Large Variations in One-Bond ¹³C^α−¹³C^β J Couplings in Polypeptides Correlate with Backbone Conformation

One-bond ¹J_CαCβ scalar couplings, measured in the protein ubiquitin, exhibit a strong dependence on the local backbone conformation. Empirically, the deviation from the ¹J_CαCβ value measured in the corresponding free amino acid, can be expressed as Δ¹J_CαCβ = 1.3 + 0.6 cos(ψ − 61°) + 2.2 cos[2(ψ − 61°)] − 0.9 cos[2(φ + 20°)] ± 0.5 Hz, where φ and ψ are the intraresidue polypeptide backbone torsion angles obtained from ubiquitin's X-ray structure. The relation between ¹J_CαCβ and backbone torsion angles is confirmed by density functional theory (DFT) calculations on the peptide analogue Ace-Ala-NMe.