= Solution
View the backbone along N–C$_\alpha$ to display $\phi=\angle(C'_{i-1},N_i,C_{\alpha i},C'_i)$ in a <Newman projection>. The front <amide> <nitrogen> carries the preceding <carbonyl> and H, while the back C$_\alpha$ carries the next <carbonyl>, H and side chain. Rotation changes the contacts among these groups. A corresponding view along C$_\alpha$–C$'$ displays $\psi$. The <peptide> C$'$–N bond itself is approximately planar and is not the freely rotating bond in either definition.
\Image[/past-exam-of-the-chemistry-b-course-of-the-university-of-cambridge/2024/paper-1-newman.png]
{title=Newman views of backbone torsions and the contrasting restrictions of glycine and proline}
\b[<glycine> replaces the side chain by a second <hydrogen>.] Removing C$_\beta$ removes many contacts that exclude backbone arrangements for other residues, so its allowed $\phi,\psi$ region is much broader and includes substantial positive-$\phi$ space. Its alpha <carbon> is also <achiral>, so the steric map is approximately mirror-symmetric between positive and negative torsions in the simple isolated-residue model.
\b[<proline> closes a five-membered ring from C$_\alpha$ through three methylenes back to <nitrogen>.] In the N–C$_\alpha$ projection, the <nitrogen>'s side-chain arm and C$_\alpha$'s C$_\beta$ arm are tied together, preventing unrestricted relative rotation. Its $\phi$ is consequently confined near the usual negative-$60^\circ$ region rather than exploring the broad range of an acyclic <amino acid>. <proline> also lacks a backbone N–H donor when incorporated into an ordinary internal <peptide>. Ring closure restricts $\phi$ strongly, but does not freeze every backbone or ring degree of freedom. These differences are naturally represented by distinct <Ramachandran plots>; the original torsion/steric analysis established the basis for such comparisons.<Stereochemistry of polypeptide chain configurations by G. N. Ramachandran and others>[1963, pp. 95–99, backbone torsions and steric restrictions]{ref}
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