EVALUATION OF DNA INTRAMOLECULAR INTERACTIONS FOR
NUCLEOSOME POSITIONING IN YEASTMICHAEL FERNANDEZ1
re0701m@bio.kyutech.ac.jp

SATOSHI FUJII1
s.fujii@bio.kyutech.ac.jp

HIDETOSHI KONO2
kono.hidetoshi@jaea.go.jp

AKINORI SARAI1
sarai@bio.kyutech.ac.jp

1

Department of Bioscience and Bioinformatics, Kyushu Institute of Technology (KIT),
Iizuka, 820-8502, Japan.
2Computational Biology Group, Japan Atomic Energy Agency, Kyoto, 619-0215, Japan
We calculated intramolecular interaction energies of DNA by threading DNA sequences aroundcrystal structures of nucleosomes. The strength of the intramolecular energy oscillations at frequency~10 bps for dinucleotides was in agreement with previous nucleosome models. The intramolecularenergy calculated along yeast genome positively correlated with nucleosome positioning
experimentally measured.

Keywords: chromatin, histone, indirect readout energy

1.

Introduction

Nucleosomes are the primary organizational units of chromatin in Eukaryotic
chromosomes. They are composed of about 147 DNA base pairs wrapped around a
histone octamer [1] joined by linker DNA ranging from 20 to 80 bps [1]. Genome
activities are largely regulated by nucleosomes together with the enzymes, which remodeland modify them. In this sense, nucleosome positioning can control the accessibility ofunderlying DNA to the nuclear environment. Translational and rotational settings define
a nucleosomal midpoint relative to a given DNA locus and the orientation of DNA helix
on the histone surface, respectively. Interaction of functional DNA sites with non-histone
proteins influences sequence-directed nucleosome positioning playing an importantfunctional role in determining the regularity of nucleosome location [2]. DNA regulatory
elements may reside in linker regions between nucleosomes or along the nucleosome
surface, where they may face inward (potentially inaccessible) or outward (potentiallyaccessible). Nucleosome locations are partly defined by the underlying DNA sequenceaccording to recent discoveries of nucleosome positioning sequences throughout the S.
cerevisiae (yeast) genome [2]. AA/TT dinucleotides recurring in 10-bp intervals and incounterphase with GC dinucleotides had been hypothesized to generate a curved DNA
structure that favours nucleosome formation [3].
Several methods have been proposed to computationally analyze nucleosome
positioning [4]. Particular interest gained the contextual specificity of nucleosome after
the first findings of DNA bending patterns related to periodic occurrences of certain

14 M. Fernandez et al.
dinucleotides [4] and differences in Fourier transform analysis between nucleosomal andrandom DNA sequence [4]. A later work detected weak consensuses in nucleosome sites
suggesting that no stringent conditions are imposed on a nucleotide sequence. However,periodicity of roughly 10 nucleotides was found in human exons and introns, and it wassuggested that nucleosome position could be accessible by measuring 10-bp periodicities[4].
The imperfection and degeneracy of nucleosomal organization in the chromatin limits
the application of classical computer analysis methods such as alignment and search forconsensus [4]. The computational recognition of nucleosome positing sites is moredifficult than transcription factor binding sites, which are characterized by consensuses
and weighting matrices [5]. The typical complex coding responsible for a specific DNA
conformation in histone complexes is rather generalizable and acceptable to many DNAsequences.
Structural analysis of a large number of protein-DNA complexes revealed a direct
readout mechanism via contacts between amino acid residues and base-pairs, which areboth redundant and flexible, suggesting that there is no simple code for the specificity of
DNA-protein interactions [6,7]. In addition, protein-DNA binding specificity has been
often modified by mutations of bases not in direct contact with amino acid residues,pointing out the importance of another indirect readout mechanism accounting forconformational changes (e.g. bending) [8] and/or flexibility [9] of DNA. These two
mechanisms of recognition via direct protein-DNA contact and via DNA deformations,have been referred as intermolecular (direct) readout and intramolecular (indirect)
readout, respectively. The specificity of intermolecular readout has been quantified basedon the statistical analysis of the structures of protein-DNA complexes [9]. The energy ofspecific interactions between bases and amino acids for protein-DNA complexes havebeen calculated by empirical potential functions. Threading different DNA sequences on
the protein-DNA framework and calculating the total energy have quantified differencesin the fitness of various DNA sequences against the protein-DNA complex structure. Thisthreading has enabled us to calculate Z-score against random sequences, as a measure of
the specificity of the protein-DNA recognition, and to predict DNA target sites forregulatory proteins [9]. This framework was applied to the evaluation of DNA
intramolecular interactions for nucleosome positioning in yeast.

2.

Method and Results

2.1. Intramolecular Interaction Energy Calculation
Nucleosome positioning for a given DNA sequence is estimated by threading theconstituent base pairs on the three-dimensional template constituted by the nucleosome
core-particle structure, and calculating an intramolecular interaction energy in terms ofthe deviations of the base-pair step parameters that make up the structure from theirEvaluation of DNA Intramolecular Interactions for Nucleosome Positioning

15

preferred equilibrium values [9]. A self-consistent component was added to the approachdescribed by Olson et al. [10]. The conformation energies were approximated using aharmonic function:
EDNA=1/2ΣΣfijΔΘiΔΘj,in which Θi represents the base-step parameters, and fij are the elastic force constants
impeding deformation of the given base step ΔΘi=Θi − <Θi>, in which <Θi> is theaverage base-step parameter. The base-step parameters used were shift, slide, rise, tilt,roll, and twist. The definitions of these parameters are given as in the literature [11]. Notethat we only gave the parameters for the ten mutually distinct base steps, while theremaining parameters were derived from symmetry relations [11]. The unknown
parameters fij and <Θi> were determined by statistical analysis of non-redundant proteinDNA complexes [9]. Setting up a covariance matrix from observed distributions of Θithus refers to an effective inverse harmonic force-constant matrix. Inversion of thismatrix transformed it to a force-constant matrix in the original coordinate basis. The total
intramolecular energy of a given complex structure was calculated as the sum of all thebase steps.
2.2. Oscillation Pattern of Dinucleotides Along the Nucleosome Structure
A total of 15 nucleosome-containing crystal structures (histone similarity indexes
lower than 30%) were retrieved from the Protein Data Bank (PDB). 3D coordinates andsequences of the nucleosome templates were extracted from the PDB files. We calculated
the indirect readout energies for ten mutually distinct DNA dinucleotides at all thepositions within the nucleosome structure, by sequence-structure threading over thenucleosome templates. Then, FFT was applied to evaluate the oscillation pattern of theindirect readout energies for all the dinucleodites (Fig. 1). The peaks are evident at ~34
degrees/base for some dinucleotides, corresponding to the turn of double-helix DNA.
Furthermore, the magnitude depends on the dinucleotide sequence (Fig. 2): CT, CC andAA exhibit the highest peak values in descending order, whereas dinucleotide GC
exhibits the lowest peak values. The peak amplitudes were normalized dividing by theaverage amplitude.

16M. Fernandez et al.

Figure 2: FFT average frequencies of indirect readout energies along nucleosome sequence for 10
dinucleotides. (Continue)

Evaluation of DNA Intramolecular Interactions for Nucleosome Positioning

17Figure 1: FFT average frequencies of indirect readout energies along nucleosome sequence for 10
dinucleotides.

Figure 2: Relative intensity of FFT peaks at ~34 degrees/base of the indirect readout energies for the 10
dinucleotides.

18M. Fernandez et al.

2.3. Intramolecular Energy Profile of Yeast Genome
We used the DNA intramolecular energy to evaluate the nucleosome occupancy profile inyeast genome. In order to evaluate the probability that a nucleosome occupies a given
position, we computed the energy by threading the corresponding DNA fragment against
the nucleosome template. A six-parameter potential including twist, tilt, roll, shift, slide
and rise dinucleotide step parameters of DNA double helix enabled us to compute theintramolecular interaction energy of DNA fragments of given sequence for the final
superhelical structure around the histone core of crystal nucleosome structures used as
templates.
ThegenomeofS.
cerevisiae
wasdownloaded
from
NCBI
(http://www.ncbi.nlm.nih.gov/) and the experimental nucleosome occupancy data for S.
cerevisiae (log2ratio) were retrieved from ref. 12). The intramolecular interaction energy
landscape for nucleosome occupancy in yeast was obtained by computing Z-score values
in windows centered at each nucleotide position along the yeast genome sequence using
the best resolution template nucleosome (PDB code: 1KX5). The ability of the theoretical
Z-scores to discriminate between nucleosome forming and inhibiting sequences wasevaluated by receiver operating characteristic ROC analysis. Sub-sequences with extreme
experimental nucleosome occupancies were labeled as nucleosome forming (high scores)
and non-forming (low scores). For the whole dataset, the ROC scores were 0.7 and 0.8
for 10% and 1% of DNA residues having extreme score values, respectively.
On a large scale, when the nucleosome occupancy patterns of all promoters areaveraged, the nucleosome-depleted region (NDR) is evident. Smoothing the energy
landscape by a window of 4 bps, corresponding to the resolution of the experimental data,
led to the energy profile, which was compared to in vivo nucleosome occupancy data as
determined by measuring the accessibility to MNase of genomic DNA in chromatin. The
average nucleosome intramolecular energy signature for yeast is clearly oriented attranscription start sites (TSSs). Precisely aligned nucleosome occupancy signal by TSSs
and averaged all genes show higher values of intramolecular energy, in good agreementwith the experimental scores (Figure 3).

Evaluation of DNA Intramolecular Interactions for Nucleosome Positioning

19Experimental scores

Calculated scores

Figure 3. Nucleosome forming profile at yeast TSSs. Intramolecular interaction energy calculated in this study
and experimental scores from ref. 12. Both scores are rescaled arbitrarily (intramolecular interaction energy
on the right axis).

3.

Discussions

Regularities of nucleosome positioning have been reported to depend on dinucleotide
frequencies in the genome. The GC/AT-richness of a sequence has been considered as thestrongest single factor among k-mer frequencies in determining its nucleosome formation
potential in S. cerevisiae genome [13]. However, some author reported a species
dependency in the nucleosome formation potential of genome. In this regards, regularity
studies in human genome reflected that dominance of oscillating GG and CC
dinucleotides in human nucleosomes and the contribution of AG(CT), GA(TC), andAA(TT) suggest a general nucleosome DNA sequence pattern-counterphase oscillation ofRR and YY dinucleotides [14].
We have applied the intramolecular energy of DNA or indirect readout energy inprotein-DNA recognition [9] to the problem of nucleosome positioning. The calculated
intramolecular energy for the dinucleotides threaded along the nucleosome structure
oscillates at frequency ~10 bps, in good agreement with previous nucleosome models
which reported distinctive sequence motifs that recur periodically at the DNA helical
repeat. However, the Fourier analysis showed that the relative strength of that peak in thepower spectrum was highest for CT followed by CC and AA, and lowest for GC and CG,
which is somewhat different from the result of sequence analysis. It remains to be seen
how important is the phase information for the nucleosome positioning, and whether the20

M. Fernandez et al.

dinucleotides intermolecular energy is sufficient or not. We are currently investigating
the relationship between the intramolecular energy profile and sequence features, and therole of periodicities or phasing in energy profile by including the effect of longer-rangeinteractions.
We also compared the intramolecular interaction energy landscape to the nucleosome
occupancy data in yeast [12]. We computed Z-score values based on the intramolecularenergy, and the ROC analysis has shown that the ability of computed Z-scores todiscriminate between nucleosome forming and inhibiting sequences is high. The energy
landscape was also compared to the in vivo nucleosome occupancy data as determined bymeasuring the accessibility of MNase to genomic DNA in chromatin. The averagenucleosome intramolecular energy signature for yeast is clearly oriented at TSSs, and theupstream NDR is evident. Precisely aligned nucleosome occupancy signal by TSSs andaveraged all genes show higher values of intramolecular energy, in good agreement withthe experimental scores, although the well-known ladder shape of nucleosomes
positioned at downstream of TSSs is not well reproduced by the intramolecularinteraction energy profile. However, the ladder might not be reflecting the intrinsic
propensity of individual nucleosome formation. It should be noted that the nulceosome
formation is a cooperative process regulated by chemical modifications, interactions withcofactors, solvent condition etc. We are currently working on a model that incorporates
not only the intrinsic nucleosome positioning but also the effects of cooperativity.
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