High Accuracy of Karplus Equations for Relating Three-Bond J Couplings to Protein Backbone Torsion Angles

(3)J(CC) and (3)J(HNH) couplings are related to the intervening backbone torsion angle phi by standard Karplus equations. Although these couplings are known to be affected by parameters other than phi, 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 phi angles and experimental (3)J(CC) and (3)J(HNH) values than does the high-resolution X-ray structure. In intrinsically disordered proteins, (3)J(CC) and (3)J(HNH) 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 phi angles sampled by each residue.