Comparison of theories for the translational and rotational diffusion coefficients of rod-like macromolecules. Application to short DNA fragments

Two theories relating the translational and rotational diffusion coefficients Dt and Dr of a rod-like macromolecule to its length and diameter, proposed by Broersma [J. Chem. Phys. 74, 6989 (1981)], and Tirado and García de la Torre [J. Chem. Phys. 71, 2581 (1979); 73, 1986 (1980)] are shown to predict different values of the coefficients for a particle of given dimensions. Next, we use the two theories to analyze existing experimental data of sedimentation coefficients s and translational and rotational diffusion coefficients of short DNA fragments, and obtain values of the hydrated diameter of DNA d which is treated as an adjustable parameter. The results are compared with the expected value, d≂26Å. This comparison favors clearly the Tirado–Garcia de la Torre theory in the case of Dt and s. For Dr, and using a rise per base pair r=3.4 Å, this theory gives best agreement for all the data examined, while when r=3.3 Å, the agreement depends on the source of data.