Article
pubs.acs.org/JPCB
Structure and Binding Energy of Double-Stranded A‑DNA Minihelices: Quantum-Chemical Study
Tetiana Zubatiuk,† Maxim A. Kukuev,† Alexandra S. Korolyova,‡ Leonid Gorb,§ Alexey Nyporko,‡
Dmytro Hovorun,§ and Jerzy Leszczynski*,∥
†
Division of Functional Materials Chemistry, SSI “Institute for Single Crystals”, National Academy of Science of Ukraine, Kharkiv
61001, Ukraine
‡
Department of Molecular Biotechnology and Bioinformatics, Institute of High Technologies, Taras Shevchenko National University
of Kyiv, Kyiv 03022, Ukraine
§
Department of Molecular Biophysics, Institute of Molecular Biology and Genetics, National Academy of Sciences of Ukraine, Kyiv
03143, Ukraine
∥
Interdisciplinary Center for Nanotoxicity, Department of Chemistry and Biochemistry, Jackson State University, Jackson, Mississippi
39217, United States
S Supporting Information
*
ABSTRACT: A-DNA is thought to play a significant biological role
in gene expression due to its specific conformation and binding
features. In this study, double-stranded mini-helices (dA:dT)3 and
(dG:dC)3 in A-like DNA conformation were investigated. M06-2X/631G(d,p) method has been utilized to identify the optimal geometries
and predict physicochemical parameters of these systems. The results
show the ability of the corresponding mini-helices to preserve their Alike conformation under the influences of solvent, charge, and Na+
counterions. Presented structural and energetic data offer evidence
that two steps of GG/CC or AA/TT are already enough to turn the
DNA helix to generate different forms by favoring specific values of
roll and slide at a local level. Our calculations support the
experimentally known fact that AA/TT steps prefer the B-form
over the A-ones, whereas GG/CC steps may be found in either the B- or A-form. The stability of mini-helices at the level of total
energy analysis, ΔE(A−B)
total , is discussed.
■
INTRODUCTION
Structural diversity of DNA molecules in a living cell is
sufficiently limited. All known DNA conformations derived
from DNA:protein complexes are variances of canonical righthanded A-DNA and B-DNA (rareleft-handed Z-form)
structural forms.1,2 The general number of complexes
containing the A-form of DNA is half of the B-form-contained
ones.2 Thus, despite A-DNA having been discovered in
nonphysiological environment (low humidity and high ionic
strength),3 the importance of both right-handed DNA forms in
biological processes is undisputed.
Since both A- and B-DNA structures belong to the family of
right-handed double helices, they have some similar structural
parameters. In the case of A-DNA, they are the following:4 11
base pairs per turn; inclination equal to ca. 70°; helical diameter
of about 20 Å. These parameters correspond with the ones that
characterize a B-DNA form: 10 pairs per turn; inclination 90°;
helical diameter of ca. 20 Å. However, in fact, the structure of
A-DNA differs significantly from the structure of the Watson−
Crick B-DNA (see Figure 1). This is because the base pairs of
the A-form displace almost half of the radius from the helical
© 2015 American Chemical Society
Figure 1. A- and B-forms of DNA macromolecule (side and top
views).
Received: May 14, 2015
Revised: September 9, 2015
Published: September 9, 2015
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DOI: 10.1021/acs.jpcb.5b04644
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Article
The Journal of Physical Chemistry B
the application of static and dynamic methods of quantum
chemistry. However, dynamic quantum chemistry methods are
much more time and resources demanding than the classical
MD simulations. The application of them is still limited even at
the DFT level.21−24
First quantum mechanical (QM) reliable data about the
structure of DNA were obtained using quantum-mechanical/
molecular-mechanical (QM/MM) hybrid methods.25−27 The
largest QM part treated at the DFT/plane waves level has the
composition of d(5′-GTGG-3′).28 Using different versions of
QM/MM techniques, the structure−relationship properties of
short DNA oligonucleotides have been successfully investigated.26
Recently we applied modern versions of DFT approximations to study structural and energetic features of mini-helices
((dG:dC)3, (dA:dT)3, (dG:dC)5, and (dA:dT)5) of B-DNA29,30
at the static quantum-chemical level. Despite the lack of the
conformational sampling, the results showed that the simplest
trideoxyribonucleoside diphosphate homopolymers are able to
adopt the classical conformation of B-type even in vacuum and,
of course, in water solution.
The current study extends the results obtained in ref 29
toward A-DNA form. This is the first comprehensive DFT
study of Watson−Crick trideoxyribonucleoside diphosphate
homopolymers (dG:dC)3 and (dA:dT)3 duplexes adopting Aconformation (Figure 3). Presented in Figure 3, DNA model
axis to the periphery of the molecules. Namely, the displacement reaches 4−5 Å (in B-DNA it is close to zero). Therefore,
A-DNA when viewed from above (along the axis of the helix)
looks like a tube, with a “hole” in the center (Figure 1). Also, BDNA conformation contains the DNA bases stacked in a
parallel fashion perpendicular to the main helix axis with
approximately zero roll, positive slide, and approximately 36°
helical twist, while the A-form possesses the conformation
where the base pair tilted with respect to the main helix axis and
has higher roll, negative slide, and lower helical twist.5
Meanwhile, crystallographers found the factors which are
responsible for the “hole” in the center of A-DNA.4 It was
shown that a pentagonal deoxyribose sugar ring has different
configurations in A- and B-DNA and plays the role of switcher
between two stable states: C-2′ endoin the B-formand C3′ endoin the A-form (Figure 2). When switching from the
first state to the second, base pairs move away from the helical
axis because sugar rings are connected directly with the bases of
the DNA.
Figure 2. Conformations of ribose ring.
To push a B-DNA form to adopt an A-conformation, one
needs to change in vitro conditions dramatically. For example,
such a transition will take place in the case of a replacement of
80% of water molecules by the molecules of ethanol, or by
changing an ionic strength of the water solutions by increasing
the concentration of surrounding ions as concluded from the
flat-film diffraction experiments.6−9 In vivo the transition to the
A-form takes place during the interaction with some enzymes.
For instance, during the interaction with DNA-polymerase (see,
for example, ref 10 and the references therein).
Since DNA undergoes an enormous amount of structural
changes and exists in multiple forms (A, BI, BII, C, D, and Z,
etc.) which differ with the helical parameters, the conformation
of backbone, and orientation of bases,11,12 resolving the DNA
structure is one of the primary steps for most investigations.
Reliable methods to perform such investigations are X-ray
diffraction, NMR spectroscopy, and such methods of computational chemistry and biology as classical molecular dynamics
(MD) and static and dynamic methods of quantum chemistry.
It is also well-known that, for many years, applications of
classical MD represented the main computational tool used to
study DNA structure and dynamics. Classical MD studies at the
atomic level have proven to be invaluable for interpreting the
results of DNA experiments.13−18 They provided an enhanced
understanding of molecular structure and dynamics in terms of
static and thermodynamic parameters.19 Moreover, MD
simulations have been used to test and confirm experimental
findings.20 However, the most serious limitation of classical
molecular dynamics is their force fields which are derived on
the basis of a molecular mechanics model of a molecule. They
are empirical in nature and are not able to reproduce, for
example, the polarization of molecules due to different kinds of
intra- and intermolecular interactions. The solution from the
previously described situation is quite straightforward. This is
Figure 3. Studied double-helical A-like trideoxyribonucleoside
diphosphates ((dG:dC)3 duplex is shown as representative example)
and site numbering for nucleobases with base-pair width [C1′C1′]
distance and λR and λY angles between the line joining the [C1′C1′]
and the N9−C1′ (purine) and N1−C1′ (pyrimidine) glycosidic
bonds.
nucleotides binding is the simplest A-type double helices (minihelices) which are large enough to describe key features of a
DNA helix yet small enough that highly accurate DFT
methods, suitable for studies of binding in DNA, can be
employed. Our study includes a comprehensive investigation of
the characteristics of helix, base-pair steps, molecular geometry,
and energetics (including calculation of binding and relative
energies) for both isolated (compensated by Na+ cations) and
hydrated (negatively charged as well as compensated by Na+
cations) duplexes. Since we used the exact same approximation
that was used in ref 29, we are also able to compare some
geometrical parameters, the binding and relative energies of the
aforementioned mini-helices adopting A- and B-forms,
revealing and distinguishing vital features of both forms.
■
COMPUTATIONAL DETAILS
We analyze fully optimized double-stranded A-DNA-like minihelices that contain three base pairs. Current study applies the
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The Journal of Physical Chemistry B
evaluated with the monomer basis set. In summary, the binding
energy is defined in the following way:
very similar computational protocols that were used in our
recent publication.29 All optimized geometries are published in
the Supporting Information (SI) (Tables S1−S6). The initial
(further referred to as “ideal”) structures of the duplexes were
constructed with the canonical A-DNA conformations using the
3DNA program.31 Initial duplex models were composed of G-C
and A-T base pairs. 5′-Terminal and 3′-terminal phosphate
groups were substituted with methyl groups, so the duplex
contained two pairs of phosphate groups and 4− charge as a
consequence (Figure 3).
The analysis was performed for the following models:
(1) Model 1 is an A-type DNA mini-helix in which the
negative charges have been compensated for by Na+ ions in
vacuum, without including additional environment effects. The
Na+ ions have been located near (approximately 2.4 Å) two
terminal phosphate oxygen atoms of the backbone.
(2) Model 2 is a negatively charged A-type duplex immersed
into continuum-type dielectric medium mimicking water. This
model includes the average influence of compensating ions (see
the explanation in ref 29).
(3) To form model 3, model 1 has been hydrated the same
way as model 2 (see ref 29 for the details).
The Gaussian09 32 program was used for geometry
optimizations and all single-point M06-2X33 calculations. The
highly parametrized, empirical exchange−correlation M06-2X
functional has been shown to describe well noncovalent
interactions (including dispersion interactions) and is currently
in common use for investigating the structure−relationship
properties of different fragments of DNA.29,30,34,35 Geometry
optimizations were carried out using the 6-31G(d,p) basis set
without inclusion of any BSSE (basis set superposition error)
correction. However, we performed preliminary optimization
with including BSSE using the pure B97-D functional. We
found that the contributions of intramolecular BSSE amount to
about 1−1.5 kcal/mol and virtually do not affect the geometry
of the studied system. In spite of the fact that intramolecular
BSSE seems to be a small value, uncorrected BSSE during
optimization is an additional source of mistake in binding
energy calculations.36 Effects due to solvent polarization
(water) have been estimated by using the polarizable
continuum model (PCM).37 The vibrational frequencies have
been calculated for all obtained structures. No imaginary
frequencies have been found for the final optimized geometries.
The interaction energy, ΔER···Y
int , of a duplex R···Y is defined as
the electronic energy difference between the duplex (ER···Y) and
the isolated single oligonucleotides (monomers) (ER, EY). The
monomer energies are computed in the basis set of the duplex
(duplex-centered basis set), assuming the geometries of the
optimized duplex.38,39 Thus, the results are corrected for the
mathematical artifact called intermolecular BSSE.
R ··· Y
ΔE int
= ER ··· Y − (ER + EY )
R ··· Y
R ··· Y
ΔE bind
= ΔE int
+ Edef
(2)
where
Edef = ErR + ErY
(3)
and
R
ErR = ER − Eopt
Y
ErY = EY − Eopt
(4)
In the case of PCM single-point calculations for isolated single
oligonucleotides the same duplex size cavity has been used, but
with charge distribution corresponding to the monomer.
Initial geometries as well as their structural parameters were
obtained using the 3DNA31 program which provides a full set
of base-pair, base-pair-step, helical, and backbone features. The
atom numbering used is shown in Figure 3. The definition of
the parameters is clear from Figures 3−5. Besides the local
Figure 4. Pictorial definitions of rigid body parameters used to
describe the geometry of complementary base pairs and sequential
base-pair steps. The base-pair reference frame is constructed such that
the x-axis points away from the (shaded) minor groove edge of a base
or base-pair and the y-axis points toward the sequence strand I.
(1)
When calculating the binding energy of the duplex, ΔER···Y
bind , it
is important to further add the duplex deformation energy,
Edef.38 The deformation energy is a sum of the repulsive
contributions due to changes of the single-oligonucleotide
geometries upon the duplex formation. The duplex deformation energy consists of relaxations of each single oligonucleotide, Er. The relaxation energy of each single oligonucleotide is
evaluated as the energy difference between the single
oligonucleotide adopting the final deformed geometry (as
adjusted in the duplex) and relaxed isolated molecule (Eopt), all
Figure 5. Schematic diagram of a duplex composed of three stacked
base pairs and a sugar phosphate backbone. Labeled torsion angles on
strands I and II belong to the nucleotides of the central base pair (base
pair 2). Phosphates are marked with black dots, and sugar O4′ atoms
are marked with open circles. Single-stranded oligonucleotides are
labeled as Y and R.
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Table 1. Base-Pair Parameters of A-Form Mini-helices Obtained at the 6-31G(d,p)/M06-2X Level of Theory Compared to BForma,b, Ideal 3DNA Structures and Molecular Dynamics Datac
model 1 (gas, Na+)
param
b
(dG:dC)3 duplex
slide (Å)
roll (deg)
twist (deg)
inclination (deg)
X-displacement (Å)
(dA:dT)3 duplex
slide (Å)
roll (deg)
twist (deg)
inclination (deg)
X-displacement (Å)
model 2 (PCM)
model 3 (PCM, Na+)
ideal
MD
A
B
A
B
A
B
A
B
−1.6
24.2
55.8
24.4
−2.8
2.2
−11.2
50.7
−12.7
3.2
−1.1
9.4
33.3
15.5
−2.9
1.4
−2.4
42.7
−2.4
1.8
−1.0
9.7
32.6
16.0
−2.8
0.7
−3.5
39.0
−4.7
2.3
−1.4
12.4
30.3
22.6
−4.4
0.5
1.7
35.9
2.8
0.5
0.1
9.9
34.7
16.8
−1.3
0.3
−4.4
39.4
−6.4
0.9
−0.6
6.2
38.6
9.3
−1.5
0.3
−2.8
42.3
−3.9
0.7
−0.5
6.1
38.3
9.2
−1.5
0.0
−4.3
44.1
−5.7
0.4
−1.4
12.4
30.3
22.4
−4.5
0.5
1.7
35.9
2.8
0.5
A
B
32.6
15.8
−4
−0.4
3.6
32.6
6.8
−1.4
32.6
15.8
−4
−0.4
3.6
32.6
6.8
−1.4
a
Data from ref 29. bThe local base-pair step (slide, roll, twist) and helical parameters (inclination, X-displacement) are averaged over two steps AA/
TT or GG/CC in (dA:dT)3 and (dG:dC)3 duplexes, correspondingly. cReference 40.
much better to the geometry of the ideal form than those
describing the geometry of mini-helices in vacuum. This is
especially true in the case of (dG:dC)3 duplexes. One may also
see that the values are sequence-specific.
The overall picture may be made clear by examining plots of
roll versus slide (as was proposed in ref 4) for considering minihelices in A- and B-forms as shown in Figure 6. The analysis of
base-pair parameters (shear, stretch, stagger, buckle, propeller,
and opening), the virtual interbase parameters (distance
d(C1′−C1′) and angles λY and λR) also characterize the
geometry of the central base pair. The local base-pair-step (rise,
slide, shift, tilt, roll, and twist) and helical parameters
(inclination, X-displacement, Y-displacement, tip) are averaged
over two steps AA/TT or GG/CC in (dA:dT)3 and (dG:dC)3
duplexes, correspondingly. We present here the analysis of
structural data based on arithmetic means because our
preliminary analysis of the full set of rigid coordinates did
reflect the same trends as provided by average values. The full
set of the rigid body parameters is given in the Supporting
Information in addition to average values (Table S7). We also
analyzed the angle of pseudorotation of the sugar ring (P) and
the main chain torsion angles (in the 5′ to 3′ direction) which
belong to the nucleotides containing the central base pair.
■
RESULTS AND DISCUSSION
Base-Stacking and Helical Parameters. We analyzed the
obtained helical parameters according to their importance in
formation A- or B-conformations of DNA. The leading role of
the sugar conformation is well-known and has already been
mentioned. We just confirm that all of the structures belonging
to models 1−3 have the sugar in the northern (C-3′ endo)
regions. The corresponding values of the phase angle of
pseudorotaion are collected in Table 3.
The next subject of our consideration is the differences in
dinucleotide steps geometry. It is well-known4 that different
sequences of bases in DNA can generate different doublehelical structures by favoring different values of roll, slide, and
twist at a local level. Almost all of the external features of the Aand B-conformations, such as the distance of base pairs from an
axis, the tilt of pairs with respect to an axis, and the rise along
the axis, are connected with their (roll, slide, and twist) values.
Also the A- and B-conformations have different inclination and
X-displacement. All of these specific angles are collected in
Table 1 for the A- and B-conformations of considered minihelices. One may see that the conditions of all three models
keep the obtained conformations of mini-helices as A-ones,
because all of them have negative slide, greater than in the Bform roll, lower than in the B-form twist, larger than in the Bform inclination, and negative X-displacement. As expected,
parameters that include an influence of water bulk correspond
Figure 6. Plots of roll versus slide for two base-pair steps of duplex
discussed. The numbers indicate the model. The dashed line from roll,
slide = −10°, −1 Å to +20°, −0.2 Å represents the break between Aand B-type DNA geometries, which lie to the left and right,
respectively, of the line (as described in Calladine and Drew4).
slide−roll correlation presented in Figure 6 reveals that roll and
slide values of considered (dG:dC)3 mini-helices belong to the
region that characterizes the A-DNA form. As one may see, the
situation with similar parameters of (dA:dT)3 mini-helix is not
so straight forward, since those parameters belong to the area
which is on the border between the A- and B-forms. There are
at least two arguments that could explain this. It is known that,
in contrast to the (dG:dC)3 sequence, the sequence (dA:dT)3
strongly prefers the B-type conformation.4,5 This is why some
geometrical parameters that characterize the AA/TT step in the
A-form could be on the border between A- and B- forms
indicating a tendency to such a preference.
It is also well-known that different A- and B-forms are
isosteric each to another one.4 In other words, they have
approximately the same C1′−C1′ distance and values of λY and
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DOI: 10.1021/acs.jpcb.5b04644
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The Journal of Physical Chemistry B
Table 2. Virtual Interbase Parameters of A-Form Mini-helices Compared to B-Forma and Ideal 3DNA Structures
model 1 (gas, Na+)
central bp
b
(dG:dC)3 duplex
d(C1′−C1′) (Å)
λY (deg)
λR (deg)
(dA:dT)3 duplex
d(C1′−C1′) (Å)
λY (deg)
λR (deg)
a
model 3 (PCM, Na+)
model 2 (PCM)
ideal
A
B
A
B
A
B
A
B
10.4
52.8
54.9
10.7
46.9
55
10.7
57.1
54
10.6
54
55.4
10.7
56.5
53.4
10.7
53.6
53.8
10.7
54.3
54.3
10.7
54.2
54.2
10.6
52.1
54.5
10.7
53
53.1
10.4
54.9
56
10.3
55.3
57.7
10.4
55
56
10.8
52.8
50.9
10.7
54.3
54.3
10.7
54.2
54.2
Data from ref 29. bbp = base pair.
Table 3. Torsion Angles and the Phase Angle of Pseudorotation (P) of Central Base Pair Averaged within Strand I and Strand II
and the Mean Experimental Values of Torsions with ESD for A- and B-Form DNA
(dG:dC)3
a
mean (ESD)a
(dA:dT)3
model 1
(gas, Na+)
model 2
(PCM)
model 3
(PCM, Na+)
model 1
(gas, Na+)
model 2
(PCM)
model 3
(PCM, Na+)
A-DNA
B-DNA
β (deg)
206
159
159
157
166
166
174 (14)
δ (deg)
83
81
80
78
82
82
81 (7)
ζ (deg)
265
281
281
266
293
292
289 (12)
χ (deg)
166
193
192
204
202
202
199 (8)
P (deg)
−9
9
10
11
10
10
−20−60
176 (9) BI
146 (8) BII
128 (13) BI
144 (7) BII
265 (10) BI
174 (14) BII
258 (14°) BI
271 (8) BII
120−190
Experimental values from ref 41.
λR angles. The data collected in Table 2 show that those
parameters of AT and GC central base pairs perfectly
correspond to the requirement of isostericity since they have
practically identical C1′−C1′ distances and λY and λR angles
between themselves.
The conformation of the sugar−phosphate backbone is the
second component which determines the differences in a DNA
shape. The role of sugar conformation is absolutely clear since
it possesses very different values of phase angle of
pseudorotation in A- and B-DNA. The conformations of the
sugar−phosphate backbone for different forms of DNA are also
well-described based on both experimental and MD data (see
refs 40 and 41). As for the values of torsional angles, it is known
that they occupy some specific regions of full conformational
space and are highly correlated.5 However, the experimental
distribution of these angles is notably broad, and sometimes the
regions of A-DNA and B-DNA intersect. It is also known12 that
the angles β, δ, ζ, and χ are conformation-specific. We present
these four torsions along with the value of the phase angle of
pseudorotation in Table 3. According to these data, the torsions
and the values of phase angle of pseudorotation for all
considered models are all in the range that corresponds to the
A-DNA form.
Other Conformational Parameters. This section presents
the analysis of other geometrical parameters which do not
directly depend on the DNA form and have similar values in
the case of A- and B-forms. According to calculated data, there
are no major differences whether (dG:dC)3 and (dA:dT)3
duplexes are immersed in continuum-type dielectric medium
or not. However, there are a few peculiarities which we would
like to highlight.
In the same way as it was observed for B-DNA mini-helices29
most of the A-DNA models are compressed due to a low value
of rise comparing to the rise in ideal structures (see also Figure
7). Additionally, one no-standard result is presented in Table 4,
Figure 7. Schematic pictures of duplexes discussed with the main
helical axes (solid lines) and local helix axes (dotted lines)
superimposed. Images generated with 3DNA build upon the principles
of Calladine and Drew. All structures were set with reference to the
middle helical frame defined by blocks 1, 2, and 3 and minor groove
facing the viewer.
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The Journal of Physical Chemistry B
Table 4. Conformational Parameters for A-Form Duplexes
Obtained from M06-2X/6-31G(d,p), 3DNA Ideal
Structuresa
Table 5. M06-2X and Experimental Hydrogen Bond
Distances (Å) in A-T and G-C Central Base Pairs of A- and
B-DNAa-like Duplexes at Equilibrium Geometry
ideal structure
parameters
model 1
(gas, Na+)
model 2
(PCM)
model 3
(PCM, Na+)
A-DNA
Local Central Base-Pair Parameters
(dG:dC)3
shear (Å)
−0.5
0.0
−0.0
0.01
stretch (Å)
−0.3
−0.1
−0.1
−0.10
stagger(Å)
−0.5
−0.1
−0.1
0.06
buckle (deg)
24.2
−7.2
−8.0
0.1
propeller (deg)
8.4
−13.9
−14.2
−10.5
opening (deg)
−4.5
−0.8
−0.2
−2.3
(dA:dT)3
shear (Å)
−0.1
0.0
−0.0
0.01
stretch (Å)
−0.3
−0.2
−0.2
−0.10
stagger(Å)
0.2
0.2
0.2
0.06
buckle (deg)
2.4
−1.5
−2.1
0.1
propeller (deg)
−20.2
−28.6
−28.7
−10.5
opening (deg)
1.4
3.0
3.2
−2.3
Averaged Base-Pair Step and Helical Parameters
(dG:dC)3
shift (Å)
−1.5
0.5
0.5
−0.01
rise (Å)
−1.6
3.1
3.1
3.30
tilt (deg)
−4.5
3.4
2.7
−0.1
Y-disp (Å)
1.3
−0.4
−0.6
−0.01
tip (deg)
4.5
−5.2
−4.1
0.0
(dA:dT)3
shift (Å)
0.2
0.1
0.1
−0.01
rise (Å)
2.9
3.1
3.1
3.30
tilt (deg)
−1.4
−0.3
−0.3
−0.1
Y-disp (Å)
−0.5
−0.1
−0.1
−0.01
tip (deg)
2.0
0.5
0.4
0.0
G-C
B-DNA
DNA
0.03
−0.10
0.09
−0.1
−15.1
−1.9
model 1
A-form
B-form
model 2
A-form
B-form
model 3
A-form
B-form
isolated base
pair
0.03
−0.10
0.09
−0.1
−15.1
−1.9
a
A-T
O(6)···
N(4)
N(1)···
N(3)
N(2)···
O(2)
N(6)···
O(4)
N(1)···
N(3)
2.754
3.021
2.887
2.824
2.885
3.03
2.841
2.926
2.731
2.896
2.918
2.923
2.922
2.933
2.870
2.957
3.107
2.912
2.783
2.964
2.923
2.848
2.788
2.909
2.896
2.922
2.854
2.91
2.913
3.097
3.115
2.951
2.775
2.756
2.789
Data from ref 29.
pairs in PCM models 2 and 3 leads to small elongation of the
outer O(6)···N(4) and N(6)···O(4) distances correspondently
compared to the isolated base pair. Given that the hydrogen
bond is very flexible and sensitive to changes in the
environmental conditions, such variations are quite natural.
There is also a clear influence of hydration: hydrogen bond
distances in model 1 are somewhat shorter than in models 2
and 3. The noticeabe shortening of all hydrogen bonds in
central G-C and A-T base pairs in vacuum (model 1) compared
to isolated base pairs could possibly be explained by the
backbone strain in the absence of hydration. However, it is
likely that the interbase distance is marginally underestimated
with the M06-2X/6-31G(d,p) optimization since the presently
used gradient procedure is not corrected for the basis set
superposition error.
Interaction and Binding Energies. The absence of
conformational sampling for both DNA duplex and DNA
single oligonucleotides makes resolving the thermodynamics of
oligonucleotides dimerization into A-DNA form a serious
challenge for the considered type of the calculations. Therefore,
in the current study, obtaining the thermodynamic parameters
of the duplex formation is omitted.
The main energy data are included in Table 6. The third
column of Table 6 shows theM06-2X/6-31G(d,p) interaction
energies calculated according to eq 1. These numbers do not
include the oligonucleotides relaxation. The next column of
Table 6 gives the intermolecular basis set superposition error
recalculated per base pair. The next two columns show the
oligonucleotides deformation contributions to the binding
R···Y
energy, ΔER···Y
bind , calculated according to eq 4. The ΔEbind values
in Table 6 were calculated with the M06-2X/6-31G(d,p)
method (gradient optimizations and energy evaluations are
done at the same level) corrected for BSSE (interaction
energies) and duplex deformation energy. As in all of our older
studies, we do not list the BSSE uncorrected binding energies,
as we consider them to be biased. Evidently, uncorrected
calculations would exaggerate the base-pair strength and bias
the relative energies (see also ref 43). The next column of
Table 6 gives the binding enthalpy (ΔHR···Y
bind ) which is based on
ΔER···Y
with
inclusion
of
zero
point
vibrational
energies. The
bind
last column of Table 6 presents the estimates of stability of the
A-form relative to the B-form, ΔE(A−B)
total . These values were
−0.01
3.36
0.1
0.01
−0.1
−0.01
3.36
0.1
0.01
−0.1
a
Obtained using comprehensive software package 3DNA.31 The local
base-pair step and helical parameters (rise, shift, tilt, Y-disp. and Tip)
are averaged over two steps AA/TT or GG/CC in (dA:dT)3 and
(dG:dC)3 duplexes, correspondingly.
where a negative average rise (−1.6 Å) is found for the Aconfiguration of (dG:dC)3 in model 1. Denoted in Figure 7, the
negative rise causes a strongly irregular conformation of dG3 in
the A-form (dG:dC)3. Indeed there is a large amount of
evidence that stacking interactions involving guanines are
considerably weaker than those affecting adjacent adenines.20,42,35 That could explain the scarce regularity of
(dG:dC)3 oligonucleotides.
Next, it looks like the central GC and AT base pairs are
overbuckled, overtilted, and overtipped in comparison with the
ideal structures (initial geometries). In contrast to (dG:dC)3
mini-helix there is a quite significant deviation of propeller for
the (dA:dT)3 mini-helix. Again, the same result was obtained
with B-DNA models.29 Indeed, experiments4 show that regions
of DNA with all adenine on one strand and all thymine bases
on the other do have an unusually high propeller of about 20°
to 30°, as opposed to 10° to 20° for other sequences.
We now turn to the analysis of another set of intermolecular
parameters which are gathered in Table 5. One can see that
hydrogen bond distances vary around 2.8−3.0 Å. This is the
manifestation of the intermediate strength of the hydrogen
bonds. The hydrogen bond distances (heavy atoms considered)
show that the high propeller of the central G-C and A-T base
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Table 6. Energetic and Thermal Effects of Binding in A- and B-DNAa along with BSSE Corrections (kcal mol−1 per Base Pair)
relaxation energy
M06-2X structure
model 1 (gas, Na+)
model 2 (PCM)
model 3 (PCM, Na+)
model 1 (gas, Na+)
model 2 (PCM)
model 3 (PCM, Na+)
a
DNA
ΔER···Y
int (with BSSE)
A
B
A
B
A
B
−38.9
−37.6
−16.8
−16.3
−17.0
−16.3
A
B
A
B
A
B
−17.3
−16.7
−10.1
−9.5
−10.5
−10.2
BSSE
ERr
(dG:dC)3 Duplex
6.5
4.6
5.9
8.9
5.3
9.0
1.1
1.7
6.2
8.3
0.9
1.5
(dA:dT)3 Duplex
4.2
3.4
4.3
1.6
1.9
1.8
2.0
0.4
1.9
1.9
2.9
1.1
EYr
ΔER···Y
bind (with BSSE)
ΔHR···Y
bind (0 K)
ΔE(A−B)
total
10.2
6.1
2.5
1.1
3.2
2.3
−24.2
−22.6
−5.3
−13.5
−5.5
−12.4
−29.9
−27.7
−10.2
−14.2
−11.2
−13.1
−38.5
12.4
2.3
3.5
1.8
3.4
2.6
−1.5
−12.8
−4.7
−7.3
−5.1
−6.5
−5.9
−16.7
−6.8
−9.0
−7.2
−9.2
−19.7
−1.4
−3.5
−1.4
−0.6
Data from ref 29.
Table 7. Energy Differences between the Single Oligonucleotides in A- and B-DNA Conformations and the Intermolecular Basis
Set Superposition Errors, Presented in kcal/mol per One Base Pair
those that are determined from gas phase interactions. Besides,
the differences between energy and enthalpy of binding also
decrease in PCM models. This result is true both for A- and Bforms of mini-helix.
(ii) Interestingly, ΔER···Y
int seems to be virtually the same in Aand B-duplexes. We expect that this is because the spatial
geometry of interacting base pairs is very similar in both A- and
B-forms. This is not easy to prove completely. However, we
direct the reader to the results presented in Table 5. One may
see that the corresponding interatomic distances in A- and Bforms are differing roughly in 0.1 Å.
(iii) The mini-helices in A-form are more sensitive to the
surrounding factors and are more susceptible to deformation.
In contrast to the B-form, inclusion of relaxation energy for the
cases of the interaction in PCM for A-DNA results in
decreasing of ΔER···Y
bind almost three times for (dG:dC)3 duplex
and almost twice for (dA:dT)3 duplex.
(iv) From the energies of oligonucleotide relaxation, one can
see the clearly expressed strand specificity. The pyrimidine
nucleotides (C3, T3) need more energy to adopt DNA-specific
conformation. Clearly, in water solution the strands relaxation
calculated simply by subtracting the total energy of the minihelix in the B-form from the corresponding value in the A-from.
According to data in Table 6, the A-configuration poses the
larger stability in all models, especially in model 1 (gas, Na+)
referring to (dG:dC)3. The A- and B-forms in model 1 (gas,
Na+) have very close BSSE errors. Since ΔER···Y
bind for the A- and
B-forms in this case differ by less than 2 kcal/mol, the larger
stability of the A-configuration may be due to larger stabilities
of the A-form unrelaxed (as well as relaxed) oligonucleotides
(see Table 7). In our opinion, this happens because of the
presence of unsolvated sodium cation which seems to
coordinate oxygens of phosphate groups in a different
unpredictable manner leading to the strong deformations of
the strands. With these data, the clear influence of hydration
and its affection on the structure and stability of A- and B-forms
of DNA is demonstrated.
The further analysis of interaction and binding energies
revealed the following:
(i) The mini-helixes are predicted to be stable in vacuum and
water solution. As expected, the values of binding energies and
enthalpies in solution are nearly two times lower compared to
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The Journal of Physical Chemistry B
favoring specific values of roll and slide at a local level. In
particular, they support the experimentally known fact that AA/
TT steps prefer the B-form over the A-ones, whereas GG/CC
steps may be found in either the B- or A-form.
happens easily. The oligonucleotides in the A-form have
stronger deformation, than in the B-form. For hydrated models
this results in less energy needed for binding of oligonucleotides into A-DNA mini-helix.
(v) One more interesting hypothesis that can be evaluated
from the presented calculation is that the DNA probably
preferred a specific base sequence (AT or GC) to form A- or Bconformation through the helix. The data in Table 6 show that
the binding energy per base pair in (dA:dT)3 is very small in
the gas phase, in contrast to (dG:dC)3. The low binding energy
of the A-form (dA:dT)3 in comparison with its B-form could
indicate a preference of this sequence to stay in the Bconformation. It may also indicate that the A-form of DNA
consists of GC base pairs and could be easily deformed (for
example turned to the B-form) on the AT sequence. The
relative energies ΔE(A−B)
total also confirmed this idea, showing that
the (dG:dC)3 duplex in the A-form is two times more stable
than the (dA:dT)3 duplex. These data are in line with the
analysis on the behavior of roll and slide correlation that has
been performed earlier.
As we already mentioned, DNA in physiological conditions
exists exclusively in the B-form. It is absolutely clear that
hydrated models 2 and 3 describe the physicochemical
conditions which are significantly closer to physiological ones
than to the properties of low hydrated films or high ionic
strength water solutions where the A-form dominates.6−9
Therefore, it would be realistic to expect that our calculations
have to predict considered mini-helices to be more stable in the
B-form. However, the data presented in Table 6 show the
oppositeat the level of total energy analysis, the A-form is the
most stable. The preference is really remarkable in the gas
phase and reaches just a few kilocalories per mole in water bulk.
To explain these data, we refer to the results published by
Beveridge and co-workers.44 On the basis of the data of classical
molecular dynamic simulations, the authors revealed that the
most important component resulting in a domination of a Bform of DNA in water solution is hydration energy. This is
completely in line with the data presented in Table 6.
Therefore, we guess that to observe predominance of the Bform, more accurate modeling of the hydration (including an
explicit one) is needed. Such hypothesis will be verified very
soon by the investigation of the complexes of homopolymers
having the structure of (dG:dC)5 and (dA:dT)5 with structural
water molecules.
■
ASSOCIATED CONTENT
S Supporting Information
*
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.jpcb.5b04644.
M06-2X/6-31G(d,p) optimized reference geometries of
(dA:dT)3 and (dG:dC)3 mini-helices (compensated and
uncompensated forms) in vacuum and immersed into a
continuum-type dielectric medium and the full set of
unaveraged base-pair step and helical parameters. (PDF)
■
AUTHOR INFORMATION
Corresponding Author
*Phone: (601) 979-3482. Fax: 60 1979 7823. E-mail: jerzy@
icnanotox.org.
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
This work was supported by NSF CREST Grant No. HRD0833178. We thank the Extreme Science and Engineering
Discovery Environment (XSEDE) for the award allocations
(Grant Nos. TG-DMR110088 and CHE140005) and the
Mississippi Center for Supercomputer Research (Oxford, MS,
USA) for a generous allotment of computer time. Computational facilities of the joint computational cluster of SSI
“Institute for Single Crystals” and Institute for Scintillation
Materials of National Academy of Science of Ukraine
incorporated into Ukrainian National Grid are gratefully
acknowledged. As presented here, the quantum-chemical
study of DNA continues the series of nucleic acids studies
started by an outstanding researcher, our friend and colleague
Dr. Oleg Shishkin. His contributions to computational
chemistry science are invaluable. Starting from the simplest
bases of nucleic acids, he influenced the whole scientific field
devoted to the key aspects of structural properties and specific
features of nucleic acids and their fragments (for review, see ref
45). His prominent ideas are involved in each of these studies.
Oleg will always be missed and we cherish the memories we
have.
■
■
CONCLUSION
DFT optimization of a fairly complex model such as (dG:dC)3,
(dA:dT)3 DNA mini-helices in the A-form is feasible using
M06-2X meta-hybrid potential combined with the comparatively undemanding 6-31G(d,p) basis set. All predicted
structural parameters that define A-DNA and distinguish it
from B-DNA are close to observable experimental values.
Namely, they are specific backbone torsion angles (β, δ, ζ, and
χ), sugar puckers (C-3′ endo), and step and base-pair
parameters. Nevertheless, numerical data itself should be
considered with necessary caution because of the strong
influence of edge effects and application of continuum model of
hydration. In particular, we guess that application of PCM, in
spite of explicit hydration, results in slight preference of relative
stability of the A-form over B-ones.
Presented structural and energetic parameters offer evidence
that two steps of GG/CC or AA/TT are already enough to
turn the DNA helix to generate different forms (A or B) by
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