Dependence of the linking deficiency of supercoiled minichromosomes upon nucleosome distortion.

The contribution from each nucleosome to the linking number of minichrosome DNA depends on two factors. These are the wrapping number, omega, which is the number of times the DNA wraps about the axis of the nucleosome; and the winding number, phi, which is the number of base pairs on the nucleosome divided by the helical repeat of the DNA. If the nucleosome is distorted with DNA surface contacts being preserved, phi remains unchanged. The wrapping number may still change, however, depending on the extent of the distortion. For example, if the usual cylindrical shape of the nucleosome is deformed into an ellipsoid while preserving the equatorial radius, then the wrapping number will increase. We apply these concepts to minichromosomes torsionally stressed by supercoiling with, for example, DNA gyrase. We analyze the experimental result that the maximum amount of supercoiling obtained by gyrase treatment of minichromosomes is the same as that of naked DNA. In particular, we show that this phenomenon can be explained by a relatively slight distortion of the nucleosome core while maintaining the surface contacts of the DNA on the core.     

Chromatin reconstitution on small DNA rings. II. DNA supercoiling on the nucleosome

DNA supercoiling on the nucleosome was investigated by relaxing with topoisomerase I mono- and dinucleosomes reconstituted on small DNA rings. Besides 359 base-pair (bp) rings whose linking differences were integers, two additional series of rings with fractional differences, 341 and 354 bp in size, were used. Mononucleosomes reconstituted on 359 bp rings were found to relax into a single mononucleosome form. In contrast, 341 and 354 bp mononucleosomes relaxed into a mixture of two forms, corresponding to two adjacent topoisomers. The observation that the ratio between these two forms was, within each ring series, virtually independent of the initial linking number of the topoisomer used for the reconstitution suggested that each partition reflected an equilibrium. Comparison with the equilibria observed for the same rings in the absence of histones showed that the formation of a single nucleosome is associated with a linking number change of -1.1(+/-0.1) turn. Dinucleosomes, in contrast, were not relaxed to completion and do not reach equilibria. The corresponding linking number change per nucleosome was, however, estimated to be similar to the above figure, in agreement with previous data from the literature obtained with circular chromatins containing larger numbers of nucleosomes. DNA structure in mononucleosomes was subsequently investigated by means of high-resolution electron microscopy and gel electrophoresis. It was found that the above linking number reduction could be ascribed to a particle with a large open extranucleosomal DNA loop and with no more than 1.5 turns of a superhelix around the histone core. A theoretical model of a nucleosome on a small ring was constructed in which one part of the DNA was wrapped around a cylinder and the other part was free to vary both in torsion and flexion. The linking number reduction predicted was found to be most consistent with experimental data when the twist of the DNA in the superhelix was between 10.5 and 10.65 pb per turn, suggesting that wrapping on the nucleosome does not alter the twist of the DNA significantly. A lower estimate of the linking number reduction associated with a two-turn nucleosome was also derived, based on an analysis of recent data obtained upon treatment of reconstituted minichromosomes with gyrase. The value, 1.6 turns, set a lower limit of 10.44 bp per turn for the twist of nucleosomal DNA, in agreement with the above estimate.(ABSTRACT TRUNCATED AT 400 WORDS)     

The elastic rod model for DNA and its application to the tertiary structure of DNA minicircles in mononucleosomes.

Explicit solutions to the equations of equilibrium in the theory of the elastic rod model for DNA are employed to develop a procedure for finding the configuration that minimizes the elastic energy of a minicircle in a mononucleosome with specified values of the minicircle size N in base pairs, the extent w of wrapping of DNA about the histone core particle, the helical repeat h(0)b of the bound DNA, and the linking number Lk of the minicircle. The procedure permits a determination of the set Y(N, w, h(0)b) of integral values of Lk for which the minimum energy configuration does not involve self-contact, and graphs of writhe versus w are presented for such values of Lk. For the range of N of interest here, 330 < N < 370, the set Y(N, w, h(0)b) is of primary importance: when Lk is not in Y(N, w, h(0)b), the configurations compatible with Lk have elastic energies high enough to preclude the occurrence of an observable concentration of topoisomer Lk in an equilibrium distribution of topoisomers. Equilibrium distributions of Lk, calculated by setting differences in the free energy of the extranucleosomal loop equal to differences in equilibrium elastic energy, are found to be very close to Gaussian when computed under the assumption that w is fixed, but far from Gaussian when it is assumed that w fluctuates between two values. The theoretical results given suggest a method by which one may calculate DNA-histone binding energies from measured equilibrium distributions of Lk.     

Effect of salt-dependent stiffness on the conformation of a stressed DNA loop containing initially coplanar bends

Closed DNA loops containing one or more bent regions are important structures that occur in the regulation of gene expression. We analyze the response of structures of this type to a change in applied rotation (change in linking deficiency, delta Lk). Our results apply to a closed loop formed from an elastic rod that is intrinsically bent in Nb discrete, 20 degrees steps up to a maximum of 240 degrees, the bent regions being initially coplanar with the plane of the relaxed DNA loop. We determine the effect of changing the intrinsic elastic resistance of the DNA loop to bending and torsional deformations. This relative resistance is expressed by Poisson's ratio v, which depends upon the ratio of bending stiffness to torsional rigidity. Poisson's ratio is primarily a function of salt type and concentration. We find that the tertiary structure of DNA loops changes with delta Lk, but that the geometric response can be either of two quite different types, depending upon the precise (Nb, v) pair. For combinations of Nb and v that are above a critical curve (the Fickel curve), the response to increasing delta Lk is nonmonotonic (NMT region): the distance between the loop closure point and its diametric opposite first decreases, then increases, as delta Lk increases. For combinations of Nb and v that are below the Fickel curve (NMT region), the corresponding diameter never increases, but always decreases with increasing delta Lk. In addition to these results, we define and implement a new measure of tertiary structure in closed DNA: the absolute writhe, AWr.     

NAP1-Assisted Nucleosome Assembly on DNA Measured in Real Time by Single-Molecule Magnetic Tweezers

While many proteins are involved in the assembly and (re)positioning of nucleosomes, the dynamics of protein-assisted nucleosome formation are not well understood. We study NAP1 (nucleosome assembly protein 1) assisted nucleosome formation at the single-molecule level using magnetic tweezers. This method allows to apply a well-defined stretching force and supercoiling density to a single DNA molecule, and to study in real time the change in linking number, stiffness and length of the DNA during nucleosome formation. We observe a decrease in end-to-end length when NAP1 and core histones (CH) are added to the dsDNA. We characterize the formation of complete nucleosomes by measuring the change in linking number of DNA, which is induced by the NAP1-assisted nucleosome assembly, and which does not occur for non-nucleosomal bound histones H3 and H4. By rotating the magnets, the supercoils formed upon nucleosome assembly are removed and the number of assembled nucleosomes can be counted. We find that the compaction of DNA at low force is about 56 nm per assembled nucleosome. The number of compaction steps and associated change in linking number indicate that NAP1-assisted nucleosome assembly is a two-step process.     

Elastic model of highly supercoiled DNA

The equilibrium shapes of supercoiled DNA are investigated by employing an elastic model. First, a set of Euler equations is derived to determine the equilibrium shapes under ring-closure conditions. Two exact solutions that describe circular and figure-8 shapes are obtained. Using these and their topological properties, the configuration change from the circular to the figure-8 form is discussed. Second, more intricate structures of supercoiling DNA are studied by a numerical analysis. Among a class of configurations, the shape that has the minimum elastic energy is explicitly determined. Poisson's ratio, the ratio of the self-avoiding radius to the total length, and the deficit (or excess) of the linking number ΔLk are found to be the important parameters. We conclude that the topology and the elastic theory of looped DNA explain the essential features of the supercoiling phenomena.     

Interactions of Drosophila DNA topoisomerase II with left-handed Z-DNA in supercoiled minicircles.

The native form of Drosophila melanogaster DNA topoisomerase II was purified from Schneider's S3 tissue culture cells and studied with two supercoiled minicircle preparations, mini and mini-CG, 354 bp and 370 bp in length, respectively. Mini-CG contains a d(CG)7 insert which assumes a left-handed Z-DNA conformation in negative supercoiled topoisomers with a negative linking number difference - delta Lk greater than or equal to 2. The interactions of topoisomerase II with topoisomer families of mini and mini-CG were studied by band-shift gel electrophoresis in which the individual topoisomers and their discrete or aggregated protein complexes were resolved. A monoclonal anti-Z-DNA IgG antibody (23B6) bound and aggregated only mini-CG, thereby confirming the presence of Z-DNA. Topoisomerase II bound and relaxed mini-CG more readily than mini. In both cases, there was a preference for more highly negatively supercoiled topoisomers. The topoisomerase II inhibitor VM-26 induced the formation of stable covalent DNA-protein intermediates. In addition, the non-hydrolyzable GTP analogue GTP gamma S inhibited the binding and relaxation activities. Experiments to detect topoisomerase cleavage sites failed to elicit specific loci on either minicircle preparation. We conclude that Drosophila topoisomerase II is able to bind and process small minicircles with lengths as short as 360 bp and negative superhelix densities, - sigma, which can exceed 0.1. Furthermore, the enzyme has a preferential affinity for topoisomers containing Z-DNA segments and relaxes these molecules, presumably by cleavage external to the inserts. Thus, a potentially functional relationship between topoisomerase II, an enzyme regulating the topological state of DNA-chromatin in vivo, and left-handed Z-DNA, a conformation stabilized by negative supercoiling, has been established.     

DNA wrapping in nucleosomes. The linking number problem re-examined.

Chromatin was assembled in vitro from relaxed closed circular DNA (SV40) and core histones at histone to DNA ratios of 0.2 to 0.3 (g/g) and incubated with topoisomerase I to relax supercoils in DNA regions not constrained by protein. Addition of histones H1 + H5 to the chromatin at an ionic strength of 0.1 M, in the presence of the solubilizing agent, polyglutamic acid, and topoisomerase I, increased the magnitude of the DNA linking number change, relative to protein-free DNA. No change in the linking number distribution occurred for relaxed protein-free DNA under these conditions. Control experiments indicated that the increase in the absolute value of the DNA linking number change in the chromatin could not be attributed to an increase in the number of nucleosomes per DNA molecule. These data suggest a solution to the linking number problem associated with models of chromatin structure.     

Computer simulation of DNA supercoiling

We treat supercoiled DNA within a wormlike model with excluded volume. A modified Monte Carlo approach has been used, which allowed computer statistical-mechanical simulations of moderately and highly supercoiled DNA molecules. Even highly supercoiled molecules do not have a regular shape, though with an increase in writhing the chains look more and more like branched interwound helixes. The averaged writhing (Wr) approximately 0.7 delta Lk. The superhelical free energy F is calculated as a function of the linking number. Lk. The calculations have shown that the generally accepted quadratic dependence of F on Lk is valid for a variety of conditions, though it is by no means universal. Significant deviations from the quadratic dependence are expected at high superhelical density under ionic conditions where the effective diameter of DNA is small. The results are compared with the available experimental data.     

Linkage reduction allows reconstitution of nucleosomes on DNA microdomains

We have established an experimental system for reconstitution of an individual nucleosome on a closed DNA microdomain (operationally defined as a DNA domain of a size so small as to be unable to establish titratable superhelical turns). The microdomain (185 base-pairs (bp), composed of 128 bp encompassing the central part of the Saccharomyces cerevisiae ADH II promoter plus 57 bp of a polylinker) was obtained by ligation under conditions that produced three circularized forms characterized by different linkage numbers. These linkomers were tested for nucleosome reconstitution with S. cerevisiae histones. It was observed that only microcircles with linkage reduction (delta Lk = 1 or 2) could form a nucleosome, as defined by protection of a 145(+/- 2) bp DNA fragment from micrococcal nuclease, relaxed forms (open or closed circles) could not.     

Structural dynamics of nucleosome core particle: comparison with nucleosomes containing histone variants

The present study provides insights on the dominant mechanisms of motions of the nucleosome core particle and the changes in its functional dynamics in response to histone variants. Comparative analysis of the global dynamics of nucleosomes with native and variant H2A histones, using normal mode analysis revealed that the dynamics of the nucleosome is highly symmetric, and its interaction with the nucleosomal DNA plays a vital role in its regulation. The collective dynamics of nucleosomes are predicted to be dominated by two types of large-scale motions: (1) a global stretching-compression of nucleosome along the dyad axis by which the nucleosome undergoes a breathing motion with a massive distortion of nucleosomal DNA, modulated by histone-DNA interactions; and (2) the flipping (or bending) of both the sides of the nucleosome in an out-of-plane fashion with respect to the dyad axis, originated by the highly dynamic N-termini of H3 and (H2A.Z-H2B) dimer in agreement with the experimentally observed perturbed dynamics of the particular N-terminus under physiological conditions. In general, the nucleosomes with variant histones exhibit higher mobilities and weaker correlations between internal motions compared to the nucleosome containing ordinary histones. The differences are more pronounced at the L1 and L2 loops of the respective monomers H2B and H2A, and at the N-termini of the monomers H3 and H4, all of which closely interact with the wrapping DNA.     

DNA Topological Context Affects Access to Eukaryotic DNA Topoisomerase I

Abstract

We have analyzed the reactivity of a 217 base pair segment of the intrinsically curved Crithidia fasciculata kinetoplast DNA towards eukaryotic DNA topoisomerase I. The substrates were open [linear fragment and nicked circle] and closed minidomains [closed relaxed circle and circles with linking differences of ?1 and ?2], We interpreted the results with the aid of a model that was used to predict the structures of the topoisomers. The modelling shows that the ΔLk(?l) form is unusually compact because of the curvature in the DNA. To determine the role of sequence-directed curvature in both the experimental and modeling studies, controls were examined in which the curved Crithidia sequence was replaced by an uncurved sequence obtained from the plasmid pBR322.

Reactivity of the Crithidia DNA [as analyzed both by the cleavage and the topoisomerization reactions] markedly varied among the DNA forms: (i) the hierarchy of overall reactivity observed is: linear fragment > nicked circular, closed circular [ΔLk(O)], interwound [ΔLk(?2)] > bent interwound [ΔLk(?l)]; (ii) the intensity of several cleavage positions differs among DNA forms.

The results show that eukaryotic DNA topoisomerase I is very sensitive to the conformation of the substrates and that its reactivity is modulated by the variation of the compactness of the DNA molecule. The C. fasciculata sequence contains a highly curved segment that determines the conformation of the closed circle in a complex way.     

Energetics of DNA twisting. II. Topoisomer analysis

A gel electrophoresis method has been developed for resolving small (approximately equal to 250 bp DNA topoisomers. In this size range only one major topoisomer band is observed, except for ligase closure conditions in which the probabilities are nearly equal for circularization by untwisting and overtwisting the corresponding linear DNA. The two probabilities are nearly equal when delta Tw is close to 0.5, if the mean helical twist of the linear DNA is n + delta Tw, where n is an integer and delta Tw is the fractional twist. We determine delta Tw of the linear DNA in standard conditions (20 degrees C, no ethidium) by titration experiments in which delta Tw is varied at the time of ligase closure, either by changing temperature or ethidium concentration. The endpoint (delta Tw = 0.5) is found when the two topoisomers formed by untwisting and overtwisting are present at equal concentrations. This analysis assumes that the net writhe is zero and the DNA helix is isotropically bendable. The results confirm the analysis of cyclization probabilities given in the preceding paper: delta Tw = 0 at the two maxima in the curve of j-factor versus DNA length and delta Tw = 0.5 at the minimum. Consequently, we can determine the DNA lengths at which Tw takes on integral values and use them to measure precisely the average helix repeat. From the difference between the delta Tw values of DNAs with 237 and 247 bp, we obtain an approximate value for the helix repeat of h = 10.4 +/- 0.1 bp/turn, in good agreement with earlier values found by the band-shift and nuclease-cutting methods. The twist is integral at 250.8 +/- 0.4 bp and from h = 10.4 +/- 0.1 we find n = 24; then 250.8/24 gives h = 10.45 +/- 0.02 bp/turn. The mean linking number (Lk) changes in a stepwise manner as delta Tw is varied for 250 bp DNAs. This result is expected when the free energy of twisting half a turn becomes large compared to thermal fluctuations. In these experiments, it is possible to obtain the mean Tw value from the mean Lk value only when delta Tw = 0.5, and consequently the mean Lk value is not simply related to DNA length for 250 bp DNAs except when delta Tw = 0.5.(ABSTRACT TRUNCATED AT 400 WORDS)