Section 23.3.2.4. Helix parameters

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.