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.