Error assessment in molecular dynamics trajectories using computed NMR chemical shifts

Accurate chemical shifts for the atoms in molecular mechanics (MD) trajectories can be obtained from quantum mechanical (QM) calculations that depend solely on the coordinates of the atoms in the localized regions surrounding atoms of interest. If these coordinates are correct and the sample size is adequate, the ensemble average of these chemical shifts should be equal to the chemical shifts obtained from NMR spectroscopy. If this is not the case, the coordinates must be incorrect. We have utilized this fact to quantify the errors associated with the backbone atoms in MD simulations of proteins. A library of regional conformers containing 169,499 members was constructed from 6 model proteins. The chemical shifts associated with the backbone atoms in each of these conformers was obtained from QM calculations using density functional theory at the B3LYP level with a 6-311+G(2d,p) basis set. Chemical shifts were assigned to each backbone atom in each MD simulation frame using a template matching approach. The ensemble average of these chemical shifts was compared to chemical shifts from NMR spectroscopy. A large systematic error was identified that affected the ¹H atoms of the peptide bonds involved in hydrogen bonding with water molecules or peptide backbone atoms. This error was highly sensitive to changes in electrostatic parameters. Smaller errors affecting the ¹³C^a and ¹⁵N atoms were also detected. We believe these errors could be useful as metrics for comparing the force-fields and parameter sets used in MD simulation because they are directly tied to errors in atomic coordinates.