Conformational Properties of the Deoxyribose and Ribose Moieties of Nucleic Acids: a Quantum Mechanical Study

J. Phys. Chem. B 1998, 102, 6669-6678 6669

Conformational Properties of the Deoxyribose and Ribose Moieties of Nucleic Acids: A Quantum Mechanical Study

Nicolas Foloppe and Alexander D. MacKerell, Jr.* Department of Pharmaceutical Sciences, School of Pharmacy, UniVersity of Maryland, Baltimore, Maryland 21201 ReceiVed: April 15, 1998

The present work analyzes the intrinsic conformational energetics associated with the puckering of the deoxyribose and ribose sugars in nucleic acids using high-level ab initio quantum mechanical calculations. A variety of model compounds have been designed to define the minimal structural unit suitable to model the sugar moiety in nucleic acids. Results suggest that all the structural features of a nucleoside are required to model the sugar moiety of nucleic acids. Stuctures calculated at the MP2 level of theory are in close agreement with experimental structural information. In deoxyribose, the south pucker (B form of double helices) is intrinsically favored over the north pucker (A form of double helices) by ∼1.0 kcal/mol. In contrast, for ribose, with torsion in an RNA-like conformation, the north pucker is favored over the south pucker by ∼2.0 kcal/mol. For both the deoxyribose and ribose of nucleic acids, the lowest energy barrier between the north and south puckers is >4.0 kcal/mol. The present calculations suggest that crossing this barrier may involve a decrease in the amplitude of the furanose ring. Implications of these results with respect to nucleic acid stucture and dynamics are discussed.

1. Introduction modate both conformations.8,9 However, condensed phase structural information from experimental approaches includes It is now well documented that nucleic acid structural possible contributions from solvent effects, crystal packing 1 variability and flexibility is related to their biological functions. interactions, or other internal degrees of freedom in the The sugar moiety occupies a central position in the structure of molecules investigated. It is thus difficult to derive the intrinsic nucleic acids, and is of crucial importance in shaping their energetic properties of the ribose or deoxyribose solely from structure and dynamics. This importance is evidenced by the statistical analysis of the condensed phase structures containing striking differences in structural properties between DNA and these moieties. Improved knowledge of the contributions of RNA, which differ only by the chemical nature of their sugar. the sugar moiety to nucleic acids energetics is, however, of Although DNA and RNA differ only by a hydroxyl group, it is general interest to better understand the conformational proper- enough to confine RNA double helices to a single structural ties of DNA and RNA. family (A form), whereas DNA is polymorphic and exists in a 1 Another limitation of available experimental data concerning variety of structural families including the A, B, and Z forms. the sugar conformational properties is their being mostly The pivotal role of the sugar in nucleic acids structures is further restricted to the north and south regions. Measurements in illustrated by the direct relationship between the deoxyribose 3,5,6,10 2 solution suggest that in nucleosides and nucleotides, as ring conformation and the overall structure of the DNA. well as in DNA,11-14 the sugar exists in a dynamic equilibrium The sugar ring conformation, or puckering, can be conve- between the north and south conformations. Consequently, the niently described by two parameters, the pseudorotation angle height of the energy barrier between the north and south energy 3 and the amplitude of pucker. In the structures of nucleosides minima of the furanose ring is expected to play an important 4-7 2 and nucleotides, as well as oligonucleotides, the sugar role in governing the dynamic behavior of the nucleic acids pseudorotation angle has been found to populate essentially two and their components. As noted earlier,9 the barrier associated ranges of conformations, referred to as the north and the south with the east quadrant is expected to lie between 2.0 and 5.0 3 ranges. The north range is associated with RNA and the A kcal/mol above the global energy minimum. The lower estimate form of DNA, and the south range is associated with the B is deduced from the scarcity of structures detected experimen- form of DNA. In the Z form of DNA, the sugar is found in tally with a pseudorotation angle falling in the east quadrant, 2 both the north and south ranges. whereas the higher estimate is compatible with the expected Although experimental approaches have yielded a wealth of interconversion between the north and south puckers at room information concerning the conformations accessible to the sugar temperature. Ro¨der et al.10 found a barrier of 4.7 ( 0.5 kcal/ in nucleic acids and its components, the relationship between mol for purine ribosides in deuteroammonia, although the these conformations and the intrinsic energetics of the sugar relevance of this result to biological situations may be questioned remains unclear. For both ribose and deoxyribose, the energy given the solvent used. To our knowledge, an equivalent study difference between the north and south conformations is for deoxyribo-containing compounds is not available. expected to be small enough to allow these sugars to accom- Theoretical calculations can complement experimental methods and provide further insights regarding the intrinsic energetics * To whom correspondence should be addressed. of the sugar in nucleic acids, independently of condensed phase S1089-5647(98)01868-9 CCC: $15.00 © 1998 American Chemical Society Published on Web 08/05/1998 6670 J. Phys. Chem. B, Vol. 102, No. 34, 1998 Foloppe and Mackerell effects, and on the entire range of pseudorotation angle values. To date, theoretical studies of the sugars in nucleic acids have been limited to semiempirical quantum mechanical15 or empirical force field investigations.8,16 Olson and Sussman9 have already discussed some discrepancies between the large body of experimental data pertaining to the sugars in nucleic acids and the results of Saran et al.15 and Levitt and Warshel.16 Olson8 has derived a potential parametrized to be compatible with experimentally observed populations in the north and south energy minima. That work stressed the usefulness of the gauche effect to explain the influence of the furanose substituents on the sugar conformational properties. The developed potential, however, remains empirical in nature and its validity for regions of the pseudorotation angle for which experimental data are scarce or nonexistent is an open question. In the present work, the conformational energetics of model compounds containing deoxyribose or ribose are examined using high-level quantum chemical calculations. Comparison of the results from the present calculations with available experimental data suggests that all the structural features of a nucleoside are required to model the sugar moiety in nucleic acids. In such a model, the deoxyribose south conformation is intrinsically more stable than the north, but the energy difference between the north and south conformations is small enough to allow for the existence of the north conformation. In contrast, the corresponding energy difference in the ribose, when is restricted to an RNA-like conformation, favors the north conformation and makes the south conformation unlikely. In addition, the Figure 1. Model compounds A, B, C, and D used to model present calculations provide a powerful alternative to experi- deoxyribose and model compound E used to model ribose. mental methods to probe the energy barriers between the north and south energy minima. For both deoxyribose and ribose, sets for the neutral and anionic compounds, respectively. All the present calculations suggest a significant potential energy pseudorotation energy surfaces were investigated at both the barrier between the north and south energy minima. A marked restricted Hartree-Fock (HF) level of theory and at the second- flattening of the furanose ring is observed when crossing the order Møller-Plesset (MP2) level of theory, except for com- energy barrier between these two energy minima. pounds D and E. For compound D, calculations were performed The present results will be useful to improve the calibration only at the HF level and for compound E they were performed of the sugar conformational properties in nucleic acid force only at the MP2 level. fields. Pseudorotation energy surfaces were obtained by fixing one endocyclic dihedral angle and performing energy minimization. 2. Methods For compounds A, B, C, and E, the dihedral C1′-C2′-C3′- C4′ was fixed at 10.0° increments from -30.0 to 30.0°. For Structures of the model compounds used to explore the compounds A, B, and D, the C3′ endo and C2′ endo conforma- deoxyribose and ribose pseudorotation properties are shown in tions were obtained by fixing the dihedral angles C4′-O4′- Figure 1. Throughout the present work each model compound C1′-C2′ and C3′-C4′-O4′-C1′ to 0.0°. For each pseudo- will be referred to by its letter designation. The nucleic acid rotation energy surface, both the south and north energy minima atom names and dihedral angle nomenclature1 is used for their were located by relaxing all constraints on the furanose model compounds counterparts. Accordingly, the dihedral endocyclic torsions. Energy surfaces were offset relative to their angles are defined as follows: global energy minimum and are presented as a function of the â γ δ ú pseudorotation angle. The pseudorotation angles and amplitudes H O5′ C5′ C4′ C3′ O3′ HorP were extracted from the energy minimized structures. The energy barrier between two energy minima is defined here as In all the model compounds except A, the base is modeled by the energy difference between the global energy minimum and an imidazole moiety because it is computationaly more tractable the point of highest energy obtained by discrete sampling than any of the natural bases present in nucleic acids. The between the two minima. No attempt was made to locate the imidazole atom names and the dihedral angle ø about the sugar- true energy maximum between two energy minima. Energy imidazole glycosidic linkage were defined in a way analogous minimizations were performed to the default tolerances in the to their definition in purines.1 Sugar puckering pseudorotation GAUSSIAN program. angles (P) and amplitudes (τm) were determined following For compounds A, B, and C, all degrees of freedom other Altona and Sundaralingam,3 using the same reference state for than the fixed endocyclic dihedral were allowed to relax during P ) 0.0°. The pseudorotation space is divided into four equally energy minimizations. When present, the dihedral angles γ, â, sized quadrants, centered around P ) 0.0°, P ) 90.0°, P ) and were initially positioned in their conformation in nucleic 180.0°, and P ) 270.0°, which are referred to as the north, east, acids, g+, t, and t, respectively. The dihedrals γ and â remained south, and west quadrants, respectively. in these conformations during energy minimization without Quantum mechanical calculations were carried out with the being constrained, except in compound D. For compound D, GAUSSIAN 94 program17 using the 6-31G* and 6-31+G* basis the pseudorotation energy surface was obtained with â (H- A Quantum Mechanical Study J. Phys. Chem. B, Vol. 102, No. 34, 1998 6671

TABLE 1: Descriptors Related to the Energy Minima in the Pseudorotation Energy Surfaces Obtained for Compounds A-Ea HF MP2 compound Pn Ps ∆EB Pn Ps ∆EB A 347.5 161.4 -2.1 3.0 331.6 219.8 -1.6 3.5 B 10.7 152.3 -0.2 1.0 352.2 160.4 -0.3 2.3 C 17.4 161.6 0.9 2.7 13.1 167.2 1.2 4.4 D 18.4 153.8 5.0 5.3 na na na na E na na na na 15.5 164.2 -2.3 5.0 a The properties listed refer to the results obtained at the HF or at the MP2 level of theory. Calculation at one of these levels of theory were not performed (na) for some model compounds. Pseudorotation angles (deg) Pn and Ps correspond, respectively, to the north and south energy minima. The experimental counterparts of Pn and Ps in DNA crystal structures are 18.0° and 158.0°, respectively (see section 3.1). ∆E (kcal/mol) is the energy of the north minimum minus the energy of the south minimum. B (kcal/mol) is the energy barrier between the south and the north energy minima through the east pseudorotation path.

O5′-C5′-C4′) fixed at 180.0°; without this constraint, reorientation of the 5′ hydroxyl group occurs, leading to formation of an intramolecular hydrogen bond with the 3′ phosphate group for some ring conformations (C3′ endo), but not all of them (C2′ endo). This hydrogen bond, which cannot be formed in DNA, significantly complicates the analysis of the pseudorotation energy surface. With compound E, calculations were designed to model RNA by initially fixing at 180.0° and a g+ conformation for H-O2′-C2′-C3′. This arrangement was made to avoid formation of an intramolecular hydrogen bond where the 3′-OH group donates a proton to the 2′-O. Following Figure 2. The four top panels show the pseudorotation energy profiles the initial minimization, was allowed to relax and remained obtained with compound A, B, C, and D, at the HF (x) or MP2 (O) in the trans conformation. The calculation with compound E level of theory. The lower panel shows the probability distribution of where the 3′-OH group donates a proton to the 2′-O acceptor the pseudorotation angle in A DNA (thick line), B DNA (thin line), was initiated with both the H-O3′-C3′-C4′ and H-O2′- and Z DNA (dotted line) crystal structures. C2′-C3′ dihedrals in the trans conformation and allowed to relax without constraints. OH group in ribose alters the conformational properties of the sugar. Distributions of the sugar puckers in crystal structures of DNA duplexes were obtained from the nucleic acids database18 as of 3.1. Model Selection. Previous studies have used full 15 8,16 May, 1996. Structures containing nonstandard DNA compo- nucleosides or a smaller model compound to model the nents, bound drugs, or proteins were excluded. The distributions sugar in nucleic acids, but no systematic comparison between are presented as probability distributions and were obtained these models has been performed. In the present work, the separately for the A, B, and Z DNA families, by sorting the importance of the chemical structure of the model compound data into 2° bins. The modal values of these distributions refer is tested by investigating a series of deoxyribose-based model - - to the center of the most highly sampled bin. compounds (A D). Compounds A D are of increasing complexity, with more DNA structural features added from compound A to compound D. The size of the model compounds 3. Results and Discussion has dictated the two levels of theory, HF/6-31G* (HF/6-31+G* In the following, we discuss the pseudorotation energy for compound D) and MP2/6-31G*, at which the calculations surfaces in term of the descriptors listed in Table 1, which were carried out. Using levels of theory more computationaly include the north (Pn) and south (Ps) minimum energy pseu- demanding than MP2/6-31G* would be difficult given the size dorotation angles, their energy difference (∆E), and the east of the model compounds and the need to carefully sample the energy barrier (B) between these minima. For most of the model pseudorotation energy surface. In this context, it is interesting compounds, the region of the pseudorotation energy surface to test if the salient features of the pseudorotation energy surface around the O4′ exo conformation has not been explored because can be derived at the less computationally demanding HF level this conformation is highly unlikely in nucleic acids (see section of theory, although the MP2 level is a priori more reliable than 3.1, compound B). the HF.19 The first part of this study aims to define a suitable model Figure 2 presents the pseudorotation energy surfaces for compound to investigate the intrinsic energetics of the sugar compounds A-D at both the HF and MP2 levels of theory, moieties in nucleic acids by comparing the calculated properties along with the pseudorotation angle distributions from oligode- of deoxyribose model compounds with experimental data. In oxyribonucleotide crystal structures. We assess the relevance the second part of this study, we use the selected model of the different models by comparing the location of the energy compound to characterize the energy barriers between the north minima in their pseudorotation energy profiles, as well as the and south energy minima in deoxyribose. In the third part, an energy differences between these energy minima, with the analogous model compound is used to investigate how the 2′- corresponding experimental populations in nucleosides, nucle- 6672 J. Phys. Chem. B, Vol. 102, No. 34, 1998 Foloppe and Mackerell otides, and DNA (vide infra). The computed energy difference levels of theory. The O4′ endo and O4′ exo regions are indeed between the north and south minima, and their location, cannot energy maxima in the MP2 ab initio surface, but the west barrier be rigorously compared with the experimental pseudorotation is lower in energy than east barrier by 0.9 kcal/mol. In nucleic angle distributions because these may include solvation or crystal acids, the west barrier is generally assumed to be of higher packing effects that are not included in the present calculations. energy than the east barrier because it brings the C4′ and the Furthermore, the experimental distributions reflect free energies C1′ substituents in close proximity, leading to unfavorable steric whereas our calculations yield potential energies. However, it interactions between these substituents. Our results, however, is expected that the condensed-phase pseudorotation angle suggest that the interaction between the amine and the methyl distributions can be reconciled with the corresponding energy group is not as unfavorable as anticipated. At the MP2 level, profiles as obtained in vacuo. the distances between the methyl carbon and the nitrogen in Experimental Reference Data. The experimental data used the O4′ exo and the global energy minimum structures are 3.17 as reference in the present study is comprised of structural and 3.53 Å, respectively. In both structures, the amino information obtained by X-ray crystallography for nucleosides hydrogens are pointing away from the methyl group, the amino 7 2 and nucleotides and DNA (Figure 2) as well as NMR solution electron lone pair is pointing toward the methyl group, and one 4,5,10,20,21 studies. The pseudorotation angle distributions ex- of the methyl hydrogens is pointing toward the amino lone- tracted from crystal structures of A, B, and Z DNA are included pair group. The distance between this methyl hydrogen and in Figure 2. It is well known that the deoxyribose sugars the nitrogen is 2.57 and 2.99 Å in the O4′ exo and the global ′ consistently populate regions in the north (containing C3 endo, energy minimum, respectively. This result suggests that the P ) 18.0°) and south (containing C2′ endo, P ) 162.0°) ranges interaction between the methyl and the amino groups may in nucleosides and nucleotides,7 as well as in DNA2 (Figure 2). involve some hydrogen-bond character, imparting the unex- The modal values of the A, B, and Z DNA crystal pseudoro- pected shape on the pseudorotation energy profile. Regardless tation angles distribution shown in the bottom of Figure 2 are of its chemical interpretation, it is apparent that the pseudoro- PA ) 18.0°, PB ) 158.0° and PZ ) 151.0°, respectively. Another structural property that can be used to assess the tation energy profile of compound A cannot be reconciled with relevance of the calculations is the well-documented correlation the conformational properties of the deoxyribose in DNA and between the sugar pucker and the conformation of the glycosidic related nucleosides and nucleotides. Indeed, none of the energy torsion in the anti orientation.2,7 In crystal structures of minima in compound A pseudorotation energy profile obtained nucleosides and nucleotides, the ø average value in purines is at the MP2 level coincides with any of the pseudorotation angle 193.3° (standard deviation ) 14.0°) for north sugars and 237.0° crystal distribution modal values (Table 1). This result prompted (standard deviation ) 24.3°) for south sugars.7 The ø modal examination of compounds with a chemical structure more values from the A DNA and B DNA oligonucleotides crystal closely related to the DNA. distributions are ø ) 208.0° and ø ) 256.0°, respectively.22 Compound B. Compound B differs from A by replacing Concerning the deoxyribose energetics, it is experimentally the amino group in A with an imidazole moiety. The imidazole documented that deoxyribonucleosides and deoxyribonucleotides was selected to mimic the base in DNA. This modification favor the south over the north conformation, both in solu- leads to a dramatic change in the general shape of the tion4,5,20,21 and in crystals,3,7 suggesting that the south energy pseudorotation energy profile (Figure 2). With compound B, minimum is intrinsically more stable than the north. The energy the east path (via P ) 90.0°) between the north and south energy difference, however, is expected to be small enough to allow minima is significantly lower in energy than the west path (via the sugar to accommodate both conformations, whether in DNA P ) 270.0°), which is in better agreement with what is expected or in its components. NMR studies of nucleosides in aqueous for DNA.1 In the O4′ exo conformations, energy minimized at solution indicate that the south conformation accounts for the HF and MP2 levels (ø adopts values of 169.6° and 160.1°, between 60%21 and 80%20 of the sugar population, and the same respectively) is significantly different from the values seen in kind of measurements for the deoxyribonucleotides have DNA experimental structures.2 Such an effect on ø in the O4′ 5 estimated the south:north ratio to be 70:30. A recent survey exo conformation also occurs when a 5′-OH group is present of the crystal geometries of deoxyribonucleosides and deoxy- in the model compound (data not shown). In oligonucleotides, 7 ∼ ∼ ribonucleotides lists 29 ( 80%) and 7 ( 20%) in the south the orientation of the base relative to the sugar also has to and north conformations, respectively. An appropriate model accommodate constraints imposed by base-base interactions, for the deoxyribose in DNA and its components is also expected making sampling of the O4′ exo conformation even more to yield an east energy barrier between 2.0 and 5.0 kcal/mol.9 unlikely than predicted by the intrinsic energy derived from Compound A. Compound A has been included in the model compounds. Therefore, the O4′ exo conformation is not present study because it represents a simple model of deoxyri- discussed further in the present work. bose in DNA and it has been used in the past to analyze the The pseudorotation energy profiles of compound B are still deoxyribose pseudorotation characteristics.8,16 The general shape of the surface computed for compound A differs strikingly in relatively poor agreement with the experimental data. from what has been proposed previously.8,16 It also stands apart Although the locations of the north and south energy minima from what is obtained in the present work with compounds B, in the HF pseudorotation energy profile (Table 1) are in C, and D. Both Levitt and Warshel16 and Olson8 obtained reasonable agreement with experiment, the east energy barrier HF ) pseudorotation energy profiles for compound A characterized (B 1.0 kcal/mol) is lower than expected, and the north by two energy wells corresponding to the C3′ endo and C2′ energy minimum is more stable than the south, in contradiction endo conformational ranges, and separated by two energy with experimentally observed trends. In the MP2 pseudorotation maxima approximately located at the O4′ endo (east barrier) energy profile of compound B the location of the north minimum MP2 ) ° and O4′ exo (west barrier) conformations; the west barrier was (Pn 352.2 ) cannot be reconciled with the experimental significantly higher in energy than the east barrier. This is in data. In addition, the MP2 calculations also yield a north energy contrast with the present calculations at both the HF and MP2 minimum more stable than the south (Table 1). In compound A Quantum Mechanical Study J. Phys. Chem. B, Vol. 102, No. 34, 1998 6673

noticeable that the differences obtained at the HF level fall outside the crystal standard deviations for these bond lengths (Table 2), in contrast with what is obtained at the MP2 level. This result is in large part because the carbonsheteroatom bond lengths depart significantly more from their experimental reference when calculated at the HF level than at the MP2 level (Table 2). When calculated at the HF level, the carbon- Figure 3. Probability distribution of the pseudorotation angle of purines heteroatom bond lengths in compound C are systematically 19 (thin line) and pyrimidines (thick line) in B DNA crystal structures. shorter than their crystal counterpart, as expected. The better agreement of the MP2 calculations and the crystal B, the ø values in the south energy minima are 219.3° and geometries, as compared with the HF calculations, is also 215.6°, at the HF and MP2 levels, respectively. These values apparent when scrutinizing the valence angles (Table 3). The are significantly lower than what is expected when the deoxy- average differences between the ab initio and crystal valence ribose is in the south conformation (see section on experimental angles are 1.1° (south) and 1.2° (north) at the HF level, and reference data). The 5′-methyl hydrogen pointing toward the 1.0° at the MP2 level in both the north and south conformations. imidazole (H-C5′-C4′-C3′ ≈ 53° at both HF and MP2 levels) Except for C2′-C3′-C4′ in the north conformation, all the in compound B may repel the imidazole, leading to the low ø endocyclic valence angles calculated at the MP2 level fall within values. This result suggests that compound B is still a poor the corresponding crystal standard deviation. At the HF level, representation of the sugar moiety in DNA as well as in the however, five out of six of the endocyclic valence angles related nucleosides and nucleotides. involving O4′ fall outside their experimental standard deviation Compound C. Compound C expands on compound B by range. Whether calculated at the HF or at the MP2 level, a addition of a hydroxyl group at the 5′ carbon. The pseudoro- majority of the exocyclic valence angles fall within the tation energy profile obtained with compound C (Figure 2) can corresponding experimental standard deviation. Overall, there be better reconciled with the experimental data obtained from is close agreement between both the MP2 calculated bond DNA and related nucleosides and nucleotides, as compared with lengths and valence angles and their experimental counterparts. compounds A and B. Compound C is itself a nucleoside Both the HF and MP2 calculated puckering amplitudes (Table analogue, differing from natural nucleosides only by the 4) in compound C are in reasonable agreement with their crystal replacement of a standard purine or pyrimidine base by an equivalents, falling within the crystal standard deviations. In imidazole moiety. The location of the north energy minimum the north conformation, the HF and MP2 calculated amplitudes HF ) ° MP2 ) ° ° ° at both the HF (Pn 17.4 ) and MP2 (Pn 13.1 ) levels is differ from the crystal average values by 0.2 and 0.8 , in reasonable agreement with the A DNA modal value, deviating respectively, and in the south conformation, the differences are from it by 0.6° and 4.9°, respectively. The south energy 2.3° and 1.3°, respectively. It is noticeable, however, that the minimum is also in better agreement with the B DNA modal MP2 amplitudes reflect the experimentally observed decrease ° HF ) ° MP2 value of 158.0 at both the HF (Ps 161.6 ) and MP2 (Ps of amplitude in the south versus the north conformation, ) ° HF MP2 although the opposite trend occurs in the HF results. 167.2 ) levels. Although Ps and Ps in compound C deviate from 158.0°, they are in the range of pseudorotation Overall, the geometric properties of compound C calculated angles that are populated in B DNA. Note that the calculated at the MP2 level are in reasonable agreement with experimental Ps values are both higher than the B DNA modal value. This results. The agreement between experimental and calculated result is consistent with the imidazole being more similar to a geometries is significantly better when these properties are purine than to a pyrimidine, and the higher pseudorotation angles calculated at the MP2 level than when calculated at the HF level. seen in purines versus pyrimidines (Figure 3). The second type of experimental information to test the In the HF and MP2 calculations with compound C, ø values validity of compound C as a model regards the relative energies are 204.4° and 205.2° in the north conformation, respectively, of the north and south conformations. Consistent with the and 234.5° and 234.8° in the south conformation, respectively. experimentally observed preference of deoxyribonucleosides and These values are in good agreement with experimental data, deoxyribonucleotides for the south conformation, both the HF showing that both the HF and MP2 calculations provide a and the MP2 calculations indicate the south energy minimum reasonable representation of the known correlation between the to be more stable than the north in compound C, with the MP2 sugar pucker and the glycosidic torsion (see section on energy difference (∆EMP2 ) 1.2 kcal/mol) larger than the HF experimental reference data). value (∆EHF ) 0.9 kcal/mol). If the sugar conformational space To further assess the relevance of the calculated results on is reduced to a very simple two-state model where only the compound C to experiment, the bond lengths (Table 2), valence energy minima are populated, a Boltzmann analysis at 298.0 K angles (Table 3), and amplitude of puckering (Table 4) can be indicates statistical weights in the north (Wn) and south (Ws) HF ) HF ) MP2 ) compared with the corresponding average geometries derived energy minima of Wn 0.2 and Ws 0.8, or Wn 0.1 MP2 ) from high-precision crystal structures of nucleosides and nucle- and Ws 0.9, when derived from the HF or MP2 energies, otides.7 Note that the calculated structures represent in vacuo respectively. Although this approximation is coarse, it indicates conditions at 0.0 K, so that even ideal calculations are not that the energy profile obtained from compound C yields expected to yield bond lengths and valence angles identical to energetic values that are in the range of what is observed their crystal counterparts. However, the crystal standard devia- experimentally. Interestingly, the NMR study that measured a tions on the bond lengths and valence angles (Table 2 and Table 80:20 south:north ratio20 was performed with a purine (adenine) 3, from Gelbin et al.7) provide a range from which the calculated deoxyribonucleoside, in line with compound C being a purine properties should not depart significantly. deoxyribonucleoside analogue and with the obtained south:north Average differences between the ab initio and crystal bond statistical weights. Thus, the energetics properties of compound lengths are 0.017 Å (south) and 0.019 Å (north) at the HF level, C are consistent with experimental data on the relative stabilities and 0.008 Å (south) and 0.007 Å (north) at the MP2 level. It is of the north and south energy minima, whereas compounds A 6674 J. Phys. Chem. B, Vol. 102, No. 34, 1998 Foloppe and Mackerell

TABLE 2: Bond Lengths (Å) for the Deoxyribose Moiety in Compound C in the South, North, and O4′ Endo Conformationsa south north O4′ endo

bond lcrys σcrys lHF lMP2 lcrys σcrys lHF lMP2 lHF lMP2 C1′sC2′ 1.518 0.010 1.529 1.527 1.519 0.010 1.535 1.530 1.541 1.540 C2′sC3′ 1.516 0.008 1.523 1.520 1.518 0.012 1.527 1.527 1.537 1.535 C3′sC4′ 1.529 0.010 1.535 1.530 1.521 0.010 1.524 1.522 1.536 1.535 C4′sO4′ 1.446 0.010 1.412 1.439 1.449 0.009 1.412 1.439 1.403 1.430 O4′sC1′ 1.420 0.011 1.398 1.425 1.418 0.012 1.394 1.422 1.391 1.417 C3′sO3′ 1.435 0.013 1.408 1.432 1.419 0.006 1.400 1.424 1.405 1.431 C4′sC5′ 1.512 0.007 1.515 1.513 1.509 0.011 1.512 1.509 1.513 1.512 C1′sN 1.468 0.014 1.438 1.445 1.488 0.013 1.450 1.458 1.439 1.449 C5′sO5′ 1.418 0.025 1.404 1.429 1.423 0.011 1.402 1.427 1.402 1.429

a lcrys refers to the average values obtained from statistical analysis (standard deviation σcrys) of crystal structures of nucleosides and nucleotides 7 (Gelbin et al. ). lHF and lMP2 refer to ab initio calculations at the HF and MP2 levels of theory, respectively; no average crystal bond lengths are available for the O4′ endo conformation.

TABLE 3: Valence Angles (deg) for the Deoxyribose Moiety in Compound C in the South, North, and O4′ Endo Conformationsa south north O4′ endo

angle θcrys σcrys θHF θMP2 θcrys σcrys θHF θMP2 θHF θMP2 C1′sC2′sC3′ 102.5 1.2 102.1 101.8 102.4 0.8 102.8 102.4 104.7 105.8 C2′sC3′sC4′ 103.1 0.9 102.5 102.6 102.2 0.7 101.1 100.9 103.8 104.8 C3′sC4′sO4′ 106.0 0.6 106.3 106.3 104.5 0.4 105.0 105.3 106.4 107.9 C4′sO4′sC1′ 110.1 1.0 112.0 110.1 110.3 0.7 112.1 110.0 110.4 111.1 O4′sC1′sC2′ 105.9 0.8 105.0 105.5 106.8 0.5 106.1 106.2 105.9 107.3 C2′sC3′sO3′ 109.4 2.5 111.9 111.5 112.6 3.3 114.8 115.0 114.4 114.0 C4′sC3′sO3′ 109.7 2.5 106.8 115.6 112.3 2.0 109.0 108.0 107.6 106.3 C5′sC4′sC3′ 114.1 1.8 114.6 114.4 115.7 1.2 116.1 115.7 115.1 113.8 C5′sC4′sO4′ 109.3 1.9 109.4 109.1 109.8 1.1 110.0 109.6 108.8 107.6 O4′sC1′sN 108.0 0.7 109.5 108.2 108.3 0.3 109.1 108.6 108.1 106.9 C2′sC1′sN 114.3 1.4 115.0 114.1 112.6 1.9 113.9 112.8 114.9 113.4 O5′sC5′sC4′ 110.9 1.7 109.3 108.4 111.0 2.5 109.6 108.7 108.9 107.6 C1′sN9sC4 126.3 1.2 126.9 127.0 123.9 1.0 125.5 125.3 127.0 127.1

a θcrys refers to the average values obtained from statistical analysis (standard deviation σcrys) of crystal structures of nucleosides and nucleotides 7 (Gelbin et al. ); θHF and θMP2 refer to ab initio calculations at the HF and MP2 levels of theory, respectively; no average crystal valence angles are available for the O4′ endo conformation. TABLE 4: Amplitude of Puckering (deg) of the Sugar the minimum energy for pseudorotation angles in the range ′ Moiety in Compounds C and E in the South, North, and O4 PHF ( 30.0°, in good agreement with the B DNA crystal Endo Conformationsa s pseudorotation angle distribution (Figure 2). The location of conformation crys σcrys CHF CMP2 E HF ) ° the north energy minimum (Pn 18.4 ) is in excellent b c HF south 36.2 3.3 36.0 37.0 33.4 /38.9 agreement with PA. However, the energy difference (∆E ) north 37.3 2.4 35.0 38.6 39.3 5.0 kcal/mol) between the north and south energy minima is O4′ endo na na 31.0 18.1 21.1 surprisingly large, and cannot be reconciled with the experi- a crys refers to the average values (standard deviation σcrys) obtained mental data mentioned previously. This discrepancy may partly from statistical analysis of crystal structures of nucleosides and 7 be explained by the energy profile for compound D being nucleotides (Gelbin et al. ). C and E refer to the model compounds ′ - ′- ′- ′ shown in Figure 1. No average crystal amplitudes are available for the obtained with the 5 -â torsion angle (H O5 C5 C4 ) fixed ° O4′ endo conformation. CHF and CMP2 are the amplitudes obtained at at 180.0 . This situation prevents formation of an intramolecular the HF and MP2 levels of theory, respectively, for compound C. The hydrogen bond between the 5′ hydroxyl group and the 3′ two amplitudes reported for compound E in the south conformation phosphate moiety. Formation of this hydrogen bond when correspond to the situation where was confined to an RNA-like compound D is energy minimized with an unconstrained 5′-â conformation (b), and the situation where the 3′-OH group was allowed to donate a proton to O2′ (c). torsion brings the north energy minimum 6.6 kcal/mol lower in energy than the south energy minimum. The magnitude of and B are not as consistent. This result strongly suggests that the energy change illustrates the pitfalls associated with increas- ′ ′ a nucleoside (or a nucleoside analogue) is the minimal chemical ing the complexity of the model compound. Possibly, a 3 ,5 - entity required to model the conformational properties of the bisphosphate nucleotide may avoid this problem, however, sugar in nucleic acids or their components. calculations on such a system are computationaly prohibited at Compound D. Because the elementary building block of this time. An additional difficulty with compound D is that, ° DNA is a nucleotide, the deoxyribose conformational energetics although remains in the 190 range in the north energy ° were also investigated with compound D,a3′-nucleotide minimum region, it adopts values in the range of 270 in the analogue. Compound D has been investigated only at the HF south energy minimum region. level of theory because of computational limitations. An Difficulties associated with the additional degrees of freedom, interesting feature of the compound D pseudorotation energy combined with a significantly increased computational burden, profile (Figure 2) is the broad south energy well, which is make compound D less attractive than compound C as a model HF ) ° centered around an energy minimum (Ps 153.8 ) deviating of the sugar conformational energetics in nucleic acids. Thus, from PB by 4.2°. The energy remains within ∼1.0 kcal/mol of of the results in the present study, those obtained at the MP2/ A Quantum Mechanical Study J. Phys. Chem. B, Vol. 102, No. 34, 1998 6675

6-31G* level with compound C can be regarded as the most In theoretical studies of the furanose presented to date, the reliable computed estimate of the deoxyribose intrinsic energet- inversion barrier has been found higher in energy than the energy ics in DNA. barriers along the pseudorotation pathway.23,24 The HF and Model compound C indicates that the deoxyribose favoring MP2 energy barriers associated with a coplanar furanose in the south conformation in condensed phase in nucleosides and compound C are 3.9 and 5.0 kcal/mol, respectively. Hence, nucleotides may be driven, in part, by the intrinsic energetics the present calculations confirm that the inversion mechanism of the sugar and its direct substituents. This intrinsic energetics in deoxyribose is more unfavorable than pseudorotation through may also be an important factor in stabilizing the B form of the east barrier (Table 1). Because the energy difference DNA over a wide range of solvent conditions.1 Furthermore, between the east and inversion barriers is only 0.6 kcal/mol in the intrinsic north/south energy difference is small enough for the present MP2 calculation, it cannot be concluded that the the deoxyribose to also populate the north conformation in DNA, inversion mechanism is forbidden. The location of the point allowing for DNA polymorphism. Even in B DNA in solution, of highest energy along the inversion path in a substituted the deoxyribose is likely to populate the north conformation, furanose, however, does not necessarily coincide with the in agreement with a growing body of experimental evi- coplanar conformation of the furanose, possibly leading to a dence.11,12,14 higher inversion barrier. 3.2. Energy Barriers Between the Deoxyribose North and 3.3. Influence of the 2′-OH Group in ribose. The extra South Conformations. Although the relevance of the computed 2′-OH group in ribose (compound E, Figure 1), as compared properties for the north and south energy minima can be assessed with deoxyribose, significantly complicates the conformational by comparison with available experimental data, experimental analysis. Indeed, the 2′-OH group can adopt a number of observations that can be directly related to the energy barrier conformations, with the possibility of intramolecular hydrogen between these two energy minima are more elusive. The quality bonds, which may or may not be relevant to the situation in of the agreement between the MP2 calculated and experimental RNA. Clearly, an intramolecular hydrogen bond where the 3′ structural and energetics properties for compound C suggests hydroxyl is the hydrogen donor and the 2′ hydroxyl the acceptor that the MP2 calculations should yield useful information for does not pertain to RNA structures, except at the 3′ termini. conformations of the furanose for which experimental informa- Because the present work is primarily concerned with the tion is scarce. The conformations representing energy barriers energetics of the sugar in nucleic acids, most of the present between the north and south energy minima are of particular calculations have been performed with (H3′-O3′-C3′-C4′) interest, and are discussed based on results for compound C. in the trans conformation, disallowing formation of a hydrogen As seen in Figure 2, the present sampling of the pseudoro- bond where the 3′-OH group is a donor. tation energy surface locates the east energy barrier in the O4′ Experimental methods alone are generally unable to unam- endo conformation in both the HF and MP2 calculations. The biguously locate the positions of the 2′-OH hydrogen in RNA. MP2 calculations predict a significant flattening of the deox- Examination of a number of experimental structures combined yribose in the O4′ endo conformation (Table 4), with an with molecular dynamics results, however, suggests that the 2′- amplitude of 18.1° and a systematic opening of all the furanose OH bond points preferentially toward the O3′ oxygen of the endocyclic valence angles (Table 3). Calculations at the HF same residue.25b Accordingly, energy minimizations of com- level also predict a flattening in the O4′ endo conformation, pound E were initiated with H2′-O2′-C2′-C3′ in the g+ although to a lesser extent than what is obtained at the MP2 conformation. In the north energy minimum, the south energy level. Strain associated with the flattening of the furanose ring minimum, and the O4′ endo conformation, H2′-O2′-C2′-C3′ may contribute to the significant O4′ endo energy barrier. is equal to -35.0°, 50.6°, and 26.7°, respectively, and is equal Both the HF (BHF ) 2.7 kcal/mol) and MP2 (BMP2 ) 4.4 to 205.0°, 202.3°, and 197.8°, respectively. In all three kcal/mol) calculated barriers for compound C fall in the expected conformations, the O3′ to H2′ distances (north: 2.07 Å, south: 2.0-5.0 kcal/mol range,9 while remaining lower than what has 2.23 Å, O4′ endo: 2.01 Å) are indicative of some hydrogen- been measured for the purine ribonucleosides.10 As noted bond character. Visual inspection of the orientation of the 2′- previously, the energy barrier is expected to be higher in ribose- OH bond relative to O3′, however, suggests that the resulting based compounds than in the deoxyribo analogues.9 The MP2 hydrogen bond is better formed in the north energy minimum calculated energy barrier for compound C is significantly higher and in the O4′ endo conformation than in the south energy than the 1.8 kcal/mol estimate of Olson8 and is closer to the minimum. 4.7 kcal/mol measured by Ro¨der et al.10 Using nucleosides and Calculated bond lengths and valence angles for compound the PCILO semiempirical quantum mechanical method, Saran E are listed in Table 5 and Table 6, respectively, together with et al.15 predicted an east energy barrier on the order of 4.0 kcal/ their crystal counterparts. The average differences between the mol. However, the current MP2 treatment combined with the ab initio and crystal bond lengths are 0.007 Å in both the north 6-31G* basis set used in the present study is more reliable than and the south conformations. The average differences between the PCILO method. Furthermore, Saran et al.15 carried out their the ab initio and crystal valence angles are 1.2° and 1.0° in the calculations with fixed bond lengths and constrained ring north and south conformations, respectively. Most of the valence angles and amplitudes. The usefulness of the present calculated bond lengths and valence angles fall within the reexamination of the east energy barrier should be seen in this corresponding crystal standard deviation (Tables 5 and 6). In context. the north energy minimum, the ribose in compound E is slightly Although the O4′ exo conformation associated with the west more puckered (Table 4) than the deoxyribose in compound C, energy barrier implies a dramatic reorientation of torsion angle which is in agreement with the trend observed in crystal ø (see compound B), this is not the case in the inversion structures.7 In the south energy minimum, however, the ribose mechanism, which proceeds through a furanose structure where in compound E is flatter than the deoxyribose in compound C all five ring atoms are coplanar. It is therefore of interest to and flatter than what is observed in crystal structures.7 This compare the energy barrier associated with the inversion discrepancy disappears if one takes into consideration a south mechanism with that from the pseudorotation east energy barrier. conformation of compound E where is oriented in a 6676 J. Phys. Chem. B, Vol. 102, No. 34, 1998 Foloppe and Mackerell

TABLE 5: Bond Lengths (Å) for the Ribose Moiety in compound E is 2.3 kcal/mol more stable than the south Compound E in the South, North, and O4′ Endo conformation. Of particular interest is the magnitude of this a Conformations energy difference, which not only favors the north conformation south north O4′ endo but makes the south conformation unlikely at room temperature.

bond lcrys σcrys lai lcrys σcrys lai lai This result contrasts the corresponding energy difference in C1′sC2′ 1.526 0.008 1.537 1.529 0.011 1.529 1.547 compound C, which favors the south conformation but does C2′sC3′ 1.525 0.011 1.530 1.523 0.011 1.523 1.552 not preclude the north conformation at room temperature. These C3′sC4′ 1.527 0.011 1.527 1.521 0.010 1.523 1.532 results suggest that the intrinsic conformational energetics of C4′sO4′ 1.454 0.010 1.444 1.451 0.013 1.437 1.431 the sugar moiety in nucleic acids may be related to the O4′sC1′ 1.415 0.012 1.419 1.412 0.013 1.422 1.416 observation that DNA can exist in both the A and B forms of C3′sO3′ 1.427 0.012 1.437 1.417 0.014 1.430 1.434 C4′sC5′ 1.509 0.012 1.513 1.508 0.007 1.509 1.512 double helices, whereas RNA is restricted to the A form. C2′sO2′ 1.412 0.013 1.413 1.420 0.010 1.419 1.414 Ribose favoring the north conformation over the south in C1′sN 1.464 0.014 1.441 1.483 0.015 1.454 1.444 RNA by as much 2.3 kcal/mol may seem to contradict a number C5′sO5′ 1.424 0.016 1.429 1.420 0.009 1.427 1.427 of experimental studies on nucleosides and nucleotides. NMR a 4,20,21 ′ 5 lcrys refers to the average values obtained from statistical analysis studies of nucleosides and 5 -nucleotides in aqueous (standard deviation σcrys) of crystal structures of nucleosides and solution have found that, although ribose favors the north 7 nucleotides (Gelbin et al. ), and lai is the counterpart in the MP2 ab conformation more than deoxyribose, ribose still significantly initio calculations. No average crystal bond lengths are available for populates the south conformation. In the statistical analysis of the O4′ endo conformation. crystal structures of nucleosides and nucleotides of Gelbin et TABLE 6: Valence Angles (deg) for the Ribose Moiety in al.,7 24 ribose compounds were found in the north conformation Compound E in the South, North, and O4′ Endo and 49 in the south. It is, however, difficult to extrapolate these Conformationsa observations to the relative stabilities of the north and south south north O4′ endo conformations of the ribose in RNA because, in nucleosides and 5′-nucleotides, the 2′ and 3′-OH groups may adopt orienta- angle θcrys σcrys θai θcrys σcrys θai θai tions that favor the south conformation but cannot exist in RNA. C1′sC2′sC3′ 101.5 0.8 102.0 101.3 0.7 102.0 104.5 C2′sC3′sC4′ 102.6 1.0 103.5 102.6 1.0 101.1 105.2 To test this hypothesis compound E was energy minimized C3′sC4′sO4′ 106.1 0.8 106.9 104.0 1.0 104.7 107.7 at the MP2 level of theory in the south conformation with the C4′sO4′sC1′ 109.7 0.7 110.3 109.9 0.8 110.1 110.7 3′-OH group allowed to donate its proton to the 2′-O, a situation O4′sC1′sC2′ 105.8 1.0 106.3 107.6 0.9 106.7 107.8 that is relevant only to nucleosides and some nucleotides but C1′sC2′sO2′ 111.8 2.6 113.1 108.4 2.4 107.6 112.4 ′- ′- ′s ′s ′ not to RNA. In this structure, the values of torsions H3 O3 C3 C2 O2 114.6 2.2 113.7 110.7 2.1 109.0 112.2 ′- ′ ′- ′- ′- ′ ° ° C2′sC3′sO3′ 109.5 2.2 108.9 113.7 1.6 115.2 111.3 C3 C4 and H2 O2 C2 C3 are 155.3 and 183.3 , C4′sC3′sO3′ 109.4 2.1 108.0 113.0 2.0 109.0 107.2 respectively. This conformation of compound E is 0.2 kcal/ C5′sC4′sC3′ 115.2 1.4 113.5 116.0 1.6 115.2 113.8 mol more stable than the north energy minimum with in an C5′sC4′sO4′ 109.1 1.2 108.4 109.8 0.9 109.4 107.3 RNA-like conformation. Furthermore, the amplitude of pucker- ′s ′s O4 C1 N 108.2 0.8 108.4 108.5 0.7 108.6 106.7 ing with the 3′-OH group donating its proton to the 2′-O is 38.9°, C2′sC1′sN 114.0 1.3 114.0 112.0 1.1 112.5 113.4 O5′sC5′sC4′ 111.7 1.9 107.5 111.5 1.6 108.6 107.2 in significantly better agreement with the crystal structures of C1′sN9sC4 127.4 1.2 127.0 126.3 2.8 125.5 126.9 ribonucleosides and ribonucleotides as compared with the

a amplitude calculated in the south conformation with in an θcrys refers to the average values obtained from statistical analysis RNA-like conformation (Table 4). This result indicates that (standard deviation σcrys) of crystal structures of nucleosides and 7 nucleotides (Gelbin et al. ), and θai is the counterpart in the MP2 ab the present calculations are compatible with the properties initio calculations. No average crystal valence angles are available for observed experimentally for RNA components. The present the O4′ endo conformation. results suggest that, although the ribose favors the north and south conformations almost equally in nucleosides, the intrinsic energetic properties of the ribose in RNA may be significantly different due to a loss of hydrogen-bond-donating capability at

k the O3′ site. The present calculations also help to clarify the influence of the ribose 2′-OH group on the magnitude of the east energy barrier, as compared with its value in deoxyribose. The empirical potential used by Olson8 predicted that the east energy Figure 4. Pseudorotation energy profile obtained at the MP2 level barrier would be approximately 2.0 kcal/mol higher in ribose for compound E. than in deoxyribose. The major contribution to the increased conformation that is not compatible with RNA structure but is barrier in ribose was the van der Waals repulsion between the possible in nucleosides and 5′-nucleotides (vide infra). As in 2′ and 3′ eclipsed hydroxyl groups.8 The east energy barrier in the MP2 calculations on compound C, compound E shows a compound E is 5.0 kcal/mol in the present calculations, in close marked flattening of the furanose in the O4′ endo conformation, agreement with the value obtained experimentally (4.7 ( 0.5 although to a lesser extent than in the deoxy compound. kcal/mol) by Ro¨der et al.10 for purine ribonucleosides. This The pseudorotation energy profile for compound E is shown agreement confirms that the east energy barrier is higher in in Figure 4. The north and south energy minima are located at ribose than in deoxyribose (Table 1) and that it is located at, or Pn ) 15.5° and Ps ) 164.2°, respectively, and the east energy close to, the O4′ endo conformation (Figure 4). However, the barrier is located at the O4′ endo conformation. The location east energy barrier in compound E is only 0.6 kcal/mol higher of the energy minima are only slightly shifted relative to their than in compound C. This result indicates that although the deoxyribose counterparts (compound C, Table 1), but their O4′ endo conformation forces the 2′- and 3′-OH groups to be relative energies are reversed. The north conformation in eclipsed, the interaction between them is not as repulsive as A Quantum Mechanical Study J. Phys. Chem. B, Vol. 102, No. 34, 1998 6677 previously described.8 In the O4′ endo structure the 2′-OH bond significantly changes the north/south relative energies. When is pointing toward the O3′ oxygen and the distance between mimicking the RNA situation by preventing the 3′-OH group the 2′-OH proton and the O3′ oxygen is 2.02 Å, suggesting that to act as an hydrogen-bond donor, the north conformation of hydrogen bonding is occurring between the two hydroxyl the ribose is more stable than the south, by an energy difference groups. The energy of compound E with a coplanar furanose on the order of 2.0 kcal/mol. This difference suggests that the (inversion mechanism) at the MP2 level is 0.8 kcal/mol higher contribution of the ribose intrinsic energetics in stabilizing the than the east energy barrier. A form of RNA may be significant. It has been argued that RNA double helices do not adopt the 4. Conclusions B form because the ribose 2′-OH group would sterically clash 16 Results have been presented on a variety of model compounds with other parts of the B helix. However, the present designed to investigate the energetics of sugar puckering in calculations suggest that the intrinsic energetics of ribose may nucleic acids using high-level ab initio calculations. Calculated be an important factor in confining RNA to the A form. properties for four compounds (A-D) with increasing nucleic Interestingly, B RNA has been found to be stable in some - 25a acid structural features were compared with a variety of molecular dynamics simulations on the 1 2 ns time scale. Such stability suggests that very unfavorable steric clashes experimental data. It should be reiterated that the present in ′ vacuo potential energies are being compared with experimental between the ribose 2 -OH and other parts of the B helix might distributions that correspond to free energies in the condensed not be the primary reason why RNA does not adopt the B form phase. The present results strongly suggest that a previously in nature. used8,16 model (compound A), substituting the base with an The present work also provides new insights concerning the amino group and lacking a 5′-OH group, is not appropriate to energetics and structure of the conformations at the east energy model the furanose ring in nucleic acids. Previous conclusions barrier between the north and south energy minima. The values drawn using this model compound should be viewed in this obtained for the east barrier fall in the higher limit of the 2.0 to context. Replacement of the amino group by an imidazole, 5.0 kcal/mol range previously suggested.9 The east barrier in without adding a 5′-OH group (compound B), yielded calculated deoxyribose (4.5 kcal/mol) is lower than in ribose (5.0 kcal/ properties in better agreement with experiment, although the mol), but only by a small difference. In both deoxyribose and agreement was still poor. Inclusion of all the structural features ribose, the east energy barrier along the pseudorotation pathway of a nucleoside (compound C) yielded significantly better is lower in energy than the barrier associated with an inversion agreement with experiment, satisfactory enough to suggest that mechanism. a nucleoside is the minimal unit to consider when modeling The present results also indicate that the furanose amplitude the conformational energetics of the sugar moiety in nucleic decreases significantly when crossing the east barrier, in both acids. Using a nucleotide (compound D) involves additional deoxyribose and ribose. Interrelationships between the furanose torsional degrees of freedom that significantly complicate the pseudorotation angle, amplitude, bond lengths, and valence modeling of the sugar conformational properties, in addition to angles have been analyzed26 and led to the proposal that the increased computational burden. pseudorotation may proceed through the O4′ endo conformation The agreement between experimental and calculated geom- with variable amplitudes. To date, this proposal has not been etries is significantly better when the geometries are calculated clearly substantiated due to the lack of high precision structures at the MP2 level compared with the HF level. Furthermore, of nucleic acids constituents in this conformation.7 The present comparison of the pseudorotation energy profiles calculated at calculations provide direct evidence that the pseudorotation path the HF and MP2 levels of theory show that they can differ of lowest energy between the north and south energy minima significantly. These differences are apparent in the locations probably involves a significant variation in the furanose ring of the energy minima (compounds A and B, Table 1) and in amplitude. the height of the energy barriers (compounds B and C, Table An important application of the present analysis is the 1). These results document the possible shortcomings of using calibration of nucleic acids molecular mechanics force fields. the HF level of theory when investigating the sugar moieties in Force field based theoretical approaches have become increas- nucleic acids, including modified sugars. Although the proper- ingly powerful for the study of DNA structure and dynamics ties discussed in the present work are expected to be modulated in solution.25,27,28 Current tests of these methods, however, by the type of base linked to the sugar, calculations at the MP2 demonstrate that for DNA simulations to realize their full level on compounds C and E suggest the following conclusions. potential, further improvement of the underlying force fields The present work confirms that the intrinsic energetics of are necessary.29,30 The available force fields are still in partial deoxyribose favors the south conformation over the north, and disagreement with experiment in their representation of the provides a quantitative estimate on the order of 1.0 kcal/mol equilibrium between the A and B forms of DNA.29 In particular, for this energy difference. Thus, the deoxyribose intrinsic the delicate balance between the A and B forms of the sugar energetics are an important factor in stabilizing the B form of ring is still not adequately modeled.25,27,29,31 It has been noted DNA, but are also compatible with DNA structures containing that a more accurate representation of the energy barrier between the north conformation of the sugar. the north and south energy minima in nucleic acid force fields As illustrated by this work, the presence an additional is of crucial importance to obtain more reliable theoretical hydroxyl group tremendously complicates the conformational models of the structure and dynamics of nucleic acids.25 The analysis of the ribose as compared with deoxyribose. When east energy barrier in an adenine nucleoside has been reported hydroxyls are allowed to orient relative to each other without to be 2.9 kcal/mol (dielectric constant of 1.0) in the AMBER conditions, as can occur in a nucleoside, the south conformation force field,32 and is 1.8 kcal/mol in Version 2233 of the is found to be slightly more stable than the north, with an energy CHARMM force field (unpublished result). This suggests that difference (0.2 kcal/mol) less than that found in the deoxyribose. the value of this barrier in the current versions of these force Treating the ribose in an RNA context puts some conditions fields may be too low. The energy profiles presented here on the relative orientations of the 2′- and 3′-OH groups, which should prove useful in this respect. 6678 J. Phys. Chem. B, Vol. 102, No. 34, 1998 Foloppe and Mackerell

Acknowledgment. This work has been financially supported (17) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; by NIH grant GM51501. We also thank the Pittsburgh Super- Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Raghavachari, K.; Al- Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, computing Center and NCI’s Frederick Biomedical Supercom- J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, puting Center for providing computational resources. P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Head-Gordon, M.; Gonzalez, C.; Pople, J. A.; 1996, Gaussian, Inc., Supporting Information Available: Tables presenting the Pittsburgh, PA. north, south, and O4′ endo MP2/6-31G* optimized Cartesian (18) Berman, H. M.; Olson, W. K.; Beveridge, D. L.; Westbrook, J.; Gelbin, A.; Demeny, T.; Hsieh, S.-H.; Srinivasan, A. R.; Schneider, B. coordinates of compounds C and E (6 pages). Ordering Biophys. J. 1992, 63, 751. information is given on any current masthead page. (19) Hehre, W. J.; Radom, L.; Schleyer, P.v. R.; Pople, J. A.; Ab Initio Molecular Orbital Theory; John Wiley & Sons: New York, 1986. (20) Uesugi, S.; Miki, H.; Ikehara, M.; Iwahashi, H.; Kyogoku, Y. References and Notes Tetrahedron Lett. 1979, 42, 4073. (1) Saenger, W. Principles of Nucleic Acid Structure; Springer- (21) Guschlbauer, W.; Jankowsky, K. Nucleic Acids Res. 1980, 8, 1421. Verlag: New York, 1984. (22) Foloppe, N.; MacKerell, A. D., Jr. manuscript in preparation. (2) Dickerson, R. E.; Drew, H. R.; Conner, B. N.; Wing, R. M.; Fratini, (23) Cremer, D.; Pople, J. A. J. Am. Chem. Soc. 1975, 97, 1358. A. V.; Kopka, M. L. Science 1982, 216, 475. (24) Cadioli, B.; Gallinella, E.; Coulombeau, C.; Jobic, H.; Berthier, G. (3) Altona, C.; Sundaralingam, M. J. Am. Chem. Soc. 1972, 94, 8205. J. Phys. Chem. 1993, 97, 7844. (4) Altona, C.; Sundaralingam, M. J. Am. Chem. Soc. 1973, 95, 2333. (25) (a) Cheatham, T. E., III.; Kollman, P. A. J. Am. Chem. Soc. 1997, (5) Davies, D. B.; Danyluk, S. S. Biochemistry 1974, 13, 4417. 119, 4805. (b) Auffinger, P.; Westhof, E. J. Mol. Biol. 1997, 274, 54. (6) Davies, D. B.; Danyluk, S. S. Biochemistry 1975, 14, 543. (26) Westhof, E.; Sundaralingam, M. J. Am. Chem. Soc. 1980, 102, 1493. (7) Gelbin, A.; Scheider, B.; Clowney, L.; Hsieh, S.-H.; Olson, W. (27) MacKerell, A. D., Jr. J. Phys. Chem. B 1997, 101, 646. K.; Berman, H. M. J. Am. Chem. Soc. 1996, 118, 519. (28) Young, M. A.; Jayaram, B.; Beveridge, D. L. J. Am. Chem. Soc. (8) Olson, W. K. J. Am. Chem. Soc. 1982, 104, 278. 1997, 119, 59. (9) Olson, W. K.; Sussman, J. L. J. Am. Chem. Soc. 1982, 104, 270. (29) Feig, M.; Pettitt, B. M. J. Phys. Chem. 1997, 101, 7361. (10) Ro¨der, O.; Lu¨demann, H.; Von Goldammer, E. Eur. J. Biochem. (30) MacKerell, A. D., Jr. Molecular Modeling of Nucleic Acids; Leontis, 1975, 53, 517. N. B.; SantaLucia, J., Jr., Eds.; American Chemical Society: Washington, (11) Wartell, R. M.; Harrell, J. T. Biochemistry 1986, 25, 2664. D.C., 1988; 304. (12) Pechenaya, V. I.; Serikov, A. A. Biopolymers 1988, 27, 1817. (31) Cheatham, T. E., III.; Crowley, M. F.; Fox, T.; Kollman, P. A. (13) Weisz, K.; Shafer, R. H.; Egan, W.; James, T. L. Biochemistry Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 9626. 1992, 31, 7477. (32) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. (14) Ulyanov, N. B.; James T. L. Appl. Magn. Reson. 1994, 7, 21. M., Jr.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; (15) Saran, A.; Perahia, D.; Pullman, B. Theor. Chim. Acta 1973, 30, Kollman, P. A. J. Am. Chem. Soc. 1995, 117, 5179. 31. (33) MacKerell, A. D., Jr.; Wio´rkiewicz-Kuczera, J.; Karplus, M. J. Am. (16) Levitt, M.; Warshel, A. J. Am. Chem. Soc. 1978, 100, 2607. Chem. Soc. 1995, 117, 11946.