Predicting chemical shifts in proteins: Structure refinement of valine residues by using ab initio and empirical geometry optimizations

We have investigated the carbon-13 solution nuclear magnetic resonance (NMR) chemical shifts of C(α), C(β) and C(γ) carbons of 19 valine residues in a vertebrate calmodulin, a nuclease from Staphylococcus aureus, and a ubiquitin. Using empirical chemical shift surfaces to predict C(α), C(β) shifts from known, X-ray φ, ψ values, we find moderate accord between prediction and experiment. Ab initio calculations with coupled Hartree-Fock (HF) methods and X-ray structures yield poor agreement with experiment. There is an improvement in the ab initio results when the side chain (χ1) torsion angles are adjusted to their lowest energy conformers, using either ab initio quantum chemical or empirical methods, and a further small improvement when the effects of peptide-backbone charge fields are introduced. However, although the theoreticai and experimental results are highly correlated (R² ~0.90), the observed slopes of ~-0.6-0.8 are less than the ideal value of -1, even when large uniform basis sets are used. Use of density functional theory (DFT) methods improves the quality of the predictions for both C(α) (slope = -1.1, R² = 0.91) and C(β) (slope = -0.93, R² = 0.89), as well as giving moderately good results for C(γ). This effect is thought to arise from a small, conformationally-sensitive contribution to shielding arising from electron correlation. Additional shielding calculations on model compounds reveal similar effects. Results for valine residues in interleukin-1β are less highly correlated, possibly due to larger crystal-solution structural differences. When taken together, these results for 19 valine residues in 3 proteins indicate that choosing the lowest energy XI conformer together with X-ray φ,ψ values enables the successful prediction of both Ca and CP shifts, with DFT giving close to ideal slopes and R² values between theory and experiment. These results strongly suggest that the most highly populated valine side-chain conformers are those having the lowest (computationally determined) energy, as evidenced by the ability to predict essentially all C(α), C(β) chemical shifts in calmodulin, SNase, and ubiquitin, as well as moderate accord for Cr. These observations suggest a role for chemical shifts and energy minimization/geometry optimization in the refinement of protein structures in solution, and potentially in the solid state as well.