The Twist,Writhe, and Linking Number Distributions in Closed Circular DNA

Abstract

We discuss the predictions which follow from the assumption of statistically independent twist and writhe distributions of given variances in circular DNA with single-strand nicks. The nature of the topoisomer distribution produced upon covalent closure of the nicks is described, as well as the nature of the twist and writhe distributions in the fully-closed molecules. In particular, we show how the distributions depend on the magnitudes of the given variances, and how the relative magnitudes of the variances can be deduced from experiment. One additional consequence of the theory is the prediction of a necessary difference between the temperature coefficient of the twist in nicked versus fully-closed circular DNA. The ratio of the two twist coefficients turns out to depend only on the ratio of the twist and writhe variances in nicked DNA.     

Effect of spontaneous twist on DNA minicircles

Monte Carlo simulations are used to study the effect of spontaneous (intrinsic) twist on the conformation of topologically equilibrated minicircles of dsDNA. The twist, writhe, and radius of gyration distributions and their moments are calculated for different spontaneous twist angles and DNA lengths. The average writhe and twist deviate in an oscillatory fashion (with the period of the double helix) from their spontaneous values, as one spans the range between two neighboring integer values of intrinsic twist. Such deviations vanish in the limit of long DNA plasmids.     

Breakage of double-stranded DNA due to single-stranded nicking

Enzymes such as pancreatic deoxyribonuclease (DNase I) nick the single strands of double-stranded DNA. Two nicks sufficiently close on opposite strands will lead to breakage of the DNA molecule. This paper gives a mathematical model for the breakage of circular, supercoiled DNA under the action of an enzyme which nicks at random sites (or at preferred sites, these being in abundance and randomly positioned around the circle). After the first nick the DNA loses its supercoiled structure; after many nicks it breaks to become topologically linear; further nicks lead to fragmentation of this linear form. Formulae are given for the proportions of DNA molecules in each of the four classes: supercoiled; nicked but still circular; linear; fragmented. Formulae are also presented for the case when there is, in addition to nicking, simultaneous action of an endonuclease which produces direct double-stranded breaks in the DNA. Finally, a general theory is given for the case where a third type of enzyme, topoisomerase I, is operative, with all three DNA modifications taking place simultaneously.     

Terminal Twist-Induced Writhe of DNA with Intrinsic Curvature

Supercoiling of a closed circular DNA rod may result from an application of terminal twist to the DNA rod by cutting the rod, rotating one of the cut faces as the other being fixed and then sealing the cut. According to White's formula, DNA supercoiling is probably accompanied by a writhe of the DNA axis. Deduced from the elastic rod model for DNA structure, an intrinsically straight closed circular DNA rod does not writhe as subject to a terminal twist, until the number of rotation exceeds a rod-dependent threshold. By contrast, a closed circular DNA rod with intrinsic curvature writhes instantly as subject to a terminal twist. This noteworthy character in fact belongs to many intrinsically curved DNA rods. By solving the dynamic equations, the linearization of the Euler–Lagrange equations governing intrinsically curved DNA rods, this paper shows that almost every clamped-end intrinsically curved DNA rod writhes instantly when subject to a terminal twist (clamped-end DNA rods include closed circular DNA rods and topological domains of open DNA rods). In terms of physical quantities, the exceptions are identified with points in ℝ⁶ whose projections onto ℝ⁵ (through ignoring the total energy density of a rod) form a subset of a quadratic hypersurface. This paper also suggests that the terminal twist induced writhe is due to the elasticity and the clamped-end boundary conditions of the DNA rods. To my sister for her 50th birthday.     

Temperature dependence of DNA persistence length

We have determined the temperature dependence of DNA persistence length, a, using two different methods. The first approach was based on measuring the j-factors of short DNA fragments at various temperatures. Fitting the measured j-factors by the theoretical equation allowed us to obtain the values of a for temperatures between 5°C and 42°C. The second approach was based on measuring the equilibrium distribution of the linking number between the strands of circular DNA at different temperatures. The major contribution into the distribution variance comes from the fluctuations of DNA writhe in the nicked circular molecules which are specified by the value of a. The computation-based analysis of the measured variances was used to obtain the values of a for temperatures up to 60°C. We found a good agreement between the results obtained by these two methods. Our data show that DNA persistence length strongly depends on temperature and accounting for this dependence is important in quantitative comparison between experimental results obtained at different temperatures.     

Structure of plectonemically supercoiled DNA

Using electron microscopy and topological methods, we have deduced an average structure for negatively supercoiled circular DNA in solution. Our data suggest that DNA has a branched plectonemic (interwound) form over the range of supercoiling tested. The length of the superhelix axis is constant at 41% of the DNA length, whereas the superhelix radius decreases essentially hyperbolically as supercoiling increases. The number of supercoils is 89% of the linking deficit. Both writhe and twist change with supercoiling, but the ratio of the change in writhe to the change in twist is fixed at 2.6:1. The extent of branching of the superhelix axis is proportional to the length of the plasmid, but is insensitive to superhelix density. The relationship between DNA flexibility constants for twisting and bending calculated using our structural data is similar to that deduced from previous studies. The extended thin form of plectonemically supercoiled DNA offers little compaction for cellular packaging, but promotes interaction between cis-acting sequence elements that may be distant in primary structure. We discuss additional biological implications of our structural data.     

Structural changes in positively and negatively supercoiled DNA

The effect of superhelical constraint on the structure of covalently closed circular DNA (cccDNA; pBR322) with positive and negative writhe (superturn) has been investigated as a function of decreasing and increasing specific linking difference (mean superhelical density sigma). At low and moderate negative superhelical densities sigma, the overall average structure is maintained in an unwound B-form slightly modified. The overwound cccDNAs with positive writhe differ from those with negative writhe by an absence of cruciform structure. At high negative densities of supercoiling different changes involving the reversal of twist handedness are shown to lead to the formation of DNA segments in a conformation identical to the left-handed component of form V DNA.     

Positive supercoiling is generated in the presence of Escherichia coli SeqA protein

In Escherichia coli, the SeqA protein is known as a negative regulator of chromosome replication. This protein is also suggested to have a role in chromosome organization. SeqA preferentially binds to hemi-methylated DNA and is by immunofluorescence microscopy seen as foci situated at the replication factories. Loss of SeqA leads to increased negative supercoiling of the DNA. We show that purified SeqA protein bound to fully methylated, covalently closed or nicked circular DNA generates positive supercoils in vitro in the presence of topoisomerase I or ligase respectively. This means that binding of SeqA changes either the twist or the writhe of the DNA. The ability to affect the topology of DNA suggests that SeqA may take part in the organization of the chromosome in vivo. The topology change performed by SeqA occurred also on unmethylated plasmids. It is, however, reasonable to suppose that in vivo the major part of such activity is performed on hemi-methylated DNA at the replication factories and presumably forms the basis for the characteristic SeqA foci observed by fluorescence microscopy.     

Method to eliminate linear DNA from mixture containing nicked circular, supercoiled, and linear plasmid DNA

Preparations of circular plasmid DNA in either supercoiled or nicked circular form often are contaminated with undesired linear DNA fragments arising from shearing/degradation of chromosomal DNA or linearization of plasmid DNA itself. We report a simple enzymatic method, using a combination of λ exonuclease and RecJ_f, for the selective removal of linear DNA from such mixtures. λ exonuclease digests one strand of linear duplex DNA in the 5′ to 3′ direction, whereas RecJ_f, a single-strand-specific exonuclease, digests the remaining complementary single strand into mononucleotides. This combination of exonucleases can remove linear DNA from a mixture of linear and supercoiled DNA, leaving the supercoiled form intact. Furthermore, the inability of λ exonuclease to initiate digestion at nicks or gaps enables the removal of undesired linear DNA when nicked circular DNA has been enzymatically prepared from supercoiled DNA. This method can be useful in the preparation of homogeneous circular plasmid DNA required for therapeutic applications and biophysical studies.     

Nuclease S1 cleavage and the primary structure of mitochondrial DNA.

The single-strand-specific nuclease S1 from Aspergillus oryzae rapidly converts superhelical mitochondrial DNA (African Green Monkey cells, Vero ATCC; CCL 81) into nicked circular DNA. These nicked mitochondrial DNA molecules contain two nicks, one in each strand. The phosphodiester backbones are cleaved during this reaction at or near sites that are alkali-labile. In a second slow reaction the circular mitochondrial DNA is converted into a linear duplex DNA. Permutation tests indicate that this linear DNA represents a nonpermutated collection of DNA molecules. These results suggest that two of the alkai-labile sites in the phosphodiester backbones of the mitochondrial chromosome are closely spaced on opposite strands and at specific positions.     

Characterization of an endonuclease activity associated with Friend-murine leukemia virus

An endonuclease activity shown to be associated with Friend leukemia virus has been characterized using double-stranded phi X174 DNA as substrate. In the presence of Mg2+, the endonuclease activity was able to convert supercoiled circular DNA duplexes to the relaxed form by introducing single-stranded nicks into the DNA. Most of the nicked DNA duplexes contained only one nick per strand, since unit length DNA was the predominant species obtained when the nicked DNA was analyzed by alkaline sucrose gradient centrifugation. The regions into which the nick could be introduced were evenly distributed around the circular DNA molecule. When Mn2+ was substituted for Mg2+ in the reaction mixture, the number of nicks introduced into circular DNA duplexes by the virus associated endonuclease was greatly increased. In contrast to circular duplexes, linear duplexes and single-stranded DNA functioned poorly as substrates for the virus-associated enzyme. The Friend leukemia virus-associated endonuclease activity is with respect to these characteristics very similar to the endonuclease activity associated with the p32 protein of the avian myeloblastosis virus [1]. The molecular weight of the Friend leukemia virus endonuclease was estimated by gel filtration on a Sephacryl S-200 column to be about 45 000.     

Topological distributions and the torsional rigidity of DNA. A Monte Carlo study of DNA circles

Distributions of the linking number of circular DNA molecules, defined as the sum of twist and the writhing number, are obtained by Monte Carlo simulations of small, randomly closed DNA circles. We estimate the relative contributions of fluctuations in twist and writhe to the linking number distribution, as functions of DNA size. Published experimental data on topoisomer distributions in circular DNA molecules are interpreted to estimate the torsional rigidity of DNA in solution. We show that ignoring the writhe component of the linking number distribution, even for DNA circles as small as 250 base-pairs, leads to an underestimate for the torsional stiffness of the double helix. The value of the torsional modulus obtained from this analysis, C = 3.4 X 10(-19) erg cm, is from 10 to 40% larger than that estimated by others and more than twice as large as the values obtained from fluorescence depolarization or other time-resolved spectroscopic measurements. We also develop further the theoretical treatment of ring closure probabilities for DNA described in the previous article. It is shown that the torsional part of the ring closure probability, phi 0,1 (tau 0) is a periodic function of DNA length that contributes strongly to the ring closure probability for short chains but makes negligible contributions for chains over 1000 base-pairs in length.     

Purification and properties of DNA endonucleases associated with Friend leukemia virus.

An endonuclease associated with the core of Friend leukemia virus (FLV) has been purified more than 10(3)-fold by ion exchange chromatography and gel filtration. Its molecular weight was determined by gel filtration to be about 40,000. Divalent cations were required for the endonuclease to function and KCl concentrations above 50 mM inhibited the enzyme activity. In the presence of Mg++ the purified enzyme nicked preferentially supercoiled circular DNA duplexes and in most of these molecules only one single-stranded nick was introduced per strand. The regions into which the nick could be introduced appeared to be randomly distributed on the circular molecule. When Mn++ was substituted for Mg++ the number of nicks introduced into DNA by the purified enzyme was greatly increased, and both relaxed circular and linear DNA duplexes were nicked as well as supercoiled circular DNA duplexes. Prior to its purification, however, in the presence of Mn++ the endonuclease activity in the virus extract was able to differentiate between circular and linear DNA duplexes, since both supercoiled and relaxed circular duplexes were nicked much more readily than linear duplexes. Single-stranded DNA functioned poorly as a substrate for the purified enzyme.     

Writhe of DNA induced by a terminal twist

This paper considers the three-dimensional structure of B-form DNA. The molecule may be open or covalently closed. For the former, its two ends are not allowed to move or rotate freely in space unless the molecule is under the influence of rigid body motions of the ambient space. Implied by the elastic rod model for DNA, the molecule writhes immediately when subject to a terminal twist as long as its axis is none of the following curves: lines, circular arcs, circular helices. This result is remarkably different from well-known results about DNA of other conformations. For example, if a DNA is regarded as an elastic rod whose axis is a circle, then it has no induced writhe when subject to a terminal twist until the latter meets a critical extent. To my mother for her 70th birthday An erratum to this article is available at .     

ISWI induces nucleosome sliding on nicked DNA.

The ATPase ISWI is the molecular motor of several remodeling factors that trigger nucleosome sliding in vitro. In search for the underlying mechanism, we found that unilateral binding of ISWI to a model nucleosome correlated with directional movement of the nucleosome toward the enzyme. It has been proposed that ISWI might loosen histone-DNA interactions through twisting DNA. However, nucleosome sliding assays on nicked DNA substrates suggest that propagation of altered twist is not involved. Surprisingly, nicks in the linker DNA in front of the nucleosome facilitate sliding. These data suggest that the rate of nucleosome sliding is limited by a conformational change other than twisting, such as the formation of a short loop, of DNA at the entry into the nucleosome.     

Involvement of Coprinus endonuclease in preparing substrate for in vitro recombination

A functional recombination assay involving the tetracycline mutant plasmids, pUW1 and pUW4, was used to assess (i) the nature of the DNA substrates needed and (ii) the involvement of Coprinus endonuclease in preparing substrate, for the RecA-directed recombination process. A gapped circular plasmid and a linear or a nicked circular plasmid are efficient substrate combinations in this system to achieve a 160-fold increase in the in vitro recombination frequency over the control levels. The Coprinus endonuclease obtained from early meiotic prophase can produce such substrates. The recombination frequency obtained with the combination of gapped pUW1 plasmids initially relaxed by the Coprinus endonuclease and linear pUW4 plasmids produced by the site-specific BamHI digest is 10-fold lower than that obtained when both substrates are digested by BamHI. The results suggest that the Coprinus endonuclease creates random nicks on plasmid DNA. Glyoxal gel electrophoretic analysis was used to confirm this random nicking activity of Coprinus endonuclease.     

Segregation of relaxed replicated dimers when DNA ligase and DNA polymerase I are limited during oriC-specific DNA replication.

An in vitro Escherichia coli oriC-specific DNA replication system was used to investigate the DNA replication pathways of oriC plasmids. When this system was perturbed by the DNA ligase inhibitor nicotinamide mononucleotide (NMN), alterations occurred in the initiation of DNA synthesis and processing of intermediates and DNA products. Addition of high concentrations of NMN soon after initiation resulted in the accumulation of open circular dimers (OC-OC). These dimers were decatenated to open circular monomers (form II or OC), which were then processed to closed circular supercoiled monomers (form I or CC) products. After a delay, limited ligation of the interlinked dimers (OC-OC to CC-OC and CC-CC) also occurred. Similar results were obtained with replication protein extracts from polA mutants. The presence of NMN before any initiation events took place prolonged the existence of nicked template DNA and promoted, without a lag period, limited incorporation into form II molecules. This DNA synthesis was nonspecific with respect to oriC, as judged by DnaA protein dependence, and presumably occurred at nicks in the template DNA. These results are consistent with oriC-specific initiation requiring closed supercoiled molecules dependent on DNA ligase activity. The results also show that decatenation of dimers occurs readily on nicked dimer and represents an efficient pathway for processing replication intermediates in vitro.     

Properties of a DNA repair endonuclease from mouse plasmacytoma cells

The properties of a DNA-repair endonuclease isolated from mouse plasmacytoma cells have been further studied. It acted on ultraviolet-light-irradiated supercoiled DNA, and the requirement for a supercoiled substrate was absolute at ultraviolet light doses below 1.5 kJ m-2. At higher doses relaxed DNA could also serve as a substrate, but the activity on this DNA was due mostly to hydrolysis of ultraviolet-light-induced apurinic/apyrimidinic (AP) sites by the AP-endonuclease activity associated with the enzyme. The latter enzyme activity did not require a supercoiled form of the DNA. The enzyme also introduced nicks in unirradiated d(A-T)n. The nicked ultraviolet-light-irradiated DNA served as a substrate for DNA polymerase I, showing that the nicks contained free 3'-OH ends. Treatment of the nicked ultraviolet-light-irradiated DNA with bacterial alkaline phosphatase followed by T4 polynucleotide kinase, resulted in the phosphorylation of the 5' ends of the nicks, indicating that the nicks possessed a 5'-phosphate group; 5'- and 3'-mononucleotide analyses of the labelled DNA suggested that the enzyme introduced breaks primarily between G and T residues. The enzyme did not act on any specific region on the supercoiled DNA molecule; it produced random nicks in ultraviolet-light-modified phi X 174 replicative form I DNA. Antibodies raised against ultraviolet-light-irradiated DNA inhibited the activity. DNA adducts such as N-acetoxy-2-acetylaminofluorene and psoralen were not recognized by the enzyme. It is suggested that the enzyme has a specificity directed toward helical distortions.     

Circular intermediates with missing nucleotides in the conversion of supercoiled or nicked circular to linear duplex DNA catalyzed by two species of BAL 31 nuclease

The extracellular nucleases from Alteromonas espejiana BAL 31 can catalyze the endonucleolytic and/or exonucleolytic hydrolysis of duplex DNA in response to a variety of alterations, either covalent or noncovalent, in DNA structure. The nuclease can exist as at least two kinetically and molecularly distinct protein species. The two species that have been studied, called the 'fast' (F) and 'slow' (S) nucleases, both readily convert negatively supercoiled DNAs to linear duplex molecules and accomplish this conversion through the formation of a circular duplex intermediate containing usually a single interruption in one strand. It is further shown that most of these intermediates contain gaps arising from the removal in a processive manner of one or more nucleotide residues after the introduction of the initial strand break (nick). Considering only the intermediates with gaps, the average number of missing residues is 6.3 +/- 0.5 and 2.8 +/- 0.3, respectively, for DNA acted upon by the F and S enzymes independently of the extent of conversion of supercoiled DNA. The nicks and gaps are bounded by 3'-hydroxyl and 5'-phosphoryl termini. When singly nicked circular DNA is used as the substrate, conversion to the linear duplex form occurs predominantly through a gapped circular intermediate with the same average numbers, within experimental error, of missing nucleotides for the respective nuclease species as found when supercoiled DNA is the substrate. The conversion to linear duplex DNA is much slower when nicked circular DNA is the substrate compared to that found when supercoiled DNA is the starting material.