Computing the Rotational Diffusion of Biomolecules via Molecular Dynamics Simulation and Quaternion Orientations

Rotational diffusion (D-rot) is a fundamental property of biomolecules that contains information about molecular dimensions and solute solvent interactions. While ab initio D-rot, prediction can be achieved by explicit all-atom molecular dynamics simulations, this is hindered by both computational expense and limitations in water models. We propose coarse-grained force fields as a complementary solution, and show that the MARTINI force field with elastic networks is sufficient to compute D-rot, in >10 proteins spanning 5-157 kDa. We also adopt a quaternion-based approach that computes Dro, orientation directly from autocorrelations of best-fit rotations as used in, e.g., RMSD algorithms. Over 2 mu s trajectories, isotropic MARTINI+EN tumbling replicates experimental values to within 10-20%, with convergence analyses suggesting a minimum sampling of >50 X tau(theor) to achieve sufficient precision. Transient fluctuations in anisotropic tumbling cause decreased precision in predictions of axisyrnmetric anisotropy and rhombicity, the latter of which cannot be precisely evaluated within 2000 X tau(theor) for GB3. Thus, we encourage reporting of axial decompositions D-x, D-y,D- D-z to ease comparability between experiment and simulation. Where protein disorder is absent, we observe close replication of MARTINI+EN Drot orientations versus CHARMM22*/TIP3p and experimental data. This work anticipates the ab initio prediction of NMR-relaxation by combining coarse-grained global motions with all -atom local motions.