A new NMR protocol for estimating protein side chain rotameric preferences using ¹H relaxation and J couplings

Herein we demonstrate the utility of measuring initial ¹H NMR relaxation rates for determining protein side chain mobility in a human Pin1 WW domain thermostable mutant. To accomplish this, a ¹H spinlock field or TOCSY element is appended to the beginning of any multidimensional NMR experiment beginning on ¹H. This initial assessment is essential for determining the appropriate side chain motional model for fitting J coupling data. NMR signal intensities arising from three-bond J couplings ³J_N,HB2/3, ³J_CO,HB2/3, and ³J_HA,HB2/3 were analyzed using a script fitting to two alternative motional models: 1) a single χ₁-dihedral angle or 2) a mixed population of the three ideally staggered rotamers (gauche-, +60°; trans, 180°; gauche+, +300°). Using existing empirically determined Karplus coefficients, we initially calculated χ₁-dihedral angles for rigid residues that differed significantly from the ideal rotamers. Switching to Karplus coefficients derived using density functional theory (DFT), we obtained dihedral angles that better matched predictions based on a 1 μs molecular dynamics (MD) simulation starting from a high-resolution X-ray crystal structure. Previous empiric models were inaccurate because they utilized information from mixed populations of rigid and mobile side chains, underscoring the importance of using ¹H NMR relaxation to discern rigid from mobile residues prior to J coupling analysis. Moreover, empirically derived Karplus coefficients relied on sparse data for χ₁-dihedral angles outside the three major rotamers, further limiting their accuracy. Of note, our revised Karplus coefficients include a phase offset term that breaks the symmetry of the Karplus relationship; they are significantly different for Ser/Thr and Val/Ile residues and for helix versus sheet residues. While there is general agreement between NMR data and MD simulations in predicting the relative rigidity/mobility of side chains, there were some pointed discrepancies, suggesting that NMR may be useful to guiding MD parametrization in the future.