The w3DNA server reports three sets of rigid-body parameters: (i) the six base-pair parameters describing the spatial arrangements of associated bases—three angles called Buckle, Propeller, and Opening and three displacements called Shear, Stretch, and Stagger; (ii) the six base-pair-step parameters specifying the configurations of spatially adjacent base pairs—two bending angles called Tilt and Roll, the dimeric rotation angle Twist, two in-plane dislocations termed Shift and Slide, and the vertical displacement Rise; and (iii) the six parameters that relate the positions of successive base pairs relative to a local helical frame—the angles Inclination and Tip and the distances x-displacement and y-displacement describing the orientation and translation of the base planes with respect to the helical axis, and the rotation about and displacement along the helical axis, referred to as Helical Twist and Helical Rise (1 (link),10 ). The numerical values describe the deviations of the base pairs in a given structure from the planar Watson–Crick base pairs in an ideal B-DNA helix, where the base-pair parameters, the dimeric bending components, and in-plane dislocations of adjacent base pairs are null (11 (link)). A fourth set of rigid-body variables—the dinucleotide Tilt, Roll, Twist, Shift, Slide, and Rise—specifies the arrangements of adjacent bases along individual strands. The computations of rigid-body parameters use the mathematical definitions of El Hassan and Calladine (5 (link)). The identification of the helical axis between adjacent base pairs follows the methodology introduced by Babcock et al. (13 (link)).
The reported output also includes the areas of overlap of adjacent bases and base pairs and the positioning of phosphorus atoms within each base-pair step. The former values quantify the stacking of neighboring base pairs, and the latter discriminate between A and B double-helical steps (17 (link)). The base-pairing information is complemented by more conventional structural data, such as the identities and lengths of hydrogen bonds, the distances and angles between atoms in hydrogen-bonded and adjacent nucleotides, the torsion angles along the chain backbone, the amplitude and phase angle of sugar pseudorotation (i.e. puckering geometry), the glycosyl torsions orienting the sugars and bases, and the widths of the major and minor grooves.
The reported output also includes the areas of overlap of adjacent bases and base pairs and the positioning of phosphorus atoms within each base-pair step. The former values quantify the stacking of neighboring base pairs, and the latter discriminate between A and B double-helical steps (17 (link)). The base-pairing information is complemented by more conventional structural data, such as the identities and lengths of hydrogen bonds, the distances and angles between atoms in hydrogen-bonded and adjacent nucleotides, the torsion angles along the chain backbone, the amplitude and phase angle of sugar pseudorotation (i.e. puckering geometry), the glycosyl torsions orienting the sugars and bases, and the widths of the major and minor grooves.
