Chemical Shifts in Nucleic Acids Studied by Density ...iqc.udg.es/articles/pdf/iqc838.pdf · The...

DOI: 10.1002/chem.201103593

Chemical Shifts in Nucleic Acids Studied by Density Functional TheoryCalculations and Comparison with Experiment

Judith M. Fonville,[a, f] Marcel Swart,[b, e] Zuzana Vok�cov�,[c] Vladim�r Sychrovsky,[c]

Judit E. Sponer,[d] Jir� Sponer,[d] Cornelis W. Hilbers,[f] F. Matthias Bickelhaupt,*[e] andSybren S. Wijmenga*[f]

Introduction

The structure determination of biomolecules such as nucleicacids and proteins by NMR spectroscopy is well establish-ed.[1] Traditionally, this is achieved by using constraints de-rived from NOEs, residual dipolar couplings, and J cou-plings to establish distances, atomic connectivities, and tor-sion angles. Another important NMR parameter is thechemical shift, which is very sensitive to local conformationand intramolecular environment. The role of the chemicalshift in biomolecular structure determination has become in-creasingly important, for example, protein secondary struc-ture is now commonly derived from heteronuclear andproton shifts.[2] Recently it was shown that the three-dimen-sional structure of proteins can be derived by using hetero-nuclear and proton shifts as the sole source of experimentalrestraints in combination with fragment replacement.[3]

However, to date, the use of chemical shifts to derive struc-tural information for nucleic acids has been limited. It isknown that ring-current and magnetic-anisotropy effects in-fluence the proton chemical shifts of nucleic acids, and ini-tial efforts showed that the associated (well-parametrized)semi-classical equations provide a way to precisely and accu-rately predict the chemical shifts of nonexchangeable pro-tons given a three-dimensional structure.[4] Extension of the

Abstract: NMR chemical shifts arehighly sensitive probes of local molecu-lar conformation and environment andform an important source of structuralinformation. In this study, the relation-ship between the NMR chemical shiftsof nucleic acids and the glycosidic tor-sion angle, c, has been investigated forthe two commonly occurring sugar con-formations. We have calculated bymeans of DFT the chemical shifts of allatoms in the eight DNA and RNAmono-nucleosides as a function ofthese two variables. From the DFT cal-culations, structures and potentialenergy surfaces were determined byusing constrained geometry optimiza-

tions at the BP86/TZ2P level of theory.The NMR parameters were subse-quently calculated by single-point cal-culations at the SAOP/TZ2P level oftheory. Comparison of the 1H and13C NMR shifts calculated for themono-nucleosides with the shifts deter-mined by NMR spectroscopy for nucle-ic acids demonstrates that the theoreti-cal shifts are valuable for the character-ization of nucleic acid conformation.For example, a clear distinction can bemade between c angles in the anti and

syn domains. Furthermore, a quantita-tive determination of the c angle in thesyn domain is possible, in particularwhen 13C and 1H chemical shift dataare combined. The approximate lineardependence of the C1’ shift on the c

angle in the anti domain provides agood estimate of the angle in thisregion. It is also possible to derive thesugar conformation from the chemicalshift information. The DFT calcula-tions reported herein were performedon mono-nucleosides, but examples arealso provided to estimate intramolecu-larly induced shifts as a result of hydro-gen bonding, polarization effects, orring-current effects.

Keywords: density functional calcu-lations · NMR spectroscopy · nucle-ic acids · structure elucidation

[a] Dr. J. M. FonvillePresent address: Department of Zoology, University of CambridgeDowning Street, Cambridge CB2 3EJ (UK)

[b] Prof. Dr. M. SwartPresent address: Instituci� Catalana de Recercai Estudis AvanÅats (ICREA)Passeig Llu�s Companys 23, E-08010 Barcelona (Spain)Institut de Qu�mica Computacional and Departament de Qu�micaUniversitat de Girona, Campus Montilivi, 17071 Girona (Spain)

[c] Dr. Z. Vok�cov�, Prof. Dr. V. SychrovskyInstitute of Organic Chemistry and BiochemistryAcademy of Sciences of the Czech Republicv.v.i, Fleming Square 2, 16610 Prague (Czech Republic)

[d] Dr. J. E. Sponer, Prof. Dr. J. SponerInstitute of Biophysics, Academy of Sciences of the Czech RepublicKr�lovopolsk� 135, 61265 Brno (Czech Republic)

[e] Prof. Dr. M. Swart, Prof. Dr. F. M. BickelhauptDepartment of Theoretical Chemistryand Amsterdam Center for Multiscale Modeling (ACMM)Scheikundig Laboratorium der Vrije UniversiteitDe Boelelaan 1083, NL-1081 HV Amsterdam (The Netherlands)E-mail : [email protected]

[f] Dr. J. M. Fonville, Prof. Dr. C. W. Hilbers, Prof. Dr. S. S. WijmengaInstitute of Molecules and MaterialsBiophysical Chemistry, Radboud University NijmegenHeyendaalseweg 135, 6525 AJ, Nijmegen (The Netherlands)E-mail : [email protected]

Supporting information for this article is available on the WWWunder http://dx.doi.org/10.1002/chem.201103593.

� 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eur. J. 2012, 18, 12372 – 1238712372

use of proton chemical shifts, which are a limited data set,to heteronuclear shifts is a highly desirable addition to thestrategies available to structure determination. Precise andaccurate structure–chemical shift relationships for heteronu-clei such as carbon and nitrogen are currently limited fornucleic acids.[2b, 5] Given the reliability and sensitivity of the-oretically calculated NMR chemical shifts,[6] these could fur-ther aid structure determination and validation by enhancedinterpretation of experimental chemical shift data. More-over, the availability of these data could also provide furtherinformation on the physical background of the chemicalshift phenomenon, in particular, on how these shifts dependon the spatial conformation of the molecule.

The glycosidic torsion angle, c, is a crucial factor in thedetermination of DNA and RNA structures because this di-hedral angle defines the orientation of the bases with re-spect to their sugar moieties (see Figure 1). Although it ispossible to extract information on the glycosidic torsionangle experimentally by means of NOEs from 3JH1’–C2/4,

3JH1’–

C6/8,[7] and 1JH1’–C1� couplings,[7c,8] or from cross-correlated re-

laxation of C�H dipolar coupling and N chemical shift ani-sotropy,[9] these experiments can be complicated, lengthy,and may not uniquely determine c. On the other hand, vir-tually every NMR experiment returns chemical shift valuesand thus a detailed knowledge of the relationship between c

and the chemical shifts in DNA and RNA nucleosides maysimplify and accelerate the determination of the glycosidictorsion angle from NMR studies and hence improve the elu-cidation of nucleic acid structures.

There have been previous efforts to establish a relation-ship between proton chemical shifts and the glycosidic tor-sion angle[1a,4] and between proton chemical shifts and thepucker of ribose and deoxyribose moieties.[11] Furthermore,attempts have been made to establish similar relationshipsfor heteronuclear shifts, for example, between 13C chemicalshifts and the pucker of ribose and deoxyribose moiet-ies.[11, 12] The relationship between the glycosidic torsionangle and carbon chemical shifts has been studied by usingexperimental data[13] and DFT calculations.[6a,14] Relation-ships have also been established between the glycosidic tor-sion angle and chemical shift anisotropies of the 13C and 15Nchemical shift tensors.[15]

In this work we have comprehensively evaluated, throughDFT calculations, the chemical shifts of 1H, 13C, 15N, and 17Oin all eight RNA and DNA mono-nucleosides as a functionof glycosidic torsion angle, c, for the two common sugarpuckers, the C2’-endo and C3’-endo conformations. In par-ticular, we have optimized the geometries of all eight DNAand RNA mono-nucleosides at each c angle/pucker combi-nation by using modern constrained optimization techni-ques.[12c,16] Then, for each value of the torsion angle we cal-culated the NMR chemical shielding of all the atoms by avalidated, well-established method.[6a,17] An in-depth com-parison was then made between the 1H and 13C chemicalshifts determined by the DFT calculations and those deter-mined experimentally for selected RNA molecules to dem-onstrate the value of the DFT-derived shifts for establishing

the conformation and structural elements in the nucleic acidmolecules. This is challenging because the calculations wereperformed for mono-nucleosides in a vacuum and partiallyalso with a dielectric continuum model (COSMO, see theExperimental Section), mimicking aqueous solution condi-tions. We find that a distinction between c angles in the antior syn domain and good estimates of their actual values canbe made on the basis of the chemical shift data. Further-more, analysis of the chemical shift values of different

Figure 1. A) Nomenclature, structures, and numbering of the fivecommon bases.[10] B) The b-(deoxy)-d-riboses of DNA and RNA are pre-sented for two commonly occurring sugar-ring conformations: the C2’-endo (2E or S-type; top) conformation is shown for adenosine and theC3’-endo (3E, or N-type; bottom) conformation is shown for uracil. Thebackbone torsion angles b, g, d, and e (for their definitions, see Table 1)are indicated as well as the glycosidic torsion angle c, the range 0�908 isreferred to as the syn region, the range 180�908 as the anti region.[10]

Chem. Eur. J. 2012, 18, 12372 – 12387 � 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.chemeurj.org 12373

FULL PAPER

www.chemeurj.org

carbon atoms provides insights into the presence or absenceof intramolecular interactions such as hydrogen bonding andbase stacking, as well as indications for the occurrence of in-ternal molecular motion. The shifts of protonated as well asof unprotonated carbon atoms in the nucleobase can now bemeasured as a result of recent developments in hardware(cryo- or cold probes with increased sensitivity for carbon)and new NMR pulse sequences.[18]

Results

We first present some methodological aspects of the DFTcalculations (see the Experimental Section for full details),namely those concerning geometry optimization and inclu-sion of the solvent. We then describe the main results of theDFT calculations, that is, the DFT chemical shifts of allatoms of all eight RNA and DNA mono-nucleosides calcu-lated as a function of c and for the two common sugars. Fi-nally, a comparison is made of the DFT results with experi-mental data, and we demonstrate how chemical shifts pro-vide structural information.

The nomenclature and numbering schemes of the IUPAC/IUB guidelines were used.[10] The numbering of the atoms inthe common DNA and RNA bases and the furanose ring ispresented in Figure 1A. The nucleic acid backbone and gly-cosidic torsion angles are indicated in Figure 1B and definedin Table 1. Figure 1B also shows a representation of the twomost important sugar conformations, the C2’-endo (alsoknown as “south” or S-type) and C3’-endo (“north” or N-type) puckers.

The DFT results were compared with the experimentalchemical shifts of four different RNA molecules for whichthe secondary structure is presented in Figure 2: HIV2-TAR

RNA,[18a] the apical stem-loop of Human and Duck Hepati-tis B Virus (human HBV[20] and duck HBV,[21] respectively),and an RNA hairpin with a UUCG tetra-loop.[9c,18b] TheseRNAs were selected because resonance assignment of theheteronuclei in these molecules also included non-hydrogen-ated heteroatoms in combination with the extensive experi-mental determination of torsion angles.

Constraints on backbone torsion angles and accounting forthe presence of solvent is useful for structure optimization :In the DFT calculations, each conformation was geometry-optimized prior to calculation of the chemical shifts. In thefirst calculations, the backbone torsion angles were not con-strained during this geometry optimization. This led, for cer-tain glycosidic torsion angles, to jumps in the energy profilesand in the computed NMR chemical shifts. These inconsis-tencies were found to result from the large rotational free-dom allowed for the backbone torsion angles in the mono-nucleosides, a freedom not available in DNA or RNA oligo-and polymer strands.

1) Most noteworthy in this respect was the behavior ofthe b backbone dihedral angle. The b torsion angle usuallyadopts values of around 1808 in nucleic acids. In our mono-nucleoside systems, a hydroxy group replaces the 5’-phos-phate present in the oligo- and polynucleotides (Figure 1)leading to rotational freedom about the O5’�C5’ bond,which permits the hydroxy group to easily form a hydrogenbond with nearby hydrogen-accepting groups; such a hydro-gen bond cannot be formed by the phosphate groups inoligo- or polynucleotides. These hydrogen bonds, caused bythe hydroxy group, greatly influenced the energy profile as afunction of the glycosidic torsion angle. We therefore decid-ed in subsequent calculations to constrain the b as well as

Figure 2. Secondary structures of the RNA molecules used in the compar-ison of the DFT-calculated chemical shifts with experimental shift values.

Table 1. Definitions of the glycosidic torsion angle, c, and the backbonedihedrals a–z (see Figure 1 for the atomic numbering).

Angle Atomsinvolved

Experimentalrange DNA[a]

[8]

Experimentalrange RNA[a]

[8]

Constraint[b]

[8]

c O4’�C1’��C2(pyrimidines)

–

O4’�C1’�N9�C4 (purines)

–

a ACHTUNGTRENNUNG(n-1)O3’�P�O5’�C5’

270–330 270–310 –

b P�O5’�C5’�C4’

135–185 165–185 180

g O5’�C5’�C4’�C3’

30–75 45–60 60

d C5’�C4’�C3’�O3’

90–180 75–90 ACHTUNGTRENNUNG(80, 140)[c]

e C4’�C3’�O3’�P

165–265 190–225 210

z C3’�O3’�P�O5’ ACHTUNGTRENNUNG(n+1)

150–310 265–305 –

[a] Estimated values for B-DNA and A-RNA from Figure 5.9 in ref. [19].[b] Value to which the backbone dihedrals were constrained (unlessnoted otherwise). [c] The d dihedral was only constrained in cases inwhich the pucker conformation changed during the scan of the glycosidictorsion angle. In these cases the d dihedral angle was constrained to avalue of 808 (C3’-endo pucker) or 1408 (C2’-endo pucker), which are theconventional values for these pucker conformations.

www.chemeurj.org � 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eur. J. 2012, 18, 12372 – 1238712374

F. M. Bickelhaupt, S. S. Wijmenga et al.

www.chemeurj.org

the g and e backbone torsion angles to the experimentallyobserved values (see Table 1).

2) Secondly, we consider the torsion angle d. The torsionangle d was, in most cases, not constrained during the opti-mization because it determines which one of the two sugarpucker conformations is adopted in the calculations. Al-though the conformation obtained generally contained thedesired pucker (i.e. , d�808 for the C3’-endo pucker and�1408 for the C2’-endo sugar pucker), some nucleosides, inparticular some of the RNA nucleosides, suffered fromspontaneous conversion of the initial into the alternativepucker somewhere during the glycosidic torsion angle scan.Note that for values of c for which the unconstrained d

angle remains close to 80 or 1408, the energy is close to aminimum. For the nucleosides in which a spontaneous con-version of the pucker took place, the d angles deviated sig-nificantly from 80 and 1408 for c angles neighboring theconversion region. For glycosidic angles with such devia-tions, the energy is relatively high and the correspondingconformations will only be encountered infrequently. For in-stances in which repuckering occurred, d was constrained inthe geometry optimization to a value of 80 (C3’-endopucker) or 1408 (C2’-endo pucker). This constraint wasfound to have only a small influence on the energy profilealthough the effect on the chemical shifts can be larger.

3) Thirdly, a further complication was posed by the O2’Hhydroxy group in the RNA nucleosides, which exhibitedalmost complete, unusual, rotational freedom and appearedto be strongly coupled to the value of the glycosidic torsionangle, c. For example, the H�O2’�C2’�H2’ dihedral angle,which would normally have a value of around 1608 (for theS pucker), was found to be in the range 250–3308 at some c-angle intervals. Although these variations did not signifi-cantly influence the energy profile, they did result in signifi-cant changes in the calculated shifts. Under physiologicalconditions, this hydroxy group will interact with the sur-rounding solvent, but this interaction is absent in the model.To overcome this, the solvent was included in our geometryoptimizations for RNA by simulating the effect of an aque-ous solution through a dielectric continuum model(COSMO, see the Experimental Section): A major improve-ment was indeed observed by its use. Although the O2’Hgroup was allowed to rotate, in this situation its motion re-tained the dihedral angle H�O2’�C2’�H2’ between 145 and1758 for the S-puckered sugars and between 80 and 1208 forthe N-puckered sugars, with concomitant smoothing of thechemical shifts as a function of the glycosidic torsion angle,c. Rotation of the O2’H group at fixed c (N pucker, c=

�1508 ; S pucker, c=�1208) leads to profiles (see Figure S1-O2’H in the Supporting Information) with a minimum in orjust above the O3’ region (60–1208) for the N (ca. 908) andS pucker (ca. 1608), respectively. For the N pucker a clearsecond minimum is seen at �508 corresponding to the baseorientation (�80–�208), which is around 1.5 kcal mol�1

(ca. 2.5 kT) higher in energy than the minimum at 908. Al-though the O3’ orientation appears to be the most commonorientation in an A-helix,[8,22] occurrence of the base orienta-

tion has also been proposed;[22, 23] in an A-helix the energyof the latter orientation may be lowered by hydrogen bond-ing to a sequential base via an H2O intermediate.[22b,c]

Because the torsion angles and structural features in thenon-COSMO calculations described above are noncanoni-cal, an interesting lesson from this is that unusual values ofchemical shifts indicate special structural elements. Further-more, solvation, as modeled by COSMO, weakens both theelectrostatic and covalent components in the hydrogenbonding between base and sugar (see, for example, FonsecaGuerra et al.[24]). Therefore, we obtain a correct medianvalue for the H�O2’�C2’�C3’ dihedral angle for the RNAnucleosides upon application of COSMO.[8]

Energy profiles : The energy profiles computed as a functionof the glycosidic torsion angle (Figure 3) show that for thetwo sugar puckers C2’-endo and C3’-endo, the energeticallyfavorable glycosidic torsion angles correspond qualitativelyto the experimentally found values, that is, for C2’-endo themost common c angle is around �1008 and for C3’-endo it isaround �1608.[25] Note that for RNA C3’-endo, this �mini-mum� at around �1608 is more like a saddle point; when weemploy a larger system, that is, with -O�PO2�OMe insteadof -OH as the terminating group, a full minimum is obtained(C3’-endo RNA: �1478, Ade; �1568, Cyt; �1458, Gua;�1558, Ura). Note also that these RNA energy profiles arewith O2’H essentially in the O3’ orientation as this corre-sponds to the lowest energy (see above). The energy profileswith O2’H fixed in the base orientation (H�O2’�C2’�H2’ at3108) are similar although translated to a higher energy (seeFigure S2-O2’H in the Supporting Information). Interesting-ly, the clear energy minimum for the c angle at about 608for the RNA mono-nucleosides (Figure 3) corresponds wellto the experimentally found torsion angle for the syn region(see below).

Chemical shifts of the hydrogen atoms in the sugar ring :The DFT-calculated chemical shifts of the hydrogen atomsof the sugar ring depend to varying degrees on the values ofthe glycosidic torsion angle and on the conformation of thesugar ring (C2’-endo or C3’-endo pucker). This is illustratedin Figure 4, in which the chemical shifts have been plottedas a function of c for H2’ and H3’ in the sugar ring of theRNA mono-nucleosides. The shifts of the H2’ and H3’atoms (but not those of H3’ of the C2’-endo-puckeredsugars) clearly change as a function of the c angle and somechanges are base-dependent. On the other hand, we findthat the H4’ chemical shift is much less sensitive to rotationabout the glycosidic bond and the nature of the base (seep. 46 of the Supporting Information). The c-dependentchemical shift variations as well as the chemical shift valuesare very similar to those obtained in previous semi-empiricalcalculations[4a,b] for both the RNA and DNA mono-nucleo-sides. As found previously,[4a] a c angle between 90 and 1508will induce strongly downfield-shifted H3’ resonances (shiftvalues at higher ppm) for C3’-endo-puckered sugars (seeFigure 4). On the other hand, C2’-endo-puckered sugars will


FULL PAPERChemical Shifts in Nucleic Acids

www.chemeurj.org

lead to large downfield shifts for H2’ when c is between 60and 1208. This is consistent with the experimental data. Forexample, for the syn-oriented G9 in the U6U7C8G9 loop ofthe hairpin in Figure 2,[9c] the experimental value of the H3’shift is 5.67 ppm, which is extraordinarily high. This highvalue immediately indicates a C3’-endo conformation forthe sugar, the most populated sugar pucker in RNA. More-over, the value of 5.67 ppm for the H3’ shift locates the gly-cosidic torsion angle in the syn range. Combining the H3’shift with that of H2’ (4.85 ppm; see Figure 4) shows thatthe glycosidic torsion angle lies between 60 and 808 (yellowband in Figure 4), in agreement with the experimental value(c=59�208).[9c]

For both the RNA and DNA nucleosides, the H2’ chemi-cal shift is always dependent on the glycosidic torsion angle,whereas the H3’ chemical shift depends strongly on c onlywhen the sugar is C3’-endo (see Figure 4). Interestingly, forthe C2’-endo conformation, this dependency of H3’ on c dis-appears almost entirely. This can be explained by stereotypi-cal considerations: For nucleosides with a C2’-endo pucker,the H3’ is directed away from the base, whereas for nucleo-

sides with a C3’-endo pucker, the H3’ atom is much closer tothe base ring and its shift thus more sensitive to ring-currentshift contributions. This is consistent with experimental fin-dings.[4a] The small “jumps”, which are occasionally observedin, for example, the H2’ RNA curve (Figure 4), correspondto regions of high energy (see Figure 3). In these conforma-tions there may exist steric (repulsive) interactions betweenbase and sugar that will affect the chemical shifts considera-bly. However, because of the high energy of these regions,they will be very sparsely populated and the correspondingvalues of the chemical shifts will hardly contribute to the ex-perimentally observed shifts. Therefore these small “jumps”are not disconcerting.

Chemical shifts of the carbon atoms : We present in Table 2the differences between the DSS-calibrated DFT shifts(DSS =2,2-dimethyl-2-silapentane-5-sulfonic acid) of themono-nucleosides in an A-helix conformation and the ex-perimental 13C shifts obtained for RNA in an A-helix con-formation. For the DSS-calibrated DFT shift in an A-helixenvironment we took the value at the standard A-helix con-

Figure 3. Energy profiles of the mono-nucleosides as a function of the glycosidic torsion angle, c, for the C3’-endo and C2’-endo puckers in DNA (top),and the C3’-endo and C2’-endo puckers in RNA (bottom). The DNA and RNA systems were geometry-optimized in the gas-phase and in a COSMO sol-vent environment, respectively (see text).



www.chemeurj.org

formation, that is, at c=�1608 and the sugar pucker C3’-endo (see also the Experimental Section). The experimentalRNA A-helix shifts were obtained as described in the Ex-perimental Section. In brief, the experimental A-helix shift

for each carbon atom was taken as the average of the meas-ured shift values of the atoms located in a pure A-helix en-vironment by using the molecules depicted in Figure 2; ter-minal nucleotides, bulges, loops, and non-C3’-endo sugarconformations were excluded. Table 2 shows that in mostcases the DSS-calibrated A-helix DFT shifts are larger thanthe experimental A-helix shifts. Furthermore, the differen-ces between the measured and DFT-derived shifts vary con-siderably from one carbon type to the next. For example,the absolute difference is the smallest for C2 of uracil (dif-ference of �0.4 ppm), which demonstrates that the meas-ured chemical shift does not differ much from the vacuumvalue obtained by the DFT calculations, whereas the abso-lute differences for C2’ (�10.2 ppm) and guanine C5(�11.1 ppm) are the largest. The average difference betweenthe calculated and experimental values amounts to around4–5 ppm, a size in accordance with other theoretical stud-ies.[6b, 17]

In considering these differences, note that the errors inthe experimentally measured shifts are quite small (ca. 0.1–0.3 ppm). Variations in helix sequence and intramolecularinteractions may give rise to an additional spread in the ex-perimental A-helix carbon chemical shifts. We find for ourdatabase of experimental shifts, that is, from the moleculesdepicted in Figure 2, that the size of this additional spreadin experimentally measured shifts is approximately equal tothe difference between the average A-helix experimentalshifts and the DSS-calibrated A-helix DFT values for basecarbon atoms, such as C2 and C5 of the pyrimidines(Table 2). For other carbon atoms, for example, in the ribosemoiety, the difference between the average A-helix experi-mental shifts and the DSS-calibrated A-helix DFT values issignificantly larger than this spread in the average A-helixexperimental shift values.

Chemical shifts of the sugar 13C resonances : The c depend-ence is clear for the chemical shifts of C1’ (Figure 5) and C2’atoms (see p. 38 of the Supporting Information), whereasthe shifts of C3’ (see p. 39 of the Supporting Information),C4’ (Figure 6), and C5’ atoms (see p. 42 of the SupportingInformation) in the DNA and RNA mono-nucleosides areless sensitive to the glycosidic torsion angle. The insensitivityof the C3’ shifts of the DNA and RNA mono-nucleosideswith an S-puckered sugar to changes in the c angle resemblethe behavior of the corresponding H3’ shifts.

The c dependencies of the C1’ DFT shifts are shown inFigure 5. The DFT C1’ shifts decrease approximately linear-ly by about 6 ppm for c between �180 and �1208. This isshown separately for the purines and pyrimidines. For theRNA pyrimidines we have omitted the part of the DFT-cal-culated curve that shows the S-puckered C1’ shift behaviorbetween �180 and �1508. The reason for this omission isthat in this region the chemical shifts rapidly increase to101 ppm (see p. 37 of the Supporting Information), althoughwe are not aware of any experimental C1’ shifts higher than96 ppm (in addition, RNA sugars are usually N-puckered inthe �180 to �1508 region). In the above, the O2’H is in the

Figure 4. DFT-derived chemical shifts of the H2’ and H3’ atoms as a func-tion of the glycosidic torsion angle, c, for all RNA mono-nucleosideswith the two main sugar puckers C3’-endo and C2’-endo. The horizontalred lines indicate the H2’ and H3’ chemical shift values measured for theG9 residue in the UUCG hairpin (Figure 2), which form the basis for thederivation of the c angle, as indicated by the vertical yellow bands (seetext).

Table 2. Differences in the DFT-calculated chemical shifts for RNA invacuum (see Experimental Section and the experimentally measuredchemical shifts for RNA in an A-helix environment (dexp�dDFT) for thedifferent carbon atoms in adenosine (A), cytosine (C), guanosine (G),and uracil (U). The chemical shifts of the sugar carbon atoms were calcu-lated as an average over the four bases.

d [ppm]A C G U

C2 �2.9 +1.0 �0.4C4 �5.4 +1.6 �1.7 +3.0C5 �7.7 +1.5 �11.1 �4.2C6 �0.8 �6.9 +2.6 �3.9C8 �1.3 �2.4C1’ �5.8 �5.8 �5.8 �5.8C2’ �10.2 �10.2 �10.2 �10.2C3’ �5.7 �5.7 �5.7 �5.7C4’ �7.4 �7.4 �7.4 �7.4C5’ �4.5 �4.5 �4.5 �4.5



www.chemeurj.org

O3’ orientation. We note that with O2’H in the base orienta-tion, the C1’ shifts show a similar profile (see Figures S3-O2’H and S4-O2’H in the Supporting Information for theC1’ versus c and C1’ versus O2’H orientation). The profileis, however, increased by approximately 2.5 (N pucker) and0.3 ppm (S pucker) compared with the O3’ orientation. Theexperimental data show that there is a slight difference be-tween the behavior of the C1’ shifts of the pyrimidines andpurines; this follows from a linear least-squares fit of the ex-perimental C1’ shifts against the c angle: sC1’=�0.115c+

115.38 (Pearson correlation coefficient r=�0.83) for pyrimi-dines (Figure 5B) and sC1’=�0.095c+77.08 (Pearson corre-lation coefficient r=�0.90) for purines (Figure 5A).

In these calculations, the outliers, designated 12 and 16for the pyrimidines, were not incorporated because of theirmotional behavior (see the Discussion section). In accord-ance with the DFT calculations, the higher c angles in the

anti domain (from about �140 to �1208), which usuallyoccur in combination with N/S- or S-puckered riboses, gavesmaller C1’ shift values than those found for N-puckeredsugars. An exception is the C1’ shift of G15 of human HBV,which has an N-puckered sugar (marked as 15 in Fig-ure 5A). The reason may be that G15, although part of aC:G Watson–Crick base pair, is part of the hexa-loop cap-ping the stem and is not flanked by regular Watson–Crickbase pairs. Furthermore, note the data point at c�608,which comes from G9 in the U6U7C8G9 loop (cf. Figure 2).This residue has a syn conformation and an N-puckeredsugar.[9c] Indeed, the experimental value is closer to theDFT curve predicted for the N than for the S conformation(data point marked as 9 in Figure 5A). We note that the synconformation cannot be predicted from the C1’ shift alonedue to the multi-valued nature of the C1’ shift as a functionof c. However, a combination of this carbon shift with theH2’ and H3’ shifts of the same molecule (see above) wouldallow the determination of c.

The DFT-calculated chemical shifts of the sugar carbonatoms also provide information on the sugar pucker. This isparticularly manifest for the C3’, C4’, and C5’ shifts, whichare not very sensitive to the value of the c torsion angle. Forthese three carbon atoms, the DFT-calculated shifts show asignificant difference between the N- and S-puckered riboseconformations. In fact, for all eight nucleosides (DNA andRNA systems) studied here, the C2’-endo pucker induces alarger chemical shift for these atoms than the C3’-endopucker (see pp. 39–41 of the Supporting Information). Thissuggests that these shifts can be used to determine the sugarconformation of individual nucleotides in a nucleic acidstructure. However, this determination is complicated by the

Figure 5. DFT-calculated chemical shifts of C1’ in RNA as a function of c

for A) adenosine and guanosine and B) cytosine and uracil. The DFTchemical shift curves were calibrated by reference to A-helix experimen-tal values (see the Experimental Section and Table 2). The experimentalchemical shifts obtained for the UUCG hairpin and the hHBV molecule(Figure 2) are: black circles: adenine; cyan diamonds: guanine; blue tri-angles: cytidine; green squares: uridine. The open and filled symbols rep-resent nucleosides with N-puckered or pure S-puckered sugars (or an ad-mixture of the N and S conformations), respectively. The labeled datapoints are discussed in the text. This notation is used in all subsequentfigures.

Figure 6. DFT-calculated chemical shifts of the sugar carbon C4’ as afunction of the glycosidic torsion angle for the four RNA nucleosides.Experimental data are shown from the UUCG hairpin. To allow a com-parison with the experimental chemical shifts, the C4’ shifts for the C3’-endo sugar conformation were calibrated to the experimental shifts ofC4’ atoms in an A-helix environment (see text). Subsequently, the DFTC4’ shifts derived for the C2’-endo sugar conformation were calibrated bythe same amount. For the notation of the symbols representing the exper-imental points, see legend of Figure 5. The data point labeled 9 refers toG9 in the UUCG hairpin.



www.chemeurj.org

influence of variables such as changes in other backboneangles and the effects of neighboring residues on Cx’ shifts(x=3–5). This is reflected, for example, in Figure 6, in whichthe experimental and DFT-calculated C4’ shifts have beenplotted against the torsion angle c. The resonances from theC4’ atoms in an A-helix environment (see the ExperimentalSection) are clustered together (open symbols), whereas theresonances of the atoms located in a non-A-helix environ-ment (filled symbols) are mostly scattered between the DFTcurves characterizing the N- and S-puckered sugars. Theselatter C4’ nuclei, that is, in sugars occurring as an admixtureof N and S puckers or as pure S puckers, resonate above83 ppm. Note that for this class of resonances, the c angleincreases within the anti range to values equal to or largerthan �150 ppm, which is also observed in plots of the C1’shifts (see above).

Chemical shifts of the base 13C atoms : The DFT chemicalshift profiles of the base carbon atoms are affected to vary-ing degrees by the sugar pucker and c. This is exemplifiedby the shift profiles of the ring carbon atoms of cytosine anduracil (see pp. 10, 11, 31, and 32 of the Supporting Informa-tion,). The shifts of C2, C4, and C5 show oscillatory behav-ior as a function of the c angle, but the amplitude is rathersmall, which means that the sensitivity to changes in c is lim-ited. Nevertheless, we found that interesting informationcould be derived from plots of C2 versus C4 shifts and C2versus C5 shifts for the C and U residues (see below). Onthe other hand, the cytosine and uracil C6 shifts and the ad-enine and guanine C8 shifts vary by almost 8 ppm (seepp. 11, 32 and 5, 18, respectively, of the Supporting Informa-tion). The increase in the shift values of these atoms when c

is located in the syn region is promising for structural analy-sis (however, see the Discussion section).

To investigate the extent to which the O2’H orientationaffects the chemical shifts, we calculated for the N puckerwith c=�1508 and for the S pucker with c=�1208 all the1H, 13C, 15N, and 17O chemical shifts for the RNA uracilmono-nucleoside as a function of the dihedral angle HO2’�O2’�C2’�H2’ (see the Supporting Information). Most basecarbons are affected to a very limited extent, that is, theshift variation is significantly smaller than 1 ppm. Further-more, with O2’H fixed in the higher-energy base orientation,the dependence of the C2, C4, C5, and C6 shifts on c is verysimilar to that for O2’H in the O3’ region (see the Support-ing Information).

The C2 shifts of cytosine show a clear separation betweenthe RNA and DNA nucleosides (see p. 10 of the SupportingInformation), which is not observed for the other ringcarbon atoms of this base. The shift differences resultingfrom the transition from the C2’-endo to the C3’-endo sugarconformation are generally small for all ring carbon atomsof the nucleosides considered.

C2 versus C4 chemical shifts—hydrogen bonding : Examina-tion of the DFT-predicted shifts shows that the chemicalshift of C4 in uracil is practically unaffected by changes in

the sugar pucker and c angle (see p. 31 of the Supporting In-formation). This is to a somewhat lesser extent also true forthe C4 shifts of cytosine, at least for c values between �175and �1008 (see p. 10 of the Supporting Information). Wefurther find that the C4 shifts of U are hardly affected bythe orientation of O2’H. In particular, the C4 shift variationis essentially zero within the most stable O3’ region. On theother hand, the DFT-predicted C2 shifts in uracil as well asin cytosine predominantly depend on the sugar pucker, atleast for values of c between �180 and �608. The same ob-servation can be made for C2 shifts when O2’H is in thebase orientation.

These observations are clear in the plot of C2 versus C4chemical shifts shown in Figure 7A. The two regions repre-senting the C2 shift values of the N-puckered, and of S-puckered and admixtures of N- and S-puckered sugars ofuracil and cytosine are indicated by the vertical dashed-dotted and solid lines, respectively. The positions of thedashed-dotted vertical lines represent the average C2 shiftsin an A-helix environment. The DFT-calculated C2 shiftsdiffer only slightly from these values: for uracil the shiftshad to be diminished by 0.4 ppm and for cytosine they hadto be increased by 1.0 ppm to match them to the experimen-tal A-helix values (see Table 2). The positions of the C2shifts of the C and U residues with S or an admixture of N/Ssugar conformations, presented by the solid lines, were ob-tained by adding the DFT-calculated difference between theC2 shifts in the N and S sugar conformations to the corre-sponding A-helix values. The C2 resonances of the uridineresidues with N-puckered sugars are all positioned close tothe dashed vertical line at 152.8 ppm. Their C4 resonancepositions, however, are spread over a region of 1.5 ppm. Thereason for this becomes clear when we consider the structur-al environment of these residues. The data points in theupper left hand corner are from residues in an A-helix. Thedata point marked 6 comes from U6 in the U6U7C8G9 hair-pin (see Figure 2). This residue is part of the reverse-wobblepair G9U6 formed in this hairpin.[9c] It retains an N-puckeredsugar conformation, but contrary to the situation in an A:Ubase pair, its C4=O group is not involved in hydrogenbonding. As a result, the C4 resonance moves from itschemical shift value in the A-helix in the direction of theposition it has in a vacuum, that is, its DFT position at166.4 ppm. The data point marked 40 arises from the basepair A22:U40 closing the stem region of the TAR-RNA frag-ment (see Figure 2). This base pair is somewhat unstableand due to fraying is partly disrupted in the course oftime.[18a] Thus, the concomitant partial disruption of the hy-drogen bond also leads to a shift of the C4 resonance awayfrom its position in an A-helix towards its value in vacuum,but to a lesser extent than observed for U6, which fullymisses this hydrogen bond. For other U residues outside thehelical structure, we predict that the sugars are S-puckeredor occur as an admixture of N and S puckers, for example,U23, U25, and U31 of the TAR-RNA fragment (marked as23TAR, 25, and 31 in Figure 7A, respectively). Their C2 reso-nance positions are close to the solid line. The C4 shift



www.chemeurj.org

values are smaller than in the A-helix, which indicates thatthe C4=O group is at least part of the time not involved inhydrogen bonding. A similar conclusion can be drawn forU14 and U23 of the stem loop of the e element of the prege-nomic RNA of human HBV (see Figure 2, marked as 14and 23hHBV in Figure 7A). These U residues are part of theloop or bulge outside the stem region of this molecule.Their sugars are involved in a rapid N and S pucker equili-brium and their C4=O groups are not involved in hydrogenbonding. The position of the data point marked 7 arisingfrom U7 in the loop of the U6U7C8G9 hairpin is an exceptionto which we return in the Discussion section.

The C2 resonances of the cytosine residues in the A-heli-cal parts of the molecules in Figure 2 fall close to thedashed line at 158.8 ppm. The C2 resonances of the cyto-sines, positioned close to the solid line at 159.9 ppm, are allfrom residues outside stem regions or from fraying basepairs. The position of the data point marked 16 is an excep-tion to which we return in the Discussion section.

C2 versus C5 chemical shifts—ring-current shifts : In the plotof C2 versus C5 chemical shifts (Figure 7B) the vertical linesindicate the C2 chemical shift positions for the N and Ssugar (N/S-mixed) conformations in uridine and cytidineresidues as in Figure 7A. For the U residues in an A-helixenvironment (open symbols), the C5 shifts vary between102.5 and 104 ppm. The spread in these shift values can beattributed to variation in ring-current effects from neighbor-ing residues. For example, the data points with C5 shiftslower than 103.2 ppm represent U residues that have a G orA as a 5’-neighbor, whereas the data points between 103.4and 104 ppm represent U residues that have a pyrimidine asa 5’-neighbor. We explicitly mention the C5 shift of residueU11 in the UUCG hairpin (marked 11)[9c] situated in the hel-ical stem, which has a G 5’-neighbor (Figure 2). Its C5 reso-nance position has shifted by 0.8 ppm below the value of theC5 from U42 in the HIV-TAR fragment (marked 42), whichhas a C 5’-neighbor; the sign and value of this shift are in ac-cordance with the experimentally validated ring-current con-tribution for this neighbor.[4a] On the other hand, the posi-tion of the C5 resonance of U6 (marked 6) is unusual; U6

partakes in the U6G9 base pair in the U6U7C8G9 hairpintetra-loop (see Figure 2) in which the C4= O group is notinvolved in hydrogen bonding. The C5 resonance position of105.1 ppm is 1.5 ppm higher than the highest C5 shift valueof U residues in an A-helix. The C5 is shifted in the direc-tion of the DSS-calibrated DFT vacuum value (Table 2), aswas observed for the C4 resonance when hydrogen bondingwas lacking. Similar conclusions can be drawn for the uri-dines U23, U25, and U31 in the TAR-RNA fragment, whichare present in bulge and loop regions and are not involvedin hydrogen bonding. Their C5 resonance positions are105.4, 105.3, and 105.4 ppm, respectively, an increase withrespect to the highest A-helix values also of around1.5 ppm. Finally, we note that this change with respect tostandard A-helix values is opposite in sign to that observedfor the C4 resonances (see above).

Figure 7. A) Experimental base carbon chemical shifts C2 versus C4 ofcytidine and uridine residues in the UUCG hairpin, the hHBV molecule,and the HIV-2 TAR molecule (Figure 2). The vertical dashed lines repre-sent the DFT-calculated resonance positions of the C2 atoms of cytosineand uracil with N-puckered sugar conformations matched to experimen-tal A-helix values (see text). The vertical solid lines represent the cali-brated DFT values for the C2 atoms of these molecules with S-puckeredsugars and sugars existing as an admixture of N and S states (see text).For the notation of symbols representing the experimental points, see thelegend of Figure 5. The data points within the large ellipse in panel A arefrom residues in Watson–Crick base pairs in an A-helix. The encircleddata points are from residues located in bulge or loop regions. The datapoints annotated with numbers are discussed separately in the text.B) Same as for (A) but for C2 versus C5 chemical shifts. C) The same asfor (A) but for C2 versus C1’ shifts. The right hand side shows a c anglescale corresponding to the C1’ shifts (see text).



www.chemeurj.org

The shifts of the C5 resonances in cytidine residuesbehave similarly: The cytidines with N-puckered sugars areall involved in G:C base pairing and their C5 resonances arespread between 96.8 and 98.6 ppm. This variation in the res-onance positions is to a large extent determined by ring-cur-rent effects from their neighbors. For example, the residueswith purines as 5’-neighbors all resonate between 96.8 and97.2 ppm, whereas the residues with pyrimidine 5’-neighborshave higher shift values (97.3–98.6 ppm). What is causingthe larger spread of the resonances of the latter group is notyet clear. The C2 shifts of the cytidine residues with S- or N/S-puckered sugars all resonate close to the solid line at159.9 ppm. The C5 shifts, clustered around 98.5 ppm, arisefrom terminal or loop cytidine residues for which the hydro-gen bonding is partly disrupted. The data point marked 16 isfrom C16 of human HBV (Figure 2), which protrudes intothe solvent. The resonances at 97.9 ppm are from residueswith G residues at their 5’-side and are therefore shifted tolower values.

C2 versus C1’ chemical shifts—determination of the c angle :Given the previous observations that the C2 chemical shiftsof uridine and cytidine are mainly determined by the stateof their sugar pucker and that the value of the C1’ shiftvaries approximately linearly as a function of the glycosidictorsion angle in the anti domain between �180 and �1208(Figure 5B), a plot of the C2 versus C1’ chemical shiftshould allow a direct estimate of the sugar conformationand the value of the c angle. This is demonstrated in Fig-ure 7C, in which these chemical shifts have been plotted forthe U and C residues with known c angles. The c scale onthe right hand side of Figure 7C was introduced by using therelationship between the C1’ shift and c derived for pyrimi-dines (see above). The c angles derived from this plot fallwithin the uncertainty limits of the experimentally deter-mined c values[9c,20a,b] with a few exceptions. These are the c

values for residues U12 and C16 (marked 12 and 16 in Fig-ure 7C) of human HBV (Figure 2). In human HBV, C16 pro-trudes into solution (Figure 5A) and is very mobile, as is res-idue U12, which is located in the loop region of human HBV(see the Discussion section).

Discussion

Earlier studies have indicated the existence of a relationshipbetween chemical shifts, in particular proton and carbonshifts, and the glycosidic and other torsion angles. Thesestudies involved experimental[1a,4, 12a,b, 13,18a] as well as theoret-ical approaches.[11,12c,d,14] In this paper we have presented aDFT study of the chemical shifts of all atoms in the eightRNA and DNA mono-nucleosides. It is the first study re-porting chemical shifts derived as a function the glycosidictorsion angle for the two common sugar puckers, the C2’-endo and C3’-endo conformations, in a comprehensivemanner using contemporary methods. In addition, the effectof the O2’H orientation was investigated for the RNA uracil

mono-nucleoside. These DFT results were used to determinethe relationships between calculated chemical shifts andstructural parameters, to provide a physical–chemical inter-pretation of these relationships when possible, and to esti-mate the values of these structural parameters (i.e. glycosi-dic torsion angle and sugar pucker). This may aid structurevalidation and structure determination as these structuralparameters may act as restraints.

A complicating factor in the comparison of the theoreticaland experimental data is that the DFT-calculated NMRshifts have been derived for mono-nucleosides in a vacuum,whereas the experimental shifts are from residues embeddedin larger nucleic acid structures dissolved in aqueous solu-tions. Thus, neither effects of neighboring residues nor sol-vent effects on the chemical shift values of a particular resi-due are manifest in the shifts calculated for the mono-nu-cleosides. The possible effects of internal motion, often pres-ent in nucleic acid structures, are also not represented in thetheoretical values. Nevertheless, the examples presented inthe Results section show that the mono-nucleoside level ofchemical shift calculation is already of value in characteriz-ing particular structural features in a molecule.

Proton shifts : The combined use of the H2’ and H3’ shifts ofresidue G9 in the loop of the U6U7C8G9 hairpin (Figure 2)allows the determination of the c angle as well as the sugarpucker of this residue (Figure 4). The result obtained here,c=70�108 and the C3’-endo sugar pucker, is in good agree-ment with the NMR experimental values, c=59�208 andsugar pucker C3’-endo, obtained by cross-correlated relaxa-tion.[9c] These DFT results also agree well with earlier pre-dictions of proton shifts[4a,b] based on the semi-empiricalmethods of Giessner-Prettre and Pullman.[11] The latter ap-proach has not only been found to be valuable for the re-finement of NMR-determined nucleic acid structures, butalso provides the possibility of determining accurate helicalnucleic acid structures solely on the basis of proton shifts.[26]

We finally note that the aforementioned results concur wellwith the c values (598) obtained by X-ray diffraction studiesof UUCG loops in a 56 nucleotide fragment of 16SrRNA.[27]

Carbon shifts

Matching of DFT-calculated and experimental shifts—in-sights into hydrogen bonding : In contrast to the 1H shifts,the shifts of non-hydrogen nuclei such as 13C, 15N, and 17Oare very sensitive to the molecular environment due to po-larization, charge transfer, and exchange effects on the wavefunctions (e.g., characterized by Giessner-Prettre[28]). Thisbecomes manifest when comparing the chemical shift valuesof nucleic acid structures in aqueous solution and the DFT-calculated shifts obtained in a vacuum. We first note thatthe differences between the carbon DFT shift values andtheir experimental counterparts are much larger for carbonatoms than for protons, which is not unexpected in view ofthe much larger spectral range covered by 13C (ca. 180 ppm)



www.chemeurj.org

than by 1H resonances (ca. 15 ppm). Secondly, these shiftdifferences vary between the structurally nonequivalentcarbon atoms. Table 2 shows that the experimental shiftvalues of C2’ and C4’ in an A-helix are 10.2 and 7.4 ppmsmaller, respectively, than the corresponding DSS-calibrated(vacuum) DFT shifts (calculated at a c angle of �1608 withan N-puckered sugar, that is, at a standard A-helix confor-mation). On the other hand, the uridine and cytidine C2shifts are only 0.4 ppm lower and 1.0 ppm higher, respective-ly, than these DSS-calibrated (vacuum) DFT values. Thus,the C2 atoms of uridine and cytidine, which are situated inthe interior of the molecule, show experimental shifts closeto the vacuum values obtained by the DFT calculations.

For the chemical shift of C2 of cytidine, the remaining dif-ference of around 1 ppm can be understood from the follow-ing considerations. In a Watson–Crick G:C base pair theC2=O is involved in hydrogen bonding, which results in alarger shift value for the C2 atom compared with the non-hydrogen-bonded situation. The effect is in good agreementwith independent experimental results: base-pair formationof the G and C nucleosides dissolved in a mixture of di-methyl sulfoxide and methanol leads to an increase of0.7 ppm for the chemical shift value of cytidine C2,[29] whichis close to the difference of 1.0 ppm between the DSS-cali-brated (vacuum) DFT value and the experimental valuesmeasured in the A-helix.

For uridine in an A:U base pair in an A-helix, the differ-ence between its experimental C2 shift and the DFTvacuum value is quite small and negative (dexp�dDFT =

�0.4 ppm, Table 2). This small negative value can be under-stood on the basis of the following considerations. In con-trast to cytidine, the C2=O group of uridine in a Watson–Crick (A:U) base pair is not involved in hydrogen bonding.In the noncanonical U:U base pairs found in some RNAs,the C2=O of uridine is sometimes involved in hydrogenbonding and sometimes not.[30] When C2=O is not hydro-gen bonded, the C2 atom resonates at the same value as inan A-helix Watson–Crick A:U base pair.[30] When the C2=

O is hydrogen-bonded, the C2 atom of the uridine resonatesat a higher chemical shift value (ca. 1.0 ppm). Thus, thiseffect is quite similar for hydrogen-bonding uridine and cyti-dine. On the other hand, the higher chemical shift values ofthe C2 atom in non-A-helix environments, such as loops orbulges, are most likely a combination of effects.

A) Switching from an A-helix to a loop/bulge conforma-tion leads to higher chemical shifts due to the following ef-fects. 1) A change from N to S pucker or to a mixture of Nand S puckers (see the Results section) may occur. 2) ForC2=O, the increased solvent exposure in a loop/bulge im-plies increased hydrogen bonding of the C2=O group bysolvent molecules compared with the situation in an A:UWatson–Crick base pair in an A-helix leading to higher shiftvalues. 3) The destacking that occurs leads in turn to a re-duction in above/below-plane ring-current effects fromneighboring bases and thus to an increase in chemical shift.

B) Switching from an A-helix to a loop/bulge conforma-tion may also lead to reduced chemical shift values, that is,

the loss of in-plane ring-current effects from the comple-mentary A base in an A:U base pair.

Thus, the conformational change from the A-helix to aloop/bulge leads to a combination of effects on the C2 reso-nance position that partly compensate each other. The�0.4 ppm difference (dexp�dDFT) for the C2 of uridine in aWatson–Crick base pair in an A-helix and in vacuum (DFTvalue) is the net outcome of the effect of in-plane andabove/below-plane ring-current effects versus the absence ofring-current effects from neighboring bases (dDFT). Quite ac-curate estimates can be made for the ring-current effectsfrom given conformations,[4a] and in-plane ring-current ef-fects are usually smaller than above/below-plane ring-cur-rent effects. Thus, one expects to find a vacuum (DFT)value that is higher than the A-helix shift, in agreement withthe aforementioned �0.4 ppm. Similarly, the cytidine C2shift is affected by a combination of in-plane and above/below-plane ring-current effects and in addition the hydro-gen-bonding effect. Finally, we note that fully solvent-ex-posed residues indeed have extra large C2 chemical shiftvalues.

The C4 and C5 resonances of residue U6 of the UUCGloop (Figure 2), which is part of the G:U base pair in thisloop, highlight a particularly interesting aspect of the differ-ence between the DFT-calculated shifts and the measuredchemical shifts in solution. The C4 resonance is at a lowervalue than the A-helix values, whereas the C5 resonanceshifts to a higher value. In this base pair, the C4= O groupof the uridine is not involved in hydrogen bonding to theguanine in contrast to the situation in an A:U base pair inan A-helix. Both the C4 and C5 resonances shift towardstheir shift values in a vacuum as calculated by DFT, whichleads to shift differences of opposite sign for C4 and C5(Table 2). This interpretation provides an explanation forthe opposite signs of the shift differences for C4 and C5 inTable 2 as well as for the sign of the shift differences withrespect to standard A-helix values as observed for the ringcarbon atoms, for example, for uridine in Figure 3 in thepaper by Carlomagno and co-workers.[18a] The authors usedthese uridine shifts to make a distinction between residuespresent in an A-helix and non-A-helix environment. Howev-er, an underlying reason for their chemical shift behaviorcould not be given.[5] The patterns of the chemical shiftchanges observed in the plots of C2 versus C4 chemicalshifts and of C5 versus C2 chemical shifts appear thus asso-ciated with hydrogen bonds and ring-current effects. Thesame patterns of C2 versus C4 chemical shift changes havebeen found in the work on RNA-containing noncanonicalU:U base pairs.[30] Also in this context, the results can beunderstood in terms of hydrogen bonds and ring-current ef-fects. From Figure 7A, we can derive for which of the part-ners in this base pair the C4= O group is involved in hydro-gen bonding. In the latter situation, C4 resonates at around169 ppm, typical of an A-helix environment. If C4= O is nothydrogen bonded, the situation for the partner uridine, itsresonance shifts to lower values in the direction of itsvacuum value. In this latter situation, the C4=O group re-



www.chemeurj.org

mains sufficiently shielded from the solvent. The U7 residueof the UUCG hairpin, with an S-puckered sugar, is an ex-ample of a base protruding into the solution.[9c,27] Its C2 res-onance is shifted significantly beyond the solid line inFigure 7. DFT shift calculations performed in a COSMO en-vironment (not shown) lead to an increase in shift value ofabout 2 ppm with respect to the vacuum value, which quali-tatively explains the anomalous C2 resonance position ofthis residue.

The G:C base pairs at the end of the double helices arecommonly involved in fraying processes, giving rise to an ad-mixture of N and S sugar conformations. All the moleculesdepicted in Figure 2 have a G:C base pair closing the 5’ and3’ termini of the helix. In Figure 7A, the resonance positionsof the C2 carbon atoms of the cytidine partners are locatedclose to the solid line, for example, the C2 resonance of C27

in the human HBV fragment is at position (159.9, 168.9). In-terestingly, this fraying process results in an effect differentto that of the A22:U40 base pair (see the Results section), forwhich the C4= O resonance of U40 shifts to a lower valueand its C2= O resonance is maintained close to 152.8 ppm.For C27, the opposite is observed: The C4=O resonance re-mains in the A-helix region and the C2=O resonancemoves from 158 to 160 ppm.

Conformational aspects : The c angle dependence of thesugar C1’ and C2’ shifts is rather strong, whereas the shiftsof the C3’, C4’, and C5’ are much less sensitive to the glyco-sidic torsion angle. In this respect, we mention the resultsobtained by Xu and Au-Yeung[14a] for the chemical shift pat-terns of the sugar carbon atoms as a function of the glycosi-dic torsion angle for cytidine with a C3’-endo conformation.The absolute values of the calculated shifts differ from thepresent calculations because different reference systems areused. The shift patterns agree reasonably well with our re-sults, despite the lack of geometry optimization prior tochemical shift calculations by Xu and Au-Yeung. However,there are some notable differences, for example, the behav-ior of the C3’ chemical shifts of cytidine as a function of c,which vary much more strongly than in our calculations, andC6, for which the opposite is true.

We now return to the syn orientation of the G9 residue inthe UUCG loop. Figures 5A and 6 show that the C1’ andC4’ shift values predicted for this particular conformation,with the sugar pucker of the guanine being C3’-endo, agreereasonably well with the experimental shift value. They de-viate by 1.0–1.5 ppm from the experimental value, and theexperimental values are clearly closer to the DFT value pre-dicted for the N conformation than for the S conformation.The experimental C1’ and C4’ shift values can, however, notbe used to distinguish between the anti and syn conforma-tions of the glycosidic torsion angle because these shiftvalues are not sufficiently distinct from those in an A-helixenvironment. In this respect, the dependency of the C8 shifton the c angle is more promising. For c values in the synregion, the C8 shift increases by about 2.1 ppm for a C3’-endo sugar conformation and by about 4 ppm for a C2’-endo

sugar conformation with respect to the chemical shift(137 ppm) in an A-helix environment (see p. 18 of the Sup-porting Information). The experimental value for the C8shift of the G9 residue in the UUCG hairpin is 142.9 ppm,which is 5.9 ppm above the A-helix value. This experimentalshift value certainly puts c into the syn region, but it ishigher than the adjusted DFT result. The reason may bethat in the UUCG hairpin loop, a hydrogen bond can beformed between the 2’-OH group of U7 and N7 of the baseof G9.[9c] In summary, the C8 shift of guanine allows a rapiddistinction between the anti and syn domains to be made,but a more accurate determination of the glycosidic torsionangle requires the inclusion of information derived from, forexample, the H2’ and H3’ shifts (Figure 4).

The glycosidic torsion angles falling in the anti region(�1808<c<�1208) can be estimated from Figure 7C. Thereare two exceptions: The residues U12 and C16 in the humanHBV molecule. The c angles predicted for these residuesdeviate significantly from the value determined by NMRmethods using the H1’–C6 and H1’–C2 coupling constant-s.[20a] The experimental c values are �123 and �1268, respec-tively, and the corresponding predicted values are �149 and�1668. The underlying reason for these two exceptions isthe mobility of these residues, which has been studied in aseries of relaxation experiments.[20c] This mobility causes anaveraging of the JH1’–C6 and JH1’–C2 couplings and thus the c

angle derived from these J couplings is an average of the c

angles belonging to different conformational states of theresidue. However, this averaging over conformational statesand thus over the c angles is likely to affect the mean valueof the c angle and the C1’ chemical shift differently due totheir nonlinear relationship. The difference will depend onthe details of the motions. For example, the relaxation ex-periments show that the mobility of the base of cytidine C16,which specifically influences the c angle, is much higherthan that of its sugar moiety, which suggests that the C1’chemical shift will not be strongly influenced. This concurswith the experimental shift value (see Figure 7C). On theother hand, for residue U12 both the base and the sugarmoiety exhibit strong motion. Thus, in this case, the C1’chemical shift is also influenced, indeed resulting in a re-duced experimental value. Hence, for residues U12 and C16,the averaging effect on the C1’ chemical shift and the JH1’–C6

and JH1’–C2 couplings may lead to highly different average c

angles.In summary, given a method to identify and exclude resi-

dues subject to such motional effects, Figure 7C may providea fast method for estimating the c angle in the anti domainfor U and C residues. We finally note that the C1’ resonanceposition of U6 (in the U6U7C8G9 hairpin loop) is shifted up-wards by around 1 ppm above the A-helix values (Fig-ure 7C). For this residue, the O2’H is oriented towards thenucleobase.[8] This shift in resonance position is in line withthe results presented in Figure S3-O2’H in the SupportingInformation, which shows that for the base orientation theC1’ shifts to higher ppm relative to the O3’ orientation forthe N-puckered state. Finally, note that the change in the



www.chemeurj.org

C1’ shift due to the O2’H reorientation is relatively smalland thus does not significantly affect the determination ofthe c angle from the C1’ shift data.

Carbon chemical shifts also allow one to distinguish be-tween N- and S-puckered sugar moieties. Ebrahimi et al.[12a]

used a linear combination of C1’, C4’, and C5’ chemicalshifts to establish the pure sugar pucker state. The relation-ship between this linear combination of shifts and the purepucker states was derived from a large number of nucleo-sides and nucleotides of known pucker conformation. How-ever, ribose sugars of biologically interesting residues are inmany instances in fast exchange between the N and Spucker states, which results in an admixture of states. Theapproach of Ebrahimi et al. may then not work that well.This problem is also illustrated in Figure 6. The C4’ shifts ofthe residues with an N-puckered conformation are clusteredaround 82.5 ppm. The shifts of residues with ribose sugarsinvolved in a fast exchange between the N and S states,which results in an admixture of states, and of residues withribose sugars in a pure S state are all greater than 83.2 ppm.The distribution of these N and S states is, however, not re-flected in the value of the shifts in comparison with the pureN and S states. The same is true for C3’ and C5’ chemicalshifts.

In contrast, these motional effects hardly influence the C2shifts of uridine and cytidine, which are relatively insensitiveto their surroundings; instead, their chemical shifts aremainly influenced by the conformations of their sugars. TheC2 resonances of the N-puckered sugars of the moleculesconsidered are around 152.8 and 158.9 ppm for uridine andcytidine, respectively (Figure 7). Somewhat unexpectedly,for S-puckered as well as for an admixture of N/S-puckeredsugars, the C2 shifts are at 154.1 and 159.9 ppm for U and C,respectively. The fact that S- and N/S-puckered sugars leadto a similar C2 chemical shift value is remarkable and notyet fully understood. A possible explanation may reside inthe fact that under these conditions the residues are oftenno longer incorporated into an A-helix, or hydrogen bondsin the base pair are temporarily absent. In summary, it maybe concluded that carbon shifts can be used to distinguishbetween residues with N-puckered sugars (present in an A-helix environment) and residues with S-puckered sugars orwith sugars existing as an admixture of N and S puckers.

We finally note that the DFT chemical shifts and energycalculations on mono-nucleosides agree well with the experi-mental shifts even when taking the O2’H group orientationinto consideration. This is illustrated by the following exam-ples. In the A-helix, the O2’H group is oriented in the O3’region (the energy differences are small within this region).In loop regions, the pucker often changes to an S or N/Spucker state. When the O2’H group remains oriented in theO3’ region, the C2 shift differences between the N and Spucker observed in the DFT calculations are around 0.8–1.0 ppm (see the Supporting Information), which fits wellwith the experimental data (difference of ca. 1.0 ppm, seeFigure 7).

Furthermore, we observe that the energy differences arevery small within the O3’ region such that conformationalaveraging within this region may well occur. Such librationmotions within a broad O3’ region will, however, not affectthe conclusions based on the analysis of the plots presentedin Figure 7.

Although the O3’ orientation of the O2’H appears themost common orientation in an A-helix,[8,22] the occurrenceof the base orientation has also been proposed.[22,23] For thelatter situation, it has been suggested that the O2’H makeshydrogen-bond contacts with the base of sequential residuesthrough an H2O intermediate.[22a,b] The energy difference be-tween the O3’ and the base orientation is relatively small inthe mono-nucleoside (see the Supporting Information) andin an A-helix the suggested hydrogen bonding may lowerthe energy of the base orientation compared with that calcu-lated in the mono-nucleoside. The stabilization of the baseorientation may potentially lead to conformational averag-ing between the base and O3’ orientations of the O2’Hgroup in certain situations. The stabilization of the base ori-entation likely leads to lower C1’ shifts and reduces the dif-ference of around 2.5 ppm (N pucker) to 0.3 ppm (S pucker)with the O3’ orientation seen in mono-nucleoside.

Taken together, the above implies that the O2’H orienta-tion does not significantly influence the position of mostcarbon resonances except for some specific conformations.

Conclusion

We have calculated by DFT the NMR chemical shifts of allatoms in eight DNA and RNA mono-nucleosides by usinggeometry-optimized DNA and RNA mono-nucleosides forthe computational determination of the glycosidic torsionangle dependency of 1H, 13C, 15N, and 17O chemical shifts forthe two commonly occurring sugar puckers, the C2’-endoand C3’-endo conformations. Comparison of the DFT resultswith experimental data for the four RNA molecules demon-strated that evaluation of the 1H and 13C chemical shifts canaid structure validation and determination. Attention wasparticularly focused on the carbon chemical shifts, which aremostly underused in NMR structural studies of nucleic acidsbecause their structural interpretation is difficult. Compari-son of the DFT-derived carbon shifts (in a vacuum) with theshifts measured for the corresponding carbon atoms in anA-helix environment showed that the differences vary forthe different carbon atom types. Interestingly, for the carbonatoms in the interior of the molecule a semi-quantitative ex-planation can be given for the NMR shift differences be-tween DFT and experiment, particularly for the uridine andcytidine residues. Valuable information can be obtained con-cerning the presence or absence of hydrogen bonds involv-ing the C2=O and C4=O groups of these residues. In addi-tion, the shifts of the C5 carbon atoms of uridine and cyti-dine residues provide a clear indication of the presence orabsence of a 5’-purine neighbor in the A-helix. Furthermore,these results show that various carbon chemical shifts, for



www.chemeurj.org

example, the C2 and C4 shifts of uridine and cytidine, canbe used to determine the sugar pucker by distinguishing be-tween a pure N-puckered sugar and the presence of S-puck-ered or an admixture of N/S-puckered sugars.

Glycosidic torsion angles occurring in the syn domain arein most cases found for adenine and guanine residues. Forthe example presented in this paper, G9 in the UUCG hair-pin, the A-helix-calibrated DFT-derived chemical shift curvefor the C8 carbon predicts that c is situated in the syndomain, but a quantitative determination of the angle re-quires the combination of this result with the chemical shiftsdetermined for the H2’and H3’ protons of this residue.

The C1’ chemical shifts can be used to estimate the valueof the c angle in the anti domain. Exceptions may occur forresidues with a high internal mobility, but other NMR meth-ods for determining the c angle, such as the use of J cou-plings or anisotropy in the chemical shift, also suffer fromthis problem. On the other hand, we have shown through anumber of examples that the carbon chemical shifts containsufficient information to establish the presence of intra-resi-due motion as well as to distinguish subtle differences in thedifferent types of intra-residue motions.

In summary, the approach described herein shows howchemical shift information may be used to generate newconstraints for the structure determination and refinementof nucleic acids, and serves as a proof of concept for the useof contemporary DFT shift calculations to aid NMR-basedstructural studies.

Experimental Section

Computational details : Geometries were optimized for each of the glyco-sidic torsion angles (c was varied in 36 steps of 108) and for both the C2’-endo and C3’-endo pucker conformations of the DNA (adenosine, cyto-sine, guanosine, and thymidine) and RNA (adenosine, cytosine, guano-sine, and uracil) mono-nucleosides, in which a hydroxy group replacedthe 3’- and 5’-phosphates present in the oligo- and polynucleotides (seeFigure 1B). In addition to the above, in which O2’H rotation was freelyadiabatically relaxed during geometry optimization in the O3’ region (seethe Results section), the O2’H was fixed in the higher-energy base orien-tation (dihedral H�O2’�C2’�H2’ at 3108) and the geometries optimizedas a function of c and pucker conformation, as described above for theRNA uracil mono-nucleoside. Finally, for the RNA uracil mono-nucleo-side, the O2’H was rotated in 208 steps and the geometry optimized fortwo conformations, namely one with C2’-endo/c= 2108 and one with C3’-endo/c=2408.

The DFT calculations on the mono-nucleosides were performed with theAmsterdam density functional (ADF, version 2007.01) program devel-oped by Baerends and co-workers.[31] The MOs were expanded in a largeuncontracted set of Slater-type orbitals (STO),[32] which is of triple-zquality (TZ2P) augmented by two sets of polarization functions (3d and4f on C, N, and O; 2p and 3d on H). In the geometry optimizations (butnot for the chemical shift calculations), the core electrons (e.g., 1s forsecond period atoms) were treated by the frozen core (FC) approxima-tion.[31a] An auxiliary set of s, p, d, f, and g STOs was used to fit the mo-lecular density and to represent the Coulomb and exchange potentials ac-curately in each self-consistent field geometry optimization cycle.

During the geometry optimizations, the energies and gradients were cal-culated by using the local density approximation (LDA; Slater exchangeand Vosko–Wilk–Nusair (VWN)[33] correlation) with nonlocal correctionsfor exchange (Becke88[34]) and correlation (Perdew86[35]) added self-con-

sistently. This BP86 exchange-correlation functional is one of the best(pure) DFT functionals for obtaining accurate geometries[36] with an esti-mated unsigned error of 0.9 pm in combination with the TZ2P basis set;furthermore, it is able to treat weak interactions correctly.[37] The NMRparameters were calculated by using the SAOP potential,[38] which hasbeen shown to give improved behavior for NMR shielding.[6a, 17] For theDNA mono-nucleosides, the geometry optimizations and the chemicalshift calculations were performed in the gas phase (vacuum). For theRNA mono-nucleosides, solvent effects (aqueous solution) were includedin the geometry optimizations through the use of a dielectric continuummodel (COSMO)[39] with the appropriate dielectric constants (e) andradii (Rsolv)

[40] of the solvent molecules used. A nonempirical approach[41]

to include solvent effects in the DFT calculations has been used, whichworks well for solvation processes.[40, 41] The actual geometry optimizationscheme was performed within the QUILD[42] (QUantum regions Inter-connected by Local Descriptions) program, which functions as a wrapperaround the ADF program.[31a, 32] Within QUILD, the constraints on thebackbone torsions (see below) were handled by using the elegant methodproposed by Baker.[16] Finally, the chemical shift calculations for theRNA mono-nucleosides with the COSMO-optimized geometries wereperformed in two ways. First, the calculations were performed in aCOSMO environment. These RNA DFT shifts are indicated as COSMOshifts. Secondly, the chemical shifts were calculated in the gas phase,which allows a direct comparison with the results for the DNA mono-nu-cleosides. This second set of RNA DFT shifts are indicated as gas-phaseor vacuum DFT shifts. For a comparison with the experimental RNAchemical shift data (see above) we used the DFT gas-phase (or vacuum)RNA shifts. When a comparison with DFT COSMO RNA shifts is made,this is specifically indicated in the text.

Chemical shift references : The chemical shifts, dNMR, were calculated bysubtracting the NMR shieldings of the nucleosides (snucl) from those ofreference compounds (sref) as follows: dNMR =sref�snucl. The followingreference compounds were used: 2,2-Dimethyl-2-silapentane-5-sulfonicacid (DSS) for 1H and 13C, NH3 for 15N, and H2O for 17O. The referenceshielding values were calculated at the SAOP/TZ2P//BP86/TZ2P level oftheory for these compounds in the gas phase: 31.67 (1H), 187.7 (13C),258.3 (15N), and 323.7 ppm (17O). For the 1H and 13C values, the averageswere taken over the three methyl groups to give a standard deviationfrom these averages of 0.13 ppm for 1H and 1.1 ppm for 13C. When thesolvent environment is included in the NMR calculations of mono-nu-cleosides through a dielectric continuum (COSMO) model, the followingreference values were determined: 31.66 (1H), 188.5 (13C), 260.5 (15N),and 332.7 ppm (17O). As above, for the 1H and 13C values, the averagewas taken over the three methyl groups to give standard deviations fromthese averages of 0.10 ppm for 1H and 1.0 ppm for 13C.

When comparing the DFT results with the experimental data, it turnedout that this DSS reference system worked quite well for protons, but notfor the other nuclei (see, for example, Table 2 in the Results section forthese “absolute” values). In many other studies similar deviations havebeen observed (e.g., Swart and co-workers[6b]). The DFT 13C and 15Nchemical shifts (for 17O, see the Supporting Information) derived in thispaper may thus significantly differ from the experimental values whenusing these DSS-calibrated DFT shifts. However, because conformationalchanges manifest themselves as changes in NMR shifts, these DSS-cali-brated DFT shifts may be less relevant. Instead, in relating conformation-al changes to changes in chemical shifts, we need a well-defined confor-mation as a reference point. To this end we employ here the standard A-helix structure, the conformation of which is well defined and accuratelyknown also in solution. Therefore the DFT shift values corresponding tothe conformational characteristics of the A-helix (c angle of �1608 andC3’-endo sugar conformation) were equated to the average experimentalshift values of atoms known to be located in an A-helix environment(Figure 2) and the rest of the theoretical curve was adjusted correspond-ingly to give the A-helix-calibrated DFT shift values. This approach ofusing A-helix-calibrated DFT shift values is appropriate because none ofthe computational approaches currently available allow calculation ofNMR shifts at the bench-mark level, including effects of solvent and mo-lecular motions. The accuracy of DFT NMR shift calculations is thereforelimited and we have to apply the best method possible for obtaining con-



www.chemeurj.org

formational dependence of NMR shifts in sizable molecular systems likenucleosides. This is similar to a procedure that is often used by quantumchemists in which the reference value is not chosen to correspond to thereference compound, but instead is optimized to give the best corre-spondence with experimental data.[17] Other investigators also had tomatch their DFT values to allow comparison with experimental shifts.[12b,-

d, 14a]

Acknowledgements

We thank the following organizations for financial support: the Nether-lands organization for Scientific Research (NWO-CW and NWO-NCF),the Spanish Ministerio de Ciencia e Innovaci�n (MICINN projectsCTQ2005-08797-C02-01/BQU, CTQ2008-06532/BQU, and CTQ2011-25086/BQU), the Catalan Ministry of Universities, Research and the In-formation Society (DURSI projects 2005SGR-00238 and 2009SGR528).J.S. acknowledges support through grants AV0Z50040507 andAV0Z50040702 from the Ministry of Education of the Czech Republic.

[1] a) S. S. Wijmenga, B. N. M. van Buuren, Prog. Nucl. Magn. Reson.Spectrosc. 1998, 32, 287 –387; b) J. Cromsigt, B. van Buuren, J.Schleucher, S. Wijmenga, Methods Enzymol. 2002, 338, 371 –399;c) B. F�rtig, J. Richter, J. Wçhnert, H. Schwalbe, Chembiochem2003, 4, 936 –962; d) M. R. Latham, D. J. Brown, S. A. McCallum,A. Pardi, Chembiochem 2005, 6, 1492 – 1505; e) F. H. T. Allain, G.Varani, J. Mol. Biol. 1997, 267, 338 – 351; f) Z. Shajani, G. Varani, Bi-opolymers 2007, 86, 348 –359; g) H. M. Al-Hashimi, Chembiochem2005, 6, 1506 – 1519; h) C. Dominguez, M. Schubert, O. Duss, S. Rav-indranathan, F. H.-T. Allain, Prog. Nucl. Magn. Reson. Spectrosc.2011, 58, 1 –61; i) M. Sattler, J. Schleucher, C. Griesinger, Prog.Nucl. Magn. Reson. Spectrosc. 1999, 34, 93 –158; j) G. Varani, F.Aboul-ela, F. H. T. Allain, Prog. Nucl. Magn. Reson. Spectrosc. P1996, 29, 51 –127; k) M. Baldus, Curr. Opin. Struc. Biol. 2006, 16,618 – 623; l) A. Mittermaier, L. E. Kay, Science 2006, 312, 224 – 228;m) V. Tugarinov, P. M. Hwang, L. E. Kay, Annu. Rev. Biochem.2004, 73, 107 – 146; n) E. R. P. Zuiderweg, Biochemistry 2002, 41, 1 –7; o) C. D. Schwieters, J. J. Kuszewski, G. M. Clore, Prog. Nucl.Magn. Reson. Spectrosc. 2006, 48, 47 –62.

[2] a) G. Cornilescu, F. Delaglio, A. Bax, J. Biomol. NMR 1999, 13,289 – 302; b) S. P. Mielke, V. V. Krishnan, Prog. Nucl. Magn. Reson.Spectrosc. 2009, 54, 141 –165.

[3] a) A. Cavalli, X. Salvatella, C. M. Dobson, M. Vendruscolo, Proc.Natl. Acad. Sci. USA 2007, 104, 9615 –9620; b) G. Kontaxis, F. Dela-glio, A. Bax, Methods Enzymol. 2005, 394, 42 –49; c) Y. Shen, R.Vernon, D. Baker, A. Bax, J. Biomol. NMR 2009, 43, 63– 78; d) Y.Shen, O. Lange, F. Delagio, P. Rossi, J. M. Aramini, G. Liu, A. Elet-sky, Y. Wu, K. K. Singarapu, A. Lemak, A. Ignatchenko, C. H. Ar-rowsmith, T. Szyperski, G. T. Montelione, D. Baker, A. Bax, Proc.Natl. Acad. Sci. USA 2008, 105, 4685 – 4690; e) D. S. Wishart, D.Arndt, M. Berjanskii, P. Tang, J. Zhou, G. Lin, Nucleic Acids Res.2008, 36, W496-W502.

[4] a) J. A. M. T. C. Cromsigt, C. W. Hilbers, S. S. Wijmenga, J. Biomol.NMR 2001, 21, 11–29; b) S. S. Wijmenga, M. Kruithof, C. W. Hil-bers, J. Biomol. NMR 1997, 10, 337 –350; c) A. Dejaegere, R. A.Bryce, D. A. Case in Modeling NMR Chemical Shifts. Gaining In-sight into Structure and Environment, Eds.: J. C. Facelli and A. C. d.Dios), American Chemical Society, Washington DC, 1999, pp. 194 –206.

[5] S. L. Lam, L. M. Chi, Prog. Nucl. Magn. Reson. Spectrosc. 2010, 56,289 – 310.

[6] a) M. Swart, C. Fonseca Guerra, F. M. Bickelhaupt, J. Am. Chem.Soc. 2004, 126, 16718 –16719; b) L. Armangu, M. Sol, M. Swart, J.Phys. Chem. A 2011, 115, 1250 – 1256; c) F. A. A. Mulder, M. Filatov,Chem. Soc. Rev. 2010, 39, 578 –590.

[7] a) J. H. Ippel, S. S. Wijmenga, R. deJong, H. A. Heus, C. W. Hilbers,E. deVroom, G. A. vanderMarel, J. H. vanBoom, Magn. Reson.

Chem. 1996, 34, S156-S176; b) L. Trant�rek, R. Stefl, J. E. Masse, J.Feigon, V. Sklenar, J. Biomol. NMR 2002, 23, 1– 12; c) Z. Vokacova,F. M. Bickelhaupt, J. Sponer, V. Sychrovsky, J. Phys. Chem. A 2009,113, 8379 –8386.

[8] S. Nozinovic, P. Gupta, B. Furtig, C. Richter, S. Tullmann, E. Duch-ardt-Ferner, H. Schwalbe, M. C. Holthausen, Angew. Chem. 2011,123, 5509 –5512; Angew. Chem. Int. Ed. 2011, 50, 5397 – 5400.

[9] a) J. Rinnenthal, C. Richter, J. Ferner, E. Duchardt, H. Schwalbe, J.Biomol. NMR 2007, 39, 17– 29; b) E. Duchardt, C. Richter, O. Oh-lenschlager, M. Gorlach, J. Wohnert, H. Schwalbe, J. Am. Chem.Soc. 2004, 126, 1962 –1970; c) S. Nozinovic, B. Furtig, H. R. A.Jonker, C. Richter, H. Schwalbe, Nucleic Acids Res. 2010, 38, 683 –694.

[10] a) IUPAC-IUB Joint Commission on Biochemical Nomeclature(JCBN), Eur. J. Biochem. 1983, 131, 9 –15; b) J. L. Markley, A. Bax,Y. Arata, C. W. Hilbers, R. Kaptein, B. D. Sykes, P. E. Wright, K.Wuthrich, J. Biomol. NMR 1998, 12, 1– 23.

[11] C. Giessner-Prettre, B. Pullman, Q. Rev. Biophys. 1987, 20, 113 –172.[12] a) M. Ebrahimi, P. Rossi, C. Rogers, G. S. Harbison, J. Magn. Reson.

2001, 150, 1 –9; b) P. Rossi, G. S. Harbison, J. Magn. Reson. 2001,151, 1– 8; c) M. Swart, F. M. Bickelhaupt, Int. J. Quantum Chem.2006, 106, 2536 –2544; d) A. P. Dejaegere, D. A. Case, J. Phys.Chem. A 1998, 102, 5280 –5289.

[13] K. L. Greene, Y. Wang, D. Live, J. Biomol. NMR 1995, 5, 333 –338.[14] a) X. P. Xu, S. C. F. Au-Yeung, J. Phys. Chem. B 2000, 104, 5641 –

5650; b) R. Ghose, J. P. Marino, K. B. Wiberg, J. H. Prestegard, J.Am. Chem. Soc. 1994, 116, 8827 – 8828.

[15] a) E. Brumovsk�, V. Sychrovsky, Z. Vokacova, J. Sponer, B.Schneider, L. Trantirek, J. Biomol. NMR 2008, 42, 209 –223; b) D.Sitkoff, D. A. Case, Prog. Nucl. Magn. Reson. Spectrosc. 1998, 32,165 – 190.

[16] J. Baker, J. Comput. Chem. 1997, 18, 1079 –1095.[17] J. Poater, E. van Lenthe, E. J. Baerends, J. Chem. Phys. 2003, 118,

8584 – 8593.[18] a) C. Far�s, I. Amata, T. Carlomagno, J. Am. Chem. Soc. 2007, 129,

15814 – 15823; b) B. F�rtig, C. Richter, W. Bermel, H. Schwalbe, J.Biomol. NMR 2004, 28, 69 –79; c) R. Fiala, V. Sklenar, J. Biomol.NMR 2007, 39, 153 –163; d) R. Fiala, M. L. Munzarova, V. Sklenar,J. Biomol. NMR 2004, 29, 477 – 490.

[19] T. Schlick, Molecular modeling and simulation: an interdisciplinaryguide, Springer, New York, 2002.

[20] a) S. Flodell, J. Schleucher, J. Cromsigt, H. Ippel, K. Kidd-Ljungg-ren, S. Wijmenga, Nucleic Acids Res. 2002, 30, 4803 – 4811; b) S. Flo-dell, M. Petersen, F. Girard, J. Zdunek, K. Kidd-Ljunggren, J.Schleucher, S. Wijmenga, Nucleic Acids Res. 2006, 34, 4449 –4457;c) K. Petzold, E. Duchardt, S. Flodell, G. Larsson, K. Kidd-Ljungg-ren, S. Wijmenga, J. Schleucher, Nucleic Acids Res. 2007, 35, 6854 –6861.

[21] a) F. C. Girard, O. M. Ottink, K. A. M. Ampt, M. Tessari, S. S. Wij-menga, Nucleic Acids Res. 2007, 35, 2800 –2811; b) K. A. M. Ampt,R. M. van der Werf, F. H. T. Nelissen, M. Tessari, S. S. Wijmenga, Bi-ochemistry 2009, 48, 10499 –10508.

[22] a) J. Fohrer, M. Hennig, T. Carlomagno, J. Mol. Biol. 2006, 356,280 – 287; b) J. Fohrer, U. Reinscheid, M. Hennig, T. Carlomagno,Angew. Chem. Int. Ed. 2006, 45, 7033 – 7036; c) M. Hennig, J.Fohrer, T. Carlomagno, J. Am. Chem. Soc. 2005, 127, 2028 –2029.

[23] J. F. Ying, A. Bax, J. Am. Chem. Soc. 2006, 128, 8372 –8373.[24] C. Fonseca Guerra, H. Zijlstra, G. Paragi, F. M. Bickelhaupt, Chem.

Eur. J. 2011, 17, 12612 –12622.[25] S. S. Wijmenga, M. M. Mooren, C. W. Hilbers in NMR of Macromo-

lecules: A Practical Approach (Ed.: G. C. K. Roberts), Oxford Uni-versity Press, New York, 1993, pp. 217 –288.

[26] R. M. van der Werf, M. Tessari, S. S. Wijmenga, J. Biomol. NMR2011, in press.

[27] E. Ennifar, A. Nikulin, S. Tishchenko, A. Serganov, N. Nevskaya, M.Garber, B. Ehresmann, C. Ehresmann, S. Nikonov, P. Dumas, J.Mol. Biol. 2000, 304, 35 –42.

[28] C. Giessner-Prettre, J. Biomol. Struct. Dyn. 1986, 4, 99– 110.[29] S. B. Petersen, J. J. Led, J. Am. Chem. Soc. 1981, 103, 5308 – 5313.



http://dx.doi.org/10.1016/S0079-6565(97)00023-X

http://dx.doi.org/10.1016/S0079-6565(97)00023-X

http://dx.doi.org/10.1016/S0079-6565(97)00023-X

http://dx.doi.org/10.1016/S0079-6565(97)00023-X

http://dx.doi.org/10.1016/S0076-6879(02)38229-6

http://dx.doi.org/10.1016/S0076-6879(02)38229-6

http://dx.doi.org/10.1016/S0076-6879(02)38229-6

http://dx.doi.org/10.1002/cbic.200300700







http://dx.doi.org/10.1006/jmbi.1996.0855



http://dx.doi.org/10.1002/bip.20650








http://dx.doi.org/10.1016/j.pnmrs.2010.10.001




http://dx.doi.org/10.1016/S0079-6565(98)00025-9

http://dx.doi.org/10.1016/S0079-6565(98)00025-9

http://dx.doi.org/10.1016/S0079-6565(98)00025-9

http://dx.doi.org/10.1016/S0079-6565(98)00025-9

http://dx.doi.org/10.1016/0079-6565(96)01028-X

http://dx.doi.org/10.1016/0079-6565(96)01028-X

http://dx.doi.org/10.1016/0079-6565(96)01028-X

http://dx.doi.org/10.1016/0079-6565(96)01028-X

http://dx.doi.org/10.1016/j.sbi.2006.08.003




http://dx.doi.org/10.1126/science.1124964



http://dx.doi.org/10.1146/annurev.biochem.73.011303.074004




http://dx.doi.org/10.1021/bi011870b







http://dx.doi.org/10.1023/A:1008392405740

http://dx.doi.org/10.1023/A:1008392405740

http://dx.doi.org/10.1023/A:1008392405740

http://dx.doi.org/10.1023/A:1008392405740





http://dx.doi.org/10.1073/pnas.0610313104




http://dx.doi.org/10.1016/S0076-6879(05)94003-2

http://dx.doi.org/10.1016/S0076-6879(05)94003-2

http://dx.doi.org/10.1016/S0076-6879(05)94003-2

http://dx.doi.org/10.1007/s10858-008-9288-5

http://dx.doi.org/10.1007/s10858-008-9288-5

http://dx.doi.org/10.1007/s10858-008-9288-5





http://dx.doi.org/10.1093/nar/gkn305

http://dx.doi.org/10.1093/nar/gkn305

http://dx.doi.org/10.1023/A:1011914132531

http://dx.doi.org/10.1023/A:1011914132531

http://dx.doi.org/10.1023/A:1011914132531

http://dx.doi.org/10.1023/A:1011914132531

http://dx.doi.org/10.1023/A:1018348123074

http://dx.doi.org/10.1023/A:1018348123074

http://dx.doi.org/10.1023/A:1018348123074





http://dx.doi.org/10.1021/ja045276b




http://dx.doi.org/10.1039/b811366c



http://dx.doi.org/10.1002/(SICI)1097-458X(199612)34:13%3CS156::AID-OMR68%3E3.0.CO;2-U

http://dx.doi.org/10.1002/(SICI)1097-458X(199612)34:13%3CS156::AID-OMR68%3E3.0.CO;2-U

http://dx.doi.org/10.1002/ange.201007844




http://dx.doi.org/10.1002/anie.201007844



http://dx.doi.org/10.1007/s10858-007-9167-5

http://dx.doi.org/10.1007/s10858-007-9167-5

http://dx.doi.org/10.1007/s10858-007-9167-5

http://dx.doi.org/10.1007/s10858-007-9167-5

http://dx.doi.org/10.1021/ja0367041




http://dx.doi.org/10.1093/nar/gkp956



http://dx.doi.org/10.1023/A:1008290618449

http://dx.doi.org/10.1023/A:1008290618449

http://dx.doi.org/10.1023/A:1008290618449

http://dx.doi.org/10.1017/S0033583500004169

http://dx.doi.org/10.1017/S0033583500004169

http://dx.doi.org/10.1017/S0033583500004169

http://dx.doi.org/10.1006/jmre.2001.2314








http://dx.doi.org/10.1002/qua.21049




http://dx.doi.org/10.1021/jp980926h




http://dx.doi.org/10.1021/jp0007538



http://dx.doi.org/10.1021/ja00098a060




http://dx.doi.org/10.1016/S0079-6565(98)00013-2

http://dx.doi.org/10.1016/S0079-6565(98)00013-2

http://dx.doi.org/10.1016/S0079-6565(98)00013-2

http://dx.doi.org/10.1016/S0079-6565(98)00013-2

http://dx.doi.org/10.1002/(SICI)1096-987X(199706)18:8%3C1079::AID-JCC12%3E3.0.CO;2-8



http://dx.doi.org/10.1063/1.1567252

http://dx.doi.org/10.1063/1.1567252

http://dx.doi.org/10.1063/1.1567252

http://dx.doi.org/10.1063/1.1567252

http://dx.doi.org/10.1007/s10858-007-9184-4

http://dx.doi.org/10.1007/s10858-007-9184-4

http://dx.doi.org/10.1007/s10858-007-9184-4

http://dx.doi.org/10.1007/s10858-007-9184-4

http://dx.doi.org/10.1093/nar/gkf603



http://dx.doi.org/10.1093/nar/gkl582



http://dx.doi.org/10.1093/nar/gkm774






http://dx.doi.org/10.1021/bi9011385




http://dx.doi.org/10.1016/j.jmb.2005.11.043







http://dx.doi.org/10.1021/ja043390o










http://dx.doi.org/10.1080/07391102.1986.10507648

http://dx.doi.org/10.1080/07391102.1986.10507648

http://dx.doi.org/10.1080/07391102.1986.10507648




www.chemeurj.org

[30] C. A. Theimer, L. D. Finger, L. Trantirek, J. Feigon, Proc. Natl.Acad. Sci. USA 2003, 100, 449 – 454.

[31] a) G. te Velde, F. M. Bickelhaupt, E. J. Baerends, C. Fonseca Guerra,S. J. A. van Gisbergen, J. G. Snijders, T. Ziegler, J. Comput. Chem.2001, 22, 931 – 967; b) E. J. Baerends, J. Autschbach, A. Brces, F. M.Bickelhaupt, C. Bo, P. L. de Boeij, P. M. Boerrigter, L. Cavallo, D. P.Chong, L. Deng, R. M. Dickson, D. E. Ellis, L. Fan, T. H. Fischer, C.Fonseca Guerra, S. J. A. van Gisbergen, J. A. Groeneveld, O. V.Gritsenko, M. Gr�ning, F. E. Harris, P. van den Hoek, C. R. Jacob,H. Jacobsen, L. Jensen, G. van Kessel, F. Kootstra, E. van Lenthe,D. A. McCormack, A. Michalak, J. Neugebauer, V. P. Osinga, S.Patchkovskii, P. H. T. Philipsen, D. Post, C. C. Pye, W. Ravenek, P.Ros, P. R. T. Schipper, G. Schreckenbach, J. G. Snijders, M. Sol, M.Swart, D. Swerhone, G. te Velde, P. Vernooijs, L. Versluis, L. Vis-scher, O. Visser, F. Wang, T. A. Wesolowski, E. van Wezenbeek, G.Wiesenekker, S. K. Wolff, T. K. Woo, A. L. Yakovlev, T. Ziegler,ADF version 2007.01, SCM, Amsterdam, The Netherlands, 2007.

[32] E. van Lenthe, E. J. Baerends, J. Comput. Chem. 2003, 24, 1142 –1156.

[33] S. H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 1980, 58, 1200 –1211.[34] A. D. Becke, Phys. Rev. A 1988, 38, 3098.[35] J. P. Perdew, Phys. Rev. B 1986, 33, 8822 – 8824; erratum: ibid. 8834,

7406.[36] M. Swart, J. G. Snijders, Theor. Chem. Acc. 2003, 110, 34– 41; erra-

tum: ibid. 111, 156.

[37] a) C. Fonseca Guerra, F. M. Bickelhaupt, J. G. Snijders, E. J. Baer-ends, Chem. Eur. J. 1999, 5, 3581 –3594; b) C. Fonseca Guerra, F. M.Bickelhaupt, J. G. Snijders, E. J. Baerends, J. Am. Chem. Soc. 2000,122, 4117 –4128; c) T. van der Wijst, C. Fonseca Guerra, M. Swart,F. M. Bickelhaupt, Chem. Phys. Lett. 2006, 426, 415 –421; d) forother DFT applications and geometry optimizations of DNA mono-nucleosides using B3LYP see, for example, N. A. Richardson, J. Gu,S. Wang, Y. Xie, H. F. Schaefer III, J. Am. Chem. Soc. 2004, 126,4404 – 4411.

[38] P. R. T. Schipper, O. V. Gritsenko, S. J. A. van Gisbergen, E. J. Baer-ends, J. Chem. Phys. 2000, 112, 1344 –1352.

[39] a) A. Klamt, G. Sch��rmann, J. Chem. Soc. Perkin Trans. 2 1993,799 – 805; b) C. C. Pye, T. Ziegler, Theor. Chem. Acc. 1999, 101,396 – 408.

[40] R. S. Bon, B. van Vliet, N. E. Sprenkels, R. F. Schmitz, F. J. J. deKanter, C. V. Stevens, M. Swart, F. M. Bickelhaupt, M. B. Groen,R. V. A. Orru, J. Org. Chem. 2005, 70, 3542 – 3553.

[41] M. Swart, E. Rçsler, F. M. Bickelhaupt, Eur. J. Inorg. Chem. 2007,3646 – 3654.

[42] M. Swart, F. M. Bickelhaupt, QUILD, Amsterdam, 2005.

Received: November 15, 2011Published online: August 16, 2012







http://dx.doi.org/10.1002/jcc.1056







http://dx.doi.org/10.1139/p80-159

http://dx.doi.org/10.1139/p80-159

http://dx.doi.org/10.1139/p80-159

http://dx.doi.org/10.1103/PhysRevA.38.3098

http://dx.doi.org/10.1103/PhysRevB.33.8822



http://dx.doi.org/10.1002/(SICI)1521-3765(19991203)5:12%3C3581::AID-CHEM3581%3E3.0.CO;2-Y



http://dx.doi.org/10.1021/ja993262d




http://dx.doi.org/10.1016/j.cplett.2006.06.057



http://dx.doi.org/10.1021/ja030487m




http://dx.doi.org/10.1063/1.480688

http://dx.doi.org/10.1063/1.480688

http://dx.doi.org/10.1063/1.480688

http://dx.doi.org/10.1039/p29930000799

http://dx.doi.org/10.1039/p29930000799

http://dx.doi.org/10.1039/p29930000799

http://dx.doi.org/10.1039/p29930000799

http://dx.doi.org/10.1007/s002140050457

http://dx.doi.org/10.1007/s002140050457

http://dx.doi.org/10.1007/s002140050457

http://dx.doi.org/10.1007/s002140050457

http://dx.doi.org/10.1021/jo050132g



http://dx.doi.org/10.1002/ejic.200700228




www.chemeurj.org

Chemical Shifts in Nucleic Acids Studied by Density ...iqc.udg.es/articles/pdf/iqc838.pdf · The...

Documents

Transcript of Chemical Shifts in Nucleic Acids Studied by Density ...iqc.udg.es/articles/pdf/iqc838.pdf · The...