Quantum Mechanical Study of Vicinal J Spin-Spin Coupling Constants for the Protein Backbone

We have performed densisty functional theory (DFT) calculations of vicinal J coupling constants involving the backbone torsional angle for the protein GB3 using our recently developed automatic fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach (Xiao He et al. J. Phys. Chem. B 2009, 113, 10380-10388). Interestingly, the calculated values based on an NMR structure are more accurate than those based on a high-resolution X-ray strucure because the NMR structure was refined using a large number of residual dipolar couplings (RDCs) whereas the hydrogen atoms were added into the X-ray structure in idealized positions, confirming that the postioning of the hydrogen atoms relative to the backbone atoms is important to the accuracy of J coupling constant prediction. By comparing three Karplus equations, our results have demonstrated that hydrogen bonding, substituent and electrostatic effects could have significant impacts on vicinal J couplings even though they depend mostly on the intervening dihedral angles. The root-mean-square deviations (RMSDs) of the calculated (3)J(H(N),H(α)), (3)J(H(N),C(β)), (3)J(H(N),C') values based on the NMR structure are 0.52, 0.25, and 0.35 Hz, respectively, after taking the dynamic effect into consideration. The excellent accuracy demonstrates that our AF-QM/MM approach is a useful tool to study the relationship between J coupling constants and the structure and dynamics of proteins.