Nmr relaxation in DNA. I. The contribution of torsional deformation modes of the elastic filament

The pertinent correlation function for nmr dipolar relaxation of 31 P by its neighboring protons in DNA is derived for a comparatively realistic model of the internal Brownian motions. These motions include the collective torsional deformation modes of the elastic filament, uncoupled local overdamped reorienting motions of the P‐H vectors in harmonic potential wells within the nucleotide unit, and the compartively slow end‐over‐end rotations of the local helix axis. These latter slow axial tumbling motions essentially completely determine T 2 but have virtually no effect on T 1 or the nuclear Overhauser effect (NOE), which are governed almost exclusively by rapid torsional deformations and local reorientations on the nanosecond time scale. The essential behavior of the relevant correlation function for the collective torsional motions has recently been determined experimentally in this laboratory using the decay of fluorescence polarization anisotropy of bound ethidium dye [J. C. Thomas et al. (1980) Biophys. Chem. 12 , 177–180]. By using that result to carry out nmr relaxation calculations for various amplitudes and time constants of the uncoupled local motions and comparing them with the experimental data, it can be demonstrated that (within this model of purely dipolar relaxation), only rather small rms amplitudes of local reorientations (<7°) occur and that their relaxation times are near 1 ns. Contrary to previous conclusions in the literature, the collective torsional deformation modes actually make the dominant contribution to T 1 and NOE. At t = 1 ns the total rms azimuthal displacement of the P‐H vector in this model is 19.5°, which results from a superposition of torsional deformations with rms displacement 18.2° and uncoupled local motions with rms displacement 7°. The contribution of pure chemical shift anisotropy (CSA) to the 1/ T 1 relaxation rate is calculated for the first time for the case when torsional deformation modes predominate, and it is predicted to be 46% of the corresponding dipolar relaxation rate or 31% of the total relaxation rate. Unusual magnetic field strength dependence of the pure CSA and dipolar contributions is predicted to arise as a consequence of the collective torsional deformation modes. This seriously weakens empirical arguments in favor of a small (<10%) CSA contribution. In any case, a detailed interpretation of T 1 and NOE incorporating both dipolar and CSA relaxation must await the evaluation of the CSA:dipolar interference term, or crossterm, contribution to the relaxation rate. The contribution of pure CSA to 1/ T 2 relaxation is likewise calculated for the case when local reorienting motions are negligible; it is found to be ≲16% of the corresponding dipolar relaxation rate for the comparatively short (300–600‐base‐pair) DNA fragments of interest. For high‐molecular‐weight DNAs we predict that the slow Rouse‐Zimm coil‐deformation modes will dominate 1/ T 2 relaxation and the linewidth. Dynamic light‐scattering and other evidence is presented that the remarkable loss of nmr signal from DNA on addition of ethidium bromide, as reported by Hogan and Jardetzky, is actually a consequence of phase separation in such concentrated solutions. A pronounced decrease in T 2 , due to greatly hindered axial tumbling in the more concentrated phase, is advanced as a plausible line‐broadening explanation for the apparent loss of nmr signal from DNA in that phase.