NMR Order Parameter Determination from Long Molecular Dynamics Trajectories for Objective Comparison with Experiment

Functional protein motions covering a wide range of time scales can be studied, among other techniques, by NMR and by molecular dynamics (MD) computer simulations. MD simulations of proteins now routinely extend into the hundreds of nanoseconds time scale range exceeding the overall tumbling correlation times of proteins in solution by several orders of magnitude. This provides a unique opportunity to rigorously validate these simulations by quantitative comparison with model-free order parameters derived from NMR relaxation experiments. However, presently there is no consensus on how such a comparison is best done. We address here how this can be accomplished in a way that is both efficient and objective. For this purpose, we analyze N-15 R-1 and R-2 and heteronuclear {H-1}-N-15 NOE NMR relaxation parameters computed from 500 ns MD trajectories of 10 different protein systems using the model-free analysis. The resulting model-free S-2 order parameters are then used as targets for S-2 values computed directly from the trajectories by the iRED method by either averaging over blocks of variable lengths or by using exponentially weighted snapshots (wiRED). We find that the iRED results are capable of reproducing the target S-2 values with high accuracy provided that the averaging window is chosen 5 times the length of the overall tumbling correlation time. These results provide useful guidelines for the derivation of NMR order parameters from MD for a meaningful comparison with their experimental counterparts.