Sequence-dependent DNA structure: the role of the sugar-phosphate backbone

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. 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. The remaining torsion angles (beta, epsilon, alpha and gamma) comprise two less important 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). Coupling is observed between the base and backbone degrees of freedom. The major base stacking mode, slide-roll-twist, is coupled to the major backbone mode, chi-P-delta-zeta. 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. 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 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 use this observation to develop a simple virtual bond model which describes the coupling of the backbone conformations and the base stacking geometry. A semi-flexible bond is used to connect the same strand C1'-C1' atoms. 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. Using this simple model for the backbone in conjunction with potential energy calculations of the base stacking interactions, we show that it is possible to predict accurately the values of these 14 base step parameters, given values of slide, shift and propeller. We also show that the base step parameters fall into three distinct groups: roll, tilt and rise are determined solely by the base stacking interactions and are independent of the backbone; twist is insensitive to the base stacking interactions and is determined solely by the constraints of a relatively rigid fixed length backbone; slide and shift are the primary degrees of freedom and cannot be predicted accurately at the dinucleotide level because they are influenced by the conformations of neighbouring steps in a sequence. We have found that the context effect on slide is mediated by the chi torsion angles while the context effect on shift results from a BI to BII transition in the backbone. We have therefore reduced the dimensionality of the dinucleotide step problem to two parameters, slide and shift.