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

Rotational diffusion (Drot) is a fundamental property of biomolecules that contains information about molecular dimensions and solute–solvent interactions. While ab initio Drot 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 Drot in >10 proteins spanning 5–157 kDa. We also adopt a quaternion-based approach that computes Drot orientation directly from autocorrelations of best-fit rotations as used in, e.g., RMSD algorithms. Over 2 μs trajectories, isotropic MARTINI+EN tumbling replicates experimental values to within 10–20%, with convergence analyses suggesting a minimum sampling of >50 × τtheor to achieve sufficient precision. Transient fluctuations in anisotropic tumbling cause decreased precision in predictions of axisymmetric anisotropy and rhombicity, the latter of which cannot be precisely evaluated within 2000 × τtheor for GB3. Thus, we encourage reporting of axial decompositions Dx, Dy, Dz 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.