Construction and electrophoretic migration of single-stranded DNA knots and catenanes

In recent years there has been growing interest in the question of how the particular topology of polymeric chains affects their overall dimensions and physical behavior. The majority of relevant studies are based on numerical simulation methods or analytical treatment; however, both these approaches depend on various assumptions and simplifications. Experimental verification is clearly needed but was hampered by practical difficulties in obtaining preparative amounts of knotted or catenated polymers with predefined topology and precisely set chain length. We introduce here an efficient method of production of various single-stranded DNA knots and catenanes that have the same global chain length. We also characterize electrophoretic migration of the produced single-stranded DNA knots and catenanes with increasing complexity.     

Electrophoretic mobility of supercoiled,catenated and knotted DNA molecules

We systematically varied conditions of two-dimensional (2D) agarose gel electrophoresis to optimize separation of DNA topoisomers that differ either by the extent of knotting, the extent of catenation or the extent of supercoiling. To this aim we compared electrophoretic behavior of three different families of DNA topoisomers: (i) supercoiled DNA molecules, where supercoiling covered the range extending from covalently closed relaxed up to naturally supercoiled DNA molecules; (ii) postreplicative catenanes with catenation number increasing from 1 to ∼15, where both catenated rings were nicked; (iii) knotted but nicked DNA molecules with a naturally arising spectrum of knots. For better comparison, we studied topoisomer families where each member had the same total molecular mass. For knotted and supercoiled molecules, we analyzed dimeric plasmids whereas catenanes were composed of monomeric forms of the same plasmid. We observed that catenated, knotted and supercoiled families of topoisomers showed different reactions to changes of agarose concentration and voltage during electrophoresis. These differences permitted us to optimize conditions for their separation and shed light on physical characteristics of these different types of DNA topoisomers during electrophoresis.     

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.     

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.     

Phage P1 Cre-loxP site-specific recombination. Effects of DNA supercoiling on catenation and knotting of recombinant products

Bacteriophage P1 contains a site-specific recombination system consisting of a site, loxP, and a recombinase protein Cre. We have shown that with purified Cre protein we can carry out recombination between two loxP sites in vitro. When that recombination occurs between two sites in direct orientation on the same DNA molecule, we observed the production of free and catenated circular molecules. In this paper we show that recombination between sites in opposite orientation leads to both knotted and unknotted circular products. We also demonstrate that the production of catenanes and knots is influenced by two factors: (1) supercoiling in the DNA substrate, supercoiled DNA substrates yield significantly more catenated and knotted products than nicked circular substrates; and (2) mutations in the loxP site, a class of mutations have been isolated that carry out recombination but result in a distribution of products in which the ratio of catenanes to free circles is increased over that observed with a wild-type site. A more detailed analysis of the products from recombination between wild-type sites indicates: (1) that the catenanes or knots produced by recombination are both simple and complex; (2) that the ratio of free products to catenanes is independent of the distance between the two directly repeated loxP sites; and (3) that for DNA substrates with four loxP sites significant recombination between non-adjacent sites occurs to give free circular products. These observations provide insights into how two loxP sites are brought together during recombination.     

Geometric arrangements of Tn3 resolvase sites

Site-specific recombination by Tn3 resolvase normally occurs in vitro and in vivo only between directly repeated res sites on the same supercoiled DNA molecule. However, with multiply interlinked catenane substrates consisting of two DNA rings each containing a single res site, resolvase efficiently carried out intermolecular recombination. The topology of the knots produced by several rounds of this reaction proves that the DNA within the synaptic intermediate is coiled in an interwound (plectonemic) fashion rather than wrapped solenoidally around resolvase as in previously characterized supercoiled DNA-protein complexes. The synaptic intermediate can contain equivalently supercoil, catenane, or knot crossings as long as the res sites have a right-handed coiling and a particular relative orientation. The structure of the product knots and catenanes also shows the path the DNA takes during strand exchange. Intermolecular recombination within multiply linked catenanes required negative supercoiling, as does the standard intramolecular reaction.     

How topoisomerase IV can efficiently unknot and decatenate negatively supercoiled DNA molecules without causing their torsional relaxation

Freshly replicated DNA molecules initially form multiply interlinked right-handed catenanes. In bacteria, these catenated molecules become supercoiled by DNA gyrase before they undergo a complete decatenation by topoisomerase IV (Topo IV). Topo IV is also involved in the unknotting of supercoiled DNA molecules. Using Metropolis Monte Carlo simulations, we investigate the shapes of supercoiled DNA molecules that are either knotted or catenated. We are especially interested in understanding how Topo IV can unknot right-handed knots and decatenate right-handed catenanes without acting on right-handed plectonemes in negatively supercoiled DNA molecules. To this end, we investigate how the topological consequences of intersegmental passages depend on the geometry of the DNA-DNA juxtapositions at which these passages occur. We observe that there are interesting differences between the geometries of DNA-DNA juxtapositions in the interwound portions and in the knotted or catenated portions of the studied molecules. In particular, in negatively supercoiled, multiply interlinked, right-handed catenanes, we detect specific regions where DNA segments belonging to two freshly replicated sister DNA molecules form left-handed crossings. We propose that, due to its geometrical preference to act on left-handed crossings, Topo IV can specifically unknot supercoiled DNA, as well as decatenate postreplicative catenanes, without causing their torsional relaxation.     

Numerical simulation of gel electrophoresis of DNA knots in weak and strong electric fields

Gel electrophoresis allows one to separate knotted DNA (nicked circular) of equal length according to the knot type. At low electric fields, complex knots, being more compact, drift faster than simpler knots. Recent experiments have shown that the drift velocity dependence on the knot type is inverted when changing from low to high electric fields. We present a computer simulation on a lattice of a closed, knotted, charged DNA chain drifting in an external electric field in a topologically restricted medium. Using a Monte Carlo algorithm, the dependence of the electrophoretic migration of the DNA molecules on the knot type and on the electric field intensity is investigated. The results are in qualitative and quantitative agreement with electrophoretic experiments done under conditions of low and high electric fields.     

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.     

Morphometric analysis of B2cAMP-induced reverse transformation in synchronized CHO cells

Summary Synchronized transformed and reverse-transformed (by 10⁻³ M B₂cAMP) CHO-K1 cells, growing adherent to plastic, are characterized by means of geometric and densitometric parameters at the level of both the entire cell and of the nuclei at various time intervals after selective mitotic detachment. Transformed and reverse-transformed cells triple-stained with Feulgen, Napthol Yellow S, and periodic acid-Schiff appeared very similar in terms of integrated optical density (IOD), related to either polysaccharides, protein, or DNA amount. On the other hand, a shift from a polygonal to a spindle-shaped morphology is accompanied by a significant decrease in both form factor and average optical density (AOD) of intact cell and nuclei, which are the most conspicuous measured changes caused by B₂cAMP, in addition to a lengthening of the cell cycle duration. In both control and treated cells, important and parallel cell-cycle-dependent modulations of geometric and densitometric parameters are also observed, for both the cytoplasmic (i.e., cell morphometry) and DNA space (i.e., nuclear morphometry). Specifically, the modulation in nuclear morphometry during G1, S, G2, andM phases confirms previous findings on synchronized HeLa cells. The optical density threshold-dependence of geometric parameters shows that, while becoming fusiform, the cytoplasm of reverse-transformed cells had a particularly low optical density precisely in the polar area. Utilization of such an approach in the development of anobjective morphological classification of all cell lines grown as monolayers “in vitro” is also discussed.     

Bisintercalators of DNA with a rigid linker in an extended configuration.

A new class of DNA bisintercalators is reported in which phenanthridinium or acridinium rings are connected by rigid and extended linkers of varied length. Cross-linking of DNA by bisintercalation is inferred from the unwinding and folding of linear DNA induced by the compound; after ligation and removal of the bisintercalator, superhelical circles, catenanes, and knots that bear an imprint of the bisintercalator are observed. These novel bisintercalators are of interest because they can be used to probe the organization of DNA in three-dimensional space, especially near sites of replication, recombination, or topoisomerase action, where two duplexes must be in close proximity.     

Novel display of knotted DNA molecules by two-dimensional gel electrophoresis

We describe a two-dimensional agarose gel electrophoresis procedure that improves the resolution of knotted DNA molecules. The first gel dimension is run at low voltage, and DNA knots migrate according to their compactness. The second gel dimension is run at high voltage, and DNA knots migrate according to other physical parameters such as shape and flexibility. In comparison with one-dimensional gel electrophoresis, this procedure segregates the knotted DNA molecules from other unknotted forms of DNA, and partially resolves populations of knots that have the same number of crossings. The two-dimensional display may allow quantitative and qualitative characterization of different types of DNA knots simply by gel velocity.     

Evidence for cross-linking DNA by bis-intercalators with rigid and extended linkers is provided by knotting and catenation.

A new series of DNA bis-intercalators is reported in which acridine moieties are connected by rigid and extended pyridine-based linkers of varied length. Cross-linking of DNA by bis-intercalation is inferred from the unwinding and folding of linear DNA induced by the compounds; after ligation and removal of the bis-intercalator, superhelical circles, catenanes and knots that bear a residual imprint of the bis-intercalator are observed. These novel bis-intercalators are of interest because they can be used to probe the spatial organization of DNA, especially near sites of replication, recombination or topoisomerase action where two duplexes must be in close proximity. Preliminary results on the effects of the various compounds on the cloning efficiency of bacteria and replication by permeabilized human cells are also presented.     

Analysis of the structure of dimeric DNA catenanes by electron microscopy.

We analyzed the structure of open-circular and supercoiled dimeric DNA catenanes generated by site-specific recombination in vitro. Electron microscopy of open-circular catenanes shows that the number of duplex crossings in a plane is a linear function of the number of catenane interlinks (Ca/2), and that the length of the catenane axis is constant, independent of Ca. These relationships are similar to those observed with supercoiled DNA. Statistical analyses reveal, however, that the conformations of the individual rings of the catenanes are similar to those of unlinked circles. The distribution of distances between randomly chosen points on separate rings depends strongly on Ca and is consistent with a sharp decrease in the center-of-mass separation between rings with increasing Ca. Singly linked supercoiled catenanes are seen by microscopy to be linked predominantly through terminal loops in the respective superhelices. The observations suggest that chain entropy is a major factor determining the conformation of DNA catenanes.     

Side-chain entropy and packing in proteins.

What role does side-chain packing play in protein stability and structure? To address this question, we compare a lattice model with side chains (SCM) to a linear lattice model without side chains (LCM). Self-avoiding configurations are enumerated in 2 and 3 dimensions exhaustively for short chains and by Monte Carlo sampling for chains up to 50 main-chain monomers long. This comparison shows that (1) side-chain degrees of freedom increase the entropy of open conformations, but side-chain steric exclusion decreases the entropy of compact conformations, thus producing a substantial entropy that opposes folding; (2) there is a side-chain “freezing” or ordering, i.e., a sharp decrease in entropy, near maximum compactness; and (3) the different types of contacts among side chains (s) and main-chain elements (m) have different frequencies, and the frequencies have different dependencies on compactness. mm contacts contribute significantly only at high densities, suggesting that main-chain hydrogen bonding in proteins may be promoted by compactness. The distributions of mm, ms, and ss contacts in compact SCM configurations are similar to the distributions in protein structures in the Brookhaven Protein Data Bank. We propose that packing in proteins is more like the packing of nuts and bolts in a jar than like the pairwise matching of jigsaw puzzle pieces.     

Description of the topological entanglement of DNA catenanes and knots by a powerful method involving strand passage and recombination

We utilize a recently discovered, powerful method to classify the topological state of knots and catenanes. In this method, each such form is associated with a unique polynomial. These polynomials allow a rigorous determination of whether knotted or catenated DNA molecules that appear distinct actually are, and indicate the structure of related molecules. A tabulation is given of the polynomials for all possible stereoisomers of many of the knotted and catenated forms that are found in DNA. The polynomials for a substrate DNA molecule and the products obtained from it by either recombination or strand passage by a topoisomerase are related by a simple theorem. This theorem affords natural applications of the polynomial method to these processes. Examples are presented involving site-specific recombination by the transposon Tn3-encoded resolvase and the phage lambda integrase, in which product structure is predicted as a function of crossover mechanism.     

Biochemistry and structural DNA nanotechnology: an evolving symbiotic relationship

Structural DNA nanotechnology is derived from naturally occurring structures and phenomena in cellular biochemistry. Motifs based on branched DNA molecules are linked together by sticky ends to produce objects, periodic arrays, and nanomechanical devices. The motifs include Holliday junction analogues, double and triple crossover molecules, knots, and parallelograms. Polyhedral catenanes, such as a cube or a truncated octahedron, have been assembled from branched junctions. Stiff motifs have been used to produce periodic arrays, containing topographic features visible in atomic force microscopy; these include deliberately striped patterns and cavities whose sizes can be tuned by design. Deliberately knotted molecules have been assembled. Aperiodic arrangements of DNA tiles can be used to produce assemblies corresponding to logical computation. Both DNA structural transitions and branch migration have been used as the basis for the operation of DNA nanomechanical devices. Structural DNA nanotechnology has been used in a number of applications in biochemistry. An RNA knot has been used to establish the existence of RNA topoisomerase activity. The sequence dependence of crossover isomerization and branch migration at symmetric sites has been established through the use of symmetric immobile junctions. DNA parallelogram arrays have been used to determine the interhelical angles for a variety of DNA branched junctions. The relationship between biochemistry and structural DNA nanotechnology continues to grow.