Error assessment in molecular dynamics trajectories using computed NMR chemical shifts

Abstract

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 13Ca 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.

Evaluating amber force fields using computed NMR chemical shifts

“…The average RMS chemical shift error is determined for each protein and each force field using the squared difference between the calculated ensemble average and the observed values at each residue position. The results for the 1 H, N, and C a chemical shift errors are presented in Figures .…”

“…These proteins are listed in Table . The list includes the 6 proteins that were used to create the original library of conformers for the template matching approach . This set was augmented with two proteins (PDB 1L2Y and 2A3D) used in folding studies.…”

“…Chemical shifts are assigned to the 1 H, N, and C a backbone atoms of the 8 model proteins listed in Table using our template matching approach . These assignments are made for every residue position in each simulation frame.…”

“…Experimentally observed chemical shifts for these same residues are obtained from the Biological Magnetic Resonance Bank (BMRB) . For 1L2Y, only the 1 H chemical shift data is available, so this protein is excluded from error analysis involving N and C a chemical shifts. The global RMS error for each protein is calculated from the difference between computed and observed chemical shifts at each residue position.…”

“…The mean RMS errors for the 1 H, C a , and 15 N atoms in the protein backbones of the original model proteins were 1.575 ppm, 3.194 ppm, and 5.479 ppm, respectively. It was also apparent that the 1 H chemical shift error was much more significant than the error associated with the C a and N chemical shifts when these errors were compared to the mean chemical shift values for these atoms (8.323 ppm, 56.878 ppm, 118.695 ppm, respectively). Chemical shift errors that are a function of the flawed atomic coordinates in MD simulation frames could be useful for evaluating force fields.…”