The local dynamics of a double stranded DNA fragment [d(CpGpCpApApApTpTpTpGpCpG)]₂ of twelve base pairs is obtained to second order in the mode-coupling expansion of the Smoluchowski diffusion theory.

The DNA is considered a fluctuating three-dimensional (3D) structure undergoing rotational diffusion. The starting structure for the calculations is the B canonical structure of the fragment, while the fluctuations are evaluated using molecular dynamics simulations, with the ensemble averages approximated by time averages along a trajectory of length 1.5 ns. The rotational dynamics of the bonds along the double strands are calculated and compared to experimental NMR relaxation rates of different ¹³C along the sequence: R(C_z), R(C_xy) and R(H_z→C_z). For a fluctuating 3D structure the mode-coupling diffusion theory is found to be in good agreement with several relative characteristics of the experimental relaxation parameters, while motivations are given for the few differences which are due mainly to poor statistics or to inaccuracies in the diffusion model. With a view to application to larger DNA fragments, discussion is dedicated to the validity of reducing the number of degrees of freedom in the double helix statistics by grouping the atoms in rigid fragments (e.g., the backbone atoms, the sugar atoms and the base atoms of each nucleotide). Consideration is given to the effect on local dynamics properties of reduced descriptions that include only three or four rigid bodies per nucleotide as well as five rigid bodies per base pair. It is found that in general these approximations almost uniformly produce slight increase in the correlation time pattern, which grows as the rigidity in the model increases. The relative effects on the dynamic pattern for the most accurate rigid body models are modest. The errors in C1' and C5' mobilities are more significant if C5; is included in the backbone rigid body.

These results offer new tools to analyse NMR relaxation behaviour and new perspectives in studying the role of dynamics in biological macromolecules.