Sequence-dependent DNA helical rise and nucleosome stability
© Pedone and Santoni; licensee BioMed Central Ltd. 2009
Received: 26 June 2009
Accepted: 27 November 2009
Published: 27 November 2009
Nucleosomes are the basic structural units of eukaryotic chromatin and play a key role in regulation of gene expression. After resolution of the nucleosome structure, the bipartite nature of this particle has revealed itself and has disclosed the presence, on the histone surface, of a symmetric distribution of positive charges, able to interact with their negative DNA phosphate counterpart.
We analyzed helical steps in known nucleosomal DNA sequences, observing a significant relationship between their symmetric distribution and nucleosome stability. Synthetic DNA sequences able to form stable nucleosomes were used to compare distances on the left and on the right side of the nucleosomal dyad axis, where DNA phosphates and charged residues of the (H3H4)2-tetramer interact. We observed a linear relationship between coincidence of distances and nucleosome stability, i. e., the more symmetric these distances the more stable the nucleosome.
Curves related to this symmetric distribution along the DNA sequence identify preferential sites for positioning of the dyad axis, which we termed palinstases. The comparison of our data with known nucleosome positions in archaeal and eukaryotic sequences shows many coincidences of location. Sequences that impair nucleosome formation and DNase I hypersensitive sites yield curves with a lower degree of symmetry. Analysis performed on DNA tracts of promoters close to the transcription start and termination sites identified peculiar patterns: in particular low affinity for nucleosome binding at the transcription start site and a high affinity exactly at the transcription termination site, suggesting a major role of nucleosomes in the termination of transcription.
The role played by the DNA sequence in determining preferred positions of individual nucleosomes has been studied using both experimental and theoretical approaches. Several global assessments of nucleosome positioning have been described in yeast [1–4], in Caenorhabditis elegans [5, 6], in Drosophila  and in humans [8–13]. Experimental mapping of nucleosomes has been performed mainly by micrococcal nuclease digestion followed either by ligation-mediated PCR analysis or by DNA microarray-based methods. Theoretical models used for nucleosome-positioning prediction include probabilistic models , the comparative genomics approach , the support vector machine classifier , energy landscapes  and DNA physical properties . During nucleosome formation, 60 bp in the central region of nucleosomal DNA become primarily associated with (H3H4)2-tetramer . The histone particle presents, on its surface, a distribution of positive charges able to interact with their negative DNA phosphate counterpart. These charges are symmetrically distributed with respect to the pseudo-dyad axis of the nucleosome and constitute a 'mask' of distances that remained constant during evolution . It is usually assumed that DNA length is the same for any DNA sequence of the same size and that the helical rise of any dinucleotide step does not shift to a large extent from the mean value of about 3.4 Å. More recent results, obtained by X-ray analysis of DNA crystals, suggest helical rise values around 2.83 ± 0.36 Å for A-DNA and 3.29 ± 0.21 Å for B-DNA . We observed that DNA oligomers having the same number of base pairs, as reported in X-ray and NMR databases, show different lengths, i.e., the length of dodecamers varies from 32 up to 37Å.
We guessed that nucleosome positioning must be related to a symmetric distribution of distances along the DNA sequence upstream and downstream of the presumed dyad-axis location. In order to measure the length of DNA sequences, as the sum of helical steps, we have collected from literature available helical rise values of the 136 possible tetranucleotide steps of DNA.
Results and Discussion
Helical rise values of tetranucleotides
Helical rise values of the 136 possible tetranucleotides.
h r (Å)
Origin of data
h r (Å)
Origin of data
ad0002, ad0003, ad0004, adh008
adh008, adh0102, adh0103, adh0105
1 d19,1 d68,1g80.1uqe
ad0003, ad0004, adh078
Data reported in table 1 show a distribution of helical rise values with a mean of 3.2 Å and a maximal and a minimal value of 4.46 Å (step 114 CGCA/TGCG) and 2.36 Å (step 96 ATGA/TCAT), respectively, with a remarkable difference of 2.1 Å between these two values. Thirteen of the values reported in the table were calculated by averaging values for tetranucleotides containing the same central dinucleotide step. For these tetranucleotides and 39 additional ones, whose helical rise values were derived by a single DNA oligomer, rmsd values are absent. Therefore, a refinement of the table is needed using new available resolvedstructures.
It is remarkable that tetranucleotides whose rmsd values are higher than 0.3 Å have central dinucleotides that can be stacked, in the DNA helix, into two different conformations; that's why they are termed 'bistable'. Hunter  reports evidence of bistability in DNA bp, mainly in the pyrimidine-purine CG and TA steps, but also in CC/GG and AG/CT. A re-classification of bistability was performed by Gardiner et al.  in a study on structural parameters of DNA oligomers, and, in tetranucleotides, the bistability turned out to be dependent of the central step according to GG, CG, CA > GC > TA > AG, GA, AC, AT, AA order. Therefore, we conclude that high variability of helical rise values for some of the tetranucleotides in table 1 is due to the presence of a central bistable dinucleotide step, which exhibits a high sensitivity to neighboring base pairs.
Dependence of helical rise on neighboring bases.
helical rise (Å)
Symmetric elements in the (H3H4)2-tetramer
Our purpose is to discover DNA sequences in which equal distances are repeatedly inverted, such as in inverted repeats of nucleotides that occur in palindromes. We term these kinds of DNA sequences "palinstases", based on the ancient Greek word "diastasis" meaning distance. It is evident that palindromic sequences are palinstasic, but the number of palinstases is expected to exceed the number of palindromes, due to the larger number of possible combinations for 136 helical rise values of tetranucleotides, when compared with the 4 possible DNA nucleotides.
Symmetric patterns of nucleosomal DNA sequences
Minimal Δls values in figure 2A, averaged over curves characterized by multiple positions, were plotted as a function of the ΔG value (figure 2C) and a linear relationship, with a correlation coefficient R = 0.89, was obtained. This result indicates that the stability of nucleosomes depends on Δls in a linear fashion and that an increase in Δls destabilizes nucleosomes. Interaction points on the (H3H4)2-tetramer and interaction points along the DNA-phosphate backbone can be less or more coincident. DNA can stretch in order to reach a distant interaction point, can increase its curvature in order to interact with a back point or the insertion of bridging water molecules may occur. In fact, X-ray analysis of nucleosomal structure at high resolution showed that, inside the minor groove of DNA strands, up to 121 water-mediated hydrogen-bonds can form . It is evident that the substitution of an electrostatic bond with a weaker hydrogen bond of a bridging water molecule substantially destabilizes the nucleosome.
Thåström et al.  reported a sixfold increase in affinity for selected synthetic sequences when compared with the most natural nucleosome positioning. We obtained a similar variation of Δls values (figure 2B) ranging from 0.7 Å, for the most stable synthetic sample, up to 5.5 Å for 5SrDNA, which represents a stable natural nucleosome forming sequence.
The symmetric length-distribution in a given DNA sequence can not be identified in a textual way, i. e., the sequence G40T30G40 is fully symmetric and supposed to have a Δls = 0 at the central TT step. This result seems to be in contrast with the observed low nucleosome positioning affinity of poly-(A/T) tracts. Actually, the Δls profile calculated for this sequence yields a minimum of 2.3 Å, due to differences in helical rise between GGGT, GGTT, GTTT tetranucleotides on the left side and TTTG, TTGG, TGGG tetranucleotides on the right side of the central TT step. It must be mentioned that a Δls = 0 value can be attained by a sequence such as G40T59G40 and the minimum will be located at the central T(30).
We observed very low Δls values (0.3 - 0.6 Å) for synthetic DNA sequences, 150-bp long and characterized by the repetition of the (A/T)3NN(G/C)3NN motif, as well as for (CTG)50 bp repeats. It has been shown that these sequences form stable nucleosomes [28, 29].
Δls values calculated for the two samples form curves very similar and symmetric with respect to the superhelix location (SHL) 0 of the nucleosomal dyad axis (figure 3). Due to the difference between the two sequences at positions 21 and 127, there are small differences on the left and the right side of the dyad, while a more relevant change occurs at SHL = 0, where NCP146 exhibits two positions with the same Δls value of 1.1 Å in comparison to NCP147, which has a single Δls value close to zero. This difference in the distribution of symmetric distances correlates to the different resolution in X-ray structures obtained for the two particles. The lower Δls value found for NCP147 suggests a higher degree of symmetry and a tighter structure in comparison to NCP146.
Asymmetric DNA sequences
Nucleosomal stability at promoters
The result related to the region close to the TSS shows the same profile identifying a low affinity for the nucleosomes around 100 bp upstream with respect to the TSS.
A completely different scenario is reported for the region related to the TTS. The plot clearly shows a very high affinity for nucleosome in corrispondence exactly with the predicted TTS. It is remarkable that the extension of the V-shaped plot, corresponding to the potential identified nucleosome, has the extension of about 150 bp, the extension of a nucleosome.
We guessed that symmetric distributions of DNA lengths could be related to nucleosome formation and suggested two novel ideas to test this hypothesis. First we used a tetranucleotide code in order to measure DNA length and then we searched for symmetric distributions of lengths according to the frame inherent to the concept of palinstase. Results previously reported show a linear relationship between nucleosome stability and symmetry measured by Δls values of known nucleosome-forming sequences. Minimal Δls values in the profiles of several analyzed DNA sequences were consistent with preferential nucleosome formation. The presence of many contiguous minimal Δls values (4-5 every 200 bp) and of flat Δls profiles severely limits the use of our results for obtaining genome-wide maps of nucleosome positions. Δls values may instead be assumed as reliable indicators of nucleosomal stability when their measurements are based on a statistical approach. In human promoters we observed low affinity for nucleosome binding at the transcription start site and a high affinity exactly at the transcription termination site. In expectation of the acquisition of more experimental data on DNA helical rise values, we consider our results as a preliminary assessment of the weight of DNA length in nucleosome positioning.
We drew on structural databases deposited at http://ndbserver.rutgers.edu/atlas to find helical rise values of naked DNA oligomers obtained by NMR analysis, since this technique suitably applies to samples in the liquid phase, which is more reliable than the crystalline phase to represent the state of DNA in living organisms.
Samples found in the database were selected by discarding those studied in aqueous dilute liquid crystalline phase, which is typically used to resolve long-range structures (> 10 Å), but yields a poor resolution at distances such as those found for helical rise. 99 values of tetranucleotide helical rise, out of the 136 possible ones, were derived this way. 14 further values were found by searching in database samples of DNA oligomers accommodating one modified base when the tetranucleotide sequence of interest was at least two steps away from the modified base. In these samples, we have verified that the presence of the modified base does not change the overall structure of the double helix and checked similarity between helical rise values found either in the modified samples and in the normal ones (data not shown). 10 of the lacking helical rise values were taken from the X-ray database and the remaining 13 were calculated by averaging values for tetranucleotides containing the same central dinucleotide step.
To express the DNA sequence as a linear array of consecutive helical steps, we read the first tetranucleotide of the sequence and derive, from table 1, the first helical rise value related to the dinucleotide step between the second and the third bp. The second tetranucleotide of the sequence yields the value of the helical rise between the third and fourth bp and so on, up to the end of the sequence. Given a sequence of n bp, the number of the elements in the array of helical rise values is equal to n-3. In order to compare positions between various DNA sequences, base-pair numbering coincides with helical-step numbering, but the first helical rise value and the last two ones are lacking. A further decrease in the original number n is due to the use of the mask (figure 1), which covers 56 helical rise values; therefore, the final number of data is n-59.
where Li and Ri correspond to the lengths shown in Figure 1.
Δls values for the two tracts L1 and R1 are always equal, due to the convention of dividing the central segment from -3 to 3 into two identical halves. The minimal Δ ls value obtained represents the maximum degree of symmetry.
DNA sequences from Archaeal nucleosomes must be requested to:
John N. Reeve at firstname.lastname@example.org
DNA sequences from literature were retrieved from:
DNA sequences that impair nucleosome formation must be requested to:
DNA sequences from DNase I hypersensitive sites were from:
DNA promoter sequences of vertebrates were retrieved from the EPD database:
DNA promoter sequences of human genome were from:
We wish to thank Prof. Paola Ballario for useful comments and suggestions.
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