Mode‐coupling Smoluchowski dynamics of a double‐stranded DNA oligomer

The local dynamics of a double‐stranded DNA d(TpCpGpCpG)₂ is obtained to second order in the mode‐coupling expansion of the Smoluchowski diffusion theory. The time correlation functions of bond variables are derived and the ¹³C‐nmr spin–lattice relaxation times T₁ of different ¹³C along the chains are calculated and compared to experimental data from the literature at three frequencies. The DNA is considered as a fluctuating three‐dimensional structure undergoing rotational diffusion. The fluctuations are evaluated using molecular dynamics simulations, with the ensemble averages approximated by time averages along a trajectory of length 1 ns. Any technique for sampling the configurational space can be used as an alternative. For a fluctuating three‐dimensional (3D) structure using the three first‐order vector modes of lower rates, higher order basis sets of second‐rank tensor are built to give the required mode coupling dynamics. Second‐ and even first‐order theories are found to be in close agreement with the experimental results, especially at high frequency, where the differences in T₁ for ¹³C in the base pairs, sugar, and backbone are well described. These atomistic calculations are of general application for studying, on a molecular basis, the local dynamics of fluctuating 3D structures such as double‐helix DNA fragments, proteins, and protein–DNA complexes. © 1999 John Wiley & Sons, Inc. Biopoly 50: 613–629, 1999