In this paper we present ProCS15: a program that computes the isotropic chemical shielding values of backbone atoms and C\(\beta\) given a protein structure in less than a second. ProCS accounts for the effect of backbone and side-chain dihedral angles of a residue and the two neighboring residues, hydrogen bonding to the backbone amide group and H\(\alpha\) as well as ring-current effects \cite{Christensen_2011} on the hydrogen atoms and assumes that these effects are additive. The backbone, side-chain and hydrogen bonding terms are based on ~2.35 million OPBE/6-31G(d,p)//PM6 calculations on tripeptides and small structural models of hydrogen-bonding.
ProCS15 reproduces the chemical shielding values computed using PCM/OPBE/6-31G(d,p)//PM6-D3H+ for Ubiquitin and GB3 with RMSD values (after linear regression) of up to 2.5 ppm for carbon atoms, 0.8 ppm for hydrogen atoms, and 4.5 ppm for nitrogen. These deviations, which presumably result from the assumption of additivity and the simplified model systems, does not appear to preclude equal or better accuracy in comparison to experiment because the accuracies of the chemical shifts computed using ProCS15 (based on linear regression of the chemical shifts, cf. Eq \ref{eqn:scaling}) are very similar to the corresponding DFT calculations using single Ubiquitin and GB3 structures. The largest RMSD values observed for carbon, hydrogen, and nitrogen are, respectively, 2.2 (2.8) ppm, 0.7 (0.6) ppm, and 4.7 (4.6) ppm for ProCS15 (PCM/OPBE/6-31G(d,p)). These accuracies are very similar to DFT-based predictions made by other researchers (e.g. \cite{Zhu_2012},\cite{Zhu_2013}, \cite{Exner_2012}) as well as CheShift-2 \cite{24082119}, which is another DFT-based chemical shift predictor for C\(\alpha\) and C\(\beta\) atoms. The RMSD values computed using ProCS15 for Ubiquitin can be reduced by as much as 0.7, 0.1, and 0.5 ppm for carbon, hydrogen, and nitrogen by using NMR-derived structural ensembles. Similar increase in accuracy is also observed for CheShift-2 (for C\(\alpha\) and C\(\beta\)) while for empirical chemical shift predictors the increase in accuracy is at most 0.3 ppm.
The latter observation is another indication that empirical chemical shift predictors are less sensitive to small structural changes, which may make them less suitable for chemical shift-guided refinement of protein structure compared to DFT-based predictors. Christensen and co-workers \cite{24391900} have already demonstrated that this is the case for amide hydrogen bonding geometries using a previous incarnation of ProCS limited to amide proton chemical shift predictions and we are now planning similar refinement studies using all backbone atoms and C\(\beta\) chemical shifts.
ProCS15 is freely available at github.com/jensengroup/procs15 and all structures and DFT calculations, including the full NMR shielding tensors, are available at erda.dk/public/archives/YXJjaGl2ZS1TYk40VXo=/published-archive.html.