-binding and cleavage core of Saccharomyces cerevisiae Topo II (also known as Top2) and a gate-DNA segment. The structure reveals that the enzyme enforces a 150 degrees DNA bend through a mechanism similar to that of remodelling proteins such as integration host factor. Large protein conformational changes accompany DNA deformation, creating a bipartite catalytic site that positions the DNA backbone near a reactive tyrosine and a coordinated magnesium ion. This configuration closely resembles the catalytic site of type IA topoisomerases, reinforcing an evolutionary link between these structurally and functionally distinct enzymes. Binding of DNA facilitates opening of an enzyme dimerization interface, providing visual evidence for a key step in DNA transport.

cin-4, a gene with homology to topoisomerase II, is required for centromere resolution by cohesin removal from sister kinetochores during mitosis

The back-to-back geometry of sister kinetochores is essential in preventing loss or damage of chromosomes during mitosis. Kinetochore orientation is generated in part by a process of resolving kinetochores at the centromere (centromere resolution) prior to spindle interactions. Because few of the genes required for centromere resolution are known, we used Caenorhabditis elegans to screen for conditional mutants defective in orienting sister kinetochores during mitosis. C. elegans is ideal for such screens because its chromosomes are holocentric. Here we identified an essential gene, cin-4, required for centromere resolution and for removal of cohesin from sites near sister kinetochores during mitosis. Given that compromised cohesin function restores centromere resolution in the absence of cin-4, CIN-4 likely acts to remove cohesin from the CENP-A chromatin enabling centromere resolution. CIN-4 has a high amino acid identity to the catalytic domain of topoisomerase II, suggesting a partial gene duplication of the C. elegans topoisomerase II gene, top-2. Similar to CIN-4, TOP-2 is also required for centromere resolution; however, the loss of TOP-2 is phenotypically distinct from the loss of CIN-4, suggesting that CIN-4 and TOP-2 are topoisomerase II isoforms that perform separate essential functions in centromere structure and function.

Local selection rules that can determine specific pathways of DNA unknotting by type II DNA topoisomerases

We performed numerical simulations of DNA chains to understand how local geometry of juxtaposed segments in knotted DNA molecules can guide type II DNA topoisomerases to perform very efficient relaxation of DNA knots. We investigated how the various parameters defining the geometry of inter-segmental juxtapositions at sites of inter-segmental passage reactions mediated by type II DNA topoisomerases can affect the topological consequences of these reactions. We confirmed the hypothesis that by recognizing specific geometry of juxtaposed DNA segments in knotted DNA molecules, type II DNA topoisomerases can maintain the steady-state knotting level below the topological equilibrium. In addition, we revealed that a preference for a particular geometry of juxtaposed segments as sites of strand-passage reaction enables type II DNA topoisomerases to select the most efficient pathway of relaxation of complex DNA knots. The analysis of the best selection criteria for efficient relaxation of complex knots revealed that local structures in random configurations of a given knot type statistically behave as analogous local structures in ideal geometric configurations of the corresponding knot type.

Holoenzyme assembly and ATP-mediated conformational dynamics of topoisomerase VI

Type II topoisomerases help disentangle chromosomes to facilitate cell division. To advance understanding of the structure and dynamics of these essential enzymes, we have determined the crystal structure of an archaeal type IIB topoisomerase, topo VI, at 4.0-A resolution. The 220-kDa heterotetramer adopts a 'twin-gate' architecture, in which a pair of ATPase domains at one end of the enzyme is poised to coordinate DNA movements into the enzyme and through a set of DNA-cleaving domains at the other end. Small-angle X-ray scattering studies show that nucleotide binding elicits a major structural reorganization that is propagated to the enzyme's DNA-cleavage center, explaining how ATP is coupled to DNA capture and strand scission. These data afford important insights into the mechanisms of topo VI and related proteins, including type IIA topoisomerases and the Spo11 meiotic recombination endonuclease.

Energy coupling in type II topoisomerases: why do they hydrolyze ATP?

Type II topoisomerases are essential enzymes in all cells. They help to solve the topological problems of DNA by passing one double helix through a transient break in another, in a reaction coupled to the hydrolysis of ATP. Members of one class of the enzymes, DNA gyrases, are configured to carry out an intramolecular reaction, removing positive supercoiling and introducing negative supercoiling into circular DNA using free energy derived from ATP hydrolysis. The nonsupercoiling class, including bacterial topoisomerase IV and eukaryotic topoisomerase II enzymes, can carry out both intra- and intermolecular reactions, and their primary role is the unlinking (decatenation) of daughter replicons before partition. In these enzymes, ATP hydrolysis is coupled to a reduction in DNA complexity (catenation, supercoiling, and knotting) below the level expected at equilibrium. This review discusses our current understanding of the mechanisms behind the coupling of the energy of ATP hydrolysis to topological changes catalyzed by both of these classes of enzyme.

Random state transitions of knots: a first step towards modeling unknotting by type II topoisomerases

Type II topoisomerases are enzymes that change the topology of DNA by performing strand-passage. In particular, they unknot knotted DNA very efficiently. Motivated by this experimental observation, we investigate transition probabilities between knots. We use the BFACF algorithm to generate ensembles of polygons in Z(3) of fixed knot type. We introduce a novel strand-passage algorithm which generates a Markov chain in knot space. The entries of the corresponding transition probability matrix determine state-transitions in knot space and can track the evolution of different knots after repeated strand-passage events. We outline future applications of this work to DNA unknotting.

Inferring global topology from local juxtaposition geometry: interlinking polymer rings and ramifications for topoisomerase action

Lattice modeling is applied to investigate how the configurations of local chain juxtapositions may provide information about whether two ring polymers (loops) are topologically linked globally. Given a particular juxtaposition, the conditional probability that the loops are linked is determined by exact enumeration and extensive Monte Carlo sampling of conformations satisfying excluded volume constraints. A discrimination factor fL, defined as the ratio of linked to unlinked probabilities, varies widely depending on which juxtaposition is presumed. /log fL/s that are large for small loop size n tend to decrease, signaling diminishing topological information content of the juxtapositions, with increasing n. However, some juxtaposition geometries can impose sufficient overall conformational biases such that /log fL/ remains significant for large n. Notably, for two loops as large as n=200 in the model, the probability that passing the segments of a hooked juxtaposition would unlink an originally linked configuration is remarkably high, approximately 85%. In contrast, segment-passage of a free juxtaposition would link the loops from an originally unlinked configuration more than 90% of the time. The statistical mechanical principles emerging from these findings suggest that it is physically possible for DNA topoisomerases to decatenate effectively by acting selectively on juxtapositions with specific "hooked" geometries.

Topological information embodied in local juxtaposition geometry provides a statistical mechanical basis for unknotting by type-2 DNA topoisomerases

Topoisomerases may unknot by recognizing specific DNA juxtapositions. The physical basis of this hypothesis is investigated by considering single-loop conformations in a coarse-grained polymer model. We determine the statistical relationship between the local geometry of a juxtaposition of two chain segments and whether the loop is knotted globally, and ascertain how the knot/unknot topology is altered by a topoisomerase-like segment passage at the juxtaposition. Segment passages at a "free" juxtaposition tend to increase knot probability. In contrast, segment passages at a "hooked" juxtaposition cause more transitions from knot to unknot than vice versa, resulting in a steady-state knot probability far lower than that at topological equilibrium. The reduction in knot population by passing chain segments through a hooked juxtaposition is more prominent for loops of smaller sizes, n, but remains significant even for larger loops: steady-state knot probability is only approximately 2%, and approximately 5% of equilibrium, respectively, for n=100 and 500 in the model. An exhaustive analysis of approximately 6000 different juxtaposition geometries indicates that the ability of a segment passage to unknot correlates strongly with the juxtaposition's "hookedness". Remarkably, and consistent with experiments on type-2 topoisomerases from different organisms, the unknotting potential of a juxtaposition geometry in our polymer model correlates almost perfectly with its corresponding decatenation potential. These quantitative findings suggest that it is possible for topoisomerases to disentangle by acting selectively on juxtapositions with "hooked" geometries.

Knotting of random ring polymers in confined spaces

Stochastic simulations are used to characterize the knotting distributions of random ring polymers confined in spheres of various radii. The approach is based on the use of multiple Markov chains and reweighting techniques, combined with effective strategies for simplifying the geometrical complexity of ring conformations without altering their knot type. By these means we extend previous studies and characterize in detail how the probability to form a given prime or composite knot behaves in terms of the number of ring segments N and confining radius R. For 50 < or =N < or =450 we show that the probability of forming a composite knot rises significantly with the confinement, while the occurrence probability of prime knots are, in general, nonmonotonic functions of 1R. The dependence of other geometrical indicators, such as writhe and chirality, in terms of R and N is also characterized. It is found that the writhe distribution broadens as the confining sphere narrows.

Topoisomerase II-DNA complexes trapped by ICRF-193 perturb chromatin structure

DNA topoisomerase II (topo II) is involved in unlinking replicating DNA and organizing mitotic chromosomes. Topo II is the target of many antitumour drugs. Topo II inhibition results in extensive catenation of newly replicated DNA and may potentially perturb chromatin assembly. Here, we show that the topo II inhibitor ICRF-193 does not prevent the bulk of nucleosome deposition, but perturbs nucleosome spacing in Xenopus egg extracts. This is due to the trapping of topo II-closed clamps on the DNA rather than increased DNA catenation. Inhibition of replicative DNA decatenation has in itself little or no effect on nucleosome deposition and spacing, suggesting that DNA can easily accommodate the sharp bending constraints imposed by the co-habitation of nucleosomes and catenane nodes. Chromatin perturbation by topo II clamps may explain some dominant cellular effects of ICRF-193. Nucleosome-driven bending of precatenane nodes may facilitate their unlinking by topo II during unperturbed replication.

Coupling ATP hydrolysis to DNA strand passage in type IIA DNA topoisomerases

Type IIA topos (topoisomerases) catalyse topological conversions of DNA through the passage of one double strand through a transient break in another. In the case of the archetypal enzyme, DNA gyrase, it has always been apparent that the enzyme couples the free energy of ATP hydrolysis to the introduction of negative supercoiling, and the structural details of this process are now becoming clearer. The homologous type IIA enzymes such as topo IV and eukaryotic topo II also require ATP and it has more recently been shown that the energy of hydrolysis is coupled to a reduction of supercoiling or catenation (linking) beyond equilibrium. The mechanism behind this effect is less clear. We review the energy coupling process in both classes of enzyme and describe recent mechanistic and structural work on gyrase that addresses the mechanism of energy coupling.

A topological view of the replicon

The replication of circular DNA faces topological obstacles that need to be overcome to allow the complete duplication and separation of newly replicated molecules. Small bacterial plasmids provide a perfect model system to study the interplay between DNA helicases, polymerases, topoisomerases and the overall architecture of partially replicated molecules. Recent studies have shown that partially replicated circular molecules have an amazing ability to form various types of structures (supercoils, precatenanes, knots and catenanes) that help to accommodate the dynamic interplay between duplex unwinding at the replication fork and DNA unlinking by topoisomerases.

Simulations of action of DNA topoisomerases to investigate boundaries and shapes of spaces of knots

The configuration space available to randomly cyclized polymers is divided into subspaces accessible to individual knot types. A phantom chain utilized in numerical simulations of polymers can explore all subspaces, whereas a real closed chain forming a figure-of-eight knot, for example, is confined to a subspace corresponding to this knot type only. One can conceptually compare the assembly of configuration spaces of various knot types to a complex foam where individual cells delimit the configuration space available to a given knot type. Neighboring cells in the foam harbor knots that can be converted into each other by just one intersegmental passage. Such a segment-segment passage occurring at the level of knotted configurations corresponds to a passage through the interface between neighboring cells in the foamy knot space. Using a DNA topoisomerase-inspired simulation approach we characterize here the effective interface area between neighboring knot spaces as well as the surface-to-volume ratio of individual knot spaces. These results provide a reference system required for better understanding mechanisms of action of various DNA topoisomerases.