Simulated and NMR-derived backbone dynamics of a protein with significant flexibility: A comparison of spectral densities for the βARK1 PH domain

A 7.6 ns molecular dynamics trajectory of the βARK1 PH domain in explicit water with appropriate ions was calculated at 300 K. Spectral densities at ω = 0, ω_N, and 0.87ω_H and the model-free parameters were evaluated from the experimental as well as the simulated data, taking the anisotropic overall motion of the protein into account. Experimental and simulated spectral densities are in reasonable general agreement for NH bond vectors, where the corresponding motions have converged within the simulation time. A sufficient sampling of the motions for NH bonds within flexible parts of the protein requires a longer simulation time. The simulated spectral densities J(0) and J(ω_N) are, on average, 4.5% and 16% lower than the experimental data; the corresponding numbers for the core residues are about 6%; the high-frequency spectral densities J(0.87ω_H) are lower by, on average, 16% (21% for the core). The simulated order parameters, S², are also lower, although the overall disagreement between the simulation and experiment is less pronounced: 1% for all residues and 6% for the core. The observed systematic decrease of simulated spectral density and the order parameters compared to the experimental data can be partially attributed to the ultrafast librational motion of the NH bonds with respect to their peptide plane, which was analyzed in detail. This systematic difference is most pronounced for J(0.87ω_H), which appears to be most sensitive to the slow, subnanosecond time scale of internal motion, whereas J(0) and J(ω_N) are dominated by the overall rotational tumbling of the protein. Similar discrepancies are observed between the experimentally measured ¹⁵N relaxation parameters (R₁, R₂, NOE) and their values calculated from the simulated spectral densities. The analysis of spectral densities provides additional information regarding the comparison of the simulated and experimental data, not available from the model-free analysis.