Protein Structure Refinement and Prediction via NMR Chemical Shifts and Quantum Chemistry

An approach utilizing Bayesian probability and NMR chemical shifts to derive structural information about proteins is presented. The method is based on measurement of a spectroscopic parameter, P (such as a chemical shift or a coupling constant), which is then transformed via use of a corresponding parameter surface, P(α,β), into an unnormalized torsion angle probability or Z surface, Z(α,β). Using empirically determined parameter surfaces, the backbone ϕ,ψ error between prediction and experiment is about 17°, but for 10 Ala residues in Staphylococcal nuclease, this reduces to ~10° when quantum mechanically computed ¹³C shielding surfaces are utilized. The Z-surface approach permits unique combination of a wide variety of spectroscopic observables for refinement and prediction of protein structure in both solution- or solid-state systems.