[Distributions of circular DNA according its topological states]. / Raspredelenie kil'tsevykh DNK po topologicheskim sostoianiiam.

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.

Mechanism of topology simplification by type II DNA topoisomerases.

Type II DNA topoisomerases actively reduce the fractions of knotted and catenated circular DNA below thermodynamic equilibrium values. To explain this surprising finding, we designed a model in which topoisomerases introduce a sharp bend in DNA. Because the enzymes have a specific orientation relative to the bend, they act like Maxwell's demon, providing unidirectional strand passage. Quantitative analysis of the model by computer simulations proved that it can explain much of the experimental data. The required sharp DNA bend was demonstrated by a greatly increased cyclization of short DNA fragments from topoisomerase binding and by direct visualization with electron microscopy.

Positive torsional strain causes the formation of a four-way junction at replication forks.

The advance of a DNA replication fork requires an unwinding of the parental double helix. This in turn creates a positive superhelical stress, a (+)-DeltaLk, that must be relaxed by topoisomerases for replication to proceed. Surprisingly, partially replicated plasmids with a (+)-DeltaLk were not supercoiled nor were the replicated arms interwound in precatenanes. The electrophoretic mobility of these molecules indicated that they have no net writhe. Instead, the (+)-DeltaLk is absorbed by a regression of the replication fork. As the parental DNA strands re-anneal, the resultant displaced daughter strands base pair to each other to form a four-way junction at the replication fork, which is locally identical to a Holliday junction in recombination. We showed by restriction endonuclease digestion that the junction can form at either the terminus or the origin of replication and we visualized the structure with scanning force microscopy. We discuss possible physiological implications of the junction for stalled replication in vivo.

Experimental and theoretical analysis of the invasive signal amplification reaction.

The invasive signal amplification reaction is a sensitive method for single nucleotide polymorphism detection and quantitative determination of viral load and gene expression. The method requires the adjacent binding of upstream and downstream oligonucleotides to a target nucleic acid (either DNA or RNA) to form a specific substrate for the structure-specific 5' nucleases that cleave the downstream oligonucleotide to generate signal. By running the reaction at an elevated temperature, the downstream oligonucleotide cycles on and off the target leading to multiple cleavage events per target molecule without temperature cycling. We have examined the performance of the FEN1 enzymes from Archaeoglobus fulgidus and Methanococcus jannaschii and the DNA polymerase I homologues from Thermus aquaticus and Thermus thermophilus in the invasive signal amplification reaction. We find that the reaction has a distinct temperature optimum which increases with increasing length of the downstream oligonucleotide. Raising the concentration of either the downstream oligonucleotide or the enzyme increases the reaction rate. When the reaction is configured to cycle the upstream instead of the downstream oligonucleotide, only the FEN1 enzymes can support a high level of cleavage. To investigate the origin of the background signal generated during the invasive reaction, the cleavage rates for several nonspecific substrates that arise during the course of a reaction were measured and compared with the rate of the specific reaction. We find that the different 5' nuclease enzymes display a much greater variability in cleavage rates on the nonspecific substrates than on the specific substrate. The experimental data are compared with a theoretical model of the invasive signal amplification reaction.

The kinetics of oligonucleotide replacements.

The formation of a duplex between two nucleic acid strands is restricted if one of the strands forms an intra- or intermolecular secondary structure. The formation of the new duplex requires the dissociation and replacement of the initial structure. To understand the mechanism of this type of kinetics we studied the replacement of a labeled DNA oligonucleotide probe bound to a complementary DNA target with an unlabeled probe of the same sequence. The replacement kinetics were measured using a gel-shift assay for 12, 14 and 16-nucleotide probes as a function of temperature and concentration of the unlabeled probe. The results demonstrate that the overall replacement rate is a combination of two kinetic pathways: dissociative and sequential displacement. The dissociative pathway occurs by the spontaneous dissociation of the initial duplex followed by association of the target and unlabeled probe. The sequential displacement pathway requires only the partial melting of the initial duplex to allow for the formation of a branched nucleation complex with the unlabeled probe, followed by the complete displacement of the labeled probe by migration of the branch point. The contribution from the dissociative pathway is predominant at temperatures close to the melting point of the labeled probe, whereas the contribution from the displacement pathway prevails at lower temperatures and when the concentration of the replacing unlabeled probe is high. The results show that at physiological conditions, duplex formation between a single-stranded oligonucleotide probe and a structured region of a target molecule occurs mainly by the sequential-displacement mechanism.

Equilibrium distributions of topological states in circular DNA: interplay of supercoiling and knotting.

Two variables define the topological state of closed double-stranded DNA: the knot type, K, and DeltaLk, the linking number difference from relaxed DNA. The equilibrium distribution of probabilities of these states, P(DeltaLk, K), is related to two conditional distributions: P(DeltaLk|K), the distribution of DeltaLk for a particular K, and P(K|DeltaLk) and also to two simple distributions: P(DeltaLk), the distribution of DeltaLk irrespective of K, and P(K). We explored the relationships between these distributions. P(DeltaLk, K), P(DeltaLk), and P(K|DeltaLk) were calculated from the simulated distributions of P(DeltaLk|K) and of P(K). The calculated distributions agreed with previous experimental and theoretical results and greatly advanced on them. Our major focus was on P(K|DeltaLk), the distribution of knot types for a particular value of DeltaLk, which had not been evaluated previously. We found that unknotted circular DNA is not the most probable state beyond small values of DeltaLk. Highly chiral knotted DNA has a lower free energy because it has less torsional deformation. Surprisingly, even at |DeltaLk| > 12, only one or two knot types dominate the P(K|DeltaLk) distribution despite the huge number of knots of comparable complexity. A large fraction of the knots found belong to the small family of torus knots. The relationship between supercoiling and knotting in vivo is discussed.

Effect of magnesium on cruciform extrusion in supercoiled DNA.

Recently, it was reported that Mg2+greatly facilitates cruciform extrusion in the short palindromes of supercoiled DNA, thereby allowing the formation of cruciform structures in vivo. Because of the potential biological importance of this phenomenon, we undertook a broader study of the effect of Mg2+on a cruciform extrusion in supercoiled DNA. The method of two-dimensional gel electrophoresis was used to detect the cruciform extrusion both in the absence and in the presence of these ions. Our results show that Mg2+shifts the cruciform extrusion in the d(CCC(AT)16GGG) palindrome to a higher, rather than to a lower level of supercoiling. In order to study possible sequence-specific properties of the short palindromes for which the unusual cruciform extrusion in the presence Mg2+was reported, we constructed a plasmid with a longer palindromic region. This region bears the same sequences in the hairpin loops and four-arm junction as the short palindrome, except that the short stems of the hairpins are extended. The extension allowed us to overcome the limitation of our experimental approach which cannot be used for very short palindromes. Our results show that Mg2+also shifts the cruciform extrusion in this palindrome to a higher level of supercoiling. These data suggest that cruciform extrusion in the short palindromes at low supercoiling is highly improbable. We performed a thermodynamic analysis of the effect of Mg2+on cruciform extrusion. The treatment accounted for the effect of Mg2+on both free energy of supercoiling and the free energy of cruciform structure per se. Our analysis showed that although the level of supercoiling required for the cruciform extrusion is not reduced by Mg2+, the ions reduce the free energy of the cruciform structure.

Mechanisms of separation of the complementary strands of DNA during replication.

This article is a perspective on the separation of the complementary strands of DNA during replication. Given the challenges of DNA strand separation and its vital importance, it is not surprising that cells have developed many strategies for promoting unlinking. We summarize seven different factors that contribute to strand separation and chromosome segregation. These are: (1) supercoiling promotes unlinking by condensation of DNA; (2) unlinking takes place throughout a replicating domain by the complementary action of topoisomerases on precatenanes and supercoils; (3) topological domains isolate the events near the replication fork and permit the supercoiling-dependent condensation of partially replicated DNA; (4) type-II topoisomerases use ATP to actively unlink DNA past the equilibrium position; (5) the effective DNA concentration in vivo is less than the global DNA concentration; (6) mechanical forces help unlink chromosomes; and (7) site-specific recombination promotes unlinking at the termination of replication by resolving circular dimeric chromosomes.

Sedimentation and electrophoretic migration of DNA knots and catenanes.

Various site-specific recombination enzymes produce different types of knots or catenanes while acting on circular DNA in vitro and in vivo. By analysing the types of knots or links produced, it is possible to reconstruct the order of events during the reaction and to deduce the molecular "architecture" of the complexes that different enzymes form with DNA. Until recently it was necessary to use laborious electron microscopy methods to identify the types of knots or catenanes that migrate in different bands on the agarose gels used to analyse the products of the reaction. We reported recently that electrophoretic migration of different knots and catenanes formed on the same size DNA molecules is simply related to the average crossing number of the ideal representations of the corresponding knots and catenanes. Here we explain this relation by demonstrating that the expected sedimentation coefficient of randomly fluctuating knotted or catenated DNA molecules in solution shows approximately linear correlation with the average crossing number of ideal configurations of the corresponding knots or catenanes.

Non-complementary DNA helical structure induced by positive torsional stress.

We have induced a local conformational transition by positive torsional stress in small synthetic circular DNA molecules containing cruciforms with immobile or tetramobile branched junctions. The immobile species correspond to the extruded and intruded extrema of the tetramobile junction. Under normal conditions the sequences of all the branched species prevent them from being re-absorbed into the circle. We have induced positive stress by addition of ethidium to the circle, in a low ionic strength medium. Alterations in gel electrophoretic mobility under increasing concentrations of ethidium suggest that the cruciforms undergo a transition under torsional stress. The product of this transition contains mispaired nucleotides, but interwound backbones. By comparing the electrophoretic mobilities of circles containing these structures with that of a completely complementary circle of the same length, we conclude that the twist in the mispairing region is similiar to that of completely paired species.

Torsional control of double-stranded DNA branch migration.

DNA branched junctions are analogues of Holliday junction recombination intermediates. Partially mobile junctions contain a limited amount of homology flanking the branch point. A partially mobile DNA branched junction has been incorporated into a synthetic double-stranded circular DNA molecule. The junction is flanked by four homologous nucleotide pairs, so that there are five possible locations for the branch point. Two opposite arms of the branched junction are joined to form the circular molecule, which contains 262 nucleotides to the base of the junction. This molecule represents a system whereby torque applied to the circular molecule can have an impact on the junction, by relocating its branch point. Ligation of the molecule produces two topoisomers; about 87% of the product is a relaxed molecule, and the rest is a molecule with one positive supercoil. The position of the branch point is assayed by cleaving the molecule with endonuclease VII. We find that the major site of the branch point in the relaxed topoisomer is at the maximally extruded position in the relaxed molecule. Upon the addition of ethidium, the major site of the branch point migrates to the minimally extruded position.

Simplification of DNA topology below equilibrium values by type II topoisomerases.

Type II DNA topoisomerases catalyze the interconversion of DNA topoisomers by transporting one DNA segment through another. The steady-state fraction of knotted or catenated DNA molecules produced by prokaryotic and eukaryotic type II topoisomerases was found to be as much as 80 times lower than at thermodynamic equilibrium. These enzymes also yielded a tighter distribution of linking number topoisomers than at equilibrium. Thus, topoisomerases do not merely catalyze passage of randomly juxtaposed DNA segments but control a global property of DNA, its topology. The results imply that type II topoisomerases use the energy of adenosine triphosphate hydrolysis to preferentially remove the topological links that provide barriers to DNA segregation.

Extension of torsionally stressed DNA by external force.

Metropolis Monte Carlo simulation was used to study the elasticity of torsionally stressed double-helical DNA. Equilibrium distributions of DNA conformations for different values of linking deficit, external force, and ionic conditions were simulated using the discrete wormlike chain model. Ionic conditions were specified in terms of DNA effective diameter, i.e., hard-core radius of the model chain. The simulations show that entropic elasticity of the double helix depends on how much it is twisted. For low amounts of twisting (less than about one turn per twist persistence length) the force versus extension is nearly the same as in the completely torsionally relaxed case. For more twisting than this, the molecule starts to supercoil, and there is an increase in the force needed to realize a given extension. For sufficiently large amounts of twist, the entire chain is plectonemically supercoiled at low extensions; a finite force must be applied to obtain any extension at all in this regime. The simulation results agree well with the results of recent micromanipulation experiments.

The effect of ionic conditions on DNA helical repeat, effective diameter and free energy of supercoiling.

We determined the free energy of DNA supercoiling as a function of the concentration of magnesium and sodium chloride in solution by measuring the variance of the equilibrium distribution of DNA linking number,<(DeltaLk)2>. We found that the free energy of supercoiling changed >1.5-fold over the range of ionic conditions studied. Comparison of the experimental results with those of computer simulations showed that the ionic condition dependence of<(DeltaLk)2>is due mostly to the change in DNA effective diameter, d, a parameter characterizing the electrostatic interaction of DNA segments. To make this comparison we determined values of d under all ionic conditions studied by measuring the probability of knot formation during random cyclization of linear DNA molecules. From the topoisomer distributions we could also determine the changes in DNA helical repeat, gamma, in mixed NaCl/MgCl2 solutions. Both gamma and d exhibited a complex pattern of changes with changing ionic conditions, which can be described in terms of competition between magnesium and sodium ions for binding to DNA.

The effect of ionic conditions on the conformations of supercoiled DNA. I. Sedimentation analysis.

We studied the conformations of supercoiled DNA as a function of superhelicity and ionic conditions by determining its sedimentation coefficient both experimentally and by calculation. To cancel out unknown parameters from both calculations and experiments, we determined the ratio of the sedimentation coefficient, s, to that of open circular DNA, s(oc). Calculations of the sedimentation coefficient were based on direct solution of the Burgers-Oseen problem for an equilibrium set of DNA conformations generated for each condition by the Metropolis Monte Carlo procedure. There were no adjustable parameters in the Monte Carlo simulations because all three parameters of the DNA model used, bending and torsional elasticity of DNA and DNA effective diameter specifying electrostatic interactions, were known from independent data. The good agreement between measured and calculated values of s/s(oc) allowed us to interpret the sedimentation results in terms of DNA conformations, with particular emphasis on the marked effect of ionic conditions. As NaCl concentration decreases, s/s(oc) increases because the superhelix becomes less regular and more compact. In the presence of just 10 mM MgCl(2), supercoiled DNA adopts essentially the same set of conformations as in moderate to high concentrations of NaCl. Our simulations showed that s is a strong function of the superhelix branching frequency. At near physiological ionic conditions, there are about four branches in the 7 kb DNA molecule used in this work. We found no indication of superhelix collapse in any ionic conditions even remotely approaching physiological ones. For all ionic conditions studied, we conclude that the electrostatic interaction of DNA segments specified by the DNA effective diameter is the primary determinant of supercoiled DNA conformations.

The effect of ionic conditions on the conformations of supercoiled DNA. II. Equilibrium catenation.

We studied the equilibrium formation of DNA catenanes to assess the conformational properties of supercoiled DNA as a function of ionic conditions and supercoiling density. Catenanes were formed by cyclizing linear DNA with long cohesive ends in the presence of supercoiled molecules. The efficiency of the catenation depends on the distance between opposing segments of DNA in the interwound superhelix. The fraction of cyclizing molecules that becomes topologically linked with the supercoiled DNA is the product of the concentration of the supercoiled DNA and a proportionality constant, B, that depends on conformations of supercoiled DNA. In parallel with these experimental studies, we calculated the values of B using Monte Carlo simulations of the equilibrium distribution of DNA conformations. There were no adjustable parameters in the calculations because all three parameters of the DNA model, bending and torsional elasticity of DNA and DNA effective diameter, specifying intersegment interactions, were known from independent studies. We found very good agreement between measured and simulated values of B for all the ionic conditions and DNA superhelix densities studied; the discrepancy was less than a factor of 2 over the 200-fold variation in B. The value of B decreases nearly exponentially with increasing superhelicity, this dependence being especially strong at low salt concentration. The dependence of B on the concentration of NaCl, MgCl(2), and spermidine can be described with good accuracy in terms of changes of the DNA effective diameter. We found no indication of superhelix collapse under any ionic conditions studied. We discuss, in light of these results, the biological importance of the effect of DNA supercoiling on the unlinking of the products of DNA replication.

[Conformational features of circular DNA with natural curvature]. / Konformatsionnye osobennosti kol'tsevykh DNK s estestvennoi kriviznoi.

Monte-Carlo modelling of DNA circles revealed that features of LK distributions must strongly depend on the DNA sequence. The effect is very significant for circles of 300-1500 bp length with a(stt) < or = 250 nm.

Conformational and thermodynamic properties of supercoiled DNA.

Work in the 1990s has substantially increased our understanding of supercoiling conformations and energetics. We now know many of the basic properties of supercoiled DNA as a result of the synergy between experimental and theoretical analyses. We conclude by summarizing the results. 1. All available data indicate a plectonemic structure for supercoiled DNA. First, three types of EM (conventional, cryo, and scanning force) show the plectonemic form. Second, the topology of the catenanes and knots generated from supercoiled DNA by the Int recombinase demands that the substrate supercoils are plectonemic, as does the topology of knotting by type-2 topoisomerases. Third, all the theoretical and computer analyses indicate that the superhelix has the interwound form. 2. The superhelix conformations are often branched, as observed using EM and Monte Carlo simulation. Moreover, branching is required to explain the distribution of knots and catenanes produced by Int or topoisomerases as well as the dependence of s and Rg on sigma. Branching frequency is very sensitive to sigma, DNA length, ionic conditions, DNA bends, and temperature. Despite the qualitative agreement, the quantitative differences between experimental and computational data point out the need for further studies of branching. 3. The results of Monte Carlo simulations, theoretical analyses, and cryo-EM show that the conformational and thermodynamic properties of supercoiled DNA depend strongly on ionic conditions. The reason for such a dependence is clear. Counterions shield DNA negative charges and decrease the repulsion of DNA segments in the tight interwound structure. The effective double-helix diameter increases from 3 to 15 nm as the salt concentration is reduced from 1.00 to 0.01 M. Experimental investigations of the dependence on ionic conditions of supercoiled DNA properties are just beginning. The following conclusions refer to conditions of moderate to high monovalent or divalent ion concentrations (> or = 0.1 M [Na+] or > or = 0.01 M [Mg2+], respectively). 1. Wr takes up about 3/4 of the delta Lk, and Wr/delta Tw is independent of sigma for DNA > or = 2.5 kb in length. A constant ratio is implied by the CD data, and Wr/delta Tw has been determined with conventional EM, cryo-EM, the Int topological method, and Monte Carlo simulation. 2. The average number of supercoils is (0.8 to 0.9) x delta Lk and is independent of DNA length. These results were obtained with EM, the Int topological method, and computer simulation.(ABSTRACT TRUNCATED AT 400 WORDS)

Testing the quality of electron microscope mapping data for DNA molecules with sequence-specific ligands.

A procedure for the testing of Electron Microscope (EM) mapping data for DNA molecules with site-specific bound ligands is suggested. The difficulty of distinguishing DNA molecule ends on electron micrographs indicates that their true orientations are not known. This in turn presents problems in obtaining correct maps relating to their alignment, and complicates checking the maps' validity. For these reasons a computer simulation of the EM study of double-stranded DNA molecules with site-specific bound ligands was carried out. The knowledge of the true orientations of the simulated DNA molecules allowed us to examine their final orientations after alignment. We used the number of improper-oriented molecules as the quantitative measure of the map quality. Detailed investigation based on this parameter permitted us to invent the criterion for the map validity, and to suggest the procedure for the testing of alignment of real DNA molecules. This procedure implies multiple randomization of initial orientations of the DNA molecules and minute analysis of the final maps. Most of the molecular, statistical and experimental parameters inherent to EM investigation of site-specific binding, such as the number of specific binding sites (N), the mean number of bound ligands (A), the length of the DNA molecules (L), the specific/non-specific ratio of binding (K), together with the standard deviation of DNA molecule lengths (HL) were tested for their influence upon the quality of EM mapping data. An empirical equation for the ultimate values of these parameters has been found, allowing us to predict the success of EM mapping.

Monte Carlo analysis of the conformation of DNA catenanes.

We used a Monte Carlo method to study the conformational properties of catenanes between two nicked DNA rings. We calculated the writhe induced by catenation as a function of the linking number between the two rings. The simulations modeled catenated rings of equal size as well as rings differing in length by a factor of 3. For both classes of catenanes, the calculated values of writhe agreed very well with the experimental measurements of catenation-induced supercoiling made by Wasserman et al. Therefore, the equilibrium value of DNA twist is not changed significantly by catenation. We found that the induced writhe increased linearly with catenane linking number, but was independent of DNA length and of effective helical diameter. We conclude that induced writhe is a general feature of catenation, and that it depends primarily on the ratio of lengths of the linked rings and the number of catenane interlocks. In contrast, catenane conformation varied qualitatively with catenation linking number, DNA length, and double helix diameter. At the values of these parameters for catenanes isolated from cells, catenane conformations were strikingly irregular. Nonetheless, the local concentration of two sites on separate but linked rings increased greatly with catenane linking number. This increase is similar to that brought about by (-) supercoiling to DNA sites in cis.