Motion of a disordered polypeptide chain as studied by paramagnetic relaxation enhancements, 15N relaxation, and molecular dynamics simulations: how fast is segmental diffusion in denatured ubiquitin?

Molecular dynamics (MD) simulations have been widely used to analyze dynamic conformational equilibria of folded proteins, especially in relation to NMR observables. However, this approach found little use in the studies of disordered proteins, where the sampling of vast conformational space presents a serious problem. In this paper, we demonstrate that the latest advances in computation technology make it possible to overcome this limitation. The experimentally validated (calibrated) MD models allow for new insights into structure/dynamics of disordered proteins. As a test system, we have chosen denatured ubiquitin in solution with 8 M urea at pH 2. High-temperature MD simulations in implicit solvent have been carried out for the wild-type ubiquitin as well as MTSL-tagged Q2C, D32C, and R74C mutants. To recalibrate the MD data (500 K) in relation to the experimental conditions (278 K, 8 M urea), the time axes of the MD trajectories were rescaled. The scaling factor was adjusted such as to maximize the agreement between the simulated and experimental (15)N relaxation rates. The resulting effective length of the trajectories, 311 μs, ensures good convergence properties of the MD model. The constructed MD model was validated against the array of experimental data, including additional (15)N relaxation parameters, multiple sets of paramagnetic relaxation enhancements (PREs), and the radius of gyration. In each case, a near-quantitative agreement has been obtained, suggesting that the model is successful. Of note, the MD-based approach rigorously predicts the quantities that are inherently dynamic, i.e., dependent on the motional correlation times. This cannot be accomplished, other than in empirical fashion, on the basis of static structural models (conformational ensembles). The MD model was further used to investigate the relative translational motion of the MTSL label and the individual H(N) atoms. The derived segmental diffusion coefficients proved to be nearly uniform along the peptide chain, averaging to D = 0.49-0.55 × 10(-6) cm(2)/s. This result was verified by direct analysis of the experimental PRE data using the recently proposed Ullman-Podkorytov model. In this model, MTSL and H(N) moieties are treated as two tethered spheres undergoing mutual diffusion in a harmonic potential. The fitting of the experimental data involving D as a single adjustable parameter leads to D = 0.45 × 10(-6) cm(2)/s, in good agreement with the MD-based analyses. This result can be compared with the range of estimates obtained from the resonance energy transfer experiments, D = 0.2-6.0 × 10(-6) cm(2)/s.