Prediction of Bond Vector Autocorrelation Functions from Larmor Frequency-Selective Order Parameter Analysis of NMR Relaxation Data

Protein molecular dynamics interpretation of the standard R-1, R-2, and heteronuclear NOE relaxation measurements has typically been limited to a single S-2 order parameter which is often insufficient to characterize the rich content of these NMR experiments. In the absence of exchange linebroadening, an optimized reduced spectral density analysis of these measurements can yield spectral density values at three distinct frequencies. Surprisingly, these three discrete spectral density values have proven to be sufficient for a Larmor frequency selective order parameter analysis of the 223 methine and methylene H-C bonds of the B3 domain of Protein G (GB3) to accurately back-calculate the entire curve of the corresponding bond vector autocorrelation functions upon which the NMR relaxation behavior depends. The C-13 relaxation values calculated from 2 mu s of CHARMM36 simulation trajectories yielded the corresponding autocorrelation functions to an average rmsd of 0.44% with only three bond vectors having rmsd errors slightly greater than 1.0%. Similar quality predictions were obtained using the CHARMM22/CMAP, AMBER ff99SB, and AMBER ff99SB-ILDN force fields. Analogous predictions for the backbone N-15 relaxation values were 3-fold more accurate. Excluding seven residues for which either experimental data is lacking or previous MD studies have indicated markedly divergent dynamics predictions, the CHARMM36-derived and experimentally derived 15N relaxation values for the remaining 48 amides of GB3 agree to an average of 0.016, 0.010, and 0.020 for the fast limit (S-f(2)) and Larmor frequency-selective (S-H(2) and S-N(2) order parameters, respectively. In contrast, for a substantial fraction of side chain positions, the statistical uncertainties obtained in the relaxation value predictions from each force field were appreciably less than the much larger differences predicted among these force fields, indicating a significant opportunity for experimental NMR relaxation measurements to provide structurally interpretable guidance for further optimizing the prediction of protein dynamics.