The contribution of phosphate-phosphate repulsions to the free energy of DNA bending

DNA bending is important for the packaging of genetic material, regulation of gene expression and interaction of nucleic acids with proteins. Consequently, it is of considerable interest to quantify the energetic factors that must be overcome to induce bending of DNA, such as base stacking and phosphate–phosphate repulsions. In the present work, the electrostatic contribution of phosphate–phosphate repulsions to the free energy of bending DNA is examined for 71 bp linear and bent-form model structures. The bent DNA model was based on the crystallographic structure of a full turn of DNA in a nucleosome core particle. A Green's function approach based on a linear-scaling smooth conductor-like screening model was applied to ascertain the contribution of individual phosphate–phosphate repulsions and overall electrostatic stabilization in aqueous solution. The effect of charge neutralization by site-bound ions was considered using Monte Carlo simulation to characterize the distribution of ion occupations and contribution of phosphate repulsions to the free energy of bending as a function of counterion load. The calculations predict that the phosphate–phosphate repulsions account for ~30% of the total free energy required to bend DNA from canonical linear B-form into the conformation found in the nucleosome core particle.     

Structural Mechanics of DNA Wrapping in the Nucleosome

Experimental X-ray crystal structures and a database of calculated structural parameters of DNA octamers were used in combination to analyse the mechanics of DNA bending in the nucleosome core complex. The 1kx5 X-ray crystal structure of the nucleosome core complex was used to determine the relationship between local structure at the base-step level and the global superhelical conformation observed for nucleosome-bound DNA. The superhelix is characterised by a large curvature (597°) in one plane and very little curvature (10°) in the orthogonal plane. Analysis of the curvature at the level of 10-step segments shows that there is a uniform curvature of 30° per helical turn throughout most of the structure but that there are two sharper kinks of 50° at ± 2 helical turns from the central dyad base pair. The curvature is due almost entirely to the base-step parameter roll. There are large periodic variations in roll, which are in phase with the helical twist and account for 500° of the total curvature. Although variations in the other base-step parameters perturb the local path of the DNA, they make minimal contributions to the total curvature. This implies that DNA bending in the nucleosome is achieved using the roll-slide-twist degree of freedom previously identified as the major degree of freedom in naked DNA oligomers. The energetics of bending into a nucleosome-bound conformation were therefore analysed using a database of structural parameters that we have previously developed for naked DNA oligomers. The minimum energy roll, the roll flexibility force constant and the maximum and minimum accessible roll values were obtained for each base step in the relevant octanucleotide context to account for the effects of conformational coupling that vary with sequence context. The distribution of base-step roll values and corresponding strain energy required to bend DNA into the nucleosome-bound conformation defined by the 1kx5 structure were obtained by applying a constant bending moment. When a single bending moment was applied to the entire sequence, the local details of the calculated structure did not match the experiment. However, when local 10-step bending moments were applied separately, the calculated structure showed excellent agreement with experiment. This implies that the protein applies variable bending forces along the DNA to maintain the superhelical path required for nucleosome wrapping. In particular, the 50° kinks are constraints imposed by the protein rather than a feature of the 1kx5 DNA sequence. The kinks coincide with a relatively flexible region of the sequence, and this is probably a prerequisite for high-affinity nucleosome binding, but the bending strain energy is significantly higher at these points than for the rest of the sequence. In the most rigid regions of the sequence, a higher strain energy is also required to achieve the standard 30° curvature per helical turn. We conclude that matching of the DNA sequence to the local roll periodicity required to achieve bending, together with the increased flexibility required at the kinks, determines the sequence selectivity of DNA wrapping in the nucleosome.     

Species-specific patterns of DNA bending and sequence.

Nucleotide sequences in the GenEMBL database were analyzed using strategies designed to reveal species-specific patterns of DNA bending and DNA sequence. The results uncovered striking species-dependent patterns of bending with more variations among individual organisms than between prokaryotes and eukaryotes. The frequency of bent sites in sequences from different bacteria was related to genomic A + T content and this relationship was confirmed by electrophoretic analysis of genomic DNA. However, base composition was not an accurate predictor for DNA bending in eukaryotes. Sequences from C. elegans exhibited the highest frequency of bent sites in the database and the RNA polymerase II locus from the nematode was the most bent gene in GenEMBL. Bent DNA extended throughout most introns and gene flanking segments from C.elegans while exon regions lacked A-tract bending characteristics. Independent evidence for the strong bending character of this genome was provided by electrophoretic studies which revealed that a large number of the fragments from C.elegans DNA exhibited anomalous gel mobilities when compared to genomic fragments from over 20 other organisms. The prevalence of bent sites in this genome enabled us to detect selectively C.elegans sequences in a computer search of the database using as probes C.elegans introns, bending elements, and a 20 nucleotide consensus sequence for bent DNA. This approach was also used to provide additional examples of species-specific sequence patterns in eukaryotes where it was shown that (A) greater than or equal to 10 and (A.T) greater than or equal to 5 tracts are prevalent throughout the untranslated DNA of D.discodium and P.falciparum, respectively. These results provide new insight into the organization of eukaryotic DNA because they show that species-specific patterns of simple sequences are found in introns and in other untranslated regions of the genome.     

Using DNA mechanics to predict in vitro nucleosome positions and formation energies

In eukaryotic genomes, nucleosomes function to compact DNA and to regulate access to it both by simple physical occlusion and by providing the substrate for numerous covalent epigenetic tags. While competition with other DNA-binding factors and action of chromatin remodeling enzymes significantly affect nucleosome formation in vivo, nucleosome positions in vitro are determined by steric exclusion and sequence alone. We have developed a biophysical model, DNABEND, for the sequence dependence of DNA bending energies, and validated it against a collection of in vitro free energies of nucleosome formation and a set of in vitro nucleosome positions mapped at high resolution. We have also made a first ab initio prediction of nucleosomal DNA geometries, and checked its accuracy against the nucleosome crystal structure. We have used DNABEND to design both strong and weak histone- binding sequences, and measured the corresponding free energies of nucleosome formation. We find that DNABEND can successfully predict in vitro nucleosome positions and free energies, providing a physical explanation for the intrinsic sequence dependence of histone–DNA interactions.     

Anisotropic flexibility of DNA and the nucleosomal structure.

Potential energy calculations of the DNA duplex dimeric subunit show that the double helix may be bent in the direction of minor and major grooves much more easily than in other directions. It is found that the total winding angle of DNA decreases upon such bending. A new model for DNA folding in the nucleosome is proposed on the basis of these findings according to which the DNA molecule is kinked each fifth base pair to the side of the minor and major grooves alternatively. The model explains the known contradiction between a C-like circular dichroism for the nucleosomal DNA and the nuclease digestion data, which testify to the B-form of DNA.     

Probing the Elasticity of DNA on Short Length Scales by Modeling Supercoiling under Tension

The wormlike-chain (WLC) model is widely used to describe the energetics of DNA bending. Motivated by recent experiments, alternative, so-called subelastic chain models were proposed that predict a lower elastic energy of highly bent DNA conformations. Until now, no unambiguous verification of these models has been obtained because probing the elasticity of DNA on short length scales remains challenging. Here we investigate the limits of the WLC model using coarse-grained Monte Carlo simulations to model the supercoiling of linear DNA molecules under tension. At a critical supercoiling density, the DNA extension decreases abruptly due to the sudden formation of a plectonemic structure. This buckling transition is caused by the large energy required to form the tightly bent end-loop of the plectoneme and should therefore provide a sensitive benchmark for model evaluation. Although simulations based on the WLC energetics could quantitatively reproduce the buckling measured in magnetic tweezers experiments, the buckling almost disappears for the tested linear subelastic chain model. Thus, our data support the validity of a harmonic bending potential even for small bending radii down to 3.5 nm.     

DNA Sequence Explains Seemingly Disordered Methylation Levels in Partially Methylated Domains of Mammalian Genomes

For the most part metazoan genomes are highly methylated and harbor only small regions with low or absent methylation. In contrast, partially methylated domains (PMDs), recently discovered in a variety of cell lines and tissues, do not fit this paradigm as they show partial methylation for large portions (20%–40%) of the genome. While in PMDs methylation levels are reduced on average, we found that at single CpG resolution, they show extensive variability along the genome outside of CpG islands and DNase I hypersensitive sites (DHS). Methylation levels range from 0% to 100% in a roughly uniform fashion with only little similarity between neighboring CpGs. A comparison of various PMD-containing methylomes showed that these seemingly disordered states of methylation are strongly conserved across cell types for virtually every PMD. Comparative sequence analysis suggests that DNA sequence is a major determinant of these methylation states. This is further substantiated by a purely sequence based model which can predict 31% (R²) of the variation in methylation. The model revealed CpG density as the main driving feature promoting methylation, opposite to what has been shown for CpG islands, followed by various dinucleotides immediately flanking the CpG and a minor contribution from sequence preferences reflecting nucleosome positioning. Taken together we provide a reinterpretation for the nucleotide-specific methylation levels observed in PMDs, demonstrate their conservation across tissues and suggest that they are mainly determined by specific DNA sequence features.     

A determining influence for CpG dinucleotides on nucleosome positioning in vitro

DNA sequence information that directs the translational positioning of nucleosomes can be attenuated by cytosine methylation when a short run of CpG dinucleotides is located close to the dyad axis of the nucleosome. Here, we show that point mutations introduced to re-pattern methylation at the (CpG)₃ element in the chicken β^A-globin promoter sequence themselves strongly influenced nucleosome formation in reconstituted chromatin. The disruptive effect of cytosine methylation on nucleosome formation was found to be determined by the sequence context of CpG dinucleotides, not just their location in the positioning sequence. Additional mutations indicated that methylation can also promote the occupation of certain nucleosome positions. DNase I analysis demonstrated that these genetic and epigenetic modifications altered the structural characteristics of the (CpG)₃ element. Our findings support a proposal that the intrinsic structural properties of the DNA at the −1.5 site, as occupied by (CpG)₃ in the nucleosome studied, can be decisive for nucleosome formation and stability, and that changes in anisotropic DNA bending or flexibility at this site explain why nucleosome positioning can be exquisitely sensitive to genetic and epigenetic modification of the DNA sequence.     

Probing the elastic limit of DNA bending

Sharp bending of double-stranded DNA (dsDNA) plays an essential role in genome structure and function. However, the elastic limit of dsDNA bending remains controversial. Here, we measured the opening rates of small dsDNA loops with contour lengths ranging between 40 and 200 bp using single-molecule Fluorescence Resonance Energy Transfer. The relationship of loop lifetime to loop size revealed a critical transition in bending stress. Above the critical loop size, the loop lifetime changed with loop size in a manner consistent with elastic bending stress, but below it, became less sensitive to loop size, indicative of softened dsDNA. The critical loop size increased from ∼60 bp to ∼100 bp with the addition of 5 mM magnesium. We show that our result is in quantitative agreement with the kinkable worm-like chain model, and furthermore, can reproduce previously reported looping probabilities of dsDNA over the range between 50 and 200 bp. Our findings shed new light on the energetics of sharply bent dsDNA.     

Prediction of nucleosome rotational positioning in yeast and human genomes based on sequence-dependent DNA anisotropy

Background

An organism’s DNA sequence is one of the key factors guiding the positioning of nucleosomes within a cell’s nucleus. Sequence-dependent bending anisotropy dictates how DNA is wrapped around a histone octamer. One of the best established sequence patterns consistent with this anisotropy is the periodic occurrence of AT-containing dinucleotides (WW) and GC-containing dinucleotides (SS) in the nucleosomal locations where DNA is bent in the minor and major grooves, respectively. Although this simple pattern has been observed in nucleosomes across eukaryotic genomes, its use for prediction of nucleosome positioning was not systematically tested.

Results

We present a simple computational model, termed the W/S scheme, implementing this pattern, without using any training data. This model accurately predicts the rotational positioning of nucleosomes both in vitro and in vivo, in yeast and human genomes. About 65 – 75% of the experimentally observed nucleosome positions are predicted with the precision of one to two base pairs. The program is freely available at http://people.rit.edu/fxcsbi/WS_scheme/. We also introduce a simple and efficient way to compare the performance of different models predicting the rotational positioning of nucleosomes.

Conclusions

This paper presents the W/S scheme to achieve accurate prediction of rotational positioning of nucleosomes, solely based on the sequence-dependent anisotropic bending of nucleosomal DNA. This method successfully captures DNA features critical for the rotational positioning of nucleosomes, and can be further improved by incorporating additional terms related to the translational positioning of nucleosomes in a species-specific manner.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-313) contains supplementary material, which is available to authorized users.     

Nucleosomes protect DNA from DNA methylation in vivo and in vitro

Positioned nucleosomes limit the access of proteins to DNA. However, the impact of nucleosomes on DNA methylation in vitro and in vivo is poorly understood. Here, we performed a detailed analysis of nucleosome binding and nucleosomal DNA methylation by the de novo methyltransferases. We show that compared to linker DNA, nucleosomal DNA is largely devoid of CpG methylation. ATP-dependent chromatin remodelling frees nucleosomal CpG dinucleotides and renders the remodelled nucleosome a 2-fold better substrate for Dnmt3a methyltransferase compared to free DNA. These results reflect the situation in vivo, as quantification of nucleosomal DNA methylation levels in HeLa cells shows a 2-fold decrease of nucleosomal DNA methylation levels compared to linker DNA. Our findings suggest that nucleosomal positions are stably maintained in vivo and nucleosomal occupancy is a major determinant of global DNA methylation patterns in vivo.     

Direct measurements of the nucleosome-forming preferences of periodic DNA motifs challenge established models

Several periodic motifs have been implicated in facilitating the bending of DNA around the histone core of the nucleosome. For example, di-nucleotides AA/TT/TA and GC at ∼10-bp periods, but offset by 5 bp, are found with higher-than-expected occurrences in aligned nucleosomal DNAs in vitro and in vivo. Additionally, regularly oscillating period-10 trinucleotide motifs non-T, A/T, G and their complements have been implicated in the formation of regular nucleosome arrays. The effects of these periodic motifs on nucleosome formation have not been systematically tested directly by competitive reconstitution assays. We show that, in general, none of these period-10 motifs, except TA, in certain sequence contexts, facilitates nucleosome formation. The influence of periodic TAs on nucleosome formation is appreciable; with some of the 200-bp DNAs out-competing bulk nucleosomal DNA by more than 400-fold. Only the nucleotides immediately flanking TA influence its nucleosome-forming ability. Period-10 TA, when flanked by a pair of permissive nucleotides, facilitates DNA bending through compression of the minor groove. The free energy change for nucleosome formation decreases linearly with the number of consecutive TAs, up to eight. We suggest how these data can be reconciled with previous findings.     

Sequence-dependent bending of DNA and phasing of nucleosomes

Conformational analysis has revealed anisotropic flexibility of the B-DNA double helix: it bends most easily into the grooves, being the most rigid when bent in a perpendicular direction. This result implies that DNA in a nucleosome is curved by means of relatively sharp bends ("mini-kinks") which are directed into the major and minor grooves alternatively and separated by 5-6 base pairs. The "mini-kink" model proved to be in keeping with the x-ray structure of the B-DNA dodecamer resolved later, which exhibits two "annealed kinks", also directed into the grooves. The anisotropy of B DNA is sequence-dependent: the pyrimidine-purine dimers (YR) favor bending into the minor groove, and the purine-pyrimidine dinucleotides (RY), into the minor one. The RR and YY dimers appear to be the most rigid dinucleotides. Thus, a DNA fragment consisting of the interchanging oligopurine and oligopyrimidine blocks 5-6 base pairs long should manifest a spectacular curvature in solution. Similarly, a nucleotide sequence containing the RY and YR dimers separated by a half-pitch of the double helix is the most suitable for wrapping around the nucleosomal core. Analysis of the numerous examples demonstrating the specific alignment of nucleosomes on DNA confirms this concept. So, the sequence-dependent "mechanical" properties of the double helix influence the spatial arrangement of DNA in chromatin.     

A computational study of nucleosomal DNA flexibility

Molecular dynamics simulations of the nucleosome core particle and its isolated DNA free in solution are reported. The simulations are based on the implicit solvent methodology and provide insights into the nature of large-scale structural fluctuations and flexibility of the nucleosomal DNA. In addition to the kinked regions previously identified in the x-ray structure of the nucleosome, the simulations support the existence of a biochemically identified distorted region of the DNA. Comparison of computed relative free energies shows that formation of the kinks is associated with little, if any, energy cost relative to a smooth, ideal conformation of the DNA superhelix. Isolated nucleosomal DNA is found to be considerably more flexible than expected for a 147 bp stretch of DNA based on its canonical persistence length of 500 A. Notably, the significant bending of the DNA observed in our simulations occurs without breaking of Watson-Crick bonds. The computed relative stability of bent conformations is sensitive to the ionic strength of the solution in the physiological range; the sensitivity suggests possible experiments that might provide further insights into the structural origins of the unusual flexibility of the DNA.