Relationships between 31P Chemical Shift Tensors and Conformation

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J. Phys. Chem. B 2007, 111, 2658-2667

Relationships between 31P Chemical Shift Tensors and Conformation of Nucleic Acid Backbone: A DFT Study Jana Prˇ ecechteˇ lova´ , Marke´ ta L. Munzarova´ , Petr Nova´ k, and Vladimı´r Sklena´ rˇ * National Centre for Biomolecular Research, Faculty of Science, Masaryk UniVersity, Kotla´ rˇska´ 2, CZ-611 37 Brno, Czech Republic ReceiVed: October 19, 2006; In Final Form: December 22, 2006

Density functional theory (DFT) has been applied to study the conformational dependence of 31P chemical shift tensors in B-DNA. The gg and gt conformations of backbone phosphate groups representing BI- and BII-DNA have been examined. Calculations have been carried out on static models of dimethyl phosphate (dmp) and dinucleoside-3′,5′-monophosphate with bases replaced by hydrogen atoms in vacuo as well as in an explicit solvent. Trends in 31P chemical shift anisotropy (CSA) tensors with respect to the backbone torsion angles R, ζ, β, and  are presented. Although these trends do not change qualitatively upon solvation, quantitative changes result in the reduction of the chemical shift anisotropy. For R and ζ in the range from 270° to 330° and from 240° to 300°, respectively, the δ22 and δ33 principal components vary within as much as 30 ppm, showing a marked dependence on backbone conformation. The calculated 31P chemical shift tensor principal axes deviate from the axes of O-P-O bond angles by at most 5°. For solvent models, our results are in a good agreement with experimental estimates of relative gg and gt isotropic chemical shifts. Solvation also brings the theoretical δiso of the gg conformation closer to the experimental gg data of barium diethyl phosphate.

Introduction 31P NMR techniques provide a powerful tool to probe the conformation of the sugar-phosphate backbone in nucleic acids.1-5 The large chemical shift anisotropy (CSA) of 31P nuclei has recently been used for constraining the orientation of phosphate groups relative to the molecular alignment tensor.6,7 The corresponding methodology is based on the knowledge of individual 31P chemical shift tensors and their orientations relative to the molecular reference frame. Such data can be obtained only by single-crystal NMR studies, which have been rare for nucleic acids.8 However, a very precise value of 31P the chemical shift tensor (principal components as well as the orientation) is available for barium diethyl phosphate.9 Since the isotropic 31P chemical shifts in nucleic acids span only a narrow range of several ppm, an assumption has been adopted that the 31P CSA tensor is uniform for all backbone phosphates in oligonucleotides and equal to the 31P CSA tensor of the diethyl phosphate.6 To be able to (1) assess the adequacy of the assumption and (2) use the 31P CSA for structure determination more effectively, an insight into the relationships between 31P chemical shift tensors and backbone torsion angles is highly desirable. Such an insight can be provided by quantum chemical calculations. The conformation of the sugar-phosphate backbone between two successive phosphorus atoms of a DNA strand is determined by six torsion angles (R, β, γ, δ, , and ζ; see Figure 1). The torsion angles R ) -60° and ζ ) -60° refer to the so-called gauche-gauche (gg) conformation of the phosphate group, whereas R ) -60° and ζ ) 180° refer to the gauche-trans (gt) conformation.10 The two conformations, gg and gt, are known as BI- and BII-DNA, respectively (Figure 2). For dimethyl

* To whom correspondence should be addressed. Phone: +420549 49 7022. Fax: +420-549 49 2556. E-mail: [email protected].

Figure 1. DNA backbone torsion angles.

phosphate, the simplest model of a phosphate group, a gg conformer with both P-O torsion angles equal to -60°, represents an idealized, symmetric case. However, the ranges of R and ζ in real structures are different. As a result, calculations of 31P chemical shift tensors as a function of the torsion angles about P-O bonds provide ζ and R trends that are not identical. Previous theoretical studies have suggested that the two P-O ester torsion angles, R (O3′-P-O5′-C5′) and ζ (C3′-O3′P-O5′), have a significant effect on δiso (31P).1,11-15 In addition to computing a 31P chemical shift-torsional angle contour map of dimethyl phosphate monoanion from CNDO electron densities,11,14 these studies have largely focused on the calculations of the difference in the chemical shift between the gg and gt 1,11,13,14 The conformers of the phosphate groups (∆δgt-gg iso ). reason for such calculations is straightforward. If ∆δgt-gg were iso known, 31P NMR measurements would provide the ratio of gg and gt conformations in the polynucleotide studied. Although has been estimated on the an approximate value of ∆δgt-gg iso

10.1021/jp0668652 CCC: $37.00 © 2007 American Chemical Society Published on Web 02/22/2007

31P

Chemical Shift Tensors, Nucleic Acid Backbone

Figure 2. BI (gg) and BII (gt) conformation. g ) 60°, -g ) -60°, t ) 180°.

Figure 3. Unsolvated models used for 31P chemical shift calculations.

basis of experimental data,1 its determination is complicated by a ggTgt exchange occurring on the nanosecond time scale16,17 and by the lack of rigid gt mononucleotides. In addition to R and ζ, the effects of the torsion angles β and  (Figure 3) on isotropic 31P chemical shifts have been studied theoretically and proved to be important as well.12,14,15 GiessnerPrettre et al. have demonstrated that σiso varies by as much as 3 ppm upon rotation within 60° around C3′-O3′ and C5′-O5′ bonds in the gg and gt regions. The qualitative trends of σiso due to the variations in β/ were shown to be identical for the gg as well as gt conformations. Gorenstein found an empirical correlation between 31P chemical shifts and the O-P-O bond angle in various phosphate esters.18 This correlation revealed an upfield shift upon increasing the O-P-O bond angle up to 108°.19 To confirm the empirical finding theoretically, Gorenstein and Kar calculated 31P chemical shifts for two sets of dimethyl phosphate conformations with the O-P-O angle set to 95° and 105°, respectively.11 However, these calculations did not provide any

J. Phys. Chem. B, Vol. 111, No. 10, 2007 2659 evidence for the dominant influence of the bond angle effect, and the computed variations were attributed rather to the coupling between bond and torsion angles. Prado et al.13 also tried to distinguish between the conformational and bond-angle dependence of the 31P chemical shift tensor. Indeed, the stretching and bending of the central phosphate unit can be driven only by the global structure. Thus, the local geometric structure should be considered and computed as given by a set of particular torsion angles. All previous theoretical studies of 31P chemical shifts in nucleic acids come from the 1970s and 1980s. They used either semiempirical11 or ab initio CHF methods.12,13,15 None of these studies included calculations of a complete 31P chemical shift tensor as a function of backbone torsion angles. So far, the solvent effect on isotropic 31P chemical shifts has not been studied theoretically. The presence of six water molecules in the first solvation shell of a phosphate group was predicted computationally20-23 and later confirmed experimentally.24,25 Pullman et al. used the ab initio SCF/STO-3G approach to calculate interaction energies for dimethyl phosphate and one water molecule to determine the principal hydration sites. 20 The calculations were followed by establishing the polyhydration scheme of the first hydration shell. The effect of hydration on the relative stabilities of the gg, gt, and tt conformers of dimethyl phosphate were studied as well.20 In the present study, we have applied density functional theory (DFT) to investigate the influence of backbone torsion angles R, ζ, β, and  on 31P CSA tensors in B-DNA. The main objectives were (1) to reveal the qualitative trends in the torsion angle dependence of 31P CSA tensors, (2) to determine the range of individual principal components of the tensor for the experimentally observed ranges of the torsion angles,26 and (3) to determine the changes of chemical shift tensor orientations upon change in the phosphate group conformation. To find an appropriate size of the backbone and the hydration shell description, we have performed calculations on dimethyl phosphate and a dinucleoside-3′,5′-monophosphate with bases replaced by hydrogen atoms. Dimethyl phosphate was calculated in vacuo as well as in explicit solvent. In the models employed, we treat the local parameters (individual bond lengths and angles) as coupled to the global parameters (a set of torsion angles). Specifically, the torsion angles are set to their particular values within the experimental ranges while the other parameters are optimized. Computational Details A chemical shift tensor, which is discussed here in detail for the case of phosphorus atoms in oligonucleotides, is typically obtained from NMR calculations as a second-rank tensor in a principal axis system (PAS). A full chemical shift tensor in principal axes can be decomposed into its isotropic and anisotropic parts,

( )(

)(

δCSA 0 0 δ11 0 0 δiso 0 0 11 CSA δ22 0 0 δ22 0 ) 0 δiso 0 + 0 0 0 δ33 0 0 δiso δCSA 0 0 33

)

(1)

where

1 δiso ) (δ11 + δ22 + δ33) 3

(2)

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TABLE 1: Starting Positions of Water Molecules before Geometry Optimizationa hydration site A1 A2 A3 B1 B2 B3

dO1(2)...Hw1/Å

θ/deg

ω/deg

φ/deg

ϑ/deg

1.45 1.50 1.45 1.50 1.45 1.45

120 120 120 120 120 120

60 -60 180 -60 60 180

180 180 180 180 180 180

180 180 180 180 180 180

a P-O2(O1)‚‚‚Hw1 ) θ; O1(O2)-P-O2(O1)‚‚‚Hw1 ) ω; O2(O1)‚‚‚Hw1Ow ) φ; P-O2(O1)-Ow-Hw2 ) ϑ. O1 and O2 are the charged oxygen atoms of dmp. Hydration sites A1, A2, A3 and B1, B2, B3 refer to water molecules bound to the oxygen atoms O1 and O2, respectively. Ow denotes an oxygen atom in a water molecule and Hw1, Hw2 refer to water hydrogen atoms (Hw1 is the hydrogen atom pointing toward one of the charged oxygen atoms in dmp).

The trace of the anisotropic part of the chemical shift tensor is equal to zero. From now on, we shall denote the anisotropic part of the full chemical shift tensor as a CSA tensor. This is not to be confused with the so-called chemical shift anisotropy (CSA, ∆σ), which is a scalar quantity defined as

1 ∆σ ) δ33 - (δ11 + δ22) 2

(3)

31P CSA tensors have been calculated for two molecular models: dimethyl phosphate (dmp) and a dinucleoside-3′,5′monophosphate (sPs; sugar-phosphate-sugar), in which nucleic acid bases were replaced by hydrogen atoms (Figure 3). This replacement is justified by the experimental evidence that 31P chemical shift tensors are approximately the same for poly(A), poly(G), poly(C), and poly(U).27 Thus, the base type does not influence the 31P chemical shift tensors, and the substitution of the bases by a hydrogen atom can only result in a systematic error. Moreover, the ring current effect on isotropic 31P chemical shifts associated with the bases in nucleic acids is known to be negligible.1 To study 31P CSA tensors in explicit solvent, we have optimized a cluster of dmp with six water molecules (three water molecules hydrogen-bonded to each of the charged oxygens). We used starting positions for the water molecules as suggested by Pullman (see Table 1).20 Two geometry minima were obtained after the geometry optimization, dmp-IC (interconnected cones of hydration) and dmp-SC (separated cones of hydration), as shown in Figure 4. The OP‚‚‚Hw-Ow bond angle and the OP‚‚‚Hw hydrogen bond distance in the optimized solvated models were in the ranges 141°-161° and 1.85-2.10 Å, respectively. The calculated structures of sPs and dmp as well as solvated dmp are provided as Supporting Information.

Figure 4. Solvated models used for hydration, respectively.

31

Molecular geometries have been optimized in Kohn-Sham DFT calculations employing the hybrid B3LYP28,29 functional and the 6-31G(d) basis set30,31 as implemented in Gaussian 98.32 The torsion angle R was constrained to 270°, 285°, 300°, 315°, and 330°. For each of these values, the dependence of 31P chemical shift tensors on ζ was calculated in the following way: the torsion angle ζ was varied within the range 240°300° (gg conformer) or 150°-210° (gt conformer), and incremented in 15° steps. The ranges of R and ζ used here were determined by a statistical survey of 34 X-ray B-DNA structures.26 The remaining backbone torsion angles were frozen to their mean values found in B-DNA.26 (A) dmp model: 180° (β), 180° () in the gg conformer and two sets of calculations were performed for the gt conformer. First, both β and  were set to 180°, and second, β and  were set to 150° and 250°, respectively. (B) sPs model: 176° (β), 48° (γ), 128° (δ), and 184° () in the gg conformer (the gt conformer was not studied in detail). All other structural parameters were relaxed. 31P CSA tensors were obtained with the modified version of the deMon-KS program,33,34 along with the deMon-NMR code.35-37 NMR calculations employed sum-over-states density functional perturbation theory with the IGLO choice of the gauge origin (SOS-DFPT-IGLO).38 The density functional calculations were carried out with Perdew and Wang’s generalized gradient approximation (GGA) for exchange39 and Perdew’s GGA for correlation (PWP86).40,41 The orbital basis set IGLOIII42 was used in combination with the corresponding experimental auxiliary basis set. The following convergence criteria were applied: 1 × 10-7 Hartree (energy), 1 × 10-6 (density) for sPs and 1 × 10-8 Hartree (energy), 1 × 10-7 (density) for dmp. The numerical grid for sPs and dmp was set to RADI64/ FINE and RADI128/EXTRAFINE, respectively. The standard reference compound for experimental 31P NMR is 85% H3PO4, for which a theoretical chemical shielding is hard to obtain.43 Therefore, following the procedure suggested by van Wu¨llen,44 we used PH3 as a secondary standard to convert the calculated chemical shieldings into chemical shifts,

δ(X, calc) ) σ(PH3, calc) - σ(X, calc) - 266.1

(4)

where X is the substance, for which we calculate a chemical shift, and 266.1 ppm is a difference in the absolute experimental chemical shieldings between PH3 (594.5 ppm) and 85% H3PO4 (328.4 ppm) at 300 K. This way of referencing typically leads to a better agreement of the calculated chemical shifts with experimental data. However, we should keep in mind that this is a consequence of the referencing method itself. The errors arising in calculations due to the approximations used are

P CSA tensor calculations. IC and SC refer to interconnected cones of hydration and separated cones of

31P

Chemical Shift Tensors, Nucleic Acid Backbone

J. Phys. Chem. B, Vol. 111, No. 10, 2007 2661

Figure 5. Dependence of the 31P isotropic chemical shift and the CSA tensor components on the torsion angle ζ studied on dmp (left column) and sPs (right column). Five curves in each plot correspond to various angles of the R torsion angle: R ) 270° (cyan triangle), 285° (black square), 300° (green circle), 315° (blue star), and 330° (red diamond).

explicitly neglected by ignoring the distance between σ(PH3,calc) and σ(PH3,exp) on the chemical shielding scale. The chemical shielding of PH3 calculated on the same theoretical level as the systems studied is 569.6 ppm. Results and Discussion Model Size. Any phosphate unit in nucleic acids is surrounded by two sugars bearing bases. Although the bases are quite far from the central phosphorus atom to introduce troughbond effects on 31P chemical shift tensors, certain orientations of bases can favor trough-space interactions. Such interactions have been observed, for example, between the H6 base proton and O5′ in RNA.45 In DNA, however, H6 does not approach O5′ as closely as in RNA, and the interaction might be weakened by solvent molecules. Therefore, the influence of base atoms

in the proximity of the phosphate group represents a secondorder effect and was not a subject of the study at this stage. On the basis of the above arguments and the reasons given in Computational Details, the removal of the bases from the model systems is justified, and sPs seems to be a straightforward choice to study 31P CSA tensors in nucleic acids. Yet, we have anticipated that a much simpler model (dmp) might as well be sufficient to reproduce qualitative trends. Therefore, calculations in vacuo have been carried out on both molecular models, and the 31P CSA tensors obtained are shown in Figure 5. The main qualitative features of δ11 and δ33 trends (the ascending and descending dependencies, respectively) are preserved upon model truncation, although a change of the slope of dependencies can be observed for δ11. The behavior of δ22 is more complicated than that of δ11 and δ33 because it includes not

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Figure 6. Dependence of 31P CSA tensor components on the R torsion angle; calculated for the gg conformation of the unsolvated dmp and solvated dmp, dmp-IC, and dmp-SC . Red diamond, ζ ) 300°; blue star, ζ ) 285°; green circle, ζ ) 270°; black square, ζ ) 255°; cyan triangle, ζ ) 240°.

Figure 7. Dependence of 31P CSA tensor components on the ζ torsion angle; calculated for the gg conformation of the unsolvated dmp and solvated dmp, dmp-IC, and dmp-SC . Red diamond, R ) 330°; blue star, 315°; green circle, 300°; black square, 285°; cyan triangle, 270°.

only the change of the slope of trends but also the shift of the δ22 minimum toward the smaller values of ζ. Switching from sPs to dmp also results in quantitative changes. The δ11 principal component decreases and δ33 increases, whereas δ22 spans a similar range of values for the two models. These changes lead to an overall increase in the isotropic chemical shift. In Figure 5, only the dependencies of

the principal components on the ζ torsion angle are provided because the changes in trends upon switching from sPs to dmp for the R torsion angle are very similar. Because the smaller model provides all important trends, is simple to understand, and is computationally more suitable for the calculations with explicit solvent, we have employed dmp in all further calculations.

31P

Chemical Shift Tensors, Nucleic Acid Backbone

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Figure 8. Dependence of 31P CSA tensor components on the R torsion angle; calculated for the gt conformation of the unsolvated dmp and solvated dmp, dmp-IC, and dmp-SC. Red diamond, ζ ) 150°; blue star, 165°; green circle, 180°; black square, 195°; cyan triangle, 210°.

Figure 9. Dependence of 31P CSA tensor components on the ζ torsion angle; calculated for the gt conformation of the unsolvated dmp and solvated dmp, dmp-IC, and dmp-SC. Red diamond, R ) 330°; blue star, 315°; green circle, 300°; black square, 285°; cyan triangle, 270°.

Dimethyl phosphate as well as its solvated analogs, dmp-IC and dmp-SC, have been used to calculate the dependencies of the 31P chemical shift tensors on the torsion angles around the P-O bonds, R and ζ. We address the issue of the solvent effect on 31P CSA tensors first, and then we continue with the discussion of the torsion angle effects.

Solvent Effect. The dependencies of 31P CSA tensor components on the R and ζ torsion angles have been compared for the solvated and unsolvated dmp in both gg and gt conformation. Figures 6-9 clearly demonstrate that the overall qualitative trends in isotropic 31P chemical shifts as influenced by R and ζ do not change upon solvation. Nevertheless, quantitative

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TABLE 2: Theoretical and Experimental Isotropic 31P Chemical Shifts and 31P Chemical Shift Tensor Componentsa δiso

δ33

CSA

dmp dmp-IC dmp-SC

gg (Calculations) 1.9 127.6 74.1 5.6 89.3 32.6 3.9 96.2 38.2

δ11

δ22

-195.9 -105.1 -122.6

-296.8 -166.1 -189.8

dmp dmp-IC dmp-SC

gt (Calculations) 8.8 125.7 78.5 11.5 86.7 40.7 7.7 92.1 40.8

-177.7 -92.8 -109.9

-279.8 -156.5 -176.4

BDEP9 poly(U)50 DNA(salmon)(Na)27

Experiment -5.0 79.0 19.0 -3.6 76.0 16.0 -2.0 83.0 23.0

-113.0 -103.0 -110.0

-162.0 -149.0 -163.0

a All values are given in ppm. The torsion angles, R, σ in barium diethyl phosphate (BDEP) and the calculated models with gg conformation (gt conformation) were 68.2°, 71.6°, and -60°, -60° (-60°, 180°), respectively.

Figure 10. Comparison of the calculated and experimentally measured full 31P chemical shift tensors. Experimental data were collected on BDEP. The torsion angles R, ζ in BDEP and the calculated models were 68.2°, 71.6°, and -75°, -75°, respectively.

differences have been encountered. These differences are caused by a charge transfer from dimethyl phosphate to the hydrogen-bonded water molecules. A charge-transfer effect has already been evidenced by the theoretical calculations of Pullman et al.20 Dmp-gg with six water molecules exhibits larger chemical shifts than dmp-gg in vacuo. The downfield shift is more pronounced for dmp-IC (∼4 ppm) than for dmp-SC (∼2 ppm). Interestingly, a similar behavior is found in the gt conformation only for dmp-IC, whereas isotropic 31P chemical shifts of dmpSC are either approximately the same or even slightly lower than that of dmp in vacuo. The difference between dmp-IC and dmp-SC of the gt conformation is a result of a random compensation of the three tensor components. If the solvent effect is examined separately for δ11, δ22, and δ33, it turns out that the individual trends are identical for dmp-gg and dmp-gt. The components δ11 and δ22 decrease, and δ33 increases upon solvation, thereby leading to the reduction of the chemical shift anisotropy. For example, in the case of the gg conformer with R, ζ ) -60°, the chemical shift anisotropy for dmp is -296.8 ppm, but it is reduced to only -166.1 ppm for dmp-IC (cf. Table 2). The sensitivity of CSA to the hydration of the phosphate group was observed in experimental studies.9,46 Herzfeld at al.9 showed that the binding of one water molecule to a diesterphospholipid resulted in the decrease of the experimental CSA value and the increase of the isotropic chemical shift, which is in agreement with our calculations. Table 2 and Figure 10 show a comparison of the calculated chemical shift tensors with experimental data for barium diethyl phosphate (BDEP). To compare experimental data with theoretical 31P chemical shifts, we used a gg conformer of the dimethyl

Figure 11. Energy differences of the two hydrated models, IC and SC.

phosphate with torsion angles R, ζ ) -75°. Considering the symmetry of dmp, these values are closest to the values of the P-O torsion angles found in the experimental structure of BDEP (68.2°, 71.6°).9 It is obvious that a better agreement with experiment is obtained if calculations are carried out in explicit solvent. The gg conformation is known to lie energetically lower than gt,1 and the same holds for dmp-IC vs dmp-SC (Figure 11). Although the difference between dmp-IC and dmp-SC is rather small (1.5 and 2.9 kcal/mol for gg and gt, respectively; see Figure 11), the chemical shift tensors for the two models differ quantitatively. In addition to water molecules, metal ions, such as Na+, are present in DNAs to compensate for the negative charge of phosphate groups. Electrostatic effects introduced by the counterions influence the global as well as the local electronic structure of nucleic acids and can be reflected in calculated 31P chemical shift tensors. However, molecular dynamics simulations show that the ions do not bind directly to the oxygen atoms of the phosphate, but the interaction is mediated via a water molecule.47,48 For this reason, we expect that the influence of metal ions on 31P chemical shift tensors is smaller than that of the solvent. Hence, the incorporation of Na+ ions into our calculations would likely represent a second-order effect, which was beyond the scope of this study. Torsion Angle Dependence. The trends in isotropic chemical shifts as well as in all principal components have been studied for the R and ζ torsion angle in the range of 60° for both gg and gt conformations. Within the experimentally observed gg range, the isotropic 31P chemical shift decreases with the increasing torsional angle, either R or ζ (see Figures 6 and 7). The same trend has also been found in the gt range for δiso as influenced by R (see Figure 8). On the contrary, the dependence of the 31P isotropic chemical shift on the ζ torsion angle in the gt conformation has its maximum around 180° and drops when going to the outer values of the ζ torsion angle range (Figure 9). The span between the smallest and largest isotropic chemical shift is as much as 5 and 10 ppm in the gg and gt conformations, respectively. Comparing our results to the chemical shift torsion angle contour map by Gorenstein,1,19 we obtain an agreement regarding (1) the relative isotropic chemical shifts of the gg and gt conformations, (2) the trend for the dependence on ζ in the gg region, and (3) a shallow dependence on ζ in the gt region. See Supporting Information for 3D plots of calculated 31P isotropic chemical shifts against R and ζ. Although there is no clear trend in the δ11 principal component, the behavior of the remaining two, δ22 and δ33, is quite simple. The δ22 component goes up and δ33 declines upon increasing the R or ζ torsion angle. As in the case of the isotropic chemical shift, the only exception to this behavior is the ζ torsion

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J. Phys. Chem. B, Vol. 111, No. 10, 2007 2665

TABLE 3: Differences in the Isotropic Chemical Shift between the gg and gt Conformations R/deg

ζ/deg

β/deg

/deg

δiso/ppm

∆δgt-gg iso /ppm

dmp (gg) dmp (gt)

-60 -60

-60 180

180 180

180 180

1.9 8.8

6.9

dmp-IC (gg) dmp-IC (gt)

-60 -60

-60 180

180 180

180 180

5.6 8.7

3.1

dmp-IC (gg) dmp-IC (gt)

-60 -60

-60 180

180 150

180 250

5.6 11.5

5.9

dmp-SC (gg) dmp-SC (gt)

-60 -60

-60 180

180 180

180 180

3.9 5.7

1.8

dmp-SC (gg) dmp-SC (gt)

-60 -60°

-60 180

180 150

180 250

3.9 7.7

3.8

conformation

Figure 12. Directions of the principal components of the 31P chemical shift tensor with respect to the Cartesian coordinate system.

angle dependence for the gt conformation. δ22 reaches its maximum and δ33 its minimum around 180°, that is, in the middle of the ζ interval (see Figure 9). For a given torsion angle (R or ζ), a given conformation type (gg or gt) and a given solvation pattern (no solvent, dmp-IC, dmp-SC), the δ11 component varies within 5-10 ppm, whereas both δ22 and δ33 vary within as much as 30 ppm. The up or down displacements of the dependencies of the δ22 and δ33 principal components on one of the P-O ester torsion angles due to changes in the other P-O torsion angle is larger for the ζ-dependencies (∼20-25 ppm) than for R-dependencies (∼5-10 ppm). Another step in assessing the influence of P-O torsion angles is the comparison of the 31P chemical shifts for the gg and

gt conformations. In agreement with previous studies,1,11,13,14 gt is more deshielded than gg (cf. Figure 7 vs Figure 9). The 31P isotropic chemical shifts of gg (R, ζ ) -60° ) and gt (R ) -60°, ζ ) 180°) are (a) for dmp-IC 5.6 and 11.5 ppm, respectively; and (b) for dmp-SC 3.9 and 7.7 ppm, respectively (cf. Table 3). Thus, the difference in the 31P chemical shift between the gg and gt conformation is larger for dmp-IC (5.9 ppm) than for dmp-SC (3.8 ppm) (see Table 3). It should be kept in mind that β and  torsion angles were set to different values in the gg and gt conformations, corresponding to the average values observed in X-ray structures of nucleic acids,26 whereas both β and  are equal to 180° in gg, β and  are equal to 150° and 250°, respectively, in gt. If β and  are set to 180° in the gt conformation (dmp-SC), as well, the 31P chemical shift reduces from 7.7 to 5.7 ppm, which in turn leads to a smaller difference in the 31P chemical shift between the gg and gt conformations (1.8 ppm) (cf. Table 3), and we can observe the same phenomenon for dmp-IC. The calculated ∆δgt-gg thus depends not only on R and ζ but also iso on the other backbone torsion angles and the solvation pattern. The 31P chemical shift difference between the BI and BII states was estimated on the basis of experimental data1 as 1.6 ppm. The estimate was made on the assumption that  ) 170° for BI and  ) 255° for BII (information about β has not been provided). Thus, we should compare the “experimental” value with the one calculated for β,  ) 180° in the case of ∆δgt-gg iso of the gg conformer and β ) 150° and  ) 250° in the case of the gt conformer. This comparison shows that calculations by 2 and 4 ppm in the case of dmp-SC overestimate ∆δgt-gg iso and dmp-IC, respectively. Table 3 shows that ∆δgt-gg decreases upon solvation, which iso is in agreement with the finding by Pullman et al.20 He showed that an increasing number of water molecules in the first solvation shell diminishes the energy gap between the gg and gt conformers by destabilizing gg relative to gt. The trends in δiso and the principal tensor components with respect to the P-O torsion angles are modified by β and . These modifications are rather quantitative; qualitative trends do not change dramatically (see Figure 13). All principal components, as well as the isotropic chemical shift, vary by ∼2 ppm if β and  are changed from 180° to 150° and 250°,

CSA CSA Figure 13. Comparison of the trends in δiso, δCSA 11 , δ22 , and δ33 obtained for dmp-SC with β ) 180°,  ) 180° (empty box), and β ) 150°,  ) 250° (filled box), respectively. The torsion angle ζ was set to 180° in all structures.

2666 J. Phys. Chem. B, Vol. 111, No. 10, 2007 respectively. The δ11 component is the only one that decreases for all values of R. The values of δ22 and δ33 change in both directions. Wu et al. have noted that the assumption of a uniform CSA tensor for all backbone phosphates in [d(CGCGAATTCGCG)]2 is appropriate because the isotropic 31P chemical shifts span only a narrow range of several ppm.6 However, the early calculations of 31P chemical shift tensors13 have already suggested a considerable dependence of each principal component upon geometry. Following these calculations, Prado et al. have emphasized that the same chemical shift anisotropy for the gg and gt conformation is a result of a fortuitous mutual compensation of the principal components.13 Our calculations support this original finding. Different phosphate conformations obviously have different CSA tensors, as discussed above. Nevertheless, the inspection of the R and ζ torsion angle ranges in [d(CGCGAATTCGCG)]2 (1NAJ, 1DUF) shows that torsion angle variations in such a regular B-DNA fall within a much narrower range of backbone torsion angles (15°-30°) than the range used in our calculations (60°). In this light, the assumption of a uniform 31P chemical shift tensor as suggested by Wu et al.6 appears to be justified. However, some unusual phosphate group conformations have been observed in noncanonical forms of nucleic acids for which the span between the lowest and the largest R and ζ torsion angle values by far exceed 60°.49 Calculations for the noncanonical conformations are currently underway and will be published elsewhere. Orientation of the CSA Tensor. We have used sPs to calculate the angular deviations of the directions of the principal components δ11, δ22, and δ33 from the axes of the Cartesian coordinate system defined so that the y axis bisects the O1-P-O2 angle, the z axis lies in the O1-P-O2 plane and is perpendicular to y, and the x axis is orthogonal to both y and z (Figure 12). The calculated deviations range approximately from 0.5° to 5°. Thus, for any choice of R, ζ, and , the directions of principal components of the 31P CSA tensors almost coincide with the axes of the Cartesian coordinate system, and the conformation of the phosphate group has a negligible influence on the orientation of 31P CSA tensors relative to the molecular reference frame. Dynamic Effects. Our static models with a regular arrangement of water molecules represent sufficiently simple, yet very rough approximations of the phosphate group surroundings in a real solution. Despite the essentially organized structure of the first and second phosphate group hydration shell,20 the positions of water molecules undergo a dynamic evolution, and hydrogen bonds continually break and reform, thereby affecting the 31P chemical shifts. This fact, as well as close energies of dmp-IC and dmp-SC models, suggests that a study combining molecular dynamics (MD) with DFT calculations is a next logical step in the theoretical treatment of the 31P CSA tensors. Conclusions Our calculations in vacuo carried out on dimethyl phosphate and dinucleoside-3′,5′-monophosphate with bases replaced by hydrogen atoms demonstrated that qualitative trends in isotropic 31P chemical shifts and all principal components of the 31P CSA tensor do not change upon model truncation. The results also demonstrate that the smaller model (1) provides a clear understanding of the conformational effects and (2) prevents the creation of artificial hydrogen bonds during geometry optimizations. Therefore, dmp can be safely employed to study the torsion angle dependence of 31P CSA tensors. It has been shown that the presence of explicit solvent does not change the qualitative trends in 31P CSA tensors as

Prˇecechteˇlova´ et al. influenced by backbone torsion angles. Although δ11 and δ22 diminish, δ33 increases upon solvation, which results in a decrease in the chemical shift anisotropy. Contrary to the complex torsion angle behavior of δ11, most of the torsion angle dependencies of δ22 and δ33 have a clear monotonic trend. For R or ζ varying in the range from 270° to 330° and from 240° to 300°, respectively, the span of δ22 and δ33 is as much as 30 ppm. The trends in the 31P CSA tensor components as influenced by the torsion angles R and ζ are preserved upon the modification of the torsion angles β and . With respect to the small torsion angle variations in a regular B-DNA, the assumption of a uniform 31P CSA tensor for all backbone phosphates in an oligonucleotide with a B-DNA conformation appears to be appropriate. Nevertheless, noncanonical nucleic acid structures possessing unusual phosphate group conformations49 have to be approached with caution. Our calculations have also demonstrated that the conformation of the phosphate group does not significantly influence the orientation of the 31P CSA tensor. The maximum deviation of the principal tensor components from the axes of OPO bond angles is ∼5°. The static models employed in the present study proved to be useful due to their simplicity. However, they do not reflect the effects of conformational dynamics and dynamic evolution of hydrogen bonds. Therefore, a combined MD/DFT study is currently in progress and will be published in a separate paper. Acknowledgment. This work was supported by the Grants MSM0021622413 to M.M. and LC06030 to V.S. from the Ministry of Education, Youth and Sports of the Czech Republic, and by the Grant 204/03/H016 from the Science Foundation of the Czech Republic to J.P. and P.N. The authors thank Martin Kaupp for helpful discussions and Petr Kulha´nek for help with solving technical problems. Deutscher Akademischer Austausch Dienst (DAAD) is acknowledged for providing a scholarship to Jana Prˇececheˇlova´ for her research stay at the University of Wu¨rzburg, Germany. Supporting Information Available: Supporting Information material includes (I) 3D plots of 31P isotropic chemical shifts against R and ζ and (II) optimized geometries of all models and conformations studied. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Gorenstein, D. G. Chem. ReV. 1994, 94, 1315. (2) Varani, G.; Aboulela, F.; Allain, F. H. T. Prog. Nucl. Magn. Reson. Spectrosc. 1996, 29, 51. (3) Wijmenga, S. S.; van Buuren, B. N. M. Prog. Nucl. Magn. Reson. Spectrosc. 1998, 32, 287. (4) Cromsigt, J.; van Buuren, B.; Schleucher, J.; Wijmenga, S. S. Methods Enzymol. 2001, 338, 371. (5) Furtig, B.; Richter, C.; Wohnert, J.; Schwalbe, H. ChemBioChem 2003, 4, 936. (6) Wu, Z.; Tjandra, N.; Bax, A. J. Am. Chem. Soc. 2001, 123, 3617. (7) Wu, Z.; Delaglio, F.; Tjandra, N.; Zhurkin, V. B. Bax, A. J. Biomol. NMR 2003, 26, 297. (8) Koehler, S. J.; Klein, M. P. J. Am. Chem. Soc. 1977, 99, 8290. (9) Herzfeld, J.; Griffin, R. G.; Haberkorn, R. A. Biochemistry 1978, 17, 2711. (10) For purposes of conveniently describing the dependence of phosphorus chemical shifts on P-O ester torsion angles, no distinction is usually made between R-O-P-O(R′) torsion angles +60° (+g) or -60° (-g). Moreover, R and ζ torsion angles of g, t; -g, t; and t, g are often grouped as g, t. Similarly, g, g includes conformers -g, -g; g, -g; and -g, g. (11) Gorenstein, D. G.; Kar, D. Biochem. Biophys. Res. Commun. 1975, 65, 1073. (12) Prado, F. R.; Giessner-Prettre, C.; Pullman, B. Int. J. Quantum Chem. Quantum Biol. Symp. 1979, 6, 491.

31P

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