Robust estimation of rotational diffusion tensors of proteins from molecular dynamics simulations

Rotational diffusion is a fundamental physical process that determines the rotational motion of proteins in solution. It plays a role, for example, in molecular association processes and in theories of spectroscopic experiments in solution. In addition to experimental methods, molecular dynamics (MD) simulations have emerged as a powerful method to investigate rotational diffusion. Diffusion models are fitted to rotational correlation functions extracted from the simulations. In this work, we conducted a time-dependent analysis of the model parameters prior to fitting, using extended all-atom MD simulations of ubiquitin as a model system. A comparison to Brownian dynamics (BD) simulations confirms whether the rotational dynamics observed in MD actually follow the theory of Brownian rigid-body diffusion. In addition, the analysis reveals correlation time intervals that are suitable for fitting anisotropic, semi-isotropic, or isotropic diffusion models. To this end, a two-step optimization scheme is employed that combines a global and a local search in parameter space. BD simulations are used to estimate uncertainties of the diffusion coefficients and directional uncertainties of the principal axes. We found that ubiquitin exhibits nearly semi-isotropic rotational dynamics, in good agreement with the experimental NMR data. The approach is general and can be used to investigate, for example, the rotational diffusion of molecules in various biomolecular environments or to compute NMR relaxation parameters of proteins. An implementation of the method is freely available at https://github.com/MolSimGroup/rotationaldiffusion.