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 It is now well documented that nucleic acid structural variability and flexibility is related to their biological functions.1 The sugar moiety occupies a central position in the structure of nucleic acids, and is of crucial importance in shaping their structure and dynamics. This importance is evidenced by the striking differences in structural properties between DNA and RNA, which differ only by the chemical nature of their sugar. Although DNA and RNA differ only by a hydroxyl group, it is enough to confine RNA double helices to a single structural family (A form), whereas DNA is polymorphic and exists in a variety of structural families including the A, B, and Z forms.1 The pivotal role of the sugar in nucleic acids structures is further illustrated by the direct relationship between the deoxyribose ring conformation and the overall structure of the DNA.2 The sugar ring conformation, or puckering, can be conveniently described by two parameters, the pseudorotation angle and the amplitude of pucker.3 In the structures of nucleosides and nucleotides,4-7 as well as oligonucleotides,2 the sugar pseudorotation angle has been found to populate essentially two ranges of conformations, referred to as the north and the south ranges.3 The north range is associated with RNA and the A form of DNA, and the south range is associated with the B form of DNA. In the Z form of DNA, the sugar is found in both the north and south ranges.2 Although experimental approaches have yielded a wealth of information concerning the conformations accessible to the sugar in nucleic acids and its components, the relationship between these conformations and the intrinsic energetics of the sugar remains unclear. For both ribose and deoxyribose, the energy difference between the north and south conformations is expected to be small enough to allow these sugars to accom* To whom correspondence should be addressed.
modate both conformations.8,9 However, condensed phase structural information from experimental approaches includes possible contributions from solvent effects, crystal packing interactions, or other internal degrees of freedom in the molecules investigated. It is thus difficult to derive the intrinsic energetic properties of the ribose or deoxyribose solely from statistical analysis of the condensed phase structures containing these moieties. Improved knowledge of the contributions of the sugar moiety to nucleic acids energetics is, however, of general interest to better understand the conformational properties of DNA and RNA. Another limitation of available experimental data concerning the sugar conformational properties is their being mostly restricted to the north and south regions. Measurements in solution suggest that in nucleosides and nucleotides,3,5,6,10 as well as in DNA,11-14 the sugar exists in a dynamic equilibrium between the north and south conformations. Consequently, the height of the energy barrier between the north and south energy minima of the furanose ring is expected to play an important role in governing the dynamic behavior of the nucleic acids and their components. As noted earlier,9 the barrier associated with the east quadrant is expected to lie between 2.0 and 5.0 kcal/mol above the global energy minimum. The lower estimate is deduced from the scarcity of structures detected experimentally with a pseudorotation angle falling in the east quadrant, whereas the higher estimate is compatible with the expected interconversion between the north and south puckers at room temperature. Ro¨der et al.10 found a barrier of 4.7 ( 0.5 kcal/ mol for purine ribosides in deuteroammonia, although the relevance of this result to biological situations may be questioned given the solvent used. To our knowledge, an equivalent study for deoxyribo-containing compounds is not available. Theoretical calculations can complement experimental methods and provide further insights regarding the intrinsic energetics 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 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 present calculations provide a powerful alternative to experimental methods to probe the energy barriers between the north and south energy minima. For both deoxyribose and ribose, the present calculations suggest a significant potential energy barrier between the north and south energy minima. A marked flattening of the furanose ring is observed when crossing the energy barrier between these two energy minima. The present results will be useful to improve the calibration of the sugar conformational properties in nucleic acid force fields. 2. Methods Structures of the model compounds used to explore the deoxyribose and ribose pseudorotation properties are shown in Figure 1. Throughout the present work each model compound will be referred to by its letter designation. The nucleic acid atom names and dihedral angle nomenclature1 is used for their model compounds counterparts. Accordingly, the dihedral angles are defined as follows:
β γ ζ δ H O5′ C5′ C4′ C3′ O3′ H or P In all the model compounds except A, the base is modeled by an imidazole moiety because it is computationaly more tractable than any of the natural bases present in nucleic acids. The imidazole atom names and the dihedral angle χ about the sugarimidazole glycosidic linkage were defined in a way analogous to their definition in purines.1 Sugar puckering pseudorotation angles (P) and amplitudes (τm) were determined following Altona and Sundaralingam,3 using the same reference state for P ) 0.0°. The pseudorotation space is divided into four equally sized quadrants, centered around P ) 0.0°, P ) 90.0°, P ) 180.0°, and P ) 270.0°, which are referred to as the north, east, south, and west quadrants, respectively. Quantum mechanical calculations were carried out with the GAUSSIAN 94 program17 using the 6-31G* and 6-31+G* basis
Foloppe and Mackerell
Figure 1. Model compounds A, B, C, and D used to model deoxyribose and model compound E used to model ribose.
sets for the neutral and anionic compounds, respectively. All pseudorotation energy surfaces were investigated at both the restricted Hartree-Fock (HF) level of theory and at the secondorder Møller-Plesset (MP2) level of theory, except for compounds D and E. For compound D, calculations were performed only at the HF level and for compound E they were performed only at the MP2 level. Pseudorotation energy surfaces were obtained by fixing one endocyclic dihedral angle and performing energy minimization. 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 compounds A, B, and D, the C3′ endo and C2′ endo conformations were obtained by fixing the dihedral angles C4′-O4′C1′-C2′ and C3′-C4′-O4′-C1′ to 0.0°. For each pseudorotation energy surface, both the south and north energy minima were located by relaxing all constraints on the furanose endocyclic torsions. Energy surfaces were offset relative to their global energy minimum and are presented as a function of the pseudorotation angle. The pseudorotation angles and amplitudes were extracted from the energy minimized structures. The energy barrier between two energy minima is defined here as the energy difference between the global energy minimum and the point of highest energy obtained by discrete sampling between the two minima. No attempt was made to locate the true energy maximum between two energy minima. Energy minimizations were performed to the default tolerances in the GAUSSIAN program. For compounds A, B, and C, all degrees of freedom other than the fixed endocyclic dihedral were allowed to relax during energy minimizations. When present, the dihedral angles γ, β, and were initially positioned in their conformation in nucleic acids, g+, t, and t, respectively. The dihedrals γ and β remained in these conformations during energy minimization without being constrained, except in compound D. For compound D, the pseudorotation energy surface was obtained with β (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
∆E
B
Pn
Ps
∆E
B
A B C D E
347.5 10.7 17.4 18.4 na
161.4 152.3 161.6 153.8 na
-2.1 -0.2 0.9 5.0 na
3.0 1.0 2.7 5.3 na
331.6 352.2 13.1 na 15.5
219.8 160.4 167.2 na 164.2
-1.6 -0.3 1.2 na -2.3
3.5 2.3 4.4 na 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 the initial minimization, was allowed to relax and remained in the trans conformation. The calculation with compound E where the 3′-OH group donates a proton to the 2′-O acceptor was initiated with both the H-O3′-C3′-C4′ and H-O2′C2′-C3′ dihedrals in the trans conformation and allowed to relax without constraints. Distributions of the sugar puckers in crystal structures of DNA duplexes were obtained from the nucleic acids database18 as of May, 1996. Structures containing nonstandard DNA components, bound drugs, or proteins were excluded. The distributions are presented as probability distributions and were obtained separately for the A, B, and Z DNA families, by sorting the data into 2° bins. The modal values of these distributions refer to the center of the most highly sampled bin. 3. Results and Discussion In the following, we discuss the pseudorotation energy surfaces in term of the descriptors listed in Table 1, which include the north (Pn) and south (Ps) minimum energy pseudorotation angles, their energy difference (∆E), and the east energy barrier (B) between these minima. For most of the model compounds, the region of the pseudorotation energy surface around the O4′ exo conformation has not been explored because this conformation is highly unlikely in nucleic acids (see section 3.1, compound B). The first part of this study aims to define a suitable model compound to investigate the intrinsic energetics of the sugar moieties in nucleic acids by comparing the calculated properties of deoxyribose model compounds with experimental data. In the second part of this study, we use the selected model compound to characterize the energy barriers between the north and south energy minima in deoxyribose. In the third part, an analogous model compound is used to investigate how the 2′-
Figure 2. The four top panels show the pseudorotation energy profiles obtained with compound A, B, C, and D, at the HF (x) or MP2 (O) level of theory. The lower panel shows the probability distribution of the pseudorotation angle in A DNA (thick line), B DNA (thin line), and Z DNA (dotted line) crystal structures.
OH group in ribose alters the conformational properties of the sugar. 3.1. Model Selection. Previous studies have used full nucleosides15 or a smaller model compound8,16 to model the sugar in nucleic acids, but no systematic comparison between these models has been performed. In the present work, the importance of the chemical structure of the model compound is tested by investigating a series of deoxyribose-based model 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 has dictated the two levels of theory, HF/6-31G* (HF/6-31+G* for compound D) and MP2/6-31G*, at which the calculations were carried out. Using levels of theory more computationaly demanding than MP2/6-31G* would be difficult given the size of the model compounds and the need to carefully sample the pseudorotation energy surface. In this context, it is interesting to test if the salient features of the pseudorotation energy surface can be derived at the less computationally demanding HF level of theory, although the MP2 level is a priori more reliable than the HF.19 Figure 2 presents the pseudorotation energy surfaces for compounds A-D at both the HF and MP2 levels of theory, along with the pseudorotation angle distributions from oligodeoxyribonucleotide crystal structures. We assess the relevance of the different models by comparing the location of the energy minima in their pseudorotation energy profiles, as well as the energy differences between these energy minima, with the corresponding experimental populations in nucleosides, nucle-
6672 J. Phys. Chem. B, Vol. 102, No. 34, 1998 otides, and DNA (vide infra). The computed energy difference between the north and south minima, and their location, cannot be rigorously compared with the experimental pseudorotation angle distributions because these may include solvation or crystal packing effects that are not included in the present calculations. Furthermore, the experimental distributions reflect free energies whereas our calculations yield potential energies. However, it is expected that the condensed-phase pseudorotation angle distributions can be reconciled with the corresponding energy profiles as obtained in vacuo. Experimental Reference Data. The experimental data used as reference in the present study is comprised of structural information obtained by X-ray crystallography for nucleosides and nucleotides7 and DNA2 (Figure 2) as well as NMR solution studies.4,5,10,20,21 The pseudorotation angle distributions extracted from crystal structures of A, B, and Z DNA are included in Figure 2. It is well known that the deoxyribose sugars consistently populate regions in the north (containing C3′ endo, P ) 18.0°) and south (containing C2′ endo, P ) 162.0°) ranges in nucleosides and nucleotides,7 as well as in DNA2 (Figure 2). The modal values of the A, B, and Z DNA crystal pseudorotation angles distribution shown in the bottom of Figure 2 are PA ) 18.0°, PB ) 158.0° and PZ ) 151.0°, respectively. Another structural property that can be used to assess the relevance of the calculations is the well-documented correlation between the sugar pucker and the conformation of the glycosidic torsion in the anti orientation.2,7 In crystal structures of nucleosides and nucleotides, the χ average value in purines is 193.3° (standard deviation ) 14.0°) for north sugars and 237.0° (standard deviation ) 24.3°) for south sugars.7 The χ modal values from the A DNA and B DNA oligonucleotides crystal distributions are χ ) 208.0° and χ ) 256.0°, respectively.22 Concerning the deoxyribose energetics, it is experimentally documented that deoxyribonucleosides and deoxyribonucleotides favor the south over the north conformation, both in solution4,5,20,21 and in crystals,3,7 suggesting that the south energy minimum is intrinsically more stable than the north. The energy difference, however, is expected to be small enough to allow the sugar to accommodate both conformations, whether in DNA or in its components. NMR studies of nucleosides in aqueous solution indicate that the south conformation accounts for between 60%21 and 80%20 of the sugar population, and the same kind of measurements for the deoxyribonucleotides have estimated the south:north ratio to be 70:30.5 A recent survey of the crystal geometries of deoxyribonucleosides and deoxyribonucleotides7 lists 29 (∼80%) and 7 (∼20%) in the south and north conformations, respectively. An appropriate model for the deoxyribose in DNA and its components is also expected to yield an east energy barrier between 2.0 and 5.0 kcal/mol.9 Compound A. Compound A has been included in the present study because it represents a simple model of deoxyribose in DNA and it has been used in the past to analyze the deoxyribose pseudorotation characteristics.8,16 The general shape of the surface computed for compound A differs strikingly from what has been proposed previously.8,16 It also stands apart from what is obtained in the present work with compounds B, C, and D. Both Levitt and Warshel16 and Olson8 obtained pseudorotation energy profiles for compound A characterized by two energy wells corresponding to the C3′ endo and C2′ endo conformational ranges, and separated by two energy maxima approximately located at the O4′ endo (east barrier) and O4′ exo (west barrier) conformations; the west barrier was significantly higher in energy than the east barrier. This is in contrast with the present calculations at both the HF and MP2
Foloppe and Mackerell levels of theory. The O4′ endo and O4′ exo regions are indeed energy maxima in the MP2 ab initio surface, but the west barrier is lower in energy than east barrier by 0.9 kcal/mol. In nucleic acids, the west barrier is generally assumed to be of higher energy than the east barrier because it brings the C4′ and the C1′ substituents in close proximity, leading to unfavorable steric interactions between these substituents. Our results, however, suggest that the interaction between the amine and the methyl group is not as unfavorable as anticipated. At the MP2 level, the distances between the methyl carbon and the nitrogen in the O4′ exo and the global energy minimum structures are 3.17 and 3.53 Å, respectively. In both structures, the amino hydrogens are pointing away from the methyl group, the amino electron lone pair is pointing toward the methyl group, and one of the methyl hydrogens is pointing toward the amino lonepair group. The distance between this methyl hydrogen and the nitrogen is 2.57 and 2.99 Å in the O4′ exo and the global energy minimum, respectively. This result suggests that the interaction between the methyl and the amino groups may involve some hydrogen-bond character, imparting the unexpected shape on the pseudorotation energy profile. Regardless of its chemical interpretation, it is apparent that the pseudorotation energy profile of compound A cannot be reconciled with the conformational properties of the deoxyribose in DNA and related nucleosides and nucleotides. Indeed, none of the energy minima in compound A pseudorotation energy profile obtained at the MP2 level coincides with any of the pseudorotation angle crystal distribution modal values (Table 1). This result prompted examination of compounds with a chemical structure more closely related to the DNA. Compound B. Compound B differs from A by replacing the amino group in A with an imidazole moiety. The imidazole was selected to mimic the base in DNA. This modification leads to a dramatic change in the general shape of the pseudorotation energy profile (Figure 2). With compound B, the east path (via P ) 90.0°) between the north and south energy minima is significantly lower in energy than the west path (via P ) 270.0°), which is in better agreement with what is expected for DNA.1 In the O4′ exo conformations, energy minimized at the HF and MP2 levels (χ adopts values of 169.6° and 160.1°, respectively) is significantly different from the values seen in DNA experimental structures.2 Such an effect on χ in the O4′ exo conformation also occurs when a 5′-OH group is present in the model compound (data not shown). In oligonucleotides, the orientation of the base relative to the sugar also has to accommodate constraints imposed by base-base interactions, making sampling of the O4′ exo conformation even more unlikely than predicted by the intrinsic energy derived from model compounds. Therefore, the O4′ exo conformation is not discussed further in the present work. The pseudorotation energy profiles of compound B are still in relatively poor agreement with the experimental data. Although the locations of the north and south energy minima in the HF pseudorotation energy profile (Table 1) are in reasonable agreement with experiment, the east energy barrier (BHF ) 1.0 kcal/mol) is lower than expected, and the north energy minimum is more stable than the south, in contradiction with experimentally observed trends. In the MP2 pseudorotation energy profile of compound B the location of the north minimum ) 352.2°) cannot be reconciled with the experimental (PMP2 n data. In addition, the MP2 calculations also yield a north energy minimum more stable than the south (Table 1). In compound
A Quantum Mechanical Study
Figure 3. Probability distribution of the pseudorotation angle of purines (thin line) and pyrimidines (thick line) in B DNA crystal structures.
B, the χ values in the south energy minima are 219.3° and 215.6°, at the HF and MP2 levels, respectively. These values are significantly lower than what is expected when the deoxyribose is in the south conformation (see section on experimental reference data). The 5′-methyl hydrogen pointing toward the imidazole (H-C5′-C4′-C3′ ≈ 53° at both HF and MP2 levels) in compound B may repel the imidazole, leading to the low χ values. This result suggests that compound B is still a poor representation of the sugar moiety in DNA as well as in the related nucleosides and nucleotides. Compound C. Compound C expands on compound B by addition of a hydroxyl group at the 5′ carbon. The pseudorotation energy profile obtained with compound C (Figure 2) can be better reconciled with the experimental data obtained from DNA and related nucleosides and nucleotides, as compared with compounds A and B. Compound C is itself a nucleoside analogue, differing from natural nucleosides only by the replacement of a standard purine or pyrimidine base by an imidazole moiety. The location of the north energy minimum MP2 at both the HF (PHF ) 13.1°) levels is n ) 17.4°) and MP2 (Pn in reasonable agreement with the A DNA modal value, deviating from it by 0.6° and 4.9°, respectively. The south energy minimum is also in better agreement with the B DNA modal MP2 value of 158.0° at both the HF (PHF s ) 161.6°) and MP2 (Ps HF MP2 ) 167.2°) levels. Although Ps and Ps in compound C deviate from 158.0°, they are in the range of pseudorotation angles that are populated in B DNA. Note that the calculated Ps values are both higher than the B DNA modal value. This result is consistent with the imidazole being more similar to a purine than to a pyrimidine, and the higher pseudorotation angles seen in purines versus pyrimidines (Figure 3). In the HF and MP2 calculations with compound C, χ values are 204.4° and 205.2° in the north conformation, respectively, and 234.5° and 234.8° in the south conformation, respectively. These values are in good agreement with experimental data, showing that both the HF and MP2 calculations provide a reasonable representation of the known correlation between the sugar pucker and the glycosidic torsion (see section on experimental reference data). To further assess the relevance of the calculated results on compound C to experiment, the bond lengths (Table 2), valence angles (Table 3), and amplitude of puckering (Table 4) can be compared with the corresponding average geometries derived from high-precision crystal structures of nucleosides and nucleotides.7 Note that the calculated structures represent in vacuo conditions at 0.0 K, so that even ideal calculations are not expected to yield bond lengths and valence angles identical to their crystal counterparts. However, the crystal standard deviations on the bond lengths and valence angles (Table 2 and Table 3, from Gelbin et al.7) provide a range from which the calculated properties should not depart significantly. Average differences between the ab initio and crystal bond lengths are 0.017 Å (south) and 0.019 Å (north) at the HF level, and 0.008 Å (south) and 0.007 Å (north) at the MP2 level. It is
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 carbonheteroatom bond lengths in compound C are systematically shorter than their crystal counterpart, as expected.19 The better agreement of the MP2 calculations and the crystal geometries, as compared with the HF calculations, is also apparent when scrutinizing the valence angles (Table 3). The average differences between the ab initio and crystal valence angles are 1.1° (south) and 1.2° (north) at the HF level, and 1.0° at the MP2 level in both the north and south conformations. Except for C2′-C3′-C4′ in the north conformation, all the endocyclic valence angles calculated at the MP2 level fall within the corresponding crystal standard deviation. At the HF level, however, five out of six of the endocyclic valence angles involving O4′ fall outside their experimental standard deviation range. Whether calculated at the HF or at the MP2 level, a majority of the exocyclic valence angles fall within the corresponding experimental standard deviation. Overall, there is close agreement between both the MP2 calculated bond lengths and valence angles and their experimental counterparts. Both the HF and MP2 calculated puckering amplitudes (Table 4) in compound C are in reasonable agreement with their crystal equivalents, falling within the crystal standard deviations. In the north conformation, the HF and MP2 calculated amplitudes differ from the crystal average values by 0.2° and 0.8°, respectively, and in the south conformation, the differences are 2.3° and 1.3°, respectively. It is noticeable, however, that the MP2 amplitudes reflect the experimentally observed decrease of amplitude in the south versus the north conformation, although the opposite trend occurs in the HF results. Overall, the geometric properties of compound C calculated at the MP2 level are in reasonable agreement with experimental results. The agreement between experimental and calculated geometries is significantly better when these properties are calculated at the MP2 level than when calculated at the HF level. The second type of experimental information to test the validity of compound C as a model regards the relative energies of the north and south conformations. Consistent with the experimentally observed preference of deoxyribonucleosides and deoxyribonucleotides for the south conformation, both the HF and the MP2 calculations indicate the south energy minimum to be more stable than the north in compound C, with the MP2 energy difference (∆EMP2 ) 1.2 kcal/mol) larger than the HF value (∆EHF ) 0.9 kcal/mol). If the sugar conformational space is reduced to a very simple two-state model where only the energy minima are populated, a Boltzmann analysis at 298.0 K indicates statistical weights in the north (Wn) and south (Ws) HF MP2 ) 0.1 energy minima of WHF n ) 0.2 and Ws ) 0.8, or Wn MP2 and Ws ) 0.9, when derived from the HF or MP2 energies, respectively. Although this approximation is coarse, it indicates that the energy profile obtained from compound C yields energetic values that are in the range of what is observed experimentally. Interestingly, the NMR study that measured a 80:20 south:north ratio20 was performed with a purine (adenine) deoxyribonucleoside, in line with compound C being a purine deoxyribonucleoside analogue and with the obtained south:north statistical weights. Thus, the energetics properties of compound C are consistent with experimental data on the relative stabilities 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′ C2′sC3′ C3′sC4′ C4′sO4′ O4′sC1′ C3′sO3′ C4′sC5′ C1′sN C5′sO5′
1.518 1.516 1.529 1.446 1.420 1.435 1.512 1.468 1.418
0.010 0.008 0.010 0.010 0.011 0.013 0.007 0.014 0.025
1.529 1.523 1.535 1.412 1.398 1.408 1.515 1.438 1.404
1.527 1.520 1.530 1.439 1.425 1.432 1.513 1.445 1.429
1.519 1.518 1.521 1.449 1.418 1.419 1.509 1.488 1.423
0.010 0.012 0.010 0.009 0.012 0.006 0.011 0.013 0.011
1.535 1.527 1.524 1.412 1.394 1.400 1.512 1.450 1.402
1.530 1.527 1.522 1.439 1.422 1.424 1.509 1.458 1.427
1.541 1.537 1.536 1.403 1.391 1.405 1.513 1.439 1.402
1.540 1.535 1.535 1.430 1.417 1.431 1.512 1.449 1.429
a lcrys refers to the average values obtained from statistical analysis (standard deviation σcrys) of crystal structures of nucleosides and nucleotides (Gelbin et al.7). 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′ C2′sC3′sC4′ C3′sC4′sO4′ C4′sO4′sC1′ O4′sC1′sC2′ C2′sC3′sO3′ C4′sC3′sO3′ C5′sC4′sC3′ C5′sC4′sO4′ O4′sC1′sN C2′sC1′sN O5′sC5′sC4′ C1′sN9sC4
102.5 103.1 106.0 110.1 105.9 109.4 109.7 114.1 109.3 108.0 114.3 110.9 126.3
1.2 0.9 0.6 1.0 0.8 2.5 2.5 1.8 1.9 0.7 1.4 1.7 1.2
102.1 102.5 106.3 112.0 105.0 111.9 106.8 114.6 109.4 109.5 115.0 109.3 126.9
101.8 102.6 106.3 110.1 105.5 111.5 115.6 114.4 109.1 108.2 114.1 108.4 127.0
102.4 102.2 104.5 110.3 106.8 112.6 112.3 115.7 109.8 108.3 112.6 111.0 123.9
0.8 0.7 0.4 0.7 0.5 3.3 2.0 1.2 1.1 0.3 1.9 2.5 1.0
102.8 101.1 105.0 112.1 106.1 114.8 109.0 116.1 110.0 109.1 113.9 109.6 125.5
102.4 100.9 105.3 110.0 106.2 115.0 108.0 115.7 109.6 108.6 112.8 108.7 125.3
104.7 103.8 106.4 110.4 105.9 114.4 107.6 115.1 108.8 108.1 114.9 108.9 127.0
105.8 104.8 107.9 111.1 107.3 114.0 106.3 113.8 107.6 106.9 113.4 107.6 127.1
aθ crys refers to the average values obtained from statistical analysis (standard deviation σcrys) of crystal structures of nucleosides and nucleotides (Gelbin et al.7); 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 Moiety in Compounds C and E in the South, North, and O4′ Endo Conformationsa conformation south north O4′ endo
crys 36.2 37.3 na
σcrys 3.3 2.4 na
CHF 36.0 35.0 31.0
CMP2
E
37.0 38.6 18.1
33.4b/38.9c 39.3 21.1
a crys refers to the average values (standard deviation σ crys) obtained from statistical analysis of crystal structures of nucleosides and nucleotides (Gelbin et al.7). C and E refer to the model compounds shown in Figure 1. No average crystal amplitudes are available for the O4′ endo conformation. CHF and CMP2 are the amplitudes obtained at the HF and MP2 levels of theory, respectively, for compound C. The two amplitudes reported for compound E in the south conformation correspond to the situation where was confined to an RNA-like conformation (b), and the situation where the 3′-OH group was allowed to donate a proton to O2′ (c).
and B are not as consistent. This result strongly suggests that a nucleoside (or a nucleoside analogue) is the minimal chemical entity required to model the conformational properties of the sugar in nucleic acids or their components. Compound D. Because the elementary building block of DNA is a nucleotide, the deoxyribose conformational energetics were also investigated with compound D, a 3′-nucleotide analogue. Compound D has been investigated only at the HF level of theory because of computational limitations. An interesting feature of the compound D pseudorotation energy profile (Figure 2) is the broad south energy well, which is centered around an energy minimum (PHF s ) 153.8°) deviating from PB by 4.2°. The energy remains within ∼1.0 kcal/mol of
the minimum energy for pseudorotation angles in the range ( 30.0°, in good agreement with the B DNA crystal PHF s pseudorotation angle distribution (Figure 2). The location of the north energy minimum (PHF ) 18.4°) is in excellent n agreement with PA. However, the energy difference (∆EHF ) 5.0 kcal/mol) between the north and south energy minima is surprisingly large, and cannot be reconciled with the experimental data mentioned previously. This discrepancy may partly be explained by the energy profile for compound D being obtained with the 5′-β torsion angle (H-O5′-C5′-C4′) fixed at 180.0°. This situation prevents formation of an intramolecular hydrogen bond between the 5′ hydroxyl group and the 3′ phosphate moiety. Formation of this hydrogen bond when compound D is energy minimized with an unconstrained 5′-β torsion brings the north energy minimum 6.6 kcal/mol lower in energy than the south energy minimum. The magnitude of the energy change illustrates the pitfalls associated with increasing the complexity of the model compound. Possibly, a 3′,5′bisphosphate nucleotide may avoid this problem, however, calculations on such a system are computationaly prohibited at this time. An additional difficulty with compound D is that, although remains in the 190° range in the north energy minimum region, it adopts values in the range of 270° in the south energy minimum region. Difficulties associated with the additional degrees of freedom, combined with a significantly increased computational burden, make compound D less attractive than compound C as a model of the sugar conformational energetics in nucleic acids. Thus, of the results in the present study, those obtained at the MP2/
A Quantum Mechanical Study 6-31G* level with compound C can be regarded as the most reliable computed estimate of the deoxyribose intrinsic energetics in DNA. Model compound C indicates that the deoxyribose favoring the south conformation in condensed phase in nucleosides and nucleotides may be driven, in part, by the intrinsic energetics of the sugar and its direct substituents. This intrinsic energetics may also be an important factor in stabilizing the B form of DNA over a wide range of solvent conditions.1 Furthermore, the intrinsic north/south energy difference is small enough for the deoxyribose to also populate the north conformation in DNA, allowing for DNA polymorphism. Even in B DNA in solution, the deoxyribose is likely to populate the north conformation, in agreement with a growing body of experimental evidence.11,12,14 3.2. Energy Barriers Between the Deoxyribose North and South Conformations. Although the relevance of the computed properties for the north and south energy minima can be assessed by comparison with available experimental data, experimental observations that can be directly related to the energy barrier between these two energy minima are more elusive. The quality of the agreement between the MP2 calculated and experimental structural and energetics properties for compound C suggests that the MP2 calculations should yield useful information for conformations of the furanose for which experimental information is scarce. The conformations representing energy barriers between the north and south energy minima are of particular interest, and are discussed based on results for compound C. As seen in Figure 2, the present sampling of the pseudorotation energy surface locates the east energy barrier in the O4′ endo conformation in both the HF and MP2 calculations. The MP2 calculations predict a significant flattening of the deoxyribose in the O4′ endo conformation (Table 4), with an amplitude of 18.1° and a systematic opening of all the furanose endocyclic valence angles (Table 3). Calculations at the HF level also predict a flattening in the O4′ endo conformation, although to a lesser extent than what is obtained at the MP2 level. Strain associated with the flattening of the furanose ring may contribute to the significant O4′ endo energy barrier. Both the HF (BHF ) 2.7 kcal/mol) and MP2 (BMP2 ) 4.4 kcal/mol) calculated barriers for compound C fall in the expected 2.0-5.0 kcal/mol range,9 while remaining lower than what has been measured for the purine ribonucleosides.10 As noted previously, the energy barrier is expected to be higher in ribosebased compounds than in the deoxyribo analogues.9 The MP2 calculated energy barrier for compound C is significantly higher than the 1.8 kcal/mol estimate of Olson8 and is closer to the 4.7 kcal/mol measured by Ro¨der et al.10 Using nucleosides and the PCILO semiempirical quantum mechanical method, Saran et al.15 predicted an east energy barrier on the order of 4.0 kcal/ mol. However, the current MP2 treatment combined with the 6-31G* basis set used in the present study is more reliable than the PCILO method. Furthermore, Saran et al.15 carried out their calculations with fixed bond lengths and constrained ring valence angles and amplitudes. The usefulness of the present reexamination of the east energy barrier should be seen in this context. Although the O4′ exo conformation associated with the west energy barrier implies a dramatic reorientation of torsion angle χ (see compound B), this is not the case in the inversion mechanism, which proceeds through a furanose structure where all five ring atoms are coplanar. It is therefore of interest to compare the energy barrier associated with the inversion mechanism with that from the pseudorotation east energy barrier.
J. Phys. Chem. B, Vol. 102, No. 34, 1998 6675 In theoretical studies of the furanose presented to date, the inversion barrier has been found higher in energy than the energy barriers along the pseudorotation pathway.23,24 The HF and MP2 energy barriers associated with a coplanar furanose in compound C are 3.9 and 5.0 kcal/mol, respectively. Hence, the present calculations confirm that the inversion mechanism in deoxyribose is more unfavorable than pseudorotation through the east barrier (Table 1). Because the energy difference between the east and inversion barriers is only 0.6 kcal/mol in the present MP2 calculation, it cannot be concluded that the inversion mechanism is forbidden. The location of the point of highest energy along the inversion path in a substituted furanose, however, does not necessarily coincide with the coplanar conformation of the furanose, possibly leading to a higher inversion barrier. 3.3. Influence of the 2′-OH Group in ribose. The extra 2′-OH group in ribose (compound E, Figure 1), as compared with deoxyribose, significantly complicates the conformational analysis. Indeed, the 2′-OH group can adopt a number of conformations, with the possibility of intramolecular hydrogen bonds, which may or may not be relevant to the situation in RNA. Clearly, an intramolecular hydrogen bond where the 3′ hydroxyl is the hydrogen donor and the 2′ hydroxyl the acceptor does not pertain to RNA structures, except at the 3′ termini. Because the present work is primarily concerned with the energetics of the sugar in nucleic acids, most of the present calculations have been performed with (H3′-O3′-C3′-C4′) in the trans conformation, disallowing formation of a hydrogen bond where the 3′-OH group is a donor. Experimental methods alone are generally unable to unambiguously locate the positions of the 2′-OH hydrogen in RNA. Examination of a number of experimental structures combined with molecular dynamics results, however, suggests that the 2′OH bond points preferentially toward the O3′ oxygen of the same residue.25b Accordingly, energy minimizations of compound E were initiated with H2′-O2′-C2′-C3′ in the g+ conformation. In the north energy minimum, the south energy minimum, and the O4′ endo conformation, H2′-O2′-C2′-C3′ is equal to -35.0°, 50.6°, and 26.7°, respectively, and is equal to 205.0°, 202.3°, and 197.8°, respectively. In all three conformations, the O3′ to H2′ distances (north: 2.07 Å, south: 2.23 Å, O4′ endo: 2.01 Å) are indicative of some hydrogenbond character. Visual inspection of the orientation of the 2′OH bond relative to O3′, however, suggests that the resulting hydrogen bond is better formed in the north energy minimum and in the O4′ endo conformation than in the south energy minimum. Calculated bond lengths and valence angles for compound E are listed in Table 5 and Table 6, respectively, together with their crystal counterparts. The average differences between the ab initio and crystal bond lengths are 0.007 Å in both the north and the south conformations. The average differences between the ab initio and crystal valence angles are 1.2° and 1.0° in the north and south conformations, respectively. Most of the calculated bond lengths and valence angles fall within the corresponding crystal standard deviation (Tables 5 and 6). In the north energy minimum, the ribose in compound E is slightly more puckered (Table 4) than the deoxyribose in compound C, which is in agreement with the trend observed in crystal structures.7 In the south energy minimum, however, the ribose in compound E is flatter than the deoxyribose in compound C and flatter than what is observed in crystal structures.7 This discrepancy disappears if one takes into consideration a south 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 in the South, North, and O4′ Endo Conformationsa south
north
O4′ endo
bond
lcrys
σcrys
lai
lcrys
σcrys
lai
lai
C1′sC2′ C2′sC3′ C3′sC4′ C4′sO4′ O4′sC1′ C3′sO3′ C4′sC5′ C2′sO2′ C1′sN C5′sO5′
1.526 1.525 1.527 1.454 1.415 1.427 1.509 1.412 1.464 1.424
0.008 0.011 0.011 0.010 0.012 0.012 0.012 0.013 0.014 0.016
1.537 1.530 1.527 1.444 1.419 1.437 1.513 1.413 1.441 1.429
1.529 1.523 1.521 1.451 1.412 1.417 1.508 1.420 1.483 1.420
0.011 0.011 0.010 0.013 0.013 0.014 0.007 0.010 0.015 0.009
1.529 1.523 1.523 1.437 1.422 1.430 1.509 1.419 1.454 1.427
1.547 1.552 1.532 1.431 1.416 1.434 1.512 1.414 1.444 1.427
al crys refers to the average values obtained from statistical analysis (standard deviation σcrys) of crystal structures of nucleosides and nucleotides (Gelbin et al.7), and lai is the counterpart in the MP2 ab initio calculations. No average crystal bond lengths are available for the O4′ endo conformation.
TABLE 6: Valence Angles (deg) for the Ribose Moiety in Compound E in the South, North, and O4′ Endo Conformationsa south
north
O4′ endo
angle
θcrys
σcrys
θai
θcrys
σcrys
θai
θai
C1′sC2′sC3′ C2′sC3′sC4′ C3′sC4′sO4′ C4′sO4′sC1′ O4′sC1′sC2′ C1′sC2′sO2′ C3′sC2′sO2′ C2′sC3′sO3′ C4′sC3′sO3′ C5′sC4′sC3′ C5′sC4′sO4′ O4′sC1′sN C2′sC1′sN O5′sC5′sC4′ C1′sN9sC4
101.5 102.6 106.1 109.7 105.8 111.8 114.6 109.5 109.4 115.2 109.1 108.2 114.0 111.7 127.4
0.8 1.0 0.8 0.7 1.0 2.6 2.2 2.2 2.1 1.4 1.2 0.8 1.3 1.9 1.2
102.0 103.5 106.9 110.3 106.3 113.1 113.7 108.9 108.0 113.5 108.4 108.4 114.0 107.5 127.0
101.3 102.6 104.0 109.9 107.6 108.4 110.7 113.7 113.0 116.0 109.8 108.5 112.0 111.5 126.3
0.7 1.0 1.0 0.8 0.9 2.4 2.1 1.6 2.0 1.6 0.9 0.7 1.1 1.6 2.8
102.0 101.1 104.7 110.1 106.7 107.6 109.0 115.2 109.0 115.2 109.4 108.6 112.5 108.6 125.5
104.5 105.2 107.7 110.7 107.8 112.4 112.2 111.3 107.2 113.8 107.3 106.7 113.4 107.2 126.9
k
aθ crys refers to the average values obtained from statistical analysis (standard deviation σcrys) of crystal structures of nucleosides and nucleotides (Gelbin et al.7), and θai is the counterpart in the MP2 ab initio calculations. No average crystal valence angles are available for the O4′ endo conformation.
Figure 4. Pseudorotation energy profile obtained at the MP2 level for compound E.
conformation that is not compatible with RNA structure but is possible in nucleosides and 5′-nucleotides (vide infra). As in the MP2 calculations on compound C, compound E shows a marked flattening of the furanose in the O4′ endo conformation, although to a lesser extent than in the deoxy compound. The pseudorotation energy profile for compound E is shown in Figure 4. The north and south energy minima are located at Pn ) 15.5° and Ps ) 164.2°, respectively, and the east energy barrier is located at the O4′ endo conformation. The location of the energy minima are only slightly shifted relative to their deoxyribose counterparts (compound C, Table 1), but their relative energies are reversed. The north conformation in
compound E is 2.3 kcal/mol more stable than the south conformation. Of particular interest is the magnitude of this energy difference, which not only favors the north conformation but makes the south conformation unlikely at room temperature. This result contrasts the corresponding energy difference in compound C, which favors the south conformation but does not preclude the north conformation at room temperature. These results suggest that the intrinsic conformational energetics of the sugar moiety in nucleic acids may be related to the observation that DNA can exist in both the A and B forms of double helices, whereas RNA is restricted to the A form. Ribose favoring the north conformation over the south in RNA by as much 2.3 kcal/mol may seem to contradict a number of experimental studies on nucleosides and nucleotides. NMR studies of nucleosides4,20,21 and 5′-nucleotides5 in aqueous solution have found that, although ribose favors the north conformation more than deoxyribose, ribose still significantly populates the south conformation. In the statistical analysis of crystal structures of nucleosides and nucleotides of Gelbin et al.,7 24 ribose compounds were found in the north conformation and 49 in the south. It is, however, difficult to extrapolate these observations to the relative stabilities of the north and south conformations of the ribose in RNA because, in nucleosides and 5′-nucleotides, the 2′ and 3′-OH groups may adopt orientations that favor the south conformation but cannot exist in RNA. To test this hypothesis compound E was energy minimized at the MP2 level of theory in the south conformation with the 3′-OH group allowed to donate its proton to the 2′-O, a situation that is relevant only to nucleosides and some nucleotides but not to RNA. In this structure, the values of torsions H3′-O3′C3′-C4′ and H2′-O2′-C2′-C3′ are 155.3° and 183.3°, respectively. This conformation of compound E is 0.2 kcal/ mol more stable than the north energy minimum with in an RNA-like conformation. Furthermore, the amplitude of puckering with the 3′-OH group donating its proton to the 2′-O is 38.9°, in significantly better agreement with the crystal structures of ribonucleosides and ribonucleotides as compared with the amplitude calculated in the south conformation with in an RNA-like conformation (Table 4). This result indicates that the present calculations are compatible with the properties observed experimentally for RNA components. The present 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 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 barrier would be approximately 2.0 kcal/mol higher in ribose than in deoxyribose. The major contribution to the increased barrier in ribose was the van der Waals repulsion between the 2′ and 3′ eclipsed hydroxyl groups.8 The east energy barrier in compound E is 5.0 kcal/mol in the present calculations, in close agreement with the value obtained experimentally (4.7 ( 0.5 kcal/mol) by Ro¨der et al.10 for purine ribonucleosides. This agreement confirms that the east energy barrier is higher in ribose than in deoxyribose (Table 1) and that it is located at, or close to, the O4′ endo conformation (Figure 4). However, the east energy barrier in compound E is only 0.6 kcal/mol higher than in compound C. This result indicates that although the O4′ endo conformation forces the 2′- and 3′-OH groups to be eclipsed, the interaction between them is not as repulsive as
A Quantum Mechanical Study previously described.8 In the O4′ endo structure the 2′-OH bond is pointing toward the O3′ oxygen and the distance between the 2′-OH proton and the O3′ oxygen is 2.02 Å, suggesting that hydrogen bonding is occurring between the two hydroxyl groups. The energy of compound E with a coplanar furanose (inversion mechanism) at the MP2 level is 0.8 kcal/mol higher than the east energy barrier. 4. Conclusions Results have been presented on a variety of model compounds designed to investigate the energetics of sugar puckering in nucleic acids using high-level ab initio calculations. Calculated properties for four compounds (A-D) with increasing nucleic acid structural features were compared with a variety of experimental data. It should be reiterated that the present in vacuo potential energies are being compared with experimental distributions that correspond to free energies in the condensed phase. The present results strongly suggest that a previously used8,16 model (compound A), substituting the base with an amino group and lacking a 5′-OH group, is not appropriate to model the furanose ring in nucleic acids. Previous conclusions drawn using this model compound should be viewed in this context. Replacement of the amino group by an imidazole, without adding a 5′-OH group (compound B), yielded calculated properties in better agreement with experiment, although the agreement was still poor. Inclusion of all the structural features of a nucleoside (compound C) yielded significantly better agreement with experiment, satisfactory enough to suggest that a nucleoside is the minimal unit to consider when modeling the conformational energetics of the sugar moiety in nucleic acids. Using a nucleotide (compound D) involves additional torsional degrees of freedom that significantly complicate the modeling of the sugar conformational properties, in addition to the increased computational burden. The agreement between experimental and calculated geometries is significantly better when the geometries are calculated at the MP2 level compared with the HF level. Furthermore, comparison of the pseudorotation energy profiles calculated at the HF and MP2 levels of theory show that they can differ significantly. These differences are apparent in the locations of the energy minima (compounds A and B, Table 1) and in the height of the energy barriers (compounds B and C, Table 1). These results document the possible shortcomings of using the HF level of theory when investigating the sugar moieties in nucleic acids, including modified sugars. Although the properties discussed in the present work are expected to be modulated by the type of base linked to the sugar, calculations at the MP2 level on compounds C and E suggest the following conclusions. The present work confirms that the intrinsic energetics of deoxyribose favors the south conformation over the north, and provides a quantitative estimate on the order of 1.0 kcal/mol for this energy difference. Thus, the deoxyribose intrinsic energetics are an important factor in stabilizing the B form of DNA, but are also compatible with DNA structures containing the north conformation of the sugar. As illustrated by this work, the presence an additional hydroxyl group tremendously complicates the conformational analysis of the ribose as compared with deoxyribose. When hydroxyls are allowed to orient relative to each other without conditions, as can occur in a nucleoside, the south conformation is found to be slightly more stable than the north, with an energy difference (0.2 kcal/mol) less than that found in the deoxyribose. Treating the ribose in an RNA context puts some conditions on the relative orientations of the 2′- and 3′-OH groups, which
J. Phys. Chem. B, Vol. 102, No. 34, 1998 6677 significantly changes the north/south relative energies. When mimicking the RNA situation by preventing the 3′-OH group to act as an hydrogen-bond donor, the north conformation of the ribose is more stable than the south, by an energy difference on the order of 2.0 kcal/mol. This difference suggests that the contribution of the ribose intrinsic energetics in stabilizing the A form of RNA may be significant. It has been argued that RNA double helices do not adopt the B form because the ribose 2′-OH group would sterically clash with other parts of the B helix.16 However, the present calculations suggest that the intrinsic energetics of ribose may be an important factor in confining RNA to the A form. Interestingly, B RNA has been found to be stable in some molecular dynamics simulations on the 1-2 ns time scale.25a Such stability suggests that very unfavorable steric clashes between the ribose 2′-OH and other parts of the B helix might not be the primary reason why RNA does not adopt the B form in nature. The present work also provides new insights concerning the energetics and structure of the conformations at the east energy barrier between the north and south energy minima. The values obtained for the east barrier fall in the higher limit of the 2.0 to 5.0 kcal/mol range previously suggested.9 The east barrier in deoxyribose (4.5 kcal/mol) is lower than in ribose (5.0 kcal/ mol), but only by a small difference. In both deoxyribose and ribose, the east energy barrier along the pseudorotation pathway is lower in energy than the barrier associated with an inversion mechanism. The present results also indicate that the furanose amplitude decreases significantly when crossing the east barrier, in both deoxyribose and ribose. Interrelationships between the furanose pseudorotation angle, amplitude, bond lengths, and valence angles have been analyzed26 and led to the proposal that pseudorotation may proceed through the O4′ endo conformation with variable amplitudes. To date, this proposal has not been clearly substantiated due to the lack of high precision structures of nucleic acids constituents in this conformation.7 The present calculations provide direct evidence that the pseudorotation path of lowest energy between the north and south energy minima probably involves a significant variation in the furanose ring amplitude. An important application of the present analysis is the calibration of nucleic acids molecular mechanics force fields. Force field based theoretical approaches have become increasingly powerful for the study of DNA structure and dynamics in solution.25,27,28 Current tests of these methods, however, demonstrate that for DNA simulations to realize their full potential, further improvement of the underlying force fields are necessary.29,30 The available force fields are still in partial disagreement with experiment in their representation of the equilibrium between the A and B forms of DNA.29 In particular, the delicate balance between the A and B forms of the sugar ring is still not adequately modeled.25,27,29,31 It has been noted that a more accurate representation of the energy barrier between the north and south energy minima in nucleic acid force fields is of crucial importance to obtain more reliable theoretical models of the structure and dynamics of nucleic acids.25 The east energy barrier in an adenine nucleoside has been reported to be 2.9 kcal/mol (dielectric constant of 1.0) in the AMBER force field,32 and is 1.8 kcal/mol in Version 2233 of the CHARMM force field (unpublished result). This suggests that the value of this barrier in the current versions of these force fields may be too low. The energy profiles presented here should prove useful in this respect.
6678 J. Phys. Chem. B, Vol. 102, No. 34, 1998 Acknowledgment. This work has been financially supported by NIH grant GM51501. We also thank the Pittsburgh Supercomputing Center and NCI’s Frederick Biomedical Supercomputing Center for providing computational resources. Supporting Information Available: Tables presenting the north, south, and O4′ endo MP2/6-31G* optimized Cartesian coordinates of compounds C and E (6 pages). Ordering information is given on any current masthead page. References and Notes (1) Saenger, W. Principles of Nucleic Acid Structure; SpringerVerlag: New York, 1984. (2) Dickerson, R. E.; Drew, H. R.; Conner, B. N.; Wing, R. M.; Fratini, A. V.; Kopka, M. L. Science 1982, 216, 475. (3) Altona, C.; Sundaralingam, M. J. Am. Chem. Soc. 1972, 94, 8205. (4) Altona, C.; Sundaralingam, M. J. Am. Chem. Soc. 1973, 95, 2333. (5) Davies, D. B.; Danyluk, S. S. Biochemistry 1974, 13, 4417. (6) Davies, D. B.; Danyluk, S. S. Biochemistry 1975, 14, 543. (7) Gelbin, A.; Scheider, B.; Clowney, L.; Hsieh, S.-H.; Olson, W. K.; Berman, H. M. J. Am. Chem. Soc. 1996, 118, 519. (8) Olson, W. K. J. Am. Chem. Soc. 1982, 104, 278. (9) Olson, W. K.; Sussman, J. L. J. Am. Chem. Soc. 1982, 104, 270. (10) Ro¨der, O.; Lu¨demann, H.; Von Goldammer, E. Eur. J. Biochem. 1975, 53, 517. (11) Wartell, R. M.; Harrell, J. T. Biochemistry 1986, 25, 2664. (12) Pechenaya, V. I.; Serikov, A. A. Biopolymers 1988, 27, 1817. (13) Weisz, K.; Shafer, R. H.; Egan, W.; James, T. L. Biochemistry 1992, 31, 7477. (14) Ulyanov, N. B.; James T. L. Appl. Magn. Reson. 1994, 7, 21. (15) Saran, A.; Perahia, D.; Pullman, B. Theor. Chim. Acta 1973, 30, 31. (16) Levitt, M.; Warshel, A. J. Am. Chem. Soc. 1978, 100, 2607.
Foloppe and Mackerell (17) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Raghavachari, K.; AlLaham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, 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., Pittsburgh, PA. (18) Berman, H. M.; Olson, W. K.; Beveridge, D. L.; Westbrook, J.; Gelbin, A.; Demeny, T.; Hsieh, S.-H.; Srinivasan, A. R.; Schneider, B. Biophys. J. 1992, 63, 751. (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. Tetrahedron Lett. 1979, 42, 4073. (21) Guschlbauer, W.; Jankowsky, K. Nucleic Acids Res. 1980, 8, 1421. (22) Foloppe, N.; MacKerell, A. D., Jr. manuscript in preparation. (23) Cremer, D.; Pople, J. A. J. Am. Chem. Soc. 1975, 97, 1358. (24) Cadioli, B.; Gallinella, E.; Coulombeau, C.; Jobic, H.; Berthier, G. J. Phys. Chem. 1993, 97, 7844. (25) (a) Cheatham, T. E., III.; Kollman, P. A. J. Am. Chem. Soc. 1997, 119, 4805. (b) Auffinger, P.; Westhof, E. J. Mol. Biol. 1997, 274, 54. (26) Westhof, E.; Sundaralingam, M. J. Am. Chem. Soc. 1980, 102, 1493. (27) MacKerell, A. D., Jr. J. Phys. Chem. B 1997, 101, 646. (28) Young, M. A.; Jayaram, B.; Beveridge, D. L. J. Am. Chem. Soc. 1997, 119, 59. (29) Feig, M.; Pettitt, B. M. J. Phys. Chem. 1997, 101, 7361. (30) MacKerell, A. D., Jr. Molecular Modeling of Nucleic Acids; Leontis, N. B.; SantaLucia, J., Jr., Eds.; American Chemical Society: Washington, D.C., 1988; 304. (31) Cheatham, T. E., III.; Crowley, M. F.; Fox, T.; Kollman, P. A. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 9626. (32) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M., Jr.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. J. Am. Chem. Soc. 1995, 117, 5179. (33) MacKerell, A. D., Jr.; Wio´rkiewicz-Kuczera, J.; Karplus, M. J. Am. Chem. Soc. 1995, 117, 11946.
