deletions | additions       diff --git a/section_Theory_ProCS_computes_the__.tex b/section_Theory_ProCS_computes_the__.tex  index c5f5153..11d0ea1 100644  --- a/section_Theory_ProCS_computes_the__.tex  +++ b/section_Theory_ProCS_computes_the__.tex 
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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  \begin{equation}  \label{eqn:sigmabb}  $$\Delta\sigma^{i-1}_{BB}=\sigma^{i-1}_{BB}(\phi^{i-1},\psi^{i-1},\chi^{i-1}_1,\chi^{i-1}_2,...)-\sigma^A(\phi_{\mathrm{std}},\psi_{\mathrm{std}})$$ \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}})  \end{equation}  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 by 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 $i+1$.   
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