13C NMR Relaxation Analysis of Protein GB3 for the Assessment of Side Chain Dynamics Predictions by Current AMBER and CHARMM Force Fields

Molecular simulations with seven current AMBER- and CHARMM-based force fields yield markedly differing internal bond vector autocorrelation function predictions for many of the 223 methine and methylene H-C bonds of the 56-residue protein GB3. To enable quantification of accuracy, C-13 R-1, R-2, and heteronuclear NOE relaxation rates have been determined for the methine and stereochemically assigned methylene C-alpha and C-beta positions. With only three experimental relaxation values for each bond vector, central to this analysis is the accuracy with which MD-derived autocorrelation curves can be represented by a 3-parameter equation which, in turn, maps onto the NMR relaxation values. In contrast to the more widely used extended Lipari-Szabo order parameter representation, 95% of these MD-derived internal autocorrelation curves for GB3 can be fitted to within 1.0% rmsd over the time frame from 30 ps to 4 ns by a biexponential Larmor frequency-selective representation (LF-S-2). Applying the LF-S-2 representation to the experimental relaxation rates and uncertainties serves to determine the boundary range for the autocorrelation function of each bond vector consistent with the experimental data. Not surprisingly, all seven force fields predict the autocorrelation functions for the more motionally restricted H-1(alpha)-C-13(alpha) and H-1(beta)-C-13(beta) bond vectors with reasonable accuracy. However, for the H-1(beta)-C-13(beta) bond vectors exhibiting aggregate order parameter S-2 values less than 0.85, only 1% of the MD-derived predictions lie with 1 sigma of the experimentally determined autocorrelation functions and only 7% within 2 sigma. On the other hand, substantial residue type-specific improvements in predictive performance were observed among the recent AMBER force fields. This analysis indicates considerable potential for the use of C-13 relaxation measurements in guiding the optimization of the side chain dynamics characteristics of protein molecular simulations.