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- Journal List
- Bioinformation
- v.7(3); 2011
- PMC3218313

# Statistical investigation of position-specific deformation pattern of nucleosome DNA based on multiple conformational properties

^{1}Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong

^{2}School of Electrical and Information Engineering, University of Sydney, NSW 2006, Australia

## Abstract

The histone octamer induced bending of DNA into the super-helix structure in nucleosome core particle, is very unique and vital for DNA packing into chromatin. We collected 48 nucleosome crystal structures from PDB and applied a multivariate analysis on the nucleosome structural data. Based on the anisotropic nature of DNA structure, a principal conformational subspace (PCS) is derived from multiple properties to represent the most significant variances of nucleosome DNA structures. The coupling of base pair-oriented parameters with sugar phosphate backbone parameters presented in principal dimensionalities reveals two main deformation modes that have supplemented the existing physical model. By using sequence alignment-based statistics, a positiondependent conformational map for the super-helical DNA path is established. The result shows that the crystal structures of nucleosome DNA have much consistency in position-specific structural variations and certain periodicity is found to exist in these variations. Thus, the positions with obvious deformation patterns along the DNA path in nucleosome core particle are relatively conservative from the perspective of statistics.

## Background

Nucleosome is the elementary structure unit of eukaryotic
chromatin, which works as the first step in packaging the large
genomes into the cell nucleus and directly influences DNA
replication, recombination, repair and transcription. It has been
proved that the bending of the core DNA along the superhelical
path is very anisotropic, in which the degree of overall
curvature is about twice of that in the uniform ideal super-helix
[1]. Compared with the highly conserved structures of the four
types of histone in the core octamer, DNA sequences are much
more varied and flexible to accommodate the sharp
conformational changes under different environments. In order
to describe the DNA microstructure, a considerable number of
conformational properties have been defined [2]. Based on these
properties, a lot of work has been done to reveal the stereochemical
traits and the deformation mechanism of DNA
molecules. These results have led to a clearer understanding of
the geometrical nature of the basic A-, B-form DNA that comes
from oligomers [3,
4] and the small DNA-protein complexes
[5,
6].
The knowledge about DNA deformation induced by the
histone octamer, however, is more complicated because it
depends on the coordination of the structural setting of each
part to finally form the 1.67-turn superhelix. Previous studies
on the nucleosome DNA structure usually choose one or several
nucleosome core particles (NCPs) to summarize the
deformation characteristics of the DNA and construct structural
and physical models for the super-helix path in terms of step
parameters, groove width, bending angle, inter-atomic forces or
deformation energy scores [7–9]. Tolstorukov *et al*. established
the roll-and-slide model in which slide makes major
contribution to the super-helical pitch and roll accounts for the
DNA bending [10]. Bishop applied a Fourier-filtering strategy
to the six base-pair step parameters from several nucleosome
crystal structures, to identify the necessary amount of Fourier
components that each parameter needs to reconstruct a highresolution
model of the nucleosome superhelix [11]. Becker *et al*.
established a mechanical model for the histone-DNA binding
by calculating forces and torques acting on each base pair along
the super-helical path [12]. Morozov *et al*. extended Olson’s
DNA elastic energy function by adding a weighted part of
histone-DNA interaction energy to build a biophysical model
for the intrinsic sequence dependence of nucleosome formation
[13]. Although a lot of interesting conclusions have been made,
they are specific to certain core particles used in the studies and
the structural measurement via one or a few properties only
emphasizes deformation in certain dimensions. With an
increasing number of determined nucleosome crystal
structures, it is now possible to study whether a consistency of
deformation patterns relative to the global organization exists
among NCPs with variant DNA and histone sources. We apply
a multivariate analysis on the nucleosome structure database
and establish a position-dependent conformational map for the
superhelical DNA paths. A principal conformational subspace
(PCS) is built to represent the most significant variances of the
original structural database. Based on the statistics of the
variation along the principal dimensionalities, the positions or
regions that have distinct deformation patterns are identified.
The statistical result shows that there is a high consistency as to
the position-specific structural contribution to the overall superhelix
among the crystal structures of nucleosome.

## Methodology

### Structural data of NCPs

The experimental database is constructed by collecting 6870 base pair steps from 48 nucleosome crystal structures in the Protein Data Bank (PDB), including 1AOI, 1EQZ, 1F66, 1ID3, 1KX5, 1KX4, 1KX3, 1M1A, 1M19, 1M18, 1P3P, 1P3O, 1P3M, 1P3L, 1P3K, 1P3I, 1P3G, 1P3F, 1P3B, 1P3A, 1P34, 1S32, 2CV5, 1U35, 1ZLA, 2F8N, 2FJ7, 2NZD, 2NQB, 2PYO, 3B6G, 3B6F, 3C1C, 3C1B, 3KUY, 3LJA, 3KWQ, 3LEL, 3AFA, 3A6N, 3MGS, 3MGR, 3MGQ, 3MGP, 3KXB, 3MVD, 3LZ0 and 3LZ1. The pdb file of 3LEL contains two spatially independent nucleosome cores and hence the actual total number of nucleosome sequences used in our study is 49. The software 3DNA is used to derive the conformational parameters from the raw pdb file [14]. In order to describe a typical base pair step unit, we incorporate three types of structural parameters: (1) sugar phosphate backbone, (2) base pair and (3) base pair step. The first type includes main-chain torsion angles (α, β, γ, δ, ε and ζ), a pseudorotation angle (amplitude τm and phase angle P) that indicates the sugar ring puckering and glycosidic bond torsion angle (χ) [2]. The second and the third type respectively describe the relative orientation of the two complementary bases (shear, stretch, stagger, buckle, propeller and opening) and the stacking interactions of two sequential base pair steps (shift, slide, rise, tilt, roll and twist) [2]. Due to the double strand nature of DNA, each unit has two sets of sugar phosphate backbone parameters, and hence a single observation in the database is a vector with 30 dimensions (see supplementary material)

### Principal component analysis

PCA is a useful tool in exploratory data analysis and it reveals
the projection of original parameters onto the direction that
stands for the largest variations. By applying PCA to the
database we aim at finding a principal conformational subspace
(PCS) to represent the most significant original structural
fluctuations [15]. Standard algorithms are used here. The
covariance matrix C with elements Cab measures the
relationship between the original structural dimensions. *C _{ab}* =
<(

*x*

_{a}― <

*x*

_{a}>) (

*x*

_{b}― <

*x*

_{b}>) > (Equation 1), where

*x*is the standardized values of original structural parameters and <> means the average over all observations in the nucleosome database. The matrix of eigenvectors U diagonalizes the covariance matrix C. U

_{T}CU = D (Equation 2), where D is the diagonal matrix of eigenvalues λ

_{1},…λ

_{30}. The eigenvectors in matrix U describe the harmonic contribution of original dimensions to each principal component and the eigenvalues measure the variances that each PC accounts for. The principal components with the largest eigenvalues are then selected to construct the principal conformational subspace (PCS). For any given observation θ

_{n}, its score in any collective dimension of the PCS is calculated as given in supplementary material.

### Statistical analysis of position-specific structural contribution

For each nucleosome, the PCS scores of its constituent parts, are
calculated and related to the positions at which they occur. The
scores are then converted to scaled scores of 0 to 1, in which 0
and 1 respectively represent the minimum and maximum score
in a certain nucleosome path. By doing so, we can highlight the
positions of relative larger geometrical fluctuations for each
nucleosome path. The conversion of the original score *υ*_{k,m} to the
scaled score *z*_{k,m} is defined as given in supplementary material.
Additionally, original scores at each position are summed up
and averaged over all the paths. The averaged results are then
analyzed using the Fourier Transform to detect whether
periodicity exists in the geometrical variation along the superhelix
path. The frequency spectrum of the position-specific
geometrical variation sequence is defined as given in
supplementary material.

## Discussion

### The principal conformational subspace

The eigenvalues of the first three principal components derived
from the nucleosome crystal structure database are all larger
than 2, which separate them from the subsequent PCs. So we
use (PC1, PC2, PC3) to define the principal conformational
subspace because in a less explicit situation the special
conformational information may just be implied in several most
significant eigenvectors. The loadings of PC1 are evenly
distributed on all the original structural parameters except for
buckle (Table 1, see supplementary material). Another
parameter τm2 also has very limited but not negligible projection
on PC1. It means that upon the fluctuation along PC1, the
buckle angle between two complementary bases and the sugar
pucker amplitude of the second backbone strand remain still,
when other torsions and displacements are changing. By
contrast, δ_{1}, ζ_{1}, χ_{1},
β_{2}, ε_{2}, χ_{2}, P_{2}, slide, roll and twist are dominant
in PC1, and from the geometrical meaning of these parameters,
the PC1 can be described as a ribose ring oriented coordinate
that emphasizes the slide-roll-twist variations. For PC2, the
loadings are also very evenly distributed on various parameters
except that the step parameter tilt almost has no reflection in
this eigenvector. From the coefficients comparison of PC2 with
PC1, we can see that the slide-roll-twist coupling is more
emphasized in PC2 while the anti-correlations of roll with slide
and twist found in both PCs are the same. It should be noted
that the five backbone torsion angles (α, β, γ, δ, ζ) of each strand
have significant and even projections. PC2 therefore can be
characterized as a backbone-torsion-oriented-coordinate that
emphasizes the slide-roll-twist and sugar- pucker variations.
For PC3, buckle, shift and ε_{2} dominate. PC3 also has
considerable loadings on stagger, opening, rise, tilt, twist and
τ_{m2}. As far as the absolute values of coefficients of
corresponding parameters are concerned, the weights on the
two strands are not in equilibrium. So overall PC3 is a collective
coordinate that is based on the glycosidic bond torsion as well
as sugar pucker of strand II and lays stress on the behaviors of
complementary base pairs and the step structural variations in
terms of shift, rise, tilt and twist, which is completely different
from PC1 and PC2. The average structure shows that the two
strands of backbone have very similar mean conformational
parameters, which indicates that the backbone on the whole
maintains a good symmetry or balance between its double
strands during DNA bending into the 1.67 super-helical turns.
From the standard deviation values, which measure the spread
of data points from their mean, it can be seen that the two
strands also have similar fluctuation levels. Nevertheless, the
coordinates of PCs, especially PC3, have some bias on one of
the two strands, which is in the form of exerting different
coefficients on the same backbone parameters of the two
strands. Thus, it is inferred that the two strands of backbone
play diverse and uneven roles in the PCs.

### Position-specific deformation pattern along the nucleosome DNA path

It can be seen that there are regular patterns in the sequential structural variations in terms of scaled PC1, PC2 and PC3 scores (Figure 1a, 1b and 1c). The histograms of the averaged original PC score, over all the nucleosome paths, give a general and statistical structural characterization of the constituent parts. We assume that the position-specific original PC scores are a function of position. By averaging PC scores on certain position over all the nucleosomes, the noise hidden in the data can be reduced greatly. The Fourier analysis on the curve of average value vs. position shows that the structural variation along the nucleosome path is periodic (Figure 1d). In the case of PC1 curve, a 10.66bp-periodicity is revealed, while for the PC2 and PC3 curve, a slightly different periodicity, 10.24bp, is obtained. We also applied the Fourier analysis on the 30 original structural parameters. It is found that stagger and roll have the 10.24bp periodicity while slide and twist have the 10.66bp periodicity. The backbone parameter ε and ζ also have obvious periodicities, but for different nucleosomes, their periodicities have some fluctuations of being either 10.24bp or 10.66bp. Another backbone parameter β has been observed to have a predominant 10.24bp or 10.66bp periodicity in some but not all nucleosomes. The rest parameters do not have any predominant periodicity. Therefore, it is concluded that despite of the significant projections of various parameters on the PCs, the global bending of nucleosome DNA is mainly implemented by stagger, roll, slide, twist, β, ε and ζ variations. The variations described in terms of these parameters, however, are not strictly synchronous with each other. Positions with extreme PC scores that exceed the standard deviation range are marked along the two halves relative to the dyad axis. Based on the probabilities of positions with extreme PC scores, it is possible to identify positions of overall importance for the nucleosome structure. Here, only those with over 40% probability of having extreme PC scores are recognized as important “building blocks”. It is found that some positions do not stand in isolation but with adjacent positions to form a short region, such as 42˜41, 25˜ 24, 15˜14, 14˜16/17, 34˜35 and 40˜41. In particular, a fair number of positions have more than one kind of extreme PC scores, which means that they have multiple deformation patterns. We separate twenty regions with relatively strong deformation patterns measured by either or some principal dimensionalities: 69˜57, 47˜41, 38, 35˜33, 29, 25˜24, 15˜14, 10, 7˜3, 3˜7, 14˜22, 25˜29, 34˜36, 40˜41, 45˜48, 52, 55˜59, 63˜64, 67˜68 and 71. Compared with other parts along the nucleosome path, these regions are more inclined to take distinct deformation patterns. It can be found that their distributions are not strictly symmetric to the dyad point and have irregular intervals between any two neighboring ones.

## Conclusion

The statistical analysis on the experimentally determined crystal structures of nucleosomes in the PDB reveals that the conformational settings along the 145˜147bp sequence are obviously position-specific. The behaviors of the base pair steps, the puckering of the ribose ring and related backbone torsions jointly represent the major structural variation that is reflected in the PCs defined in our study. The structural variation characterized by the PC scores is periodic along the nucleosome path. The periodicity 10.66bp and 10.24bp acquired in our research are consistent with the 10˜11bp periodicity reported in previous research, but our result is based purely on the structural properties while the commonly accepted 10˜11bp periodicity is usually the product of genome sequence content analysis. Finally, the significant structural contributors that are evaluated by their scores on PC1, PC2 and PC3 have been proven to follow certain distribution patterns. Some positions are highlighted by more than one kind of PC score, implying that the local structures on these positions have multiple deformation patterns. The high probabilities of certain positions (or regions) having extreme PC values prove that the crystal structures of nucleosome DNA have much consistency in position-specific structural variations.

## Acknowledgments

This wok is supported by the Hong Kong Research Grant Council (Project CityU 123408).

## Footnotes

**Citation:**Yang & Yan, Bioinformation 7(3): 120-124 (2011)

## References

**Biomedical Informatics Publishing Group**

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