The intrinsic curvature of DNA in solution

We propose a detailed quantitative scheme for explaining the anomalous electrophoretic mobility in polyacrylamide gels of repeating sequence DNA. We assume that such DNA adopts a superhelical configuration in these circumstances, and migrates less quickly than straight DNA of the same length because it can only pass through larger holes. The retardation is maximal when the length of the DNA reaches one superhelical turn, but is less for shorter pieces. We attribute the curvature of the superhelix to different angles of roll at each kind of dinucleotide step, i.e. an opening up of an angle by an increased separation on the minor-groove side. The main effect is due to a difference of about 3 degrees in roll values between AA/TT and other steps, together with a difference of about 1 degree in the angle of helical twist: we deduce these values explicitly from some of the available data on gel-running. The scheme involves a simple calculation of the superhelical parameters for any given repeating sequence, and it gives a good correlation with all of the available data. We argue that these same base-step angular parameters are also consistent with observations from X-ray diffraction of crystallized oligomers, and particularly with the recent data on CGCA6GCG from Nelson et al. We are concerned here with the intrinsic curvature of unconstrained DNA, as distinct from the curvature of DNA in association with protein molecules; and this paper represents a first attempt at an absolute determination.     

Bending and curvature calculations in B-DNA.

A simple program, BEND, has been written to calculate the magnitude of local bending and macroscopic curvature at each point along an arbitrary B-DNA sequence, using any desired bending model that specifies values of twist, roll and tilt as a function of sequence. The program has been used to evaluate six different DNA bending models in three categories. Two are bent non-A-tract models: (a) A new model based on the nucleosome positioning data of Satchwell et al 1986 (J. Mol. Biol. 191, 659-675), (b) The model of Calladine et al 1988 (J. Mol. Biol. 201, 127-137). Three are bent A-tract models: (c) The wedge model of Bolshoy et al 1991 (Proc. Natl. Acad. Sci. USA 88, 2312-2316), (d) The model of Cacchione et al 1989 (Biochem. 28, 8706-8713), (e) A reversed version of model (b). The last is a junction model: (f) The model of Koo & Crothers 1988 (Proc. Natl. Acad. Sci. USA 85, 1763-1767). Although they have widely different assumptions and values for twist, roll and tilt, all six models correctly predict experimental A-tract curvature as measured by gel retardation and cyclization kinetics, but only the new nucleosome positioning model is successful in predicting curvature in regions containing phased GGGCCC sequences. This model--showing local bending at mixed sequence DNA, strong bends at the sequence GGC, and straight, rigid A-tracts--is the only model consistent with both solution data from gel retardation and cyclization kinetics and structural data from x-ray crystallography.     

Comparison of analyses of DNA curvature

Popular programs for characterizing DNA structure include Curves 5.1 (Lavery, R. and Sklenar, H., J. Biomol. Struct. Dyn. 6, 63-91, 1988; Lavery, R. and Sklenar, H., J. Biomol. Struct. Dyn. 6, 655-67, 1989) and Freehelix98 (Dickerson, R. E., Nucleic Acids Res. 26, 1906-1926, 1998), along with the more recent 3DNA (X. J. Lu, Z. Shakked and W. K. Olson., J. Mol. Biol. 300, 819-840 (2000). Given input of structural coordinates, all of these programs return values of the local helical parameters, such as roll, tilt, twist, etc. The first two programs also provide characterization of global curvature. Madbend (Strahs, D. and Schlick, T., J. Mol. Biol. 301, 643-663, 2000), a program that computes global curvature from local roll, tilt, and twist parameters, can be applied to the output of all three structural programs. We have compared the curvature predicted by the three programs with and without the use of Madbend. Global bend magnitudes and directions as well as values of helical kinks were calculated for four high-resolution DNA structures and four model DNA helices. Global curvature determined by Curves 5.1 without Madbend was found to differ from values obtained using Freehelix98 with or without Madbend or 3DNA and Curves 5.1 with Madbend. Using model helices, this difference was attributed the fact that Curves 5.1 is the only program sensitive to changes in axial displacement, such as shift and slide. Madbend produced robust values of bend magnitude and direction, and displayed little sensitivity to axis displacement or the source of local helical parameters. Madbend also appears to be the method of choice for bending comparisons of high-resolution structures with results from cyclization kinetics, a method that measures DNA curvature as a vectorial sum of local roll and tilt angles.     

DNA bending: the prevalence of kinkiness and the virtues of normality.

DNA bending in 86 complexes with sequence-specific proteins has been examined using normal vector plots, matrices of normal vector angles between all base pairs in the helix, and one-digit roll/slide/twist tables. FREEHELIX, a new program especially designed to analyze severely bent and kinked duplexes, generates the foregoing quantities plus local roll, tilt, twist, slide, shift and rise parameters that are completely free of any assumptions about an overall helix axis. In nearly every case, bending results from positive roll at pyrimidine-purine base pair steps: C-A (= T-G), T-A, or less frequently C-G, in a direction that compresses the major groove. Normal vector plots reveal three well-defined types of bending among the 86 examples: (i) localized kinks produced by positive roll at one or two discrete base pairs steps, (ii) three-dimensional writhe resulting from positive roll at a series of adjacent base pairs steps, or (iii) continuous curvature produced by alternations of positive and negative roll every 5 bp, with side-to-side zig-zag roll at intermediate position. In no case is tilt a significant component of the bending process. In sequences with two localized kinks, such as CAP and IHF, the dihedral angle formed by the three helix segments is a linear function of the number of base pair steps between kinks: dihedral angle = 36 degrees x kink separation. Twenty-eight of the 86 examples can be described as major bends, and significant elements in the recognition of a given base sequence by protein. But even the minor bends play a role in fine-tuning protein/DNA interactions. Sequence-dependent helix deformability is an important component of protein/DNA recognition, alongside the more generally recognized patterns of hydrogen bonding. The combination of FREEHELIX, normal vector plots, full vector angle matrices, and one-digit roll/slide/twist tables affords a rapid and convenient method for assessing bending in DNA.     

DNA Sequence-Directed Organization of Chromatin: Structure-Based Computational Analysis of Nucleosome-Binding Sequences

The folding of DNA on the nucleosome core particle governs many fundamental issues in eukaryotic molecular biology. In this study, an updated set of sequence-dependent empirical “energy” functions, derived from the structures of other protein-bound DNA molecules, is used to investigate the extent to which the architecture of nucleosomal DNA is dictated by its underlying sequence. The potentials are used to estimate the cost of deforming a collection of sequences known to bind or resist uptake in nucleosomes along various left-handed superhelical pathways and to deduce the features of sequence contributing to a particular structural form. The deformation scores reflect the choice of template, the deviations of structural parameters at each step of the nucleosome-bound DNA from their intrinsic values, and the sequence-dependent “deformability” of a given dimer. The correspondence between the computed scores and binding propensities points to a subtle interplay between DNA sequence and nucleosomal folding, e.g., sequences with periodically spaced pyrimidine-purine steps deform at low cost along a kinked template whereas sequences that resist deformation prefer a smoother spatial pathway. Successful prediction of the known settings of some of the best-resolved nucleosome-positioning sequences, however, requires a template with “kink-and-slide” steps like those found in high-resolution nucleosome structures.     

Geometry of the nucleosomal DNA superhelix

Nucleosome stability is largely an indirect measure of DNA sequence based on the material properties of DNA and the ability of a sequence to assume the required left-handed superhelical conformation. Here we focus attention only on the geometry of the superhelix and present two distinct mathematical expressions that rely on the DNA helical parameters (Shift, Slide, Rise, Tilt, Roll, Twist). One representation requires torsion for superhelix formation; the other requires shear. To compare these mathematical expressions to experimental data we develop a strategy for Fourier-filtering the helical parameters that identifies necessary and sufficient conditions to achieve a high-resolution model of the nucleosome superhelix. We apply this filtering strategy to 24 high-resolution structures of the nucleosome and demonstrate that all structures have a highly conserved distribution of Roll, Slide and Twist that involves two length scales. One length scale spans the entire length of nucleosomal DNA. The other is associated with the helix repeat. Our strategy also enables us to identify ground state or simple nucleosomes and altered nucleosome structures. These results form a basis for characterizing structural variations in the emerging family of nucleosome structures and a method for further developing structure-based models of nucleosome stability.     

Kinking the double helix by bending deformation

DNA bending and torsional deformations that often occur during its functioning inside the cell can cause local disruptions of the regular helical structure. The disruptions created by negative torsional stress have been studied in detail, but those caused by bending stress have only been analyzed theoretically. By probing the structure of very small DNA circles, we determined that bending stress disrupts the regular helical structure when the radius of DNA curvature is smaller than 3.5 nm. First, we developed an efficient method to obtain covalently closed DNA minicircles. To detect structural disruptions in the minicircles we treated them by single-strand-specific endonucleases. The data showed that the regular DNA structure is disrupted by bending deformation in the 64–65-bp minicircles, but not in the 85–86-bp minicircles. Our results suggest that strong DNA bending initiates kink formation while preserving base pairing.     

A novel roll-and-slide mechanism of DNA folding in chromatin: implications for nucleosome positioning

How eukaryotic genomes encode the folding of DNA into nucleosomes and how this intrinsic organization of chromatin guides biological function are questions of wide interest. The physical basis of nucleosome positioning lies in the sequence-dependent propensity of DNA to adopt the tightly bent configuration imposed by the binding of the histone proteins. Traditionally, only DNA bending and twisting deformations are considered, while the effects of the lateral displacements of adjacent base pairs are neglected. We demonstrate, however, that these displacements have a much more important structural role than ever imagined. Specifically, the lateral Slide deformations observed at sites of local anisotropic bending of DNA define its superhelical trajectory in chromatin. Furthermore, the computed cost of deforming DNA on the nucleosome is sequence-specific: in optimally positioned sequences the most easily deformed base-pair steps (CA:TG and TA) occur at sites of large positive Slide and negative Roll (where the DNA bends into the minor groove). These conclusions rest upon a treatment of DNA that goes beyond the conventional ribbon model, incorporating all essential degrees of freedom of "real" duplexes in the estimation of DNA deformation energies. Indeed, only after lateral Slide displacements are considered are we able to account for the sequence-specific folding of DNA found in nucleosome structures. The close correspondence between the predicted and observed nucleosome locations demonstrates the potential advantage of our "structural" approach in the computer mapping of nucleosome positioning.     

Principles of sequence-dependent flexure of DNA

The curvature of a bent rod may be defined in several different, but equivalent ways. The best way of describing the curvature of double-helical DNA is by an angle of turning per base step. Curvature comes mainly from the angle of roll between successive base-pairs, and this is defined as positive when the angle opens up on the minor groove side of the bases. DNA forms a plane curve if the roll angle values along the molecule alternate periodically between positive and negative, with a complete period equal to the helical repeat. It is known from studies of crystallized oligomers that the roll angles for particular dinucleotide steps have preferred values, or lie in preferred ranges of values. Therefore the formation of a plane curve will be easier with some base sequences of DNA than with others. We set up a computer algorithm for determining the ease with which DNA of given sequence will adopt a curved form. The algorithm has two different sets of constants: in model 1 the base step parameters come from an inspection of crystallized oligomers, and in model 2 data from a statistical survey of the incidence of dinucleotide steps in a large number of samples of chicken erythrocyte core DNA is incorporated. Both forms of the algorithm successfully locate the dyad of the nucleosome sequence (modulo 10) in a frog gene, and suggest strongly that sequence-dependent flexural properties of DNA play a part in the recognition of binding sites by nucleosome cores.     

Nucleosome “phasing” and cruciform structures in circular supercoiled pBR322 DNA

Cruciform structures have been detected in pBR322 supercoiled DNA, both in its naked state and when complexed with histone octamer, using S1 endonuclease cleavage and EcoRI restriction. An inspection of the DNA sequence shows that the S1-hypersensitive sites are very near to AT-rich regions of pBR322 genome. A nucleosome “phasing” in these regions, as found on AT-rich regions of SV40 DNA (15), has been shown by restriction enzymes analysis. On the basis of these results it can be proposed that cruciform structures protrude on the nucleosome surface. This model explains the reason why these structures, which need high superhelical density, can exist in supercoiled DNA partially relaxed by nucleosome formation.     

Structure of the nucleosome core particle at 8 A resolution

The x-ray crystallographic structure of the nucleosome core particle has been determined using 8 A resolution diffraction data. The particle has a mean diameter of 106 A and a maximum thickness of 65 A in the superhelical axis direction. The longest chord through the histone core measures 85 A and is in a non-axial direction. The 1.87 turn superhelix consists of B-DNA with about 78 base pairs or 7.6 helical repeats per superhelical turn. The mean DNA helical repeat contains 10.2 +/- 0.05 base pairs and spans 35 A, slightly more than standard B-DNA. The superhelix varies several Angstroms in radius and pitch, and has three distinct domains of curvature (with radii of curvature of 60, 45 and 51 A). These regions are separated by localized sharper bends +/- 10 and +/- 40 base pairs from the center of the particle, resulting in an overall radius of curvature about 43 A. Compression of superhelical DNA grooves on the inner surface and expansion on the outer surface can be seen throughout the DNA electron density. This density has been fit with a double helical ribbon model providing groove width estimates of 12 +/- 1 A inside vs. 19 +/- 1 A outside for the major groove, and 8 +/- 1 A inside vs. 13 +/- 1 A outside for the minor groove. The histone core is primarily contained within the bounds defined by the superhelical DNA, contacting the DNA where the phosphate backbone faces in toward the core. Possible extensions of density between the gyres have been located, but these are below the significance level of the electron density map. In cross-section, a tripartite organization of the histone octamer is apparent, with the tetramer occupying the central region and the dimers at the extremes. Several extensions of histone density are present which form contacts between nucleosomes in the crystal, perhaps representing flexible or "tail" histone regions. The radius of gyration of the histone portion of the electron density is calculated to be 30.4 A (in reasonable agreement with solution scattering values), and the histone core volume in the map is 93% of its theoretical volume.     

Structural flexibility of the nucleosome core particle at atomic resolution studied by molecular dynamics simulation

Comparative explicit solvent molecular dynamics (MD) simulations have been performed on a complete nucleosome core particle with and without N-terminal histone tails for more than 20 ns. Main purpose of the simulations was to study the dynamics of mobile elements such as histone N-terminal tails and how packing and DNA-bending influences the fine structure and dynamics of DNA. Except for the tails, histone and DNA molecules stayed on average close to the crystallographic start structure supporting the quality of the current force field approach. Despite the packing strain, no increase of transitions to noncanonical nucleic acid backbone conformations compared to regular B-DNA was observed. The pattern of kinks and bends along the DNA remained close to the experiment overall. In addition to the local dynamics, the simulations allowed the analysis of the superhelical mobility indicating a limited relative mobility of DNA segments separated by one superhelical turn (mean relative displacement of approximately +/-0.2 nm, mainly along the superhelical axis). An even higher rigidity was found for relative motions (distance fluctuations) of segments separated by half a superhelical turn (approximately +/-0.1 nm). The N-terminal tails underwent dramatic conformational rearrangements on the nanosecond time scale toward partially and transiently wrapped states around the DNA. Many of the histone tail changes corresponded to coupled association and folding events from fully solvent-exposed states toward complexes with the major and minor grooves of DNA. The simulations indicate that the rapid conformational changes of the tails can modulate the DNA accessibility within a few nanoseconds.     

Computer Analysis of Conformational and Physicochemical Properties of Nucleotide Sequences Cleavable by DNA Topoisomerase I

DNA binding with enzymes is followed by specific adaptation of the DNA structure, including partial or almost complete melting, structural changes in the sugar-phosphate backbone, stretching, compressing, bending or kinking, base flipping, etc. The set of conformational changes is individual for each enzyme and is aimed at efficiently adjusting the orbitals of the reacting groups of the enzyme and the specific DNA site to 10°–15°. The efficiency of nucleotide sequence adaptation determined by the enzyme depends on several structural characteristics. Optimal adjustment is achieved only in the case of specific DNA sequences; as a result, the reaction rate is four to eight orders of magnitude higher with specific than with nonspecific sequences. DNA topoisomerase I (Topo) is a sequence-dependent enzyme. Although less efficiently, Topo cleaves sequences which differ considerably from the optimal sequence. A method based on the analysis of conformational and physicochemical properties of the DNA helix was used to examine many nucleotide sequences cleavable by Topo. The method yields detailed information on similarity or difference of DNA structural units. The cleavable sequences proved to be similar in roll, slide, twist, and rise. In addition, all sequences had sterically disadvantageous contacts between N3 and NH₂ of guanines and N3 of adenines in the minor groove, which corresponded to the presence of dinucleotides Py-Pu in the cleavage site. DNA bending towards the major groove is easier in the case of the optimal sequence. This method is promising for analyzing the efficiency of nucleic acid cleavage by various DNA- and RNA-dependent enzymes.__________Translated from Molekulyarnaya Biologiya, Vol. 39, No. 3, 2005, pp. 488–496.Original Russian Text Copyright © 2005 by Oshchepkov, Bugreev, Kolchanov, Nevinsky.     

Evidence for opposite groove-directed curvature of GGGCCC and AAAAA sequence elements.

The repetitive sequence (AGGGCCCTAGAGGGGCCC-TAG)n was previously shown to be curved by gel mobility assays. Here we show, using hydroxy radical/DNase I digestion and differential helical phasing experiments that the curvature is directed towards the major groove and is located in the GGGCCC, but not the CTAGAG segments. The effect of the GC step in the context of the GGGCCC motif is apparently about as large as that of AA/TT, i.e. enough to cancel the macroscopic curvature of helically phased A-tracts. These data are in agreement with positive roll-like curvature of the GCC/GGC motif, predicted from nucleosome packing data and the 3D structure of the GGGGCCCC octamer, but they are not in agreement with the dinucleotide-based roll angle values predicted for AG/CT, TA, GG/CC and GC steps. Our results thus indicate the importance of interactions beyond the dinucleotide steps in predictive models of DNA curvature.     

Local sequential minimization of double stranded B-DNA using Monte Carlo annealing

A software algorithm has been developed to investigate the folding process in B-DNA structures in vacuum under a simple and accurate force field. This algorithm models linear double stranded B-DNA sequences based on a local, sequential minimization procedure. The original B-DNA structures were modeled using initial nucleotide structures taken from the Brookhaven database. The models contain information at the atomic level allowing one to investigate as accurately as possible the structure and characteristics of the resulting DNA structures. A variety of DNA sequences and sizes were investigated containing coding and non-coding, random and real, homogeneous or heterogeneous sequences in the range of 2 to 40 base pairs. The force field contains terms such as angle bend, Lennard-Jones, electrostatic interactions and hydrogen bonding which are set up using the Dreiding II force field and defined to account for the helical parameters such as twist, tilt and rise. A close comparison was made between this local minimization algorithm and a global one (previously published) in order to find out advantages and disadvantages of the different methods. From the comparison, this algorithm gives better and faster results than the previous method, allowing one to minimize larger DNA segments. DNA segments with a length of 40 bases need approximately 4 h, while 2.5 weeks are needed with the previous method. After each minimization the angles between phosphate–oxygen-carbon A₁, the oxygen–phosphate–oxygen A₂ and the average helical twists were calculated. From the generated fragments it was found that the bond angles are A₁=150°±2°and A₂=130°±10°, while the helical twist is 36.6°±2° in the A strand and A₁=150°±6° and A₂=130±6° with helical twist 39.6°±2° in the B strand for the DNA segment with the same sequence as the Dickerson dodecamer.Figure The final minimized DNA segment of the Dickerson dodecamer sequence represented by ball drawings and viewed (left) perpendicular and (right) down the helical axis     

Unpaired structures in SCA10 (ATTCT)n.(AGAAT)n repeats

A number of human hereditary diseases have been associated with the instability of DNA repeats in the genome. Recently, spinocerebellar ataxia type 10 has been associated with expansion of the pentanucleotide repeat (ATTCT)(n).(AGAAT)(n) from a normal range of ten to 22 to as many as 4500 copies. The structural properties of this repeat cloned in circular plasmids were studied by a variety of methods. Two-dimensional gel electrophoresis and atomic force microscopy detected local DNA unpairing in supercoiled plasmids. Chemical probing analysis indicated that, at moderate superhelical densities, the (ATTCT)(n).(AGAAT)(n) repeat forms an unpaired region, which further extends into adjacent A+T-rich flanking sequences at higher superhelical densities. The superhelical energy required to initiate duplex unpairing is essentially length-independent from eight to 46 repeats. In plasmids containing five repeats, minimal unpairing of (ATTCT)(5).(AGAAT)(5) occurred while 2D gel analysis and chemical probing indicate greater unpairing in A+T-rich sequences in other regions of the plasmid. The observed experimental results are consistent with a statistical mechanical, computational analysis of these supercoiled plasmids. For plasmids containing 29 repeats, which is just above the normal human size range, flanked by an A+T-rich sequence, atomic force microscopy detected the formation of a locally condensed structure at high superhelical densities. However, even at high superhelical densities, DNA strands within the presumably compact A+T-rich region were accessible to small chemicals and oligonucleotide hybridization. Thus, DNA strands in this "collapsed structure" remain unpaired and accessible for interaction with other molecules. The unpaired DNA structure functioned as an aberrant replication origin, in that it supported complete plasmid replication in a HeLa cell extract. A model is proposed in which unscheduled or aberrant DNA replication is a critical step in the expansion mutation.     

Characteristics of nucleosome core DNA and their applications in predicting nucleosome positions

By analyzing dinucleotide position-frequency data of yeast nucleosome-bound DNA sequences, dinucleotide periodicities of core DNA sequences were investigated. Within frequency domains, weakly bound dinucleotides (AA, AT, and the combinations AA-TT-TA and AA-TT-TA-AT) present doublet peaks in a periodicity range of 10-11 bp, and strongly bound dinucleotides present a single peak. A time-frequency analysis, based on wavelet transformation, indicated that weakly bound dinucleotides of core DNA sequences were spaced smaller (∼10.3 bp) at the two ends, with larger (∼11.1 bp) spacing in the middle section. The finding was supported by DNA curvature and was prevalent in all core DNA sequences. Therefore, three approaches were developed to predict nucleosome positions. After analyzing a 2200-bp DNA sequence, results indicated that the predictions were feasible; areas near protein-DNA binding sites resulted in periodicity profiles with irregular signals. The effects of five dinucleotide patterns were evaluated, indicating that the AA-TT pattern exhibited better performance. A chromosome-scale prediction demonstrated that periodicity profiles perform better than previously described, with up to 59% accuracy. Based on predictions, nucleosome distributions near the beginning and end of open reading frames were analyzed. Results indicated that the majority of open reading frames’ start and end sites were occupied by nucleosomes.