Rotational friction on small globular proteins: Combined dielectric and hydrodynamic effect

Rotational friction on proteins and macromolecules is known to derive contributions from at least two distinct sources -- hydrodynamic (due to viscosity) and dielectric friction (due to polar interactions). In the existing theoretical approaches, the effect of the latter is taken into account in an {\it ad hoc} manner, by increasing the size of the protein with the addition of a hydration layer. Here we calculate the rotational dielectric friction on a protein ($ζ_{DF}$) by using a generalized arbitrary charge distribution model (where the charges are obtained from quantum chemical calculation) and the hydrodynamic friction with stick boundary condition, ($ζ_{hyd}^{stick}$) by using the sophisticated theoretical technique known as tri-axial ellipsoidal method, formulated by Harding [S. E. Harding, Comp. Biol. Med. {\bf 12}, 75 (1982)]. The calculation of hydrodynamic friction is done with only the dry volume of the protein (no hydration layer). We find that the total friction obtained by summing up $ζ_{DF}$ and $ζ_{hyd}^{stick}$ gives reasonable agreement with the experimental results, i.e., $ζ_{exp} \approx ζ_{DF} + ζ_{hyd}^{stick}$.

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