ProCS15 computes the chemical shift of an atom in residue \(i\) by \[\label{eqn:scaling} \delta^i = b-a\sigma^i\] where \(a\) and \(b\) are empirically determined parameters as discussed further below and \(\sigma^i\) is the isotropic chemical shielding of an atom in residue \(i\). \(\sigma^i\) is computed from the protein structure using the following equation (some of these terms only contribute for certain atom types as described below) \[\label{eqn:procs} \sigma^i=\sigma^i_{BB}+\Delta\sigma^{i-1}_{BB}+\Delta\sigma^{i+1}_{BB}+\Delta\sigma^{i}_{HB}+\Delta\sigma^{i}_{H\alpha B}+\Delta\sigma^{i}_{RC}+\Delta\sigma^{i}_{w}\] Here \(\sigma^i_{BB}=\sigma^i_{BB}(\phi^i,\psi^i,\chi^i_1,\chi^i_2,...)\) is the chemical shielding computed for an Ac-AXA-NMe tripeptide (AXA for short, Figure \ref{fig:bb}), where X is residue \(i\), for a given combination of \(\phi\), \(\psi\), and \(\chi_1\), \(\chi_2\), ... values as described further in Section \ref{subsec:bbscan}. \(\Delta\sigma^{i-1}_{BB}\) is the change in chemical shielding of an atom in residue \(i\) due to the presence of the side-chain of residue \(i-1\). It is computed as \[\label{eqn:sigmabb} \Delta\sigma^{i-1}_{BB}=\sigma^{i-1}_{BB}(\phi^{i-1},\psi^{i-1},\chi^{i-1}_1,\chi^{i-1}_2,...)-\sigma^A(\phi_{\mathrm{std}},\psi_{\mathrm{std}})\] Here \(\sigma^{i-1}_{BB}\) is the chemical shielding computed for an AXA tripeptide where X is residue \(i-1\), and \(\sigma^A\) is from the corresponding calculation on the AAA tripeptide but using \(\phi_{\mathrm{std}}\) = -120° and \(\psi_{\mathrm{std}}\) = 140° for all \(\phi\) and \(\psi\) angles. For example, if residue \(i\) is a Ser and residue \(i-1\) is a Val then the effect of the Val side-chain on the C\(\beta\) chemical shielding of the Ser residue is computed as the difference in the chemical shielding of the C\(\beta\) atom in the C-terminal Ala residue computed for an AVA and AAA tripeptide. This approach assumes that the effect of the \(i-1\) side chain on the chemical shielding values of the atoms in residue \(i\) are independent of the conformations \(\phi_i\) and \(\psi_i\) angles and the nature of residue \(i\). \(\sigma^{i+1}_{BB}\) is the corresponding change in chemical shielding of an atom in residue \(i\) due to the presence of the side-chain of residue \(i+1\).