These preliminary recommendations were made at the Tsukuba Workshop on Nucleic Acid Structure and Interactions held on January 12-14, 1999 at the AIST-NIBHT Structural Biology Centre in Tsukuba, Japan. The meeting was funded by the COE program of the Science and Technology Agency, Japan and the CREST program of the Japan Science and Technology Corporation. The meeting was organized by Masashi Suzuki of the National Institute of Bioscience and Human-Technology and Helen M. Berman and Wilma K. Olson of the Nucleic Acid Database Project (supported by National Science Foundation (USA) grant DBI 95 10703).A common point of reference is needed to describe the three-dimensional arrangements of bases and base pairs in nucleic acid structures. . For example, parts of a structure, which appear "normal" according to one computational scheme, may be highly unusual according to another and vice versa. It is thus difficult to carry out comprehensive comparisons of nucleic acid structures and to pinpoint unique conformational features in individual structures. In order to resolve these issues, a group of researchers who create and use the different software packages have proposed the standard base reference frames outlined below for nucleic acid conformational analysis. The definitions build upon qualitative guidelines established previously to specify the arrangements of bases and base pairs in DNA and RNA structures . Base coordinates are derived from a survey of high resolution crystal structures of nucleic acid analogs stored in the Cambridge Structural Database . The coordinate frames are chosen so that complementary bases form an ideal, planar Watson-Crick base pair in the undistorted reference state with hydrogen bond donor-acceptor distances, C1'×××C1' virtual lengths, and purine N9C1'×××C1' and pyrimidine N1C1'×××C1' virtual angles consistent with values observed in the crystal structures of relevant small molecules. Conformational analyses performed in this reference frame lead to interpretations of local helical structure that are essentially independent of computational scheme. A compilation of base-pair parameters from representative A-DNA, B-DNA, and protein-bound DNA structures from the Nucleic Acid Database (NDB)  provides useful guidelines for understanding other nucleic acid structures.
Participants at the workshop included Manju Bansal (Indian Institute Science, Bangalore), Helen M. Berman (Rutgers University), Stephen K. Burley (Rockefeller University), Richard E. Dickerson (University of California, Los Angeles), Mark Gerstein (Yale University), Stephen C. Harvey (University of Alabama at Birmingham), Udo Heinemann (Max-Delbrück-Centrum), Stephen Neidle (Institute of Cancer Research), Wilma K. Olson (Rutgers University), Zippora Shakked (Weizmann Institute), Heinz Sklenar (Max-Delbrück-Centrum), Masashi Suzuki (AIST-NIBHT Structural Biology Centre), Chang-Shung Tung (Los Alamos National Laboratory), Eric Westhof (Strasbourg), and Cynthia Wolberger (Johns Hopkins University). The survey of small molecule crystal structures was performed by John Westbrook and Helen M. Berman. The optimization of standard base-pair geometry and the calculation of derived parameters were carried out by Xiang-Jun Lu and Wilma K. Olson with support from U.S.P.H.S. grant GM20861.
Base coordinates. Models of the five common bases (A, C, G, T, U) were generated from searches of the crystal structures of small molecular weight analogse.g., free bases, nucleosides, and nucleotidesin the most recent version of the Cambridge Structural Database . The internal geometries and associated uncertainties in this data set closely match numerical values reported in the recent survey of nucleic acid base analogs by Clowney et al. . Because the minor changes in chemical structure have essentially no effect on either the ideal base-pair frame or the computed rigid body parameters, the Clowney et al. bases are retained as standards.
Coordinate frame. The right-handed coordinate frame attached to each base (Figure 1) follows established qualitative guidelines . The x-axis points in the direction of the major groove along what would be the pseudo-dyad axis of an ideal Watson-Crick base pair, i.e., the perpendicular bisector of the C1'×××C1' vector spanning the base pair. The y-axis runs along the long axis of the idealized base pair in the direction of the sequence strand, parallel to the C1'×××C1' vector, and displaced so as to pass through the intersection on the (pseudo-dyad) x-axis of the vector connecting the pyrimidine Y(C6) and purine R(C8) atoms. The z-axis is defined by the right-handed rule, i.e., z = x ¥ y. For right-handed A- and B-DNA, the z-axis accordingly points along the 5'- to 3'-direction of the sequence strand.
Figure 1 Illustration of idealized base-pair parameters, dC1'×××C1' and l, used respectively to displace and pivot complementary bases in the optimization of the standard reference frame for right-handed A- and B-DNA, with the origin at · and the x- and y-axes pointing in the designated directions.
The location of the origin depends upon the width of the idealized base pair, i.e., the C1'×××C1' spacing, dC1'×××C1', and the pivoting of complementary bases, l, in the base-pair plane (see Figure 1). The coordinates of the C1' atoms establish the pseudo-dyad axis, i.e., the line in the base-pair plane where y = 0. The rotations of each base about a normal axis passing through the C1' glycosyl atoms determine the Y(C6) and R(C8) positions used to define the line where x = 0.
Optimization. The atomic coordinates in Table 1 are expressed in the base-pair reference frames which optimize hydrogen-bond donor-acceptor distances, dHB, and base "pivot" angles, lY and l R, against corresponding standards (d0 = 3.0 Å and l0 = 54.5°). The departures from ideality are measured by the sum of the absolute values of the relative deviations,
where the last term runs over two (T×A) or three (C×G) hydrogen bonds. (Optimization in terms of the sum of the squares of the relative deviations of the lY, lR, and dHB yields similar results.) Virtual distances and angles characterizing the optimized configurations are detailed in Table 2. The minor changes in chemical bonding between T versus C and A versus G in combination with the constraints of two or three hydrogen bonds, give rise to slightly different standard orientations of T×A and C×G base pairs (compare dC1'×××C1', l Y, and lR values in Table 2). Notably, the hydrogen bonds closer to the minor groove edges of all base pairs are shorter than those nearer the major groove edges, as is observed in high resolution structures of Watson-Crick base-pair co-crystal complexes [6,7]. The hydrogen bonds are slightly shorter on average in the small molecule analogs, which are in turn distorted to a small degree from the perfectly planar base-pair geometry assumed here (see  and Table 2 for numerical values). Minor changes in the imposed configurational constraints have almost no influence on the preferred base-pair arrangements, e.g., the increase of l0 from 54.5° to 55.5° shortens dC1'××× C1' by less than 0.1 Å and perturbs hydrogen bond lengths by less than 0.05 Å. The assignment of different rest states for N×××H-N versus O×××H-N hydrogen bonds consistent with the hydrogen bonding observed in the crystal structures of small organic compounds [9-11], e.g., d N××× H-N 3.0 Å and d O××× H-N = 2.9 Å, fails to reproduce the trends in hydrogen bond lengths noted above. These differences in standard configurations also have a slight effect on derived complementary base-pair parameters in representative oligonucleotide structures, but virtually no effect on base-pair step parameters.
Computational independence. Local complementary base-pair and dimer step parameters computed with respect to the standard reference frames are nearly independent of analytical treatment (Figure 2). The only significant discrepancies in derived values, illustrated here for the DNA complexed with the TATA-box binding protein (TBP) , involve the Rise at highly kinked base-pair steps, which, as noted previously , reflects an inconsistency in definition. The small differences in Slide, Tilt, and Twist in this example stem from minor differences in definition and in the choice of "middle frame."
Figure 2 Comparative analysis of local base-pair (left) and dimer step (right) parameters (see schematic insets for definitions) of the DNA associated with the yeast TATA-box binding protein (TBP) in the 1.8 Å X-ray crystal complex  (NDB entry:pdt012). Parameters are calculated with the seven different analysis schemes within 3DNA (Lu & Olson, in preparation) using the standard reference frame detailed in Tables 1 and 2. Dotted line connects Rise values computed using the Curves definition . Numerical values are tabulated at the following URL: http://rutchem.rutgers.edu/~olson/Tsukuba
Base-pair geometry in high resolution A-DNA and B-DNA crystal structures similarly shows limited dependence on computational methodology. The average values and dispersion of individual parameters in Table 3 are representative of numerical values obtained with the algorithms used in many nucleic-acid-analysis programs. A complete listing of local A- and B-DNA parameters, expressed in terms of the standard reference frame and computed within 3DNA (Lu & Olson, in preparation) using the mathematical definitions of several different programsCEHS/SCHNAaP[13,14]CompDNA [15,16], Curves [17,18], FREEHELIX , NGEOM [20,21], NUPARM [22,23], and RNA [24-26], is reported at our website (see below). Since the angular parameters differ by no more than 0.1° and most distances by 0.02 Å or less, the general trends in the table can be used in combination with the characteristic patterns of A- and B-DNA backbone and glycosyl torsion angles  to classify local, right-handed, double helical conformations.The subtle mathematical differences among nucleic-acid-analysis programs, however, become critical in the construction of DNA models. Seemingly minor numerical discrepancies can be magnified in polymeric chains  and in knowledge-based potentials  derived from the fluctuations and correlations of structural parameters. Duplex models and simulations must accordingly be based on the algorithm from which parameters are derived. Conformational classification. The average values of Roll, Twist, and Slide in Table 3 confirm conformational distinctions known since the earliest studies of A- and B-DNA crystal structures [30,31]. Namely, the transformation from B- to A-DNA tends to decrease Twist, increase Roll, and reduce Slide. The standard deviations in recently accumulated crystallographic data, however, show that only Slide retains the discriminating power anticipated previously. Values of Slide below 0.8 Å are typical of most A-DNA dimer steps and those greater than 0.8 Å are found in the majority of B-forms. Slide is also more variable in B-DNA vs. A-DNA dimer steps. The observed Twist and Roll angles, by contrast, show significant overlaps over a broad range of values. Specifically, Twist angles between 20° and 40° and Roll angles between 0° and 15° are found in both A- and B-DNA structures. The values of Twist and Roll are coupled with changes in Slide so that conformational assignments should be made in the context of all three parameters . The three remaining step parameters and the six complementary base-pair parameters are unaffected by helical conformation. The mean values and scatter of these values are roughly equivalent in high resolution A- and B-DNA structures (Table 3). The constraints of hydrogen bonding presumably give rise to the more limited variations in Opening and Stretch compared to other complementary base-pair angles and distances. Buckle, while fixed on average at zero, shows more pronounced fluctuations than Propeller, which is decidedly perturbed from ideal, i.e., 0°, planar geometry in all double helical structures. Helical parameters. Parameters relating consecutive residues with respect to a local helical axis can be computed using CompDNA [15,16], NUPARM [22,23], RNA [24-26], and 3DNA (Lu & Olson, in preparation), or in terms of a global axis with CEHS  (as implemented in the SCHNAaP software package ), NEWHELIX , and Curves [17,18]. These angles and distances depend on how the helical axis is defined, particularly in deformed segments of the double helical structure . The local helical parameters of high resolution A- and B-DNA structures in Table 3 complement the dimeric descriptions of these structures. The x-displacement shares the same discriminating power as Slide in differentiating A-DNA from B-DNA, as anticipated from model building , whereas Inclination and Helical Twist span overlapping ranges of values. The different mathematical definitions of local helical parameters yield numerical similarities equivalent to those found with dimer step parameters. Global helical parameters, which reflect a best-fit linear or overall curved molecular axis, are not necessarily comparable with these values (data not shown). Intrinsic correlations. As is well known [1,25], dimer step parameters depend on the choice of base-pair reference frame and can be significantly perturbed by distortions of complementary base-pair geometry. The base-pair reference frame in most nucleic-acid-analysis programs is an intermediate between the coordinate frames of the constituent bases . The origin of this "middle frame" is shifted by significant distortions in Buckle and Opening, while the long y-axis is rotated by perturbations of base-pair Shear and Stagger (Figure 3). These changes, in turn, influence the step parameters describing the orientation and positions of neighboring base pairs.
Figure 3 Schematic illustrations and scatter plots of the intrinsic correlations of A- and B-DNA base-pair and dimer step parameters associated with the standard reference frame. Large distortions of Buckle and Opening move the origin (·) of the base-pair reference frame, while significant changes in Shear and Stagger reposition the long y-axis () of the base-pair frame.
The effects of complementary base-pair deformations on dimer step parameters are most pronounced when perturbations of the same type, but of the opposite sense, occur in successive residues, i.e., Buckle, Opening, Shear, or Stagger is negative at base pair i and positive at base pair i+1 or vice versa. For example, a large negative difference in the buckle of consecutive base pairs, Buckle = Buckle(i+1) Buckle(i), sometimes called Cup , adds to the computed base-pair Rise of "extreme" dimer steps of high resolution A- and B-DNA crystal structures (Figure 3). Similarly, a large positive value of Opening increases Shift, while large negative values of Stagger and large positive values of Shear respectively enhance Tilt and Twist. Conversely, Rise, Shift, Tilt, and Twist can be depressed, respectively, by large +Buckle, Opening, +Stagger, and Shear (Figure 3). On the other hand, Roll and Slide are not appreciably influenced by base-pair deformations.Thus, extreme values of base-pair step parameters may simply reflect distorted or altered, i.e., non-Watson-Crick, base-pairing schemes. As a result, the computed Rise of a buckled dimer step with a partially intercalated amino acid side chain in a protein-DNA complex such as TBP-DNA  may approach the base-pair separation found at a planar, fully drug-intercalated step. The dispersion of step parameters is similarly influenced by occasional deformations of complementary base-pair geometry. That is, Rise, Shift, Tilt, and Twist may appear intrinsically flexible in sets of structures with distorted base pairing. Non-Watson-Crick base pairs. Direct application of the proposed reference frame to the analysis of non-Watson-Crick base pairs yields numerical parameters characteristic of the particular hydrogen-bonding scheme. For example, "wobble" G×T and A+×C base pairs are "sheared" ~2 Å relative to the Watson-Crick configuration, the displacement being positive for the Y×R pair and negative for the R×Y association. These large displacements, in turn, affect Twist along the lines described in Figure 3. For example, the G×T mismatches in the d(CGCGAATTTGCG)2 duplex structure (NDB entry: bdl009)  introduce ~15° under- and overtwisting in the associated CG and GA dimer steps since Shear is negative at the former step and positive at the latter step. The same principles apply in RNA structures where the G×U wobble assumes an important role . On the other hand, Twist can be constrained to typical A- or B-like values by proper choice of an intrinsic "wobble" base-pair frame . The latter approach necessitates a carefully chosen frame for each mode of base pairing. In the future, it may be necessary to define standards for common non-Watson-Crick base-pairing schemes. Protein-DNA interactions. Characterizing the geometry of nucleic acids interacting with proteins, obviously, brings up a whole new host of geometrical issues. However, the standard description of base-pair geometry described here can be carried over, to a large degree, to this problem, and many of the geometrical issues involved in describing the protein are somewhat simpler than for the DNA, e.g., the description of helical geometry for an a-helix versus that for the DNA double helix.
Supplementary tables and figures are available at: http://rutchem.rutgers.edu/~olson/Tsukuba
Questions regarding the construction of the standard frames and the computation of local base-pair parameters can be addressed to:
1. Lu, X.-J. & Olson, W. K. (1999) "Resolving the discrepancies among nucleic acid conformational analyses," J. Mol. Biol. 285, 1563-1575.
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4. Berman, H. M., Olson, W. K., Beveridge, D. L., Westbrook, J., Gelbin, A., Demeny, T., Hsieh, S. H., Srinivasan, A. R. & Schneider, B. (1992) "The nucleic acid database: a comprehensive relational database of three dimensional structures of nucleic acids," Biophys. J. 63, 751-759.
5. Clowney, L., Jain, S. C., Srinivasan, A. R., Westbrook, J., Olson, W. K. & Berman, H. M. (1996) "Geometric parameters in nucleic acids: nitrogenous bases," J. Am. Chem. Soc. 118, 509-518.
6. Fujita, S., Takenaka, A. & Sasada, Y. (1984) "A model for interactions of amino acid side chains with Watson-Crick base pair of guanine and cytosine. Crystal structrure of 9-(2-carboxyethyl)guanine and its crystalline complex with 1-methylcytosine," Bull. Chem. Soc. Jpn. 57, 1707-1712.
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15. Gorin, A. A., Zhurkin, V. B. & Olson, W. K. (1995) "B-DNA twisting correlates with base pair morphology," J. Mol. Biol. 247, 34-48.
16. Kosikov, K. M., Gorin, A. A., Zhurkin, V. B. & Olson, W. K. (1999) "DNA stretching and compression: large-scale simulations of double helical structures," J. Mol. Biol. 289, 1301-1326.
17. Lavery, R. & Sklenar, H. (1988) "The definition of generalized helicoidal parameters and of axis of curvature for irregular nucleic acids," J. Biomol. Struct. Dynam. 6, 63-91.
18. Lavery, R. & Sklenar, H. (1989) "Defining the structure of irregular nucleic acids: conventions and principles," J. Biomol. Struct. Dynam. 6, 655-667.
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21. Tung, C.-S., Soumpasis, D. M. & Hummer, G. (1994) "An extension of the rigorous base-unit oriented description of nucleic acid structures," J. Biomol. Struct. Dynam. 11, 1327-1344.
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31. Calladine, C. R. & Drew, H. R. (1984) "A base-centered explanation of the B-to-A transition in DNA," J. Mol. Biol. 178, 773-782.
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33. Lu, X.-J., Babcock, M. S. & Olson, W. K. (1999) "Mathematical overview of nucleic acid analysis programs," J. Biomol. Struct. Dynam. 16, 833-843.
34. Yanagi, K., Privé, G. C. & Dickerson, R. E. (1991) "Analysis of local helix geometry in three B-DNA decamers and eight dodecamers," J. Mol. Biol. 217, 201-214.
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37. Privé, G. G., Yanagi, K. & Dickerson, R. E. (1991) "Structure of the B-DNA dodecamer C-C-A-A-C-G-T-T-G-G and comparison with the isomorphous decamers C-C-A-A-G-A-T-T-G-G and C-C-A-G-G-C-C-T-G-G," J. Mol. Biol. 217, 177-199.