Analysis of the X-ray crystal structure database, simple geometric considerations and model building experiments all show that this bond is flexible with respect to slide, shift and propeller but rigid with respect to the other 14 local base stacking parameters. A semi-flexible bond is used to connect the same strand C1'-C1' atoms. We use this observation to develop a simple virtual bond model which describes the coupling of the backbone conformations and the base stacking geometry. The slide-roll-twist motion relates to changes in the mean backbone length, C, and the shift-tilt motion to the difference between the lengths of the two backbone strands, DeltaC. We show that the length of the backbone, C, given by the same strand C1'-C1' separation, is an excellent single parameter descriptor for the conformation of the backbone and the way in which it is coupled to the base stacking geometry. The secondary base stacking mode, shift-tilt, is coupled to epsilon and zeta and to a lesser extent to the chi-P-delta-zeta mode. The major base stacking mode, slide-roll-twist, is coupled to the major backbone mode, chi-P-delta-zeta. Coupling is observed between the base and backbone degrees of freedom. The base stacking interactions show three degrees of freedom: slide-roll-twist, shift-tilt, and rise (which is more or less constant). The remaining torsion angles (beta, epsilon, alpha and gamma) comprise two less important degrees of freedom. In X-ray crystal structures of oligonucleotides, the backbone shows one major degree of freedom, consisting of the torsion angles chi, delta, zeta and the pseudorotation phase angle, P. A detailed analysis of the coupling between the conformational properties of the sugar-phosphate backbone and the base stacking interactions in dinucleotide steps of double helical DNA is described.