Guanine Bases in DNA G-Quadruplex Adopt Nonplanar Geometries

Apr 3, 2012 - parallel G-quadruplex with NDB ID UDF062 is analyzed and explained with theoretical calculations. The extent of the pyramidalization ...
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Guanine Bases in DNA G-Quadruplex Adopt Nonplanar Geometries Owing to Solvation and Base Pairing Vladimír Sychrovský,*,† Zuzana Sochorová Vokácǒ vá,† and Lukás ̌ Trantírek‡ †

Institute of Organic Chemistry and Biochemistry, v.v.i., Academy of Sciences of the Czech Republic, Flemingovo square 2, 166 10 Prague 6, Czech Republic ‡ Bijvoet Center for Biomolecular Research, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands S Supporting Information *

ABSTRACT: The effect of base pairing and solvation on pyramidalization of the glycosidic nitrogen found in the residues of parallel G-quadruplex with NDB ID UDF062 is analyzed and explained with theoretical calculations. The extent of the pyramidalization depends on the local geometry of the 2′-deoxyguanosine residues, namely on their glycosidic torsion and sugar pucker, which are predetermined by the 3D-architecture of G-quadruplex. Pyramidal inversion of the glycosidic nitrogen found in 2′-deoxyguanosines of G-quadruplex is induced owing to site-specifically coordinated solvent. Different adiabatic structural constraints used for fixing the base-to-sugar orientation of 2′-deoxyguanosine in geometry optimizations result in different extents of pyramidalization and induce pyramidal inversion of the glycosidic nitrogen. These model geometry constraints helped us analyze the effect of real constraints represented by explicit molecular environment of selected residues of the G-quadruplex. The maximal extent of the glycosidic nitrogen pyramidalization found in the high-resolution crystal structure corresponds to the calculation to deformation energy of only 1 kcal mol−1. The out-of-plane deformations of nucleobases thus provide a way for compensating the site-specific external environmental stress on the G-quadruplex.

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INTRODUCTION The nucleic acid (NA) bases are mostly regarded as planar units of NA structure. The reason for accepting this assumption is that the out-of-plane deviations of the inner-ring atoms observed in the crystal structures of isolated bases were rather small and abundances of the opposite out-of-plane deviations were statistically similar, so their overall geometries were classified as planar.1 The picture was basically accepted with the exception of intrinsically pyramidal amino group that was recognized theoretically and studied rather extensively.2−4 Recently, several theoretical studies suggested the existence of nonplanar geometries also for the inner-ring atoms of NA bases, in particular for the effective conformations of different vibration states.5,6 In addition, hydration7−9 and stacking interactions10 of isolated bases and interactions between NA base and phosphate in nucleotides11,12 were found to promote nonplanarity of the NA bases. Rather extreme deformations of base geometries were also calculated for the electronic excited states of NA bases.13,14 Experimental observation of nonplanar NA bases is a challenging task. The individual populations of different © 2012 American Chemical Society

vibration states with distinct nonplanar geometries indicated by the above-mentioned theoretical studies most likely average to overall geometry that can be characterized as planar and as such it is also observed in experiment. Similarly, the effect of hydration proposed theoretically for arrangement of solvent surrounding isolated bases without experimentally validated sustainability of such pattern most probably average out as result of solvent dynamics. Experimental observation of nonplanar bases therefore critically depends on whether the effects perturbing their intrinsically planar geometries are sustainable during experiment. Although existence of nonplanar geometries of the NA base in oligonucleotides was suggested by several nuclear magnetic resonance (NMR) spectroscopic observations,15−18 the direct experimental evidence was missing until recently. In 2009, we performed a comprehensive statistical analysis of the X-ray structural data obtained at ultrahigh resolution for NA Received: November 15, 2011 Revised: March 28, 2012 Published: April 3, 2012 4144

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oligonucleotides.19 The study complemented by theoretical calculations revealed a novel structural property of NA nucleobases, namely, pyramidalization at the glycosidic nitrogen of purine and pyrimidine RNA and DNA bases. The pyramidalization was shown to be dependent on the local geometry of a nucleoside, namely on orientation of the glycosidic bond. The glycosidic linkage thus clearly provides one of the ways the pyramidalization induced. Interestingly, the previous analysis showed that reorientation of the glycosidic torsion from the syn to anti region inverted the configuration of the glycosidic nitrogen.19 It follows that the rules for interpretation of NMR data not respecting the pyramidalization could bias structural information obtained with this widely used technique. This clearly concerns the NMR scalar couplings across the glycosidic bond20 but the same can be expected also for NMR cross-correlated relaxation rates21,22 or residual dipolar couplings.17 Our very recent study suggests that the pyramidalization not only is the structural property of a NA base but also is important for its reactivity during the glycosidic bond cleavage (Sebera, Trantirek, Tanaka, Sychrovsky; unpublished data). Although the dependences on glycosidic torsion angle and sugar pucker calculated previously explained major trends observed for the pyramidalization in NA crystal structures, notable fraction of the experimental data still violated the theoretical model proposed.19 In particular, the two antipodal pyramidalizations of the glycosidic nitrogen observed for nucleosides with the same base-to-sugar orientation were not explained satisfactory. Some factors, other than constrained glycosidic torsion angle and adiabatically relaxed predefined sugar pucker clearly had to modulate the stereochemistry at the glycosidic nitrogen in the crystal structures. In this study we therefore focused on determination of these factors such as base-pairing, hydration, and ion-base interactions. The highresolution criterion of the crystallographic data had to be applied not only for selected nucleosides but particularly for their molecular surroundings. It turned out that the crystallographic data for parallel DNA G-quadruplex with NDB ID UDF062 is the most relevant data set in this respect. The results obtained highlight interplay between deformation of NA base and its specific solvation showing thus the mechanism of how the complex environmental effects are propagated into local structure of NAs.

using the concept of pseudorotation.25 Conformations with pseudorotation phase angle P = 0° ± 90° and P = 180° ± 90° are denoted as N and as S conformation, respectively. The magnitude of the pyramidalization of the glycosidic nitrogen, called further N9-pyramidalization or simply the pyramidalization, was monitored with the improper torsion angle κ′ (Figure 1). According to the definition, κ′ = 0° corresponds to idealized planar configuration of the glycosidic nitrogen. The opposite signs of the κ′ torsion are clearly coherent with the two antipodal pyramidalizations of glycosidic nitrogen. QM Calculations. As mentioned, the pyramidalization in G nucleoside is virtually close to zero and deformation of NA base can be obtained only as an effect of some external factors, which are typically the base−base interactions. Orientation of the glycosidic bond was shown to affect the pyramidalization.19 To model the effect of such external factors fixing the base-tosugar orientation of the G nucleosides, two kinds of the geometry constraints were applied. The real constraints were adopted directly from the NDB UDF062 X-ray structure. The model constraints were represented by different torsion angles defined for the atoms in G nucleoside, like the glycosidic torsion χ but also others. The real constraints reflecting explicit intermolecular noncovalent interactions of selected nucleoside with the surrounding molecules involved base−base hydrogen bonding and interactions with the solvent molecules. The model constraints were achieved simply by fixing the value of selected torsion angle in a nucleoside during its geometry optimization, whereas the β (C4′−C5′−O5′−H(O5′) = 176°) and γ (C3′−C4′−C5′−O5′ = 48°) torsion angles (Figure 1) were always fixed to the values known for B-DNA. The C2′-endo and C3′-endo sugar pucker was adiabatically preserved during geometry optimization. The application of real constraints proceeded in four steps: (1) a selected G nucleoside with two G bases interacting via the Watson−Crick/ Hoogsteen (WC/H) and H/WC type of base pairing (called hereafter the base−base constraint) including coordinated solvent molecules was extracted from the NDB ID UDF062 structure,26 (2) the complex was complemented with hydrogen atoms and the C1′ carbon atoms of the two bases representing base−base constraints were replaced by methyl groups (see Figure 7), and the resulting molecular model was used in all subsequent calculations, (3) only the geometries of hydrogen atoms were relaxed in preliminary geometry optimization, (4) the geometry of the guanine base in the selected nucleoside including the geometry of all hydrogen atoms was optimized, keeping the geometry of the rest of the atoms fixed. Alternatively, the X-ray geometry of O6 oxygen in the target guanine base was fixed to account for the effect arising from the interaction with Na+ ions in the central channel of the Gquadruplex. All the geometry optimizations were conducted with the B3LYP method and the 6-31++G** basis. Performance of other methods was tested (see below). All calculations were done with the Gaussian 09 program package.27

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METHODS Terminology. The atoms in 2′-deoxyguanosine (G) were labeled and numbered according to the IUPAC (Figure 1).23 The 50° < χ < 80° and 180° < χ < 280° regions of the glycosidic torsion angle χ were referred to as syn and anti, respectively.24 The sugar ring conformations were described

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RESULTS AND DISCUSSION The pyramidalization calculated in nucleosides with geometries corresponding to the energy optimum was small.19,20 Only the departure from optimal geometry was accompanied by the pyramidalization increase. The κ′ torsion angles measured previously in the crystallography data varied between −20.5° and 23.7°.19 Considering the structure of the NA nucleoside,

Figure 1. Schematic representation of the 2′-deoxyguanosine, χ = O4′−C1′−N9−C4, κ′ = C4−N9−C1′−C8 − 180°. 4145

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290°) or increased with the quality of the basis (χ = 40°). The same trends calculated with all the three methods ensure qualitatively correct description of N9-pyramidalization with the B3LYP/6-31++G** method in this work. Coupling of N9-Pyramidalization with Sugar Pucker. The dependences of κ′ torsion on base-to-sugar orientation are virtually independent of sugar pucker, displaying a global minimum for the low-syn G, local minimum near the low-anti G, and global maximum for the high-anti G nucleoside (Figure 2). A closer look, however, revealed that the maximum for the G nucleoside with the S-type sugar conformation was a little larger, by 4°, as compared to the G nucleoside with the N-type sugar. The minima of the κ′ torsion were essentially the same for both sugar puckers. Similar trends were calculated for other nucleosides previously.20 These data suggest that the degree of pyramidalization is affected by sugar pucker in a systematic way. The sugar puckers of G nucleosides were adiabatically preserved along the complete revolution of the χ torsion. The pseudorotation angles (P-angles) ranged from 132° to 200° and from −23° to 47° for G nucleosides with S-type and Ntype sugar puckers, respectively. The amplitudes of pseudorotation (P-amplitudes) ranged from 31° to 41° in both cases (Figure 2). The calculated P-amplitudes appeared in the range typical for NAs.25 Note the P-amplitude indicates sensitively the out-of-plane deformation of a sugar ring. The larger the Pamplitude is, the larger is the deformation of sugar. The calculated P-angles moderately differed from the canonical values (Figure 2). For the global energy minimum the difference was 4° and 6° for G with S-type and N-type sugars, respectively. For the local energy minimum where the deformation of sugar ring was rather extreme the difference was 31° (G with S-type sugar pucker) and −31° (G with N-type sugar pucker). The analysis of the extreme deformations revealed their equivalence despite the opposite signs of P-angles because the absolute differences of P-angle from the canonical value provide good qualitative measure of the sugar ring deformation. The existence of structural coupling between the base and 2′deoxyribose can be followed from the simultaneous increases or decreases of the κ′ torsion and both P-angle and P-amplitude calculated in the both S- and N-type nucleosides (Figure 2). The coherent behavior of the two geometry descriptors of sugar suggests that structural deformation enforced by the model constraint χ is distributed according to actual rigidity of the sugar that is dependent on its pucker. The pyramidalization of the two low-syn G nucleosides was essentially the same and the deformations of their sugar rings were also the same (Figure 2). The same holds qualitatively also for the geometries around χ ∼ 180° although the pyramidalization calculated here was much smaller. The highanti nucleosides violated this rule because, as mentioned, the κ′ for the S-type G nucleoside was larger by 4°. Also the deformations of the two sugar rings differed, the absolute difference of P-angle from the canonical value was 23° and 1° for S- and N-type sugar, respectively, whereas the P-amplitudes were both around 33°. Taken together, the structural deformations of base and sugar are tightly coupled via glycosidic linkage allowing distribution of the overall deformation between the two units according to actual rigidity of sugar for given orientation of χ-torsion. In other words, when the sugar deformations are equivalent the pyramidalizations are also equivalent. The nonequivalent rigidity of the S-type and N-type sugar rings is the reason for

there are two obvious ways how the pyramidalization can be induced to nucleobases, via the glycosidic bond and via the interactions with external environment including other bases, solvent molecules, and counterions. To address impact of these factors on the pyramidalization, we first systematically analyzed the effect of sugar pucker and base-to-sugar orientation. Then we analyzed the effect of various model constraints for fixing the base-to-sugar orientation, which mimicked the site-specific action of hypothetical external constraints on G nucleoside. These calculations highlighted the relationship between different external deformation forces and induced N9-pyramidalizations, which fully explained the trends observed in the ensemble of X-ray data previously.19 Lastly, the calculations employing the real constraints adopted from the NDB UDF062 crystal structure unveiled their specific effect on N9-pyramidalization in the Gquadruplex. Testing the Performance of Different Calculation Methods. To validate use of the B3LYP/6-31++G** method in this study, we compared its performance with the performances of other methods. The N9-pyramidalization was calculated for three distinct base-to-sugar orientations of G nucleoside having N-type sugar pucker with the HF, B3LYP, and MP2 method and the 6-31G, 6-31G*, 6-31G**, 6-31+ +G**, 6-311++G**, cc-pVDZ, and cc-pVTZ atomic basis (Table 1). Table 1. κ′ Torsion and Glycosidic Torsion Angle χ Calculated for Three Distinct Base-to-Sugar Orientations of dG Nucleoside with N-Type Sugar Pucker Where the Glycosidic Torsion Angle χ Was Unconstrained, Fixed to 40° and 290° global minimum

χ = 40°

χ = 290°

method

atomic basis

κ′

χ

κ′

κ′

HF

6-31++G** 6-311++G** 6-31G* 6-31G** 6-31++G** 6-311++G** cc-pVDZ cc-pVTZ cc-pVDZ 6-31++G** 6-311++G**

1.7 2.2 0.9 0.8 1.7 1.7 0.2 1.3 2.5 1.0 4.8

208.4 208.8 212.1 212.5 216.9 217.9 213.8 215.8 202.4 209.5 206.5

17.6 18.5 13.9 14.1 17.2 18.0 14.1 16.1 15.1 22.6 22.3

−15.9 −16.3 −14.2 −14.3 −14.6 −13.8 −14.3 −12.8 −10.2 −9.4 −8.3

B3LYP

MP2

For the geometry corresponding to global energy minimum and for the geometries where the glycosidic torsion χ was fixed to 40° and 290° the κ′ torsion angle calculated with different methods varied up to 4°, 8°, and 9°, respectively. The maximal values of κ′ torsion for the three conformers were 4.8°, −16.3°, and 22.6°, respectively. Performances of the three methods differ. The absolute maximal pyramidalization was calculated exclusively only with either the HF or MP2 method. The pyramidalizations calculated with the B3LYP method thus should not be overestimated. When the quality of the atomic basis increased, the pyramidalization remained small (the global minimum), increased (χ = 40°), or decreased (χ = 290°). The dependence on the atomic basis was larger for HF and MP2 methods than for B3LYP. Importantly, the absolute pyramidalization calculated with the B3LYP method and different basis either remained almost same (the global minimum and χ = 4146

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Figure 2. Top: dependences of κ′ torsion angle on glycosidic torsion χ calculated for the 2′-deoxyguanosine with the S-type (left) and N-type (right) sugar puckers. Middle: dependence of total energy relative to the global energy minima on the glycosidic torsion χ (solid line) and its numerical derivative with respect to the χ torsion (dashed line). Bottom: dependence of pseudorotation angle (P-angle, black, left y-axis) and pseudorotation amplitude (P-amplitude, blue, right y-axis) on glycosidic torsion χ. The geometry parameters are in degrees and energies in kcal mol−1. The curves were fitted with the calculated data available in the Supporting Information.

such as the base ring and sugar deformations. The force associated with constraint can be therefore called deformation force. Dependence of the deformation force on the glycosidic torsion χ was calculated as a numerical derivative of the energy with respect to the χ-coordinate. The extremes indicate geometries where deformation force approached local maxima and induced extreme pyramidalization (Figure 2). Although choice of the glycosidic torsion as structural constraint is obvious, many other geometry parameters can be used instead. One can anticipate that different constraints might be associated with different forces and their action thus may induce nonequivalent structural deformations. Indeed, the κ′ torsion ranging from −3° to 22° was calculated with the constraints employing different atoms of the anti G nucleoside with S-type sugar pucker (Table 2). Although the χ-torsion little varied once unconstrained, the overall conformation of nucleoside was preserved. Importantly, the calculated pyramidalization depended on directionality of the structural constraints in a systematic way; the κ′ torsion decreased when directionality of the linked atoms changed from the sugar edge via the Watson−Crick edge to the Hoogsteen edge

nonequivalent pyramidalization calculated in high-anti G nucleosides with S-type and N-type sugar ring conformation. Furthermore, the larger the deformation of the sugar ring, the smaller the pyramidalization and vice versa. Distinct conformation of sugar with rigidity depending on base-to-sugar orientation thus effectively controls the degree of the structural deformation of nucleobases. Effect of Deformation Forces on the Pyramidalization: The Model Constraints. The model structural constraints fixing the base-to-sugar orientation in fact simulate the action of external forces on the nucleoside. These forces must act against the potential energy (Figure 2) to keep the orientation of the nucleoside different from that corresponding to the energy optimum. The only constraint applied so far was exclusively the χ-torsion angle; so its terminal atoms O4′ and C4 are pulled together or pushed apart in a tangential direction with respect to the C1′−N9 bond and the force acting on the C4 carbon of base is perpendicular with respect to the base plane. Except for the four atoms, geometries of the other atoms in the G nucleoside relax during geometry optimization. Such adiabatic geometry relaxation concerns particularly the “soft” coordinates 4147

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Table 2. κ′ Torsion Angle Calculated with Different Model Geometry Constraints Fixing the Base-to-Sugar Orientation in the dG Nucleoside with S-Type Sugar Puckera

a

geometry constraint

κ′

χ

O4′−C1′−N9−H8 = 104.4 O4′−C1′−N9−H2 = 287.6 O4′−C1′−N9−N2 = 281.5 O4′−C1′−N9−C4 = 282.9 O4′−C1′−N9−C8 = 105.9 C4′−O4′−N9−H1 = 197.4 O4′−C1′−C4−C8 = 111.8 O4′−C1′−C8−C4 = 274.8 O4′−C1′−N9−O6 = 277.3 C4′−O4′−N9−C4 = 194.6 C4′−O4′−N9−C8 = 328.7 C4′−O4′−N9−H2 = 187.8 C4′−O4′−N9−N1 = 198.6

5.5 17.2 16.5 22.1 −3.1 16.6 5.7 13.4 15.6 15.7 0.6 12.1 16.1

286.8 283.7 285.1 282.9 282.9 279.6 287.8 288.4 255.3 282.6 279.9 282.9 280.7

considering separately the effect of O4′−C1′−N9−C4 and O4′−C1′−N9−C8 constraints differing only in the terminal atom. Suppose the two forces associated with the constraints acting on a nearly planar base like that calculated for the global energy minimum. The clockwise rotation of a base induced by the force “pushing” selectively either C4 or C8 carbon clockwise with respect to the O4′−C1′−N9 linkage leaves the other atom free for relaxation. When the C4 carbon was constrained, it was pushed out of the base plane and the C8 carbon relaxed via an increase of the N9-pyramidalization. When the C8 carbon was constrained, creating the same clockwise rotation of a base, the C4 carbon relaxed and induced the antipodal, energetically more favorable N9-pyramidalization because the two forces acting on either the C4 or C8 carbon were directed oppositely with respect to base plane. The ability of the two constraints to induce inverse configurations at the N9-pyramidalization remained conserved along adiabatic rotation of the glycosidic bond (Figure 4). The two κ′-dependences therefore appeared as mutual mirror images only slightly shifted owing to the shift of their potential energy surfaces. Hence, the stereoinversion of glycosidic nitrogen can be clearly induced independently of base-tosugar orientation in accord with the experimental observation. Noteworthy, the two mirror images confining the area with the majority of the crystallographic data form de facto “an envelope” indicating possible extend of the structural deformation that is consistent with the experimental data (Figure 4). The deformation energy required for such pyramidalization where κ′ ∼ 20° is only ∼1 kcal mol−1 (Figure 5). The calculated harmonic-like potential energy has rather conservative shape what could be in favor of adjusting relevant force-field parameters describing reliably the pyramidalization. N9-Pyramidalization in the DNA G-Quadruplex. The model calculations suggested that the two configurations of the N9 could be induced with the specific structural constraints acting on the two edges of a nucleoside. In nucleic acids, such constraints involve various interactions of a nucleoside with the surrounding molecules. To investigate their effect, we searched the nucleic acid database (NDB) for ultrahigh resolution structure of nucleic acids where solute−solvent interactions were resolved with sufficient accuracy. On the basis of the stringent criteria (vide infra), we selected three residues from the parallel G-quadruplex (NDB ID UDF062) for the following reasons: (i) the structure is of ultrahigh resolution (0.95 Å), (ii) it reveals the positions of the water molecules and counterions interacting site-specifically with the nucleosides, and (iii) the architecture of the supermolecule involves the Watson−Crick and Hoogsteen types of base pairing, thus saturating all of the interaction edges of the selected nucleobase. Importantly, both the canonical and noncanonical pyramidalizations were found in the crystal structure. We anticipated that both the existence and knowledge of such tight constraints as in the G-quadruplex is necessary for our analysis bearing in mind that the deformation energy for modulating the N9-pyramidalization is small. It follows that the selection of residues from the same crystal structure allows a systematic investigation of the hydration, counterion and base-pairing effects without a bias owing to such experimental factors as crystallization, the measurement conditions or crystal packing forces that might be influential. Three nucleosides selected from the UDF062 structure were residues no. 12 (r12), 13 (r13), and 112 (r112). The r12 and r13 nucleosides are especially important. Although r12 and r13

All of the parameters are in degrees.

(Figure 3). Noteworthy, the O4′−C1′−N9−C8 constraint directed to the Hoogsteen edge induced stereoinversion of

Figure 3. Schematic picture of the κ′-dependence on directionality of the model constraints in Table 1.

the glycosidic nitrogen pyramidalization, κ′ = −3.1°. Both the magnitude of pyramidalization and configuration of the glycosidic nitrogen thus could be altered by suitable structural constraints. All of the applied constraints induced the positive sign of the κ′ torsion except for the O4′−C1′−N9−C8 one (Table 2). The predominant configuration of the N9-pyramidalization is thus the same as the N9-configurations predominantly observed for the anti nucleosides in the crystal structures.19 We therefore hypothesize that the O4′−C1′−N9−C8 constraint associated with the distinct configuration of glycosidic nitrogen for the anti-2′-deoxyguanosine is a special case because such N9configuration appeared rarely both among the randomly selected constraints and also in real NAs. The predominantly populated N9-pyramidalization associated with positive κ′ for anti and negative κ′ for syn nucleosides is therefore called here canonical pyramidalization and the antipodal pyramidalization is called noncanonical. Rise of the antipodal pyramidalizations observed in crystal geometries can be now explained on a purely mechanistic basis 4148

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Figure 5. Dependences of energy E in kcal mol−1 on torsion angle κ′ in degrees calculated for 2′-deoxyguanosine having N-type sugar pucker with the glycosidic torsion fixed to 40° (blue), 216.9° (green), and 290° (red). The two profiles were also centered at κ′ = 0° corresponding to the idealized planar geometry for their better comparison (dashed lines).

hydration are manifested by the distinct number of water molecules in the first hydration shell of the nucleosides and their locations. The distances between the O6 atom and Na+ ions indicated possible differences of the constraints on the three nucleosides because of the ion binding (Figure 6). To analyze the complex effect of hydration, ion binding and base pairing on the N9-pyramidalization, we performed three kinds of geometry optimizations that gradually included these interactions: (1) the hydrogen bonding arising from the WC/ H and H/WC base-pairing constraints only, (2) the basepairing constraints with the X-ray geometry of the O6 oxygen fixed, and (3) the same constraints including complete solvation (Table 3). The N9-pyramidalization calculated for the r112 nucleoside was small, in agreement with the model calculations. The κ′ torsion angles for the r112 nucleoside calculated without a solvent were larger than in the crystal structure and only the inclusion of solvent brought the absolute N9-pyramidalization close to that observed in the crystal; the same holds also for the χ torsion angles (Table 3). The stereoinversion of the N9 nitrogen obtained with complete set of the constraints (κ′ = −1.2°) could still be considered as good agreement with the pyramidalization in crystal (κ′ = 0.7°), because we must consider that the corresponding energy difference (Figure 5) allows such a small discrepancy. The rather extreme sensitivity of the N9-pyramidalization with respect to the different model constraints was also predicted (Figure 3). The N9-pyramidalization calculated for the r13 nucleoside was in good agreement with the data in the crystal, and somewhat larger magnitudes obtained with a gradually increasing level of the constraints confirmed the canonical type of the N9-pyramidalization. The N9-pyramidalization calculated for the r12 nucleoside without solvent was still canonical even when the X-ray geometry of the O6 oxygen was constrained and the κ′ torsion came much closer to the value observed in the crystal structure. Only when the solvent saturating particularly the sugar edge of the r12 nucleoside was involved was the N9-stereoinversion obtained. The noncanonical pyramidalization of the r12 nucleoside with a κ′ torsion of −2.6° was therefore induced

Figure 4. Dependences on the glycosidic torsion χ calculated with the χ = O4′−C1′−N9−C4 (full line) and the O4′−C1′−N9−C8 (dashed line) model constraints for the 2′-deoxyguanosine with a S-type sugar pucker. Top: dependence of the κ′ torsion angle plotted along with the experimental crystallographic data19 for the 2′-deoxyguanosine. Middle: dependence of the total electronic energy relative to the global energy minima. Bottom: dependence of the pseudorotation angle (P-angle, black, left y-axis) and the pseudorotation amplitude (Pamplitude, blue, right y-axis) of the sugar. All of the geometry parameters are in degrees and the energies in kcal mol−1. The curves were fitted with the calculated data in the Supporting Information.

had very similar geometries (S-type sugar pucker and similar glycosidic torsions), their N9-pyramidalizations were antipodal (Table 3). The r12 nucleoside had less frequently observed noncanonical pyramidalization whereas that of the r13 nucleoside was canonical, typical for the high-anti nucleosides. The r112 nucleoside with a slightly deformed N-type sugar pucker and χ torsion angle close to 180° is a typical representative of a nucleoside with a small pyramidalization, which should be very constraint-dependent (Figure 4). The water molecules and counterions around the three nucleosides were coordinated site-specifically (Figure 6A−C) along with the differences in the binding of nucleobase O6 oxygen to Na+ ions in the central G-quadruplex channel (Figure 6A′−C′). As can be seen, the three nucleosides clearly differed in both hydration and ion binding. The differences in the 4149

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Table 3. κ′ and χ Torsion Angles in Degrees of the Selected Nucleosides in the DNA G-Quadruplex κ′

χ

nucleosidea

X-ray

calcb

calcc

calcd

X-ray

calcb

calcc

calcd

r12 r13 r112

−5.5 8.1 0.7

10.2 10.8 6.7

0.7 9.1 5.9

−2.6 13.8 −1.2

239.7 253.9 181.9

246.3 256.6 190.8

243.3 255.8 191.4

246.7 262.7 178.5

a

The nucleosides with the numbers 12, 13, and 112 in the NDB UDF062 structure had P-angles 178°, 162°, and 34°, and P-amplitudes 37°, 34°, 44°, respectively. bThe geometry optimization with the WC/WC and WC/Hoogsteen constraints (Figures 6 and 7). cThe geometry optimization with the WC/WC and WC/Hoogsteen constraints, with the X-ray geometry of the O6 oxygen being fixed. dThe geometry optimization with the WC/WC and WC/Hoogsteen constraints including solvent (Figure 7).

Figure 6. Distribution of water molecules from the first hydration shell (red) and Na+ ions from the central channel (yellow) around the residues r12 (A), r13 (B), and r112 (C) of the parallel G-quadruplex indicated by the arrow. The interatomic distances between O6 and Na+ in Å are displayed at the bottom.

molecules together with the base−base constraints and the fixed X-ray geometry of the O6 oxygen, the noncanonical pyramidalization of the r12 nucleoside with a κ′ of −2.4° was confirmed again. The stereoinversion of the glycosidic nitrogen was therefore in the case of the r12 nucleoside induced by the C6O6···Na+ interaction and the hydration of its SE. The site-specific structural constraints including the baseparing and solvent interactions were shown to alter the pyramidalization in accord with the structural data in the UDF062 DNA G-quadruplex. In particular, the application of incomplete structural constrains only in the form of the basepairing interactions induced the same N9-pyramidalizations of the r12 and r13 nucleoside with the κ′ equal to 10.2° and 10.8°, respectively. The additional constraints reflecting the solvent interactions inverted the N9-stereoinversion of the r12 nucleoside, whereas the r13 nucleoside maintained its canonical N9-pyramidalization in accord with the X-ray data. The out-ofplane deformations of the glycosidic nitrogen observed in the crystal of the DNA G-quadruplex can thus be attributed to the specific topology of the metals in the central channel of the Gquadruplex and to the site-specific hydration.

Figure 7. r12 nucleoside of the UDF062 DNA G-quadruplex interacting via the WC/Hoogsteen and Hoogsteen/WC type of hydrogen bonding with two neighboring guanine bases, the base−base constraint (left), and the same nucleoside including the solvent (the green atom is Ca2+) in sugar edge.

by the coordination of the specific bulk solvent and the metal ions inside the G-quadruplex. To support this finding, we conducted further geometry optimizations with the slightly modified complete constraints used in the (d) calculations in Table 3. When the O6 oxygen was freely optimized, the N9pyramidalizatioin again became canonical (κ′ = 6.3°), indicating that accounting for the C6O6···Na+ interaction is essential. Then, we modified the constraints by a solvent. The two water molecules bridging the N3 nitrogen of the base and the O4′ oxygen of the sugar in the SE of the r12 nucleoside were considered to be particularly important, because they seemed to act similarly to the model constraints (Figure 3). Further, such a base-to-sugar bridge from water molecules was found only for the r12 nucleoside. When we included only these two water

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CONCLUSIONS The structural data obtained and analyzed in this study provided new insight into the modulation of nonplanarity of NA bases. The pyramidalization of glycosidic nitrogen was investigated theoretically by considering the effects by complex external factors including site-specific solvation and base pairing derived from the high-resolution crystal structure of DNA Gquadruplex. Our calculations suggest that the effective structure of a nucleobase is controlled by structural rigidity of the 4150

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Article

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adjoined sugar moiety and that the structurally nonequivalent S- and N-type sugars induce a nonequivalent pyramidalization of the glycosidic nitrogen for the same base-to-sugar orientation. To the best of our knowledge the dependence of base nonplanarity like the N9-pyramidalization on explicit environmental factors derived from the experimental data was not analyzed before. The geometry relaxation of the NA base that is virtually planar depends on the character and directionality of the constraints/interactions coming from molecular surroundings of NA nucleoside. The stereoinversion of the glycosidic nitrogen configuration can be induced independently of the base-to-sugar orientation only with suitable structural constraints acting on NA nucleoside. The dependences calculated with different model constraints explained all of the trends for the N9-pyramidalization observed in the NA crystal structures and revealed that the maximal pyramidalization in the crystal structures corresponds to deformation energy of about 1 kcal mol−1. The N9stereoinversion in the DNA G-quadruplex UDF062 results from real structural constraints consisting of the Watson− Crick/Hoogsteen and Hoogsteen/Watson−Crick base-pairing and particularly of the site-specific interactions with the molecules of solvent. Neither the base-pairing nor the solvent interactions alone induced the N9-stereoinversion, i.e., the noncanonical pyramidalization with a negative value of the κ′ torsion observed for the anti-nucleosides in the G-quadruplex. The rise of the N9-stereoinversion in DNA G-quadruplex was attributed to the site-specific environmental stress.

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ASSOCIATED CONTENT

S Supporting Information *

The dependences of κ′ torsion angle, energy E, pseudorotation angle P-angle, and pseudorotation amplitude P-amplitude on torsion angles χ and O4′−C1′−N9−C8 calculated for the 2′deoxyguanosine with S-type and N-type sugar pucker. The complete ref 27. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Grant Agency of the Czech Republic P205/10/0228 and the Academy of Sciences of the Czech Republic, Institutional grants AV0Z40550506 and AV0Z50520701. V.S. was supported by the Young Investigator’s Grant of the Human Frontier Science Program (HFSP).

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REFERENCES

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dx.doi.org/10.1021/jp2110049 | J. Phys. Chem. A 2012, 116, 4144−4151