J. Biomedical Science and Engineering, 2010, 3, 331-339 JBiSE
doi:10.4236/jbise.2010.34046 Published Online April 2010 (http://www.SciRP.org/journal/jbise/).
Published Online April 2010 in SciRes. http://www.scirp.org/journal/jbise
Statistical analysis of conformational properties of periodic
dinucleotide steps in nucleosomes
Xi Yang1, Hong Yan1,2
1Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China;
2School of Electrical and Information Engineering, University of Sydney, Sydney, Australia.
Email: xiyang3@student.cityu.edu.hk
Received 15 January 2010; revised 25 January 2010; accepted 27 January 2010.
ABSTRACT
Deformability of DNA is important for its superheli-
cal folding in the nucleosome and has long been
thought to be facilitated by periodic occurrences of
certain dinucleotides along the sequences, with the
period close to 10.5 bases. This study statistically
examines the conformational properties of dinucleo-
tides containing the 10.5 - base periodicity and those
without that periodicity through scanning all nu-
cleosome structures provided in PDB. By categoriz-
ing performances on the distribution of step parame-
ter values, averaged net values, standard deviations
and deformability based on step conformational en-
ergies, we give a detailed description as to the defor-
mation preferences correlated with the periodicity
for the 10 unique types of dinucleotides and summa-
rize the possible roles of various steps in how they
facilitate DNA bending. The results show that the
structural properties of dinucleotide steps are influ-
enced to various extents by the periodicity in nu-
cleosomes and some periodic steps have shown a
clear tendency to take specific bending or shearing
patterns.
Keywords: Deformability of DNA; Nucleosome; Dinu-
cleotides; 10.5-Base Periodicity; Deformation Prefer-
ences; Flexibility; DNA Bending
1. INTRODUCTION
Numerous studies of nucleosome positioning have
demonstrated that the arrangement of nucleosomes on
DNA is nonrandom. The periodic occurrences of cer-
tain base pairs or motifs have been proven to be ubiq-
uitous in nucleosomes [1-5]. The periodicity of dinu-
cleotide steps can be considered as an important signal
for nucleosome identification, and it is widely consid-
ered to be closely related to the superhelical structure
of nucleosomal DNA [6-9]. On the other hand, the
stereochemical characteristics of DNA fragments de-
cide their individual behaviors of deformation when
being located at certain sites along the DNA sequence
[1,10-13]. Anisotropic deformation along a superheli-
cal path implies some dimers may play the role of
“hinge” and others facilitate “hinges” adhering to the
histone octamer core or just simply follow the “hinge”
wrapping around the core. From this point of view,
there exist some base steps that are geometrically more
significant than others, which are mainly reflected by
the special structural parameter settings of these im-
portant “building blocks”.
Although in previous studies, various methods, such
as molecular dynamics simulations, energy surface
calculation and deformability statistics based on dimer
energy function, have already been used to decipher
the conformational roles of the ten independent types
of dinucleotides [11,13,14], statistics which focus on a
large number of nucleosome samples whose crystal
structures are experimentally determined is still scarce.
Here, we choose 35 crystal structures of nucleosomes
published in Protein Data Bank (PDB) as the subject of
the statistical survey. The aim of our research is to
observe the overall conformational patterns measured
by the distribution and variability of base pair step
parameters and step conformation energies and build
interrelationships between periodicity and deform-
ability of base-pair steps.
2. MATERIALS AND METHODS
2.1. Crystal Structure and Dinucleotide Step
Parameters
There are 35 crystal structures of nucleosomes avail-
able in the Protein Date Bank (PDB) currently. All of
them belong to the typical complex between histone
core particle (H3, H4, H2A and H2B) and DNA se-
quence which is organized into a superhelix around the
core. The PDB ID of the 35 histone-DNA complexes
are 1AOI, 1EQZ, 1F66, 1ID3, 1KX3, 1KX4, 1KX5,
1M1A, 1M18, 1M19, 1P3A, 1P3B, 1P3F, 1P3G, 1P3I,
1P3K, 1P3L, 1P3M, 1P3O, 1P3P, 1P34, 1S32, 1U35,
X. Yang et al. / J. Biomedical Science and Engineering 3 (2010) 331-339
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332
1ZBB, 1ZLA, 2CV5, 2F8N, 2FJ7, 2NQB, 2NZD,
2PYO, 3B6F, 3B6G, 3C1B and 3C1C. The software
3DNA [15] is used to calculate the six step parameters
of nucleosome DNA: Shift, Slide, Rise, Roll, Tilt and
Twist.
2.2. Periodicity and Deformability of
Dinucleotide Steps
The periodic occurrence of dinucleotides observed in
nucleosomes has long been thought to be closely re-
lated with the sequence-dependent helical anisotropy
of DNA. AA/TT was firstly thought to be a step with
intrinsic curvature characteristic when it is periodically
repeated [16]. Correctly phased repeats (10.5 bp) of
AG/CT, CG, GA/TC and GC can also cause apprecia-
ble curvature [10]. The 10.5 bp periodicity, which is
widely acknowledged to be closely related to super-
helix structure, tends to be 11 bp in bacteria and 10 bp
in archaea and eukaryotes [17] and even for the same
type of dinucleotides in the same nucleosome, being
located at different places of the core DNA sequence,
such as at the two ends or in the middle section, can
make the periodicity fluctuate slightly [18].
In order to take the diversity of periodicity into ac-
count, the 10 ~ 11 bp are comprehensively considered
as the separation standard, that is, any step having
been separated with another step of the same type by
10 ~ 11 bp will be recognized as a periodic step and
marked with “1”, while if the distance between the
neighbouring steps of the same type goes beyond or is
not up to this standard, they will be marked with “0”.
The ten types of steps collected from 35 nucleosomes
are separated into the corresponding “0” and “1”
groups accordingly.
In the above method for extracting the periodic di-
nucleotides, we consider only one period. That is, any
neighbouring occurrence of the same type of dinucleo-
tides with a distance of 10 ~ 11 bp will be considered a
desired periodic pattern. More sophisticated methods,
such as the matched mirror position filter (MMPF)
[19], can be used to take several periods and their rela-
tions into account in a long DNA sequence. In this
paper, since we deal with short nucleosome sequences
from the PDB, there are not many long periodic pat-
terns. Thus, we detect one-period patterns only. Noise
and bias in these patterns and related parameter values
can be reasonably assumed to be random and should
not affect the overall distribution.
2.3. Separation of the Groups in Plots
Statistical analysis on the structural characteristics of
the “0” and “1” groups is made by producing the value
distribution histograms of the six base pair step pa-
rameters. By categorizing the distribution trends, we
can give a detailed description as to the deformation
preferences of dinucleotide steps in terms of angular
and translational parameters and summarize the possi-
ble roles of the significant steps which facilitate DNA
bending.
2.4. Calculation of Deformability based on Step
Conformational Energy
The conformational energies reflect the fluctuations
and correlations of structural parameters and also de-
scribe the deformability of dinucleotides at the global
level rather than in one dimension. The conformational
energy for each base-pair step is estimated by the
function based on the fluctuations of step parameters
from their equilibrium values [14]
1
2
T
i
EF

All the dinucleotides collected from the 35 nu-
cleosomes are considered as a set of experimental ob-
servations, and parameter values averaged over this
dataset represent the equilibrium geometrical states of
steps. Thus the deviation matrix ΔΘ and its transpose
ΔΘT can be obtained: ΔΘ = (Δθ1 ,…, Δθ6) and Δθi = θi
θi° (i = 1 ,…, 6). The covariance matrix of the step
parameters M calculated over the same set of DNA
structures is used to deduce the dimmer stiffness ma-
trix F: M = kTF-1 [13]. For simplicity, the Boltzmann’s
constant k and absolute temperature T is recognized as
unity and set to 1 because the relative deformability of
steps is not influenced by the value of kT, and in this
sense, the calculation result is a kind of energy score
rather than the real energy unit in joule.
3. RESULTS AND DISCUSSION
3.1. Frequency Distribution of Step Parameter
Values
The number of CG steps is especially limited in all the
35 nucleosomes. 1KX4 is a special one in which four
CGs are found. For 25 nucleosomes there are only two
CGs in each sequence with an interval of 7 ~ 8 bp
while for the remaining 9 nucleosomes, no CG can be
found at all. This explains why all the CG steps in the
35 nucleosomes are categorized into the CG0 group.
The values of Shift, Slide, Roll and Tilt distribute
over both negative and positive ranges. Twist pre-
dominantly takes a positive value with two exceptions:
–138.4º and –179.1º of TC/GA occurring in 1S32 and
3C1C respectively. Rise is generally considered as the
most conserved parameter not only at each step type
but also between the types in order to keep the hydro-
phobic interaction between two base pairs when a di-
nucleotide conformation changes [20,21]. It is also the
case in nucleosomes since the averaged Rise values for
the 10 types of steps are restricted into 3.2 ~ 3.5 Å
with very small SD values. However, there still exist a
X. Yang et al. / J. Biomedical Science and Engineering 3 (2010) 331-339
Copyright © 2010 SciRes. JBiSE
333
few steps with negative Rise values as well as values
exceeding 6 Å. Finally, for all the 10 unique steps,
their “0” groups have very similar distributions with
their respective “1” groups on the parameter Rise, Tilt
and Twist, and hence the “0” versus “1” differences in
terms of the value distribution pattern on these three
parameters are not discussed here.
For the value of Shift, AA/TT, AC/GT, AG/CT, AT,
CA/TG and TA have no significantly different distri-
bution patterns between the 0 and 1 groups and the
overall preferences of value signs of these steps are not
obvious in the distribution plots. But for GA/TC, GC
and GG/CC (Figures 1(a) to 1(c)), the “0” and “1”
distinction that “1” group tends to assume extreme
values in both directions, does exist. In comparison
with the relatively evenly distributed values of
GG/CC0, GG/ CC1 group has two modes around 1Å
and –1 Å meaning that most GG/CC steps in compli-
ance with the 10~11 bp periodicity tend to take large
Shift value, and GC follows in the same way. Al-
though the peak of GA/TC1 distribution does not oc-
cupy values as large as GG/CC1 or GC1, the “1” group
of GA/TC still shows clear preferences of taking
non-zero Shift values. In addition, most CG steps tend
to take positive Shift values.
For the values of Slide, AA/TT, AC/GT, AT, CA/TG,
GA/TC and TA have no significantly different distribu-
tion patterns between the 0 and 1 group. On the other
hand, AG/CT, GC and GG/CC have very similar Slide
value distribution modes: “1” groups mainly distribute
over the positive Slide range while their “0” groups span
a relatively wider range towards both directions (Fig-
ures 1(d) to 1(f)). With very few exceptions, CG dinu-
cleotides predominantly take positive Slide values.
For the value of Roll, the “0” groups of AA/TT, AC/
GT, CA/TG, GA/TC and GG/CC have similar distribu-
tion patterns with their corresponding “1” groups. On the
other hand, AG/CT, AT, GC and TA show relatively
prominent differences in their respective “0” versus “1”
groups (Figures 1(g) to 1(j)). Particularly, the Roll val-
ues of “1” group in AG/CT mainly fall into the negative
range while most Roll values in the “0” group have a
positive sign. The “1” group of GC also chiefly takes a
negative Roll value but its “0” group has a more even
distribution towards both positive and negative direc-
tions. The distribution patterns of “0” and “1” groups in
AT and TA, in which the majority in the “1” groups are
positive and “0” groups subtly incline to negative, seems
to be the opposite of AG/CT and GC.
3.2. Average and Standard Deviation of the
Absolute Values of Parameters
Table 1 summarizes the average values and standard
deviations of the absolute values of base-pair parame-
ters for the 10 unique sequential base-pair steps in
their “1” and “0” groups. Calculations on absolute
values of the parameters ignore the effects of rota-
tional and translational direction and only take the
degree of deformation into consideration. The per-
formances on the average degree of deformation in
terms of net rotational and translational parameters can
be divided into the following four kinds: 1) GC: steps
with periodicity have larger net values than those
without periodicity on five of six parameters. 2) TA,
AG/CT and GG/CC: steps with periodicity have larger
net values on four of six parameters. 3) CA/TG and
AC/GT: steps with periodicity exceed those without
periodicity only on three of six parameters, in other
words, in terms of three parameters, steps having no
periodicity have greater net values than steps with pe-
riodicity. 4) AA/TT, GA/TC and AT: steps without
periodicity exceed those with periodicity on five of six
parameters which is exactly contrary to 1). It might
also be noted that CG has remarkable average values
of Shift, Slide and Twist. The averaged net Roll and
SD values of the GG/CC0 group are significantly
higher than those of the GG/CC1 group. Similarly, the
GA/TC0 group has much larger averaged net Tilt value
and SD than the GA/TC1 group.
3.3. Helical Parameters Reflect Structural
Features of Dinucleotide Steps with
Periodicity
In our studies, the statistical result of the value distri-
bution frequency of the “0” and “1” groups of the 10
independent dinucleotide steps indicates that apparent
differences between dinucleotides with periodicity and
those without periodicity exist mainly in three helical
parameters: Shift, Slide and Roll. They can be recog-
nized as key parameters that drive the structural vari-
ability of periodic steps from others of the same type
but without periodicity. Our finding supports Suzuki
and Tolstorukov’s theories [9,21] that Roll and Slide
are the most important media by which particular di-
nucleotides exert their deformation properties on the
overall structure of naked DNA or nucleosomes, and
moreover, for types like AG/CT, GC, GG/CC, AT and
TA in nucleosomes, their regular occurrences with the
10.5 bp periodicity along the DNA sequence endow
these two parameters with unusual values and distribu-
tion trends. Indeed, Twist is an especially important
parameter for describing dinucleotides’ local behavior
of “kinks”. “Kinks” have impacts on the overall
stretching of DNA sequence and to some extent influ-
ence dinucleotide periodicity. However, our results
show that differences on Twist between the periodic
and the non-periodic are not that obvious. Shift, which
used to be excluded from the collection of key pa-
rameters, is in our conclusion another essential indi-
cator of periodicity-dependent conformational attrib-
X. Yang et al. / J. Biomedical Science and Engineering 3 (2010) 331-339
Copyright © 2010 SciRes. JBiSE
334
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i) (j)
Figure 1. Frequency distribution of step parameter values.
Roll(°)
Number of Dinucleotides
Number of Dinucleotides
Shift(Å)
Number of Dinucleotides
Shift(Å)
Number of Dinucleotides
Shift(Å)
Number of Dinucleotides
Slide(Å)
Number of Dinucleotides
Slide(Å)
Number of Dinucleotides
Slide(Å)
Number of Dinucleotides
Roll(°)
Number of Dinucleotides
Roll(°)
Number of Dinucleotides
Roll(°)
X. Yang et al. / J. Biomedical Science and Engineering 3 (2010) 331-339
Copyright © 2010 SciRes. JBiSE
335
Ta b le 1 . Average and standard deviation of the absolute values of base-pair parameters for the “0” and “1”
groups of the 10 dinucleotide steps.
Step N Shift (Å) Slide (Å) Rise (Å) Roll (º) Tilt (º) Twist (º)
CA/TG0 497 0.620.47 ‡ 0.950.80 3.550.45 * 11.47.5 ‡ 4.0.3.5 ‡ 37.46.9
CA/TG1 468 0.560.48 *‡ 1.410.92 3.410.59 9.112.3 ‡ 5 .414.3 *‡ 41.110.6
CG0 56 0.790.46 1.380.42 3.440.22 4.93.5 3.42.7 40.94.4
CG1 0
TA0 108
‡ 0.390.38 ‡ 0.470.53 3.550.47 ‡ 8.47.1 ‡ 3.83.9 38.55.8
TA1 124
‡ 0.540.54 ‡ 0.490.38 3.410.40 ‡ 9.76.7 ‡ 4.84.0 35.65.3
AA/TT0 630 0.440.35 0.340.30 3.360.54 ‡ 5.44.6 3.83.2 36.26.1
AA/TT1 355 0.410.32 0.330.30 3.340.40 ‡ 6.95.3 3.33.1 35.05.7
GA/TC0 371 0.830.60 0.690.61 ‡ 3.33 0.65 6.54.9 *7.719.6 36.714.3
GA/TC1 262 0.680.40 0.360.26 ‡ 3.39 0.55 4.43.0 4.23.4 35.95.5
AG/CT0 351
‡ 0.700.49 ‡ 0.430.38 ‡ 3.390.30 8.25.1 4.43.8 ‡ 33.34.2
AG/CT1 249
‡ 0.890.55 ‡ 0.860.48 ‡ 3.410.46 6.14.6 3.93.2 ‡ 37.05.6
GG/CC0 348
‡ 0.660.47 ‡ 0.690.52 3.340.59 10.19.2 ‡ 4.54.6 ‡ 33.27.0
GG/CC1 144
*‡ 1.110.42 ‡ 0.720.39 3.240.36 4.94.2 ‡ 5.8 4.2 ‡ 33.55.0
AT0 381 0.450.37 0.740.33 3.190.36 ‡ 3.73.0 3.22.6 32.04.8
AT1 144 0.410.36 0.610.29 3.110.27 ‡ 4.34.0 2.92.5 28.33.7
GC0 224
‡ 0.780.54 ‡ 0.620.43 ‡ 3.350.46 ‡ 5.44.4 4.84.2 ‡ 36.84.7
GC1 68
‡ 0.930.47 ‡ 0.950.56 *‡ 3.610.56 ‡ 6.65.2 3.83.1 ‡ 37.68.1
AC/GT0 263
‡ 0.520.38 ‡ 0.590.39 3.300.45 ‡ 4.83.2 4.14.2 31.35.3
AC/GT1 196
‡ 0.540.43 ‡ 0.670.35 3.170.46 ‡ 5.93.7 4.13.2 29.55.5
Absolute value of every step on each parameter is calculated, and then the mean parameter value and standard deviation for
each group are calculated.
Number of subscript represents standard deviation.
* Maximum mean value for each parameter selected from all groups.
‡ Situation in which the mean value of the “1” group on one parameter is higher than that of “0” group.
utes of dinucleotides. Despite the fact that the mean Shift
values are very small for all groups, the standard devia-
tions are fairly considerable which means Shift values
vary greatly even within each type and within each group,
and this phenomenon of small mean values but large SD
can be explained by the fact that the large positive values
and large net negative values cancel each other out. Sta-
tistics on the value range and averaged absolute value
support this interpretation as well and prove that in the
case of nucleosomes, Shift distance is nearly comparable
to Slide in respect of deformation degree and value vari-
ability.
3.4. Deformability of Steps
The six structural parameters are in fact interdependent
and the one-dimensional study is quite limited in charac-
terizing the flexibility of various dinucleotide steps. The
step conformational energies incorporate these structural
features and well outline the deformability of the peri-
odic and the non-periodic dinucleotides. For a certain
type of dinucleotide in each nucleosome, the representa-
tive energy score for the “0” or “1” group of this type is
defined as the average product of energy values of all the
steps in this group. A complete list of dinucleotide en-
ergy scores calculated in this way over the 35 nu-
cleosomes is given in Appendix. For dinucleotides of
AA/TT, AT, AG/CT, CA/TG and GC type, the number
of periodic groups having higher energy scores than the
corresponding non-periodic groups is close to or ap-
proximately the same with that of non-periodic groups
having higher energy scores than periodic groups of the
same type among all the nucleosome samples. In a sta-
tistical sense the observed deformabilities of periodic
dinucleotides of these types are almost identical with
their non-periodic counterparts. It is also found that in
most of the 35 nucleosome cases the GA/TC0 and
GG/CC0 groups have greater energy scores than corre-
sponding GA/TC1 and GG/CC1 groups, with the pro-
portions up to 88.5% and 79.4% of the total samples
respectively. On the contrary, the quantity of nu-
cleosomes in which the energy scores of AC/GT1 and
TA1 groups exceed those of AC/GT0 and TA0 groups
accounts for 80% and 87.8% of the total number of nu-
cleosomes respectively. It is concluded that periodic
GA/TC and GG/CC steps have greater deformability
than their non-periodic counterparts while periodic
AC/GT and TA steps appear more rigid than the
non-periodic AC/GT and TA steps.
X. Yang et al. / J. Biomedical Science and Engineering 3 (2010) 331-339
Copyright © 2010 SciRes. JBiSE
336
4. SUMMARY
AA/TT steps belong to the type whose conformational
settings are not very susceptible to the 10.5 periodicity.
In the parameter value frequency histogram, AA/TT
steps with periodicity have no clear differences from
those without periodicity. The mean absolute values,
value variabilities for the periodic and non-periodic steps
are also very close to each other. Although statistics on
step conformational energy reveals that the probability of
the non-peiodic group requiring higher amount of energy
to deform is higher than that of the periodic group re-
quiring higher energy, it is still not predominant enough
to discriminate the non-periodic group from the periodic
group. The above results may suggest that the periodicity
of AA/TT steps, on the whole, does not produce particu-
lar effects on their conformation features. AA/TT or
A-tracts are most likely to play the role of exerting con-
text influences on their neighbor dinucleotides and oc-
cupy specific positions to facilitate the bending of DNA
around the histone core [22,23].
AC/GT can also be categorized into the periodicity-
unsusceptible type. The relations and comparisons of the
six parameters between periodic AC/GT and non-peri-
odic AC/GT on value frequency plots, averaged net val-
ues and their standard deviations are quite similar to that
of AA/TT. Compared with the non-periodic ones, to
some extent periodic AC/GT steps are more rigid.
AG/CT steps can be characterized as very susceptible
to the 10.5 periodicity. Firstly, there are obvious differ-
ences in the plots of value occurrences on Slide and Roll
between the 10.5 bp-periodic AG/CT steps and the
non-periodic ones. Secondly, periodic AG/CT steps have
clearly different performances from non-periodic ones on
averaged net values and value standard deviations, fur-
ther testifying that the structural feature of AG/CT in
terms of some parameters is correlated with periodic step
occurrences in the DNA sequence.
AT steps have limited structural susceptibility to the
10.5 periodicity. On the frequency plots of parameter
values, periodic steps are different from non-periodic
steps on the parameter Roll, but non-periodic AT steps
exceed periodic ones on five of the six parameters in the
measurement of the mean net values. It can be concluded
that the 10.5 periodicity is a structural feature of AT but
may not necessarily contribute to sharp deformation in
nucleosomes.
CA/TG steps are also susceptible to the 10.5 perio-
dicity. Although the periodic group does not show any
apparent differences from the non-periodic group on
distribution plots of value occurrences and averaged
values, the periodic group has much larger standard
deviations than the non-periodic group. This implies
that the 10.5 periodicity expressed in CA/TG steps have
very large parameter value variability. CA/TG is ac-
knowledged by most reports as being the most flexible
steps that may act as “hinge” fitting the duplex to the
protein surface due to its great structural variability and
low energy consumption for bending [9,10,14,20,24].
CG steps are all marked as non-periodic, but notably
they have distinct preferences of parameter value occur-
rences. Most CG steps take negative Shift and Roll val-
ues and positive Slide values. CG also has a large aver-
aged net value on Twist which is only slightly lower than
CA/TG1, while the corresponding standard deviation for
net Twist values is much smaller than that of CA/TG1. It
means that CG steps uniformly have a large degree of
Twist.
GA/TC steps also have a certain degree of structural
susceptibility to the 10.5 periodicity. Compared with
non-periodic ones, GA/TC steps with 10.5 bp periodicity
display a slightly different value distribution on Shift and
obviously more deformability than the non-periodic
ones.
The GC step is another kind of dinucleotides par-
ticularly sensitive to the 10.5 periodicity. Periodic GC
steps have clearly distinguishing distribution patterns
from non-periodic steps on value occurrences statistical
plots of Shift, Roll and Slide. The periodic group also
has larger averaged net values and standard deviations
than the latter on five of the six parameters.
The GG/CC steps also belong to the periodicity-susceptible
type. Steps with 10.5 bp periodicity have different distri-
butions of value occurrences from non-periodic ones on
Shift and Slide. The averaged net values of periodic ones
are higher than those of non- periodic ones on four of the
six parameters. The periodic GG/CC steps also have ob-
viously more deformability than non-periodic ones.
However, it still should be noted that the standard devia-
tions of non-periodic GG/CC steps are higher than those
of periodic ones on six parameters in case of mean net
values, and the non-periodic group has far larger aver-
aged net Roll value and standard deviations than the pe-
riodic group. Thus, the influence of periodicity on
GG/CC is interpreted as partially reinforcing the de-
formability while restricting bending and shearing vari-
ability.
TA steps have a certain degree of sensitivity to the
10.5 bp periodicity. Differences between periodic ones
and non-periodic ones on Roll value distribution fre-
quency plots can be observed but are relatively subtle.
The mean net values of periodic steps exceed those of
the non-periodic ones on four of the six parameters, and
standard deviations on each parameter for the two groups,
however, are quite close to each other. The result of en-
ergy score calculation also reveals periodic TA steps are
more rigid than non-periodic ones. The periodicity, by all
counts, has limited influences on TA steps.
To summarize all the above analysis comprehensively,
the dinucleotide steps AG/CT, GC and GG/CC are most
immediately affected by the 10.5 bp periodicity. Periodic
occurrences along the nucleosomal DNA sequence as-
X. Yang et al. / J. Biomedical Science and Engineering 3 (2010) 331-339
Copyright © 2010 SciRes. JBiSE
337
sign them distinct shearing and bending preferences,
greater degrees of deformation and variability. Steps
CA/TG, GA/TC and TA can be divided into the second
category that is modestly influenced by the 10.5 perio-
dicity. Undoubtedly, special conformational trends on
some aspects do appear for periodic ones in this category,
compared with the first class above, however, trends for
the separation of periodic ones from non-periodic ones
are not prominent enough or all the separation standards
cannot be satisfied at the same time. Steps AA/TT,
AC/GT and AT fall into the third category that is least
structurally influenced by the 10.5 periodicity, which
means that the structural attributes of periodic steps in
this category is similar to non-periodic ones. Finally,
susceptibility of CG to 10.5 bp periodicity cannot be
evaluated because of lack of enough nucleosome samples,
but as a YR-type dimer it should have considerable in-
fluence on DNA deformation.
5. ACKNOWLEDGEMENT
This work is supported by the Hong Kong Research Grant Council
(Project CityU 123408).
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X. Yang et al. / J. Biomedical Science and Engineering 3 (2010) 331-339
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Appendix
aa0 aa1 ac0 ac1 ag0 ag1 at0 at1 ca0 ca1 cg0
1AOI 1.92 2.00 2.43 1.95 3.23 3.50 1.97 2.26 3.37 2.95
1EQZ 1.85 1.83 1.34 3.01 3.77 2.49 2.43 4.59 3.98 3.57 2.11
1F66 2.26 1.53 2.36 1.39 2.88 2.34 2.18 2.53 3.39 3.54 2.03
1ID3 2.46 1.59 1.86 4.82 2.62 3.86 2.09 1.31 3.89 3.01 4.24
1KX3 1.65 1.52 1.82 3.00 1.90 2.34 5.62 2.53 3.82 3.19
1KX4 3.05 2.85 2.01 2.71 1.50 3.54 2.41 3.01 6.44 2.68 2.46
1KX5 2.11 2.21 1.30 2.91 2.90 3.50 2.43 2.05 4.12 2.81
1M18 2.22 1.92 2.64 4.38 3.88 3.85 2.51 2.56 3.17 3.73 3.09
1M19 2.21 1.36 3.88 4.06 4.04 2.86 2.14 1.82 2.68 6.28 3.22
1M1A 1.63 2.29 4.90 3.63 2.77 2.54 1.93 2.47 3.49 4.45 2.59
1P34 2.22 2.30 1.88 2.91 2.02 2.87 1.93 1.70 3.89 3.61 2.26
1P3A 2.41 2.15 1.47 1.78 2.68 2.11 2.17 1.87 3.63 3.89 2.84
1P3B 2.03 1.11 1.48 2.78 2.61 1.95 1.60 1.20 3.04 5.22 2.33
1P3F 1.76 2.16 2.00 2.39 2.62 3.68 2.58 2.58 3.69 4.05 3.82
1P3G 2.02 2.65 1.76 3.26 2.30 3.46 2.08 1.61 3.22 4.22 2.06
1P3I 1.77 1.38 1.83 3.26 3.06 2.15 2.00 2.66 3.64 3.75 2.45
1P3K 2.20 1.32 1.83 2.70 2.76 2.75 2.40 1.54 3.23 2.91 4.07
1P3L 2.34 1.60 2.47 3.12 2.59 1.86 2.67 3.55 4.03 3.95 3.58
1P3M 1.92 2.03 1.97 3.21 2.70 2.53 2.56 1.32 4.15 4.08 3.90
1P3O 1.94 2.52 2.02 2.76 2.98 2.99 1.89 1.70 3.70 4.01 3.00
1P3P 1.85 2.74 2.31 2.36 3.36 2.76 2.14 1.95 3.82 4.20 2.90
1S32 2.25 0.53 1.58 1.23 2.15 2.05 1.85 1.63 3.24 7.79 1.48
1U35 1.76 1.53 7.55 3.66 2.49 4.25 1.90 2.41 3.70 5.64 1.73
1ZBB 2.25 1.96 1.71 3.35 2.25 2.90 2.36 1.87 3.89 2.64 1.30
1ZLA 1.07 0.94 1.08 2.17 1.77 2.38 1.45 1.40 3.67 7.89 2.47
2CV5 1.85 1.81 1.88 2.11 1.93 5.07 2.98 2.41 3.87 3.74
2F8N 1.72 2.51 3.35 3.86 2.25 6.04 2.01 1.61 3.36 4.75 2.41
2FJ7 2.61 2.86 2.42 2.91 2.96 2.96 3.54 2.00 2.83 3.33
2NQB 2.11 0.84 1.48 1.96 1.34 1.60 1.59 1.20 2.44 8.94 1.69
2NZD 1.68 1.15 1.39 2.15 1.96 2.42 3.32 1.60 5.55 2.97
2PYO 2.08 2.40 1.56 2.38 2.28 4.47 2.36 3.12 4.14 2.83
3B6F 3.09 2.75 0.66 2.07 2.56 2.69 3.22 1.84 2.36 4.09
3B6G 3.06 1.52 4.54 2.47 2.21 4.01 2.73 3.05 3.91 3.38
3C1B 2.16 0.63 1.34 1.57 1.29 1.64 1.44 1.14 2.30 8.11 2.25
3C1C 1.55 0.81 2.49 1.71 1.28 2.24 1.71 1.41 3.16 6.88 3.18
AV E . 2.09 1.81 2.25 2.74 2.51 2.99 2.35 2.10 3.62 4.37 2.67
aa0>aa1 aa0<aa1 ac0>ac1 ac0<ac1 ag0>ag1 ag0<ag1at0>at1 at0<at1 ca0>ca1 ca0<ca1
Number 23 12 7 28 13 22 23 12 15 20
Percent-
age 65.70% 34.30% 20.00% 80.00% 37.10%62.90%65.70% 34.30% 42.90% 57.10%
X. Yang et al. / J. Biomedical Science and Engineering 3 (2010) 331-339
Copyright © 2010 SciRes. JBiSE
339
ga0 ga1 gc0 gc1 gg0 gg1 ta0 ta1
1AOI 3.86 2.81 4.96 3.10 4.68 4.27 2.41 3.77
1EQZ 3.13 2.30 4.94 2.94 2.66 4.99 2.49 5.07
1F66 5.71 1.48 3.37 2.03 5.88 2.93 1.86 3.13
1ID3 2.64 1.73 2.60 5.44 5.36 4.98 1.65
1KX3 3.13 1.72 4.72 2.01 4.37 3.66 1.50 5.46
1KX4 3.36 2.19 3.13 3.29 4.38
1KX5 7.51 1.68 2.97 2.97 2.38 4.00 2.14 2.88
1M18 3.57 2.02 3.64 2.53 3.08 3.85 2.43 2.31
1M19 2.28 2.04 2.36 3.31 2.96 2.35 2.18 3.60
1M1A 2.99 1.93 5.28 2.77 3.22 3.18 2.99 3.09
1P34 4.47 2.83 2.13 2.95 5.32 3.58 2.24 4.14
1P3A 3.83 2.22 3.16 2.35 5.26 4.75 3.52 3.94
1P3B 5.19 2.17 3.20 4.36 6.19 4.16 2.07 2.78
1P3F 3.57 2.00 3.99 2.01 4.73 3.37 1.67 3.70
1P3G 3.23 2.91 1.75 2.25 5.68 4.74 1.92 4.77
1P3I 3.59 2.91 3.43 4.14 6.09 2.87 1.42 4.63
1P3K 3.40 3.28 2.57 4.04 5.65 5.39 2.01 5.76
1P3L 2.59 2.45 2.51 2.57 4.42 4.07 1.22 5.28
1P3M 2.35 2.59 3.45 4.08 4.51 3.50 3.93 4.53
1P3O 2.94 2.29 2.18 3.36 5.87 4.03 1.72 4.38
1P3P 3.13 2.29 4.38 2.55 3.88 2.76 1.72 4.50
1S32 8.72 1.15 1.87 1.98 1.89 2.18 1.12 4.00
1U35 1.52 1.81 2.79 3.33 2.36 0.79 3.34
1ZBB 5.82 0.89 2.55 6.95 2.12 4.07 6.07 2.36
1ZLA 9.07 1.32 2.48 2.05 3.59 2.70 0.75 2.86
2CV5 3.32 2.86 3.94 5.05 3.22 4.65 2.36 2.44
2F8N 2.44 1.76 2.73 4.34 3.38 2.30 6.74 1.97
2FJ7 2.53 4.69 2.93 2.92 3.76 3.66 6.34
2NQB 9.18 1.21 1.74 1.94 4.60 2.54 1.54 1.07
2NZD 2.66 2.63 2.24 8.64 3.65 3.16 2.20
2PYO 6.42 1.69 3.34 3.60 3.20 3.04 2.11 2.19
3B6F 3.42 4.06 2.56 3.01 3.45 2.66 2.77 3.03
3B6G 2.61 1.64 4.10 3.61 2.90 2.60 1.94 2.07
3C1B 9.82 1.73 1.72 1.43 4.83 2.16 1.06 1.49
3C1C 8.98 1.93 2.68 2.24 3.57 2.23 1.46 1.74
AV E . 4.37 2.21 3.10 3.16 4.20 3.48 2.37 3.48
ga0>ga1 ga0<ga1 gc0>gc1 gc0<gc1 gg0>gg1 gg0<gg1 ta0>ta1 ta0<ta1
Number 31 4 14 17 27 7 4 29
Percentage 88.60% 11.40% 45.20% 54.80% 79.40% 20.60% 12.10% 87.90%