A rigorous basepair oriented description of DNA structures

We propose new, rigorous definitions for (i) basepair fixed coordinate systems and (ii) the twist, tilt, and roll angles (called tau, t, rho) describing the relative orientation of adjacent basepairs and bases in a pair, in arbitrary DNA structures obtained from x-ray diffraction, 2D NMR, or energy calculations. In contrast to the corresponding angular parameters (tg, theta T, theta R) and coordinate systems introduced by Dickerson and co-workers and currently in use, our angular parameters and coordinate systems, together with a set of three displacement parameters, dx, dy, dz, provide a mathematically correct and general description of DNA conformations at the basepairs and/or base level. For instance, our description is applicable when the DNA structure considered is inherently curved, irregular, and/or does not possess dyad (or pseudodyad) axes. We develop a computationally convenient algorithm for rigorous DNA conformational analysis and apply it to some of the known crystal structures. We establish the connection to the currently used parameters and test the consistency and efficiency of our methodology by reconstructing the Dickerson B dodecamer using only the sequence and the set of parameters obtained from the atomic coordinates. The six parameter (tau, t, rho, dx, dy, dz) basepair level reconstruction is good but not perfect. Perfect reconstruction is obtained when one also considers each base in a basepair (consideration of propeller twist alone is not sufficient). The variation of the rigorous parameters proposed along the sequence is much larger, but their average values agree with fiber and solution data much better than in the case of the currently used set. The results of our analysis do not support Trifonov's AA.TT wedge model for DNA curvature but provide some evidence in favor of the Crothers junction-bend model. We point out some of the limitations of basepair level approaches when applied to DNA structure prediction and quantitative understanding of sequence-dependent variations in structure.