Distributions of circular DNA according its topological states

A distinctive feature of closed circular DNA molecules is their particular topological state, which cannot be altered by any conformational rearrangement short of breaking at least one strand. This topological constraint opens unique possibilities for experimental studies of the distributions of topological states created in different ways. Primarily, the equilibrium distributions of topological properties are considered in the review. It is described how such distributions can be obtained and measured experimentally, and how they can be computed. Comparison of the calculated and measured equilibrium distributions over the linking number of complementary strands, equilibrium fractions of knots and links formed by circular molecules has provided much valuable information about the properties of the double helix. Study of the steady-state fraction of knots and links created by type II DNA topoisomerases has revealed a surprising property of the enzymes: their ability to reduce these fractions considerably below the equilibrium level.     

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.     

Novel topologically knotted DNA from bacteriophage P4 capsids: studies with DNA topoisomerases.

DNA molecules isolated from bacteriophage P4 are mostly linear with cohesive ends capable of forming circular and concatemeric structures. In contrast, almost all DNA molecules isolated form P4 tailless capsids (heads) are monomeric DNA circles with their cohesive ends hydrogen-bonded. Different form simple DNA circles, such P4 head DNA circles contain topological knots. Gel electrophoretic and electronmicroscopic analyses of P4 head DNA indicate that the topological knots are highly complex and heterogeneous. Resolution of such complex knots has been studied with various DNA topoisomerases. The conversion of highly knotted P4 DNA to its simple circular form is demonstrated by type II DNA topoisomerases which catalyze the topological passing of two crossing double-stranded DNA segments [Liu, L. F., Liu, C. C. & Alberts, B. M. (1980) Cell, 19, 697-707]. The knotted P4 head DNA can be used in a sensitive assay for the detection of a type II DNA topoisomerase even in the presence of excess type I DNA topoisomerases.     

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.     

Protein-induced local DNA bends regulate global topology of recombination products

The tyrosine family of recombinases produces two smaller DNA circles when acting on circular DNA harboring two recombination sites in head-to-tail orientation. If the substrate is supercoiled, these circles can be unlinked or form multiply linked catenanes. The topological complexity of the products varies strongly even for similar recombination systems. This dependence has been solved here. Our computer simulation of the synapsis showed that the bend angles, phi, created in isolated recombination sites by protein binding before assembly of the full complex, determine the product topology. To verify the validity of this theoretical finding we measured the values of phi for Cre/loxP and Flp/FRT systems. The measurement was based on cyclization of the protein-bound short DNA fragments in solution. Despite the striking similarity of the synapses for these recombinases, action of Cre on head-to-tail target sites produces mainly unlinked circles, while that of Flp yields multiply linked catenanes. In full agreement with theoretical expectations we found that the values of phi for these systems are very different, close to 35 degrees and 80 degrees, respectively. Our findings have general implications in how small protein machines acting locally on large DNA molecules exploit statistical properties of their substrates to bring about directed global changes in topology.     

Predicting knot and catenane type of products of site-specific recombination on twist knot substrates

Site-specific recombination on supercoiled circular DNA molecules can yield a variety of knots and catenanes. Twist knots are some of the most common conformations of these products, and they can act as substrates for further rounds of site-specific recombination. They are also one of the simplest families of knots and catenanes. Yet, our systematic understanding of their implication in DNA and important cellular processes such as site-specific recombination is very limited. Here, we present a topological model of site-specific recombination characterizing all possible products of this reaction on twist knot substrates, extending the previous work of Buck and Flapan. We illustrate how to use our model to examine previously uncharacterized experimental data. We also show how our model can help determine the sequence of products in multiple rounds of processive recombination and distinguish between products of processive and distributive recombinations.This model studies generic site-specific recombination on arbitrary twist knot substrates, a subject for which there is limited global understanding. We also provide a systematic method of applying our model to a variety of different recombination systems.     

Computational analysis of the chiral action of type II DNA topoisomerases

It was found recently that bacterial type II DNA topoisomerase, topo IV, is much more efficient in relaxing (+) DNA supercoiling than (-) supercoiling. This means that the DNA-enzyme complex is chiral. This chirality can appear upon binding the first segment that participates in the strand passing reaction (G segment) or only after the second segment (T segment) joins the complex. The former possibility is analyzed here. We assume that upon binding the enzyme, the G segment forms a part of left-handed helical turn. This model is an extension of the hairpin model introduced earlier to explain simplification of DNA topology by these enzymes. Using statistical-mechanical simulation of DNA properties, we estimated different consequences of the model: (1) relative rates of relaxation of (+) and (-) supercoiling by the enzyme; (2) the distribution of positions of the G segment in supercoiled molecules; (3) steady-state distribution of knots in circular molecules created by the topoisomerase; (4) the variance of topoisomer distribution created by the enzyme; (5) the effect of (+) and (-) supercoiling on the binding topo II with G segment. The simulation results are capable of explaining nearly all available experimental data, at least semiquantitatively. A few predictions obtained in the model analysis can be tested experimentally.     

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.     

Predicting knot or catenane type of site-specific recombination products

Site-specific recombination on supercoiled circular DNA yields a variety of knotted or catenated products. Here, we present a topological model of this process and characterize all possible products of the most common substrates: unknots, unlinks, and torus knots and catenanes. This model tightly prescribes the knot or catenane type of previously uncharacterized data. We also discuss how the model helps to distinguish products of distributive recombination and, in some cases, determine the order of processive recombination products.     

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 chirality of ground DNA knots and links.

The chirality of ground DNA knots and links is described and characterized in terms of color symmetry groups (CSG), i.e. color symmetry groups I and II, which correspond to topochirality (topological chirality) and topoachirality (topological achirality) which bear an uncanny resemblance to point groups I (proper) and point groups II (improper) used for testing geochirality (geometrical chirality) and geoachirality (geometrical achirality), respectively. By regarding these two crossing modes in mirror images as white and black vertices, DNA knots and links with minimal crossings can be mapped to vertex-bicolored graphs under a working hypothesis that DNA knots and links exist in ground states with minimal energy m0. The color symmetry group of a vertex-bicolored graph G is defined as the set of all permutations and permutation asymmetrizations of the vertices of G that preserve its topology (connectivity), where asymmetrization, denoted as (a), is the operation of changing vertices' colors, and a permutation followed by an (a) is a permutation asymmetrization. The color symmetry groups I contains only permutations, whereas color symmetry groups II comprise permutation asymmetrizations as well as permutations. Four DNA knots and links in nature are analyzed and tabulated consisely. In addition, the well-known figure-of-eight knot and Borromean rings are discussed in much the same way.     

Unlinked strands as a topological constraint on chromosomal DNA,plasmid integration,and DNA repair

It is proposed that circular chromosomal DNA must be constrained such that the two strands are topologically unlinked. This structure can be replicated without strand breakage (nicking) by locally acting enzymes. The recently discovered form V DNA satisfies this topological constraint. The structure is likely to consist of left-handed and right-handed segments of double helix. The constraint of zero linkage has to be preserved by DNA repair, plasmid insertion and by crossing over. The argument presented in this paper is a topological one, following W. F. Pohl, that linkage is a global property that cannot be measured by locally acting enzymes. In contrast to Pohl no argument in favor of a side-by-side structure is presented. A zero linkage constraint would be hereditary and compatible with a multitude of local structures.     

Physicochemical properties of kinetoplast DNA from Crithidia acanthocephali. Crithidia luciliae, and Trypanosoma lewisi

The protozoa Crithidia and Trypanosoma contain within a mitochondrion a mass of DNA known as kinetoplast DNA (kDNA) which consists mainly of an association of thousands of small circular molecules of similar size held together by topological interlocking. Using kDNA from Crithidia acanthocephali, Crithidia luciliae, and Trypanosoma lewisi, physicochemical studies have been carried out with intact associations and with fractions of covalently closed single circular molecules, and of open single circular and unit length linear molecules obtained from kDNA associations by sonication, sucrose sedimentation, and cesium chloride-ethidium bromide equilibrium centrifugation. Buoyant density analyses failed to provide evidence for base composition heterogeneity among kDNA molecules within a species. The complementary nucleotide strands of kDNA molecules of all three species had distinct buoyant densities in both alkaline and neutral cesium chloride. For C. acanthocephali kDNA, these buoyant density differences were shown to be a reflection of differences in base composition between the complementary nucleotide strands. The molar ratios of adenine: thymine:guanine:cytosine, obtained from deoxyribonucleotide analyses were 16.8:41.0:28.1:14.1 for the heavy strand and 41.6:16.6:12.8:29.0 for the light strand. Covalently closed single circular molecules of C. acanthocephali (as well as intact kDNA associations of C. acanthocephali and T. lewisi) formed a single band in alkaline cesium chloride gradients, indicating their component nucleotide strands to be alkaline insensitive. Data from buoyant density, base composition, and thermal melting analyses suggested that minor bases are either rare or absent in Crithidia kDNA. The kinetics of renaturation of 32P labeled C. acanthocephali kDNA measured using hydroxyapatite chromatography were consistent with at least 70% of the circular molecules of this DNA having the same nucleotide sequence. Evidence for sequence homologies among the kDNAs of all three species was obtained from buoyant density analyses of DNA in annealed mixtures containing one component kDNA strand from each of two species.     

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.     

Duplex DNA knots produced by Escherichia coli topoisomerase I. Structure and requirements for formation

We investigated systematically the knotting of nicked circular duplex DNA by Escherichia coli topoisomerase I. Agarose gel electrophoresis of knots forms a ladder of DNA bands. Each rung is made up of a variety of knots with the same number of nodes, or segment crossings; knots in adjacent rungs differ by one node. We extended the technique of electron microscopy of recA protein-coated DNA to the visualization of the complex knots tied by topoisomerase I. The striking result is that the enzyme produces every knot theoretically possible. The requirement for excess enzyme to form complex knots suggests a role for topoisomerase I in contorting the DNA in addition to promoting strand passage. We conclude that nodes formed are equally likely to be positive or negative and that topoisomerase I can pass DNA strands through a transient enzyme-generated break without regard to orientation of the passing strand. The results are interpreted in terms of a formulation for the topological requirements for knotting.     

Replication initiation and DNA topology: The twisted life of the origin

Genomic propagation in both prokaryotes and eukaryotes is tightly regulated at the level of initiation, ensuring that the genome is accurately replicated and equally segregated to the daughter cells. Even though replication origins and the proteins that bind onto them (initiator proteins) have diverged throughout the course of evolution, the mechanism of initiation has been conserved, consisting of origin recognition, multi‐protein complex assembly, helicase activation and loading of the replicative machinery. Recruitment of the multiprotein initiation complexes onto the replication origins is constrained by the dense packing of the DNA within the nucleus and unusual structures such as knots and supercoils. In this review, we focus on the DNA topological barriers that the multi‐protein complexes have to overcome in order to access the replication origins and how the topological state of the origins changes during origin firing. Recent advances in the available methodologies to study DNA topology and their clinical significance are also discussed. J. Cell. Biochem. 110: 35–43, 2010. © 2010 Wiley‐Liss, Inc.     

A new Euler's formula for DNA polyhedra

DNA polyhedra are cage-like architectures based on interlocked and interlinked DNA strands. We propose a formula which unites the basic features of these entangled structures. It is based on the transformation of the DNA polyhedral links into Seifert surfaces, which removes all knots. The numbers of components μ, of crossings c, and of Seifert circles s are related by a simple and elegant formula: s + μ = c + 2. This formula connects the topological aspects of the DNA cage to the Euler characteristic of the underlying polyhedron. It implies that Seifert circles can be used as effective topological indices to describe polyhedral links. Our study demonstrates that, the new Euler's formula provides a theoretical framework for the stereo-chemistry of DNA polyhedra, which can characterize enzymatic transformations of DNA and be used to characterize and design novel cages with higher genus.