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Each base has two unique faces, arising from molecular asymmetry (53,54), which can be distinguished with the standard nucleic acid base reference frame. One face, which is hatched in Figure 2, corresponds to the positive z‐axis of the base plane, and the opposing face, which is unshaded, to the negative z‐axis. For Watson–Crick base pairs, such as the A–U pair in Figure 2a, the faces of the two bases are of the opposite sense, corresponding to two antiparallel strands. More generally, when the two bases (M and N) forming a pair have opposing faces, the scalar product of their z‐axes is negative. 3DNA designates such pairs, e.g. Watson–Crick A–U, A–T and G–C pairs, as M–N with the ‘–’ symbol used to emphasize the opposing directions. If the M and N bases in a pair share the same face, such as in the Hoogsteen base pair in Figure 2b, the pair is recorded as M+N, with the ‘+’ symbol used to emphasize the similar directions of the bases. This convention is simpler but in essence the same as the normal versus flipped concept of base pairing introduced by Burkard et al. (55).
To calculate the six complementary base pair parameters of an M–N pair (Shear, Stretch, Stagger, Buckle, Propeller and Opening), where the two z‐axes run in opposite directions, the reference frame of the complementary base N is rotated about the x2‐axis by 180°, i.e. reversing the y2‐ and z2‐axes in Figure 2a. Under this convention, if the base pair is reckoned as an N–M pair, rather than an M–N pair, the x‐axis parameters (Shear and Buckle) reverse their signs. For an M+N pair, e.g. the Hoogsteen A+U in Figure 2b, the x2‐, y2‐ and z2‐axes do not change sign; thus all six parameters for an N+M pair are of opposite sign from those for an M+N pair.
Since the six base pair parameters uniquely define the relative position and orientation of two bases, they can be used to reconstruct the base pair. Moreover, the parameters provide a simple mechanism for classification of structures (55) and database searching (X.‐J. Lu, Y. Xin and W.K. Olson, unpublished data). Among the six base pair parameters, only Shear, Stretch and Opening are critical in characterizing key hydrogen bonding features, i.e. base pair type: Shear and Stretch define the relative offset of the two base origins in the mean base pair plane and Opening is the angle between the two x‐axes with respect to the average normal to the base pair plane (see upper left panel in Fig. 1). For the Hoogsteen A+U base pair shown in Figure 2b, Shear is 0.5 Å, Stretch –3.5 Å and Opening 70°. Buckle, Propeller and Stagger, in contrast, are secondary parameters, which simply describe the imperfections, i.e. non‐planarity, of a given base pair.
Created and maintained by Dr. Xiang-Jun Lu [律祥俊] (xiangjun@x3dna.org)
The Bussemaker Laboratory at the Department of Biological Sciences, Columbia University.