Motions and entropies in proteins as seen in NMR relaxation experiments and molecular dynamics simulations

Molecular dynamics simulations of E. coli glutaredoxin1 in water have been performed to relate the dynamical parameters and entropy obtained in NMR relaxation experiments, with results extracted from simulated trajectory data. NMR relaxation is the most widely used experimental method to obtain data on dynamics of proteins, but it is limited to relatively short timescales and to motions of backbone amides or in some cases (13)C-H vectors. By relating the experimental data to the all-atom picture obtained in molecular dynamics simulations, valuable insights on the interpretation of the experiment can be gained. We have estimated the internal dynamics and their timescales by calculating the generalized order parameters (O) for different time windows. We then calculate the quasiharmonic entropy (S) and compare it to the entropy calculated from the NMR-derived generalized order parameter of the amide vectors. Special emphasis is put on characterizing dynamics that are not expressed through the motions of the amide group. The NMR and MD methods suffer from complementary limitations, with NMR being restricted to local vectors and dynamics on a timescale determined by the rotational diffusion of the solute, while in simulations, it may be difficult to obtain sufficient sampling to ensure convergence of the results. We also evaluate the amount of sampling obtained with molecular dynamics simulations and how it is affected by the length of individual simulations, by clustering of the sampled conformations. We find that two structural turns act as hinges, allowing the α helix between them to undergo large, long timescale motions that cannot be detected in the time window of the NMR dipolar relaxation experiments. We also show that the entropy obtained from the amide vector does not account for correlated motions of adjacent residues. Finally, we show that the sampling in a total of 100 ns molecular dynamics simulation can be increased by around 50%, by dividing the trajectory into 10 replicas with different starting velocities.