Ab Initio Study of the Effects of Torsion Angles on Carbon-13 Nuclear Magnetic Resonance Chemical Shielding in N-Formyl-L-alanine Amide, N-Formyl-L-valine Amide, and Some Simple Model Compounds: Applications to Protein NMR Spectroscopy

In order to understand better the origins of the chemical shift nonequivalencies observed in proteins due to folding, we have investigated the effects of torsion angles on ¹³C nuclear magnetic resonance shielding in a series of compounds, using a gauge-including atomic orbital (GIAO) method. We regard the naturally occurring L-amino acids as ethane derivatives C^βHABC^αHCD, and we have computed the effects of χ¹ (HC^βC^αH) on C^α, C^β shielding in ethane, propane, 2-methylpropane, aminoethane, propanal, and 2-aminopropanal, as well as the effects of φ, ψ, and χ¹ torsion angles on C^α, C^β shielding in the peptide models N-formyl-L-alanine amide and N-formyl-L-valine amide. Our results show for the simpler model compounds that C^α substitution causes a much larger effect on C^β shielding (as a function of χ¹) than on C^α shielding. For the two peptide model compounds, φ, ψ torsions strongly affect C^α, C^β shielding, with the largest χ¹ effect being seen with valine C^β. These dependencies are discussed in relation to some of the chemical shift nonequivalencies due to folding observed in the ¹³C NMR spectra of Drosophila melanogaster calmodulin and Staphylococcal nuclease.