Molecular Dynamics-Assisted Optimization of Protein NMR Relaxation Analysis

NMR relaxation analysis of the mobile residues in globular proteins is sensitive to the form of the experimentally fitted internal autocorrelation function, which is used to represent that motion. Different order parameter representations can precisely fit the same set of ¹⁵N R₁, R₂, and heteronuclear NOE measurements while yielding significantly divergent predictions of the underlying autocorrelation functions, indicating the insufficiency of these experimental relaxation data for assessing which order parameter representation provides the most physically realistic predictions. Molecular dynamics simulations offer an unparalleled capability for discriminating among different order parameter representations to assess which representation can most accurately model a wide range of physically realistic autocorrelation functions. Six currently utilized AMBER and CHARMM force fields were applied to calculate autocorrelation functions for the backbone H-N bond vectors of ubiquitin as an operational test set. An optimized time constant-constrained triexponential (TCCT) representation was shown to markedly outperform the widely used (S_f²,τ_s,S²) extended Lipari-Szabo representation and the more closely related (S_f²,S_H², S_N²) Larmor frequency-selective representation. Optimization of the TCCT representation at both 600 and 900 MHz ¹H converged to the same parameterization. The higher magnetic field yielded systematically larger deviations in the back-prediction of the autocorrelation functions for the mobile amides, indicating little added benefit from multiple field measurements in analyzing amides that lack slower (∼ms) exchange line-broadening effects. Experimental ¹⁵N relaxation data efficiently distinguished among the different force fields with regard to their prediction of ubiquitin backbone conformational dynamics in the ps-ns time frame. While the earlier AMBER 99SB and CHARMM27 force fields underestimate the scale of backbone dynamics, which occur in this time frame, AMBER 14SB provided the most consistent predictions for the well-averaged highly mobile C-terminal residues of ubiquitin.