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\section{Theory}  ProCS computes the chemical shift of an atom in residue \textit{i} by  $$ \begin{equation}  \label{eqn:procs}  \delta^i = b-a\sigma^i$$ b-a\sigma^i  \end{equation}  where \textit{b} and \textit{a} are empirically determined parameters as discussed further below and σi is the isotropic chemical shielding of an atom in residue \textit{i}. $\sigma^i$ is computed from the protein structure the following equation  $$\sigma^i=\sigma^i_{BB}+\Delta\sigma^{i-1}_{BB}+\Delta\sigma^{i+1}_{BB}+\Delta\sigma^{i}_{HB}+\Delta\sigma^{i}_{H\alpha B}+\Delta\sigma^{i}_{RC} $$  Here $\sigma^i_{BB}=\sigma^i_{BB}(\phi^i,\psi^i,\chi^i_1,\chi^i_2,...)$ is the chemical shielding computed for a Ac-AXA-NMe tripeptide (AXA for short, Figure 1), where X is residue $i$, for a given combination of $\phi$, $\psi$, and $\chi_1$, $\chi_2$, ... values as described further in Section 4.1. 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  $$\Delta\sigma^{i-1}_{BB}=\sigma^{i-1}_{BB}(\phi^{i-1},\psi^{i-1},\chi^{i-1}_1,\chi^{i-1}_2,...)-\sigma^A(\phi_{\mathrm{std}},\psi_{\mathrm{std}})$$  i.e. $\sigma^{i-1}_{BB}$ is the chemical shielding computed for a 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 CB chemical shielding of the Ser residue is computed by as the difference in the chemical shielding of the CB 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 the residue $i$. is the corresponding change in chemical shielding of an atom in residue i due to the presence of the side-chain of residue $i+1$.