Proline is a unique amino acid because its side chain is cyclic, forming a ring with the nitrogen atom of the amino backbone. This cyclic structure, called the pyrrolidine ring, significantly impacts the flexibility around the peptide bond.

Proline Structure and Angles

In any amino acid within a polypeptide chain, there are dihedral angles that describe the rotation around bonds in the backbone:

• The $\varphi$ (phi) angle represents the rotation around the bond between the nitrogen atom (N) and the alpha carbon ($\text{C}_\alpha$).
• The $\psi$ (psi) angle represents the rotation around the bond between the alpha carbon ($\text{C}_\alpha$) and the carbonyl carbon (C).

For most amino acids, these angles have a wide range of possible values, although some angles are unfavorable due to steric clashes (as shown in a Ramachandran plot).

In proline, the pyrrolidine ring is formed by the side chain connecting back to the nitrogen atom. This ring includes the nitrogen, $\text{C}_\alpha$, $\text{C}_\beta$, $\text{C}_\gamma$, and $\text{C}_\delta$ atoms. The formation of this ring locks the $\varphi$ angle into a very narrow range, typically around $-60^{\circ}$. This makes the backbone significantly less flexible at proline residues compared to other amino acids.

Reducing the Pyrrolidine Ring

When the pyrrolidine ring of proline is reduced to a linear form, it means the cyclic structure is broken. Specifically, the bond connecting the $\delta$-carbon ($\text{C}_\delta$) back to the nitrogen atom is cleaved or opened up. This process would convert the cyclic side chain into a linear side chain attached to the $\text{C}_\alpha$ carbon, and the nitrogen atom would now have its standard three bonds (to $\text{C}_\alpha$, to the preceding carbonyl carbon, and a hydrogen atom), similar to other amino acids like leucine or isoleucine (depending on the exact linear structure formed).

Impact on Dihedral Angles

With the pyrrolidine ring opened, the restriction it imposed on the rotation around the $\text{N}-\text{C}_\alpha$ bond is removed. The nitrogen atom and the $\text{C}_\alpha$ carbon are now free to rotate relative to each other over a much wider range of angles, just like in standard amino acids. This means the constraint on the $\varphi$ angle is significantly reduced.

The $\psi$ angle is the rotation around the $\text{C}_\alpha-\text{C}$ bond. While the ring structure in proline does somewhat influence the allowed values for $\psi$, the most dramatic effect is on $\varphi$. When the ring is broken, the freedom of rotation around $\text{C}_\alpha-\text{C}$ (the $\psi$ angle) might also change compared to proline, but the primary consequence of breaking the ring connected to the nitrogen is the relaxation of the $\varphi$ angle constraint.

Let's analyze the options:

• Option 1: constrained $\varphi$ than proline. Incorrect, the constraint is removed or reduced.
• Option 2: constrained $\psi$ than proline. Incorrect, the primary effect is on $\varphi$, and it doesn't necessarily become *more* constrained $\psi$.
• Option 3: relaxed $\varphi$ than proline. Correct, breaking the ring allows more freedom of rotation for the $\varphi$ angle.
• Option 4: unaffected $\varphi$ and $\psi$. Incorrect, the angles are definitely affected, particularly $\varphi$.

Therefore, reducing the pyrrolidine ring of proline to a linear form leads to a relaxed $\varphi$ angle compared to the highly constrained $\varphi$ angle found in proline.