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

Abstract

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, 13C R1, R2, and heteronuclear NOE relaxation rates have been determined for the methine and stereochemically assigned methylene Cα and Cβ 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-S2). Applying the LF-S2 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 1Hα–13Cα and 1Hβ–13Cβ bond vectors with reasonable accuracy. However, for the 1Hβ–13Cβ bond vectors exhibiting aggregate order parameter S2 values less than 0.85, only 1% of the MD-derived predictions lie with 1 σ of the experimentally determined autocorrelation functions and only 7% within 2 σ. 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 13C relaxation measurements in guiding the optimization of the side chain dynamics characteristics of protein molecular simulations.

Molecular Dynamics-Assisted Optimization of Protein NMR Relaxation Analysis

“… 8 Furthermore, for positions exhibiting order parameter values below the rigid limit ( S i 2 = 1), the root-mean-square deviation of the experimental uncertainties in the NMR relaxation measurements was found to closely match the resultant rmsd on the ( S f 2 , S H 2 , S X 2 ) order parameters that were derived from the Monte Carlo analysis of those measurements. 7 …”

“…While in all cases, the calculation of NMR relaxation values utilizes the full range of the complete autocorrelation function, in statistical analysis of the quality of fit between the order parameter-derived autocorrelation functions and those obtained from the MD trajectories, the standard deviation was calculated starting from 30 ps in recognition of the fact that conformational dynamics that are substantially faster than the 1 H Larmor frequency cannot be adequately characterized by this method. 7 …”

“…However, in this regard, it may be noted that even in the context of a single field relaxation analysis, the most commonly invoked four-parameter unconstrained biexponential ( S f 2 ,τ f , S s 2 ,τ s ) representation can underperform an alternative three-parameter expression that is based upon a simplified version of the time constant-constrained triexponential (TCCT) representation. 7 These results indicate the potential for further optimization of the form of the model autocorrelation function without expanding the number of adjustable parameters.…”

Fitting side-chain NMR relaxation data using molecular simulations

“…A common approach to compare MD and NMR relaxation experiments involves calculating order parameters from the simulations and comparing to those extracted from the experiments. The results of such comparisons have shown that while MD simulations generally give a relatively good agreement with order parameters for the backbone amide groups, the agreement for methyl bearing side chains is more variable (Bremi et al, 1997;Skrynnikov et al, 2002;Best et al, 2005;Showalter et al, 2007;Liao et al, 2012;O'Brien et al, 2016;Bowman, 2016;Anderson et al, 2020).…”

“…Comparison to experiments revealed systematic deviations from simulations with several different force fields, and corrections to the methyl torsion potential were developed based on quantum calculations and shown to increase agreement with experiments ( Hoffmann et al, 2018a , 2020 ). Despite these improvements and a substantial body of work on studies of side chain dynamics ( Lee et al, 1997 ; Palmer III, 1997 ; Ming and Brüschweiler, 2004 ; Cousin et al, 2018 ; Anderson et al, 2020 ), the agreement remains imperfect and further improvements would be desirable.…”