Section 23.3.2. Helix parameters

Before making detailed comparisons of the three helix types, one must define the parameters by which the helices are characterized. The fundamental feature of all varieties of nucleic acid double helices is two antiparallel sugar–phosphate backbone chains, bridged by paired bases like rungs in a ladder (Fig. 23.3.2.1). Using the convention that the positive direction of a backbone chain is from 5′ to 3′ within a nucleotide, the right-hand chain in Fig. 23.3.2.1 runs downward, while the left-hand chain runs upward. A- or B-DNA is then obtained by twisting the ladder into a right-handed helix. But Z-DNA cannot be obtained from Fig. 23.3.2.1 simply by giving it a left-handed twist; both backbone chains run in the wrong direction for Z-DNA. A more complex adjustment is required, and this will be addressed again later.

Figure 23.3.2.1| top | pdf | Unrolled schematic of A- or B-DNA, viewed into the minor groove. Paired bases are attached to backbone chains that run in opposite directions: downward on the right and upward on the left. Z-DNA differs from A- and B-DNA in that the two backbone chains run in opposite directions from those shown here. Hence, Z-DNA cannot be obtained from A- or B-DNA by simple twisting around the helix axis.

The conformation of the backbone chain along each nucleotide is described by six torsion angles, labelled α through ζ, as shown in Fig. 23.3.2.2. An earlier convention termed these same six angles as ω, φ, ψ, ψ′, φ′, ω′ (Sundaralingam, 1975), but the alphabetical nomenclature is now generally employed. Torsion angles are defined in Fig. 23.3.2.3, which also shows three common configurations: gauche ⁻ (−60°), trans (180°) and gauche ⁺ (+60°). These three configurations are especially favoured with sp³ hybridization or tetrahedral ligand geometry at the two ends of the bond in question, because their `staggered' arrangement minimizes ligand–ligand interactions across the bond. An `eclipsed' arrangement with ligands at −120°, 0° (cis), and 120° is unfavourable because it brings substituents at the two ends of the bond into opposition. Table 23.3.2.1 lists the mean values and standard deviations of all six main-chain torsion angles for A-, B- and Z-DNA, as recently observed in 96 oligonucleotide crystal structures (Schneider et al., 1997).

Table 23.3.2.1| top | pdf | Average torsion-angle properties of A-, B- and Z-DNA (°) Values listed are mean torsion angles, with standard deviations in parentheses. Conformations are only approximate; — indicates a non-gauche/trans conformation. BII and ZII are less common variants. For δ, the sugar ring geometry is quoted in place of gauche/trans. χ for B-DNA combines pyrimidines and purines. Values were obtained from a sample of 30 A-DNAs, 34 B-DNAs, 22 Z-DNAs and ten nonstandard DNAs in the Nucleic Acid Database. From Schneider et al. (1997).   A-DNA 293 (17) 174 (14) 56 (14) 81 (7) 203 (12) 289 (12) 199 (8) Conformation g− t g+ C3′-endo t g− t B-DNA 298 (15) 176 (9) 48 (11) 128 (13) 184 (11) 265 (10) 249 (16) Conformation g− t g+ C1′-exo t g− g−                 BII-DNA   146 (8)   144 (7) 246 (15) 174 (14) 271 (8) Conformation   —   C2′-endo g− t g− ZI-DNA – purines 71 (13) 183 (9) 179 (9) 95 (8) 95 (8) 301 (16) 63 (5) Conformation g+ t t O4′-endo g+ g− g+                 ZII-DNA – purines         189 (12) 52 (14) 58 (5) Conformation         t g+ g+                 ZI-DNA – pyrimidines 201 (20) 225 (16) 54 (13) 141 (8) 267 (9) 75 (9) 204 (98) Conformation t — g+ C2′-endo g− g+ t                 ZII-DNA – pyrimidines 168 (16) 166 (14)           Conformation t t

Figure 23.3.2.2| top | pdf | Sugar–phosphate backbone of RNA and DNA polynucleotides. One nucleotide begins at a phosphorus atom and extends just short of the phosphorus atom of the following nucleotide, with the conventional positive direction being PO5′—C5′—C4′—C3′—O3′P, as indicated by the arrows. Main-chain torsion angles are designated α through ζ, and torsion angles about the five bonds of the ribose or deoxyribose ring are through , as shown. If one imagines atoms O3′—P—O5′ as a hump-backed bridge, as one crosses the bridge in a positive chain direction, oxygen atom O1 is to the left and O2 is to the right. These oxygens, accordingly, are sometimes designated OL and OR. The —OH group attached to the C2′ atom of the ribose ring in RNA shown here is replaced by —H in the deoxyribose ring of DNA. Atom N to the right is part of the base attached to the sugar ring: N1 in pyrimidines and N9 in purines. Torsion angle χ is defined by O4′—C1′—N1—C2 in pyrimidines and O4′—C1′—N9—C4 in purines.

Figure 23.3.2.3| top | pdf | Definition of torsion angles. A positive angle results from clockwise rotation of the farther bond, holding the nearer bond fixed. Torsion angle +60° is designated as gauche+ or g+, angle 180° is trans or t and angle −60° is gauche− or g−.

The type of ligand–ligand clash just mentioned is an important element in ensuring that five-membered rings, such as ribose and deoxyribose, are not ordinarily planar, even though the internal bond angle of a regular pentagon, 108°, is close to the 109.5° of tetrahedral geometry. A stable compromise is for one of the four ring atoms to lie out of the plane defined by the other four, as in Fig. 23.3.2.4. This is termed an `envelope' or E conformation, by analogy with a four-cornered envelope having a flap at an angle. Intermediate `twist' or T forms are also possible, in which two adjacent atoms sit on either side of the plane defined by the other three, but this discussion will focus on the simple envelope conformations. In most cases, the accuracy of a nucleic acid crystal structure determination is such that it would be difficult to distinguish clearly between a given E form and its flanking T forms. For this reason, most structure reports consider only the E alternatives.

Figure 23.3.2.4| top | pdf | The three most common furanose ring geometries. The planar form of the five-membered ribose or deoxyribose ring is unstable because of steric hindrance from side groups; one of the five atoms prefers to pucker out-of-plane on one side of the ring or the other. Puckering toward the same side of the ring as the C5′ atom is termed endo, and puckering toward the opposite `outside' surface is termed exo. The main-chain torsion angle δ is related to sugar ring conformation because of the motion undergone by the C3′—O3′ bond during changes in puckering.

A convenient and intuitive nomenclature is to name the conformation after the out-of-plane atom and then specify whether it is out of plane on the same side as the C5′ atom (endo) or the opposite side (exo). Ten such conformations exist: five endo and five exo. In Fig. 23.3.2.4 (top), pushing the C3′ atom of the C3′-endo conformation into the plane of the ring would tend to push C2′ below the ring, passing through a T state and creating a C2′-exo conformation. C2′ can, in turn, be returned to the ring plane if C1′ is pushed above the ring, forming C1′-endo, and so on, around the ring. In this way, a contiguous series of alternating endo/exo conformations is produced, as listed in Table 23.3.2.2.

This ten-conformation endo/exo cycle can be generalized to a continuous distribution of intermediate conformations, characterized by a pseudorotation angle, P (Altona et al., 1968; Altona & Sundaralingam, 1972), with the ten endo/exo conformations spaced 36° apart (Table 23.3.2.2). Fig. 23.3.2.5 shows the calculated potential energy of conformations around the pseudorotation cycle (Levitt & Warshel, 1978). Note that C2′-endo and C3′-endo are most stable, that the pathway between them along the right half of the circle remains one of low energy, but that a large 6 kcal mol⁻¹ potential energy barrier (1 kcal mol⁻¹ = 4.184 kJ mol⁻¹) effectively forbids conformations around the left half of the circle.

Figure 23.3.2.5| top | pdf | Potential plot of all furanose ring conformations. Energies are in kcal mol −1. The distance from the central point gives the maximum displacement of the out-of-plane atom from the plane of the other four. The circle is a constant-displacement trajectory chosen to pass through the potential minima on the right three-quarters of the plot. C2′-endo and C3′-endo are especially favoured, whereas O1′-exo on the left is highly disfavoured. The path from C2′-endo through C1′-exo, O1′-endo and C4′-exo to C3′-endo is a low-energy path, and many examples all along this path are known in B-DNA helices. Reprinted with permission from Levitt & Warshel (1978). Copyright (1978) American Chemical Society.

As Fig. 23.3.2.4 indicates, the main-chain torsion angle, δ, is sensitive to ring conformation, because the C5′—C4′ and C3′—O3′ bonds that define the angle shift as ring puckering changes. The idealized relationship between torsion angle, δ, and pseudorotation angle, P (Saenger, 1984), is Fig. 23.3.2.6 shows the observed torsion angles, δ, and pseudorotation angles, P, from X-ray crystal structure analyses of synthetic DNA oligonucleotides: 296 examples from A-DNA and 280 from B-DNA. The most striking aspect of this plot is the radically different behaviour of A- and B-DNA. The prototypical sugar conformation for A-DNA obtained from fibre diffraction modelling, C3′-endo, is, in fact, adhered to quite closely in A-DNA crystal structures.

Figure 23.3.2.6| top | pdf | Plot of observed sugar conformations in 296 nucleotides of A-DNA (crosses) and 280 of B-DNA (open circles). Open squares mark ideal relationships between torsion angle δ (vertical axis) and pseudorotation angle P (horizontal axis) from the expression . Deviations from this ideal curve for real helices arise, because the amplitude of pseudorotation (or displacement of one atom from the mean plane of the others) varies from one ring to another. Note the tight clustering of A-DNA points around C3′-endo and the broader distribution of B-DNA conformations.

However, B-DNA shows a quite different behaviour. Although earlier fibre diffraction led one to expect C2′-endo sugars, the actual experimental distribution is quite broad, extending up the right-hand side of the pseudorotation circle of Fig. 23.3.2.5, through C1′-exo, O1′-endo and C4′-exo, in some cases all the way to C3′-endo itself. Indeed, the mean value of δ observed in B-DNA oligomer crystal structures is 128° rather than 144° (Table 23.3.2.1), making C1′-exo a better description of sugar conformation in B-DNA than C2′-endo. Old habits die hard, however, and the B-DNA sugar conformation is still colloquially termed C2′-endo, a designation of historical significance but of little practical value. The apparent greater malleability of the B helix compared to A may indeed be one feature that makes B-DNA particularly suitable for expressing its base sequence to drugs and control proteins via local helix structure changes.

The key to the biological role of DNA is that one of the two purines can pair with only one of the pyrimidines: A with T, and G with C. Hence, genetic information present in one strand is passed on to the complementary strand. The standard two-base pairs are shown in Fig. 23.3.2.7 along with the conventional numbering of the atoms. Backbone sugar and phosphate atoms are primed while base atoms are unprimed, as, for example, C1′ and N9 at opposite ends of a purine glycosydic bond. The G·C base pair is held together by three hydrogen bonds, whereas an A·T pair has only two. This means that A·T pairs show less resistance to propeller twisting (counter-rotation of the two bases about their common long axis), and this will have an effect on minor groove width, as seen later. The patterns of hydrogen-bond acceptors (A) and donors (D) on the major and minor groove edges of base pairs are important elements in recognition of base sequence by drugs and control proteins.

Figure 23.3.2.7| top | pdf | A·T and G·C base pairs with minor groove edge below and major groove edge above. A is a hydrogen-bond acceptor, D is as hydrogen-bond donor.

Other related but nonstandard base pairs are compared in Fig. 23.3.2.8. Inosine (I) is useful in studying properties of DNA in that, when paired with cytosine (C), it creates a G·C-family base pair having overall similarity to A·T. Similarly, diaminopurine (DAP) [also known as 2-aminoadenine (2aA)], when paired with thymine (T), creates a G·C-like pair from A·T-family bases. Hence, in a given experimental situation, one can unscramble the relative significance of number of hydrogen bonds versus identity and location of exocyclic groups.

Figure 23.3.2.8| top | pdf | Alternative purines and pyrimidines, and possible base pairings. Purines: P = purine; AP = 2-aminopurine; A = adenine or 6-aminopurine; DAP = 2,6-diaminopurine (also known as 2aA = 2-aminoadenine); G = guanine; I = inosine. Pyrimidines: T = thymine (uracil if methyl group is absent); C = cytosine. DAP–T is a nonstandard AT-family analogue of G–C, and I–C is a nonstandard GC-family analogue of A–T.

The conventional Watson–Crick base pairing of Fig. 23.3.2.7 uses the hexamer `end' of the purine base. A different type of base pairing was proposed many years ago by Hoogsteen (1963), in which the upper edge of the purine was used: N7 and N6/O6. Hoogsteen base pairing is shown between the left-hand two bases in each part of Fig. 23.3.2.9. Note that in Hoogsteen base pairing of A and T, each ring provides both a hydrogen-bond donor and an acceptor. Guanine cannot do this, since both its N7 and O6 positions are acceptors. As a consequence, in a G·C pair, C must supply both of the hydrogen-bond donors. It can only form a Hoogsteen base pair with G when the cytosine ring is protonated. This would lead one to expect triplex formation only at low pH. However, the stability of a triplex can, to a certain extent, alter the pK_a of the N—H proton itself. (Recall the shift in pK_a of buried Asp and His groups in the active sites of enzymes.) Hence, with a single-chain DNA, G-A-G-A-G-A-A-C-C-C-C-T-T-C-T-C-T-C-T-T-T-C-T-C-T-C-T-T, that folds back upon itself twice to build a triplex, NMR experiments indicate a significant amount of triplex remaining even at pH 8.0 (Sklenár & Feigon, 1990; Feigon, 1996).

Figure 23.3.2.9| top | pdf | Watson–Crick pairing of a purine (A or G) with a pyrimidine to its right (T or C), and Hoogsteen pairing of the same purine with a pyrimidine above it. This combination of Watson–Crick and Hoogsteen pairing is found in triple helices or triplexes. Note that Hoogsteen pairing of G and C can only occur at a pH at which C is protonated, because the extra proton is essential for the second hydrogen bond.

An important advantage of single-crystal oligonucleotide structures over fibre-based models is that one can actually observe local sequence-based departures from ideal helix geometry. B-DNA fibre models indicated a mean twist of ca 36° per step, or ten base pairs per turn, whereas A-DNA fibre patterns indicated less winding: ca 33° per step or 11 base pairs per turn. Twist, rise per base pair along the helix axis, horizontal displacement of base pairs off that axis, and inclination of base pairs away from perpendicularity to the axis are all intuitively obvious parameters. But when single-crystal structures began appearing in great numbers in the mid-1980s, it became imperative that uniform names and definitions be used for these and for less obvious, but increasingly significant, local helix parameters.

An EMBO workshop on DNA curvature and bending, held at Churchill College, Cambridge, in September 1988, led to an agreement on definitions and conventions that was published simultaneously in four journals (Dickerson et al., 1989). Fig. 23.3.2.10 shows the reference frames for two successive base pairs, and Figs. 23.3.2.11 and 23.3.2.12 illustrate local helix parameters involving rotation and translation, respectively. Subsequent experience has shown the most useful parameters to be inclination, propeller, twist and roll among the rotations, and x displacement, rise and slide among the translations. As mentioned at the beginning of this chapter, inclination and x displacement are the two properties that best differentiate A- from B-DNA. The four most widely used computer programs for calculation of local helix parameters are NEWHELIX by Dickerson (B7, B46), CURVES by Lavery & Sklenar (1988, 1989), BABCOCK by Babcock & Olson (Babcock et al., 1993, 1994; Babcock & Olson, 1994) and FREEHELIX (Dickerson, 1998c). NEWHELIX was the earliest of these, but it performs all calculations relative to a best overall helix axis. This is satisfactory for single-crystal DNA structures, but makes the program unusable for the 180° bending observed in some protein–DNA complexes. CURVES is especially convenient for mapping the axis of a bent or curved helix. FREEHELIX, which evolved from NEWHELIX, calculates all parameters relative to local base-pair geometry, without assuming an overall axis, and permits display of normal vector plots that are especially useful in analysing bending in DNA–protein complexes (Dickerson & Chiu, 1997).

Figure 23.3.2.10| top | pdf | Definitions of local reference axes (x, y, z) at the first two base pairs of an n-base-pair double helix. Base 1 is paired with base 2n, base 2 with base 2n − 1 etc. Shaded corners represent attachment points to sugar rings. Curved arrows denote 5′-to-3′ `positive' directions of each backbone chain. Note that when looking into the minor groove, as here, the two strands illustrate a clockwise rotation, upwards on the left and downwards on the right. This is true for A- and B-DNA, but for Z-DNA, the sense of the two backbone strands is reversed.

Figure 23.3.2.11| top | pdf | Local helix parameters involving rotations. Tip and inclination describe the orientation of a base pair relative to the helix axis, produced by rotation about the base-pair long axis or short axis, respectively. Opening, propeller and buckle describe rotations of the two bases of a pair relative to one another. Twist, roll and tilt describe changes of orientation from one base pair to the next, via rotations about the z, y and x axes, respectively.

Figure 23.3.2.12| top | pdf | Local helix parameters involving translations. y and x displacements describe shifts of a lone base pair along its long or short axis, respectively. Stagger, stretch and shear describe displacements of the two bases of a pair relative to one another. Rise, slide and shift describe displacements from one base pair to the next, via translations along the z, y and x axes, respectively.

The glycosyl bond angle, χ, about the bond connecting a sugar ring to a base is a special case of torsion angle, and is defined by O4′—C1′—N1—C2 for pyrimidines and O4′—C1′—N9—C4 for purines. In A- and B-DNA, the normal range of χ is 160 to 300°. This is known as the anti conformation (right-hand side of Fig. 23.3.2.13) and swings the sugar ring out away from the minor groove edge of the base pair. In Z-DNA, pyrimidines also exhibit the anti glycosyl bond conformation, but purines adopt the syn geometry shown on the left-hand side of Fig. 23.3.2.13. Now the sugar ring is rotated so that it intrudes into the minor groove, and χ lies in the range 50 to 90°.

Figure 23.3.2.13| top | pdf | Syn versus anti orientation about the glycosyl bond connecting sugar and base. Right: anti conformation, with χ ca 210°. Left: syn conformation, with χ around 60°. Both A- and B-DNA only employ the anti geometry; Z-DNA uses anti for pyrimidines and syn for purines, as shown here. Note that the 5′-to-3′ direction in both rings is down into the paper. Hence, antiparallel backbone chains can be achieved only by a zigzag chain geometry with local chain reversals, as shown later in Fig. 23.3.3.4. Black dots labelled A, B and Z indicate the position of the helix axis relative to the base pairs in A-, B- and Z-DNA.