High accuracy of Karplus equations for relating three-bond J couplings to protein backbone torsion angles.

(3) JC'C' and (3) JHNHα couplings are related to the intervening backbone torsion angle ${\varphi }$ by standard Karplus equations. Although these couplings are known to be affected by parameters other than ${\varphi }$, including H-bonding, valence angles and residue type, experimental results and quantum calculations indicate that the impact of these latter parameters is typically very small. The solution NMR structure of protein GB3, newly refined by using extensive sets of residual dipolar couplings, yields 50-60 % better Karplus equation agreement between ${\varphi }$ angles and experimental (3) JC'C' and (3) JHNHα values than does the high-resolution X-ray structure. In intrinsically disordered proteins, (3) JC'C' and (3) JHNHα couplings can be measured at even higher accuracy, and the impact of factors other than the intervening torsion angle on (3) J will be smaller than in folded proteins, making these couplings exceptionally valuable reporters on the ensemble of ${\varphi }$ angles sampled by each residue.