Structure and Binding Energy of Double-Stranded A-DNA Mini-helices

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Structure and Binding Energy of Double Stranded A-DNA Mini-Helices: Quantum-Chemical Study Tetiana A Zubatiuk, Maxim A. Kukuev, Alexandra S. Korolyova, Leonid Gorb, Alexey Nyporko, Dmytro Mykolayovich Hovorun, and Jerzy Leszczynski J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b04644 • Publication Date (Web): 09 Sep 2015 Downloaded from http://pubs.acs.org on September 14, 2015

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The Journal of Physical Chemistry

Structure and Binding Energy of Double Stranded A-DNA Mini-Helices: QuantumChemical 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, 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, MS 39217, USA.

ACS Paragon Plus Environment

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ABSTRACT

The 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/6-31G(d,p) method has been utilized to identify the optimal geometries and predict physico-chemical parameters of these systems. The results show the ability of the corresponding mini-helices to preserve their A-like conformation under the influences of solvent, charge, and Na+ counterions. Presented structural and energetic data offers 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, Slide at a local level. Our calculations support the experimentally known fact that AA/TT steps prefer B-form over A-ones, whereas GG/CC steps may be found in either the B- or A-form. The stability of ( A− B ) mini-helices at the level of total energy analysis ∆Etotal is discussed.

KEYWORDS: nucleic acids, DNA, DFT calculations, structure-relationship properties.

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 right-handed ADNA and B-DNA (rare – left-handed Z-form) structural forms.1,2 The general number of complexes containing A-form of DNA is half of B-form contained ones.2 Thus, despite A-DNA has been discovered in non-physiological environment (low humidity, high ionic strength),3 the importance of both right-handed DNA forms in biological processes is undisputed.


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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 c.a. 70°, helical diameter is about 20 Å. These parameters correspond with the ones that characterize a B-DNA form: 10 pairs per turn, inclination 90°, helical diameter equal to c.a. 20 Å. However, in fact, the structure of A-DNA differs significantly from the structure of the Watson-Crick B-DNA (see Fig. 1). This is because the base pairs of A-form displace almost half of the radius from the helical 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 (Fig. 1). Also, B-DNA conformation contains the DNA bases stacked in parallel fashion perpendicular to the main helix axis with approximately zero Roll, positive Slide and approximately 36° helical Twist, while A-form possesses the conformation where the base pair tilted with respect to the main helix axis and have 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 C-3' endo - in the A-form (Fig. 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 DNA.


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Figure 1. The A- and B-form of DNA macromolecule (side and top view).

Figure 2. The 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 A-form takes place during the interaction with some enzymes. For instance, during the interaction with DNA-polymerase (see for example 10

and the references therein ). Since DNA undergoes enormous amount of structural changes and exists in multiple forms

(A, BI, BII, C, D, Z, etc.) which differ with the helical parameters, conformation of backbone, and orientation of bases, 11,12 the resolving of the DNA structure is one of the primary steps for most investigations. The reliable methods to perform such investigations are X-ray diffraction,


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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 represent the main computational tool used to study DNA structure and dynamics. Classical MD studies at the atomic level 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 used to test and confirm experimental findings.20 However, the most serious limitation of classical molecular dynamics is their force fields which are derived based on 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 above described situation is quite straightforward. This is 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 DFT level.21–24 First quantum mechanical (QM) reliable data about the structure of DNA was 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-DNA 29,30 at static quantum-chemical level. Despite the lack of the conformational sampling, the results showed


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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 29 towards 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 A-conformation (Fig. 3). Presented in Fig. 3, DNA model nucleotides binding is the simplest A-type double helices (mini-helices) 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 29 we are also able to compare some geometrical parameters, the binding and relative energies of aforementioned mini-helices adopting A- and B-forms, revealing and distinguishing vital features of both forms.

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.


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COMPUTATIONAL DETAILS We analyze fully optimized double stranded A-DNA-like mini-helices that contain 3 base pairs. Current study applies the very similar computational protocols that were used in our recent publication.29 All optimized geometries are published in SI (Tables S1–S6). The initial (further referred as “ideal”) structures of the duplexes were constructed with the canonical A-DNA conformations using 3DNA program,.31 Initial duplex models were composed of G-C and A-T base pairs. 5'- and 3'-terminal phosphate groups were substituted with methyl groups, so duplex contained 2 pairs of phosphate groups and 4– charge as consequence (Fig. 3). The analysis was performed for the following models: Model 1 is A-type DNA mini-helix in which the negative charges have been

•

compensated by Na+ ions in vacuum, without including additional environment effects. The Na+ ions have been located near (approx. 2.4 Å) two terminal phosphate oxygen atoms of the backbone. •

Model 2 is negatively charged A-type duplex immersed into continuum type dielectric

medium mimicking water. This model includes average influence of compensating ions (see the explanation in 29). •

To form Model 3, Model 1 has been hydrated the same way as Model 2 (see 29 for the

details). The Gaussian09 32 program was used for geometry optimizations and all single point M06-2X 33

calculations. The highly parameterized, empirical exchange–correlation M06-2X functional

has been shown to describe well non-covalent 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 6-31G(d,p) basis set


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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 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 ∆ EintR...Y 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) and assuming the geometries of the optimized duplex. 38,39 Thus, the results are corrected for the mathematical artifact called intermolecular BSSE. ∆E intR...Y = E R...Y − ( E R + E Y )

(1)

R...Y When calculating the binding energy of duplex ∆ Ebind it is important to further add the duplex

deformation energy Edef. 38 The deformation energy is a sum of repulsive contribution 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 evaluated with the monomer basis set. In summary, the binding energy is defined in the following way:


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R ...Y R ...Y ∆Ebind = ∆E int + E def ,

(2)

where Edef = E rR + E Yr

(3)

and

R E rR = E R − Eopt Y E rY = E Y − 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 3DNA 31 program which provides a full set of base-pair, base-pair step, helical and backbone features. The atom numbering used is shown in Fig. 3. The definition of the parameters is clear from Figures 3-5. Besides the local base-pair parameters (Shear, Stretch, Stagger, Buckle, Propeller, Opening), the virtual inter-base parameters (distance dC1′ - C1′ and angles λY, λR) also characterize the geometry of the central base pair. The local base-pair step (Rise, Slide, Shift, Tilt, Roll, 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 analyze of 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 sugar ring (P) and the main chain torsion angles (in the 5' – 3' direction) which belong to the nucleotides containing the central base pair.


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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.

Figure 5. Schematic diagram of a duplex composed of three stacked base pairs and a sugar phosphate backbone. Labelled torsion angles on strands I and II belong to the nucleotides of central base pair (base pair 2). Phosphates are marked with black dots and sugar O4ʹ atoms are marked with open circles. Single stranded oligonucleotides are labelled as Y and R.

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 sugar conformation is well known and has already been mentioned. We just confirm that all the


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structures belonging to Models 1-3 have the sugar in northern (C-3' endo) regions. The corresponding values of 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 known 4 that different sequences of bases in DNA can generate different double-helical structures by favoring different values of Roll, Slide, and Twist at a local level. Almost all of the external features of the A and 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 mini-helices. 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 B-form Roll, lower than in B-form Twist, larger than in B-form Inclination, and negative X-displacement. As expected, parameters that include an influence of water bulk correspond much better to geometry of ideal form than those describing the geometry of minihelices in vacuum. This is especially true in the case of (dG:dC)3 duplexes. One may also see that the values are sequence specific.

Table 1. Base Pair Parameters of A-form Mini-Helices Obtained at 6-31G(d,p)/M06-2X Level of Theory Compared to B-forma,b, Ideal 3DNA Structures and Molecular Dynamics Datac. Parametersb (dG:dC)3 duplex Slide (Å) Roll (deg.) Twist (deg.) Inclination (deg.)

Model 1 (gas, Na+) А B

Model 2 (PCM) A B

Model 3 (PCM, Na+) A B

A

B

-1.6 24.2 55.8 24.4

-1.1 9.4 33.3 15.5

-1.0 9.7 32.6 16.0

-1.4 12.4 30.3 22.6

0.5 1.7 35.9 2.8

2.2 -11.2 50.7 -12.7

1.4 -2.4 42.7 -2.4

0.7 -3.5 39.0 -4.7

Ideal

MD A

B

32.6 15.8

-0.4 3.6 32.6 6.8


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X-displacement (Å) -2.8 3.2 -2.9 1.8 -2.8 2.3 -4.4 0.5 -4 (dA:dT)3 duplex Slide (Å) 0.1 0.3 -0.6 0.3 -0.5 0.0 -1.4 0.5 Roll (deg.) 9.9 -4.4 6.2 -2.8 6.1 -4.3 12.4 1.7 Twist (deg.) 34.7 39.4 38.6 42.3 38.3 44.1 30.3 35.9 32.6 Inclination (deg.) 16.8 -6.4 9.3 -3.9 9.2 -5.7 22.4 2.8 15.8 X-displacement (Å) -1.3 0.9 -1.5 0.7 -1.5 0.4 -4.5 0.5 -4 a Data from ref. 29 b The local base-pair step (Slide, Roll, Twist) and helical parameters (Inclination, Xdisplacement) are averaged over two steps AA/TT or GG/CC in (dA:dT)3 and (dG:dC)3 duplexes, correspondingly. c Ref. 40

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-1.4 -0.4 3.6 32.6 6.8 -1.4

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 A- and B-type DNA geometries, which lie to the left and right, respectively, of the line (Calladine & Drew 4). The overall picture may be made clear by examining plots of Roll versus Slide (as was proposed in 4) for considering mini-helices in A- and B-forms as shown in Fig. 6. The analysis of Slide-Roll correlation presented in the Fig. 6 reveals that Roll and Slide values of considered (dG:dC)3 mini-helices belong to the region that characterizes A-DNA form. As one may see, the situation with similar parameters of (dA:dT)3 mini-helix is not so straight forwarded, since those parameters belong to the area which are on the border between A- and B-forms. There are at least two arguments that could explain this. It is known that in contrast to (dG:dC)3 sequence, the


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sequence (dA:dT)3 strongly prefer the B-type conformation.4,5 This is why some geometrical parameters that characterize AA/TT step in A-form could be on the border between A- and Bform indicating 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 λR angles. The data collected in Table 2 shows 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.

Table 2. Virtual Inter-Base Parameters of A-form Mini-Helices Compared to B-forma, and Ideal 3DNA Structures.

Central bp (dG:dC)3 duplex dC1′ - C1′ (Å) λY (deg.) λR (deg.) (dA:dT)3 duplex dC1′ - C1′ (Å) λY (deg.) λR (deg.) a Data from Ref. 29

Model 1 (gas, Na+) A B

Model 2 (PCM) A B

Model 3 (PCM, Na+) 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

10.6 52.1 54.5

10.7 53 53.1

10.4 54.9 56

10.3 55.3 57.7

10.4 55 56

Ideal A

B

10.7 53.6 53.8

10.7 54.3 54.3

10.7 54.2 54.2

10.8 52.8 50.9

10.7 54.3 54.3

10.7 54.2 54.2

The conformation of 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 sugar–phosphate backbone for different forms of DNA are also well described based on both experimental and MD data (see ref. 40,41). 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


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sometimes the regions of A-DNA and B-DNA intersect. It is also known 12 that the angles β, δ, ζ and χ are conformation specific. We present these four torsions along with the value of phase angle of pseudorotation in Table 3. According to this data, the torsions and the values of phase angle of pseudorotation for all considered models are all in the range that corresponds to the ADNA form.

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-, B-form DNA. (dA:dT)3 (dG:dC)3 Mean (ESD)a Model 1 Model 2 Model 3 Model 1 Model 2 Model 3 A-DNA B-DNA + + (gas, Na ) (PCM) (PCM, Na ) (gas, Na+) (PCM) (PCM, Na+) 176° (9°) BI β 206° 159° 159° 157° 166° 166° 174° (14°) 146° (8°) BII 128° (13°) BI δ 83° 81° 80° 78° 82° 82° 81° (7°) 144° (7°) BII 265° (10°) BI ζ 265° 281° 281° 266° 293° 292° 289° (12°) 174° (14°) BII 258° (14°) BI χ 166° 193° 192° 204° 202° 202° 199° (8°) 271° (8°) BII P -9° 9° 10° 11° 10° 10° -20°–60° 120°–190° a 41 Experimental values from Ref.

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 case of Aand 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 below. In the same way as it was observed for B-DNA mini-helices 29 most of the A-DNA models are compressed due to low value of Rise comparing to the Rise in ideal structures (see also Fig.7).


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Additionally, one no-standard result presented in Table 4, where a negative average Rise (-1.6 Å) is found for A-configuration of (dG:dC)3 in Model 1. Denoted in Figure 7, the negative Rise causes a strongly irregular conformation of dG3 in 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 over buckled, over tilted and over tipped comparing to the ideal structures (initial geometries). In contrast to (dG:dC)3 mini-helix there is a quite significant deviation of Propeller for (dA:dT)3 mini-helix. Again, the same result was obtained with B-DNA models 29. Indeed, experiments 4 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°, against 10° to 20° for other sequences.

Table 4. Conformational Parameters for A-form Duplexes Obtained from M06-2X/631G(d,p), 3DNA Ideal Structuresa. Model 1 (gas, Na+) Local central base-pair parameters Parameters

Model 2 (PCM)

Model 3 (PCM, Na+)

(dG:dC)3 -0.0 -0.1 -0.1 -8.0 -14.2 -0.2 (dA:dT)3 Shear (Å) -0.1 0.0 -0.0 Stretch (Å) -0.3 -0.2 -0.2 Stagger(Å) 0.2 0.2 0.2 Buckle (deg.) 2.4 -1.5 -2.1 Propeller (deg.) -20.2 -28.6 -28.7 Opening (deg.) 1.4 3.0 3.2 Averaged base-pair step and helical parameters Shear (Å) Stretch (Å) Stagger(Å) Buckle (deg.) Propeller (deg.) Opening (deg.)

-0.5 -0.3 -0.5 24.2 8.4 -4.5

0.0 -0.1 -0.1 -7.2 -13.9 -0.8

Ideal structure A-DNA B-DNA

0.01 -0.10 0.06 0.1 -10.5 -2.3

0.03 -0.10 0.09 -0.1 -15.1 -1.9

0.01 -0.10 0.06 0.1 -10.5 -2.3

0.03 -0.10 0.09 -0.1 -15.1 -1.9


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(dG:dC)3 Shift (Å) -1.5 0.5 0.5 -0.01 -0.01 Rise (Å) -1.6 3.1 3.1 3.30 3.36 Tilt (deg.) -4.5 3.4 2.7 -0.1 0.1 Y-disp. (Å) 1.3 -0.4 -0.6 -0.01 0.01 Tip (deg.) 4.5 -5.2 -4.1 0.0 -0.1 (dA:dT)3 Shift (Å) 0.2 0.1 0.1 -0.01 -0.01 Rise (Å) 2.9 3.1 3.1 3.30 3.36 Tilt (deg.) -1.4 -0.3 -0.3 -0.1 0.1 Y-disp. (Å) -0.5 -0.1 -0.1 -0.01 0.01 Tip (deg.) 2.0 0.5 0.4 0.0 -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. Let us 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 central G–C and A-T base pairs in PCM Models 2 and 3 leads to small elongation of 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 noticeably 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.


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Figure 7. Schematic pictures of duplexes discussed with the main helical axes (solid line) and local helix axe (dotted line) 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.

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. DNA

O(6)· ·N(4)

Model 1 A-form 2.754 B-form 3.021 Model 2 A-form 2.918 B-form 2.923 Model 3 A-form 2.923 B-form 2.848 Isolated base pair 2.788 a 29 Data from

G-C N(1) ··N(3)

N(2) ··O(2)

A-T N(6) ··O(4) N(1) ··N(3)

2.887 2.824

2.885 3.03

2.841 2.926

2.731 2.896

2.922 2.933

2.870 2.957

3.107 2.912

2.783 2.964

2.909 2.896

2.854 2.91

3.097 3.115

2.775 2.756

2.922

2.913

2.951

2.789


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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 current study, obtaining the thermodynamic parameters of the duplex formation is omitted. The main energy data is included in Table 6. The third column of Table 6 shows theM062X/6-31G(d,p) interaction energies calculated according to (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 R...Y R...Y deformation contributions to the binding energy ∆Ebind calculated according to (4). The ∆Ebind

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 43). The next column of R...Y R...Y ) which is based on ∆Ebind with inclusion of zero Table 6 gives the binding enthalpy ( ∆H bind

point vibrational energies. The last column of Table 6 presents the estimates of stability of A( A− B ) form relatively to the B-form, ∆Etotal . These values were calculated simply by subtracting total

energy of mini-helix in B-form from corresponding in A-from.

Table 6. The Energetic and Thermal Effects of Binding in A- and B-DNAa along with BSSE Corrections (kcal mol-1 per Base Pair). M06-2X structures

DNA

∆E intR...Y

BSSE

(with BSSE)

Relaxation energy

E

R r

E

Y r

R...Y ∆Ebind

(with BSSE)

R...Y ∆H bind

( A− B ) ∆Etotal

(0K)

(dG:dC)3 duplex


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Model 1 (gas, Na+) Model 2 (PCM) Model 3 (PCM, Na+)

A B A

-38.9 -37.6 -16.8

6.5 5.9 5.3

4.6 8.9 9.0

10.2 6.1 2.5

-24.2 -22.6 -5.3

B A B

-16.3 -17.0 -16.3

1.1 6.2 0.9

1.7 8.3 1.5

1.1 3.2 2.3

-13.5 -5.5 -12.4

A B

-17.3 -16.7

4.2 4.3

3.4 1.6

12.4 2.3

-1.5 -12.8

A B A B

-10.1 -9.5 -10.5 -10.2

1.9 2.0 1.9 2.9

1.8 0.4 1.9 1.1

3.5 1.8 3.4 2.6

-4.7 -7.3 -5.1 -6.5

-29.9 -27.7 -10.2 -14.2

-38.5

-11.2 -13.1

-3.5

-1.4

(dA:dT)3 duplex Model 1 (gas, Na+) Model 2 (PCM) Model 3 (PCM, Na+) a

-5.9 -16.7 -6.8 -9.0 -7.2 -9.2

-19.7 -1.4 -0.6

Reprint from. 29

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+) R...Y have very close BSSE errors. Since binding energies ( ∆Ebind ) 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 different unpredictable manner leading to the strong deformations of the strands. With this data, the clear influence of hydration and its affection on the structure and stability of A- and B-forms of DNA is demonstrated.

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. Single strand

Model 1 (gas, Na+)

Model 2 (PCM)

A-DNA

A-DNA B-DNA A-DNA Relaxed oligonucleotides Eopt(A-DNA)-Eopt(B-DNA)

B-DNA

Model 3 (PCM, Na+) B-DNA


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A3 T3 G3 C3

-19.9 -11.0 -20.5 -15.8

A3 T3 G3 C3

-18.1 -1.0 -16.7 -20.5

A3 T3 G3 C3

1.5 2.7 3.3 3.3

1.5 2.7 3.0 2.9

-1.4 -2.8 0.4 -6.1 Unrelaxed oligonucleotides Esp (A-DNA)-Esp(B-DNA) 0.1 -0.9 2.1 -3.0 Intermolecular BSSE 0.2 0.2 0.2 1.6 1.8 1.6 0.2 0.1 0.1 5.2 1.0 6.1

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-0.4 -2.6 0.7 -6.0

0.9 -1.3 1.7 -4.4

0.7 2.2 0.1 0.8

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 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 for B-form of mini-helix. (ii)

Interestingly, that the energy of interaction ( ∆E intR...Y ) seems to be virtually the

same in A- and 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 would like to direct the reader to the results presented in Table 5. One may see that the corresponding interatomic distances in A- and B-forms 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 B-form, inclusion of relaxation energy for the


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R...Y cases of the interaction in PCM for A-DNA results in decreasing of ∆Ebind 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 happen easily. The oligonucleotides in A-form have stronger deformation, than in 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 specific base sequence (AT or GC) to form A- or B-conformation through the helix. The data in Table 6 shows that the binding energy per base pair in (dA:dT)3 is very small in gas phase, in contrast to (dG:dC)3. The low binding energy of A-form (dA:dT)3 comparing to its B-form could indicate a preference of this sequence to stay in B-conformation. It may also indicate that A-form of DNA consists of GC base pairs and could be easily deformed (for example turned to B-form) on the AT sequence. The relative energies ( A− B ) ∆Etotal also confirmed this idea, showing that (dG:dC)3 duplex in A-form is two times more

stable than (dA:dT)3 duplex. This data is in line with the analysis on the behavior of Roll and Slide correlation that has been performed above. As we already mentioned, DNA in physiological conditions exists exclusively in B-form. It is absolutely clear that hydrated Models 2 and 3 describe the physico-chemical conditions which are significantly closer to physiological ones than to the properties of low hydrated films or high ionic strength water solutions where 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 B-form. However, the data presented in Table 6 shows opposite – at the level of total energy analysis, A-


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form is the most stable. The preference is really remarkable in gas phase and reaches just few kcal/mol in water bulk. To explain this data, we would like to refer to the results published by D. L. Beveridge with coworkers.44 Based on the data of classical molecular dynamic simulations, the authors revealed that the most important component resulting in a domination of a B-form 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 B-form, more accurate modeling of the hydration (including 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.

CONCLUSION DFT optimization of fairly complex model such as (dG:dC)3, (dA:dT)3 DNA mini-helices in A-form is feasible using M06-2X meta-hybrid potential combined with 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), step and base-pair parameters. Nevertheless, numerical data itself should be considered with necessary caution because of strong influence of edge effect 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 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 favoring specific values of Roll, Slide at a local level. In particular, they support the


22

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experimentally known fact that AA/TT steps prefer B-form over A-ones, whereas GG/CC steps may be found in either the B- or A-form.

AUTHOR INFORMATION Corresponding Author *Phone: (601) 979-3482. Fax: 60 1979 7823. E-mail: [email protected].

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT This work was supported by NSF CREST Grant# HRD-0833178. Authors also thank the Extreme Science and Engineering Discovery Environment (XSEDE) for the award allocations (TG-DMR110088 and CHE140005) and the Mississippi Center for Supercomputer Research (Oxford, MS) for a generous allotment of a computer time. Computational facilities of 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. 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


23


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structural properties and specific features of nucleic acids and their fragments (for review see 45). His prominent ideas are involved in each of these studies. Oleg will always be missed and we cherish the memories we have.

Supporting Information Available 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 continuum type of dielectric medium; the full set of unaveraged base-pair step and helical parameters. This material is available free of charge via the Internet at http://pubs.acs.org.

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TABLE OF CONTENTS ARTWORK


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Figure 1. The A- and B-form of DNA macromolecule (side and top view). 81x57mm (300 x 300 DPI)



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Figure 2. The conformations of ribose ring. 81x26mm (300 x 300 DPI)


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Figure 3. Studied double-helical A-like trideoxyribonucleoside diphosphates (d(GpGpG) 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. 81x39mm (300 x 300 DPI)



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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. 81x43mm (300 x 300 DPI)


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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 A- and Btype DNA geometries, which lie to the left and right, respectively, of the line (Calladine & Drew). 81x50mm (300 x 300 DPI)



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Figure 7. Schematic pictures of duplexes discussed with the main helical axes (solid line) and local helix axe (dotted line) 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. 81x77mm (300 x 300 DPI)


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73x43mm (300 x 300 DPI)


Structure and Binding Energy of Double-Stranded A-DNA Mini-helices

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