Ramachandran Angles in Protein Conformation and Structure

Why are Ramachandran angles of first and the last amino acid not necessary to define the full 3D structure of a protein chain?

The Ramachandran angles, also known as φ (phi) and ψ (psi), describe the rotations of the peptide backbone around the N-Cα and Cα-C bonds, respectively. These angles determine the conformation of the protein chain and play a crucial role in defining its three-dimensional structure. However, the φ and ψ angles of the first and last amino acids are not necessary to fully define the protein’s 3D structure.

The reason for this lies in the nature of peptide bonds and the constraints they impose on the protein backbone. A peptide bond forms between the carboxyl group (C=O) of one amino acid and the amino group (N-H) of another amino acid, creating a rigid planar structure. This planar geometry restricts the free rotation around the peptide bond, resulting in a relatively fixed conformation

For the first amino acid in a protein, the φ angle represents the rotation around the N-Cα bond, and since there is no preceding amino acid, this angle is not pertinent. Similarly, the ψ angle represents the rotation around the Cα-C bond, and in the case of the last amino acid, there is no subsequent amino acid to interact with, making the ψ angle irrelevant

These first and last residues in a protein chain typically adopt secondary structure elements, such as an alpha helix or beta strand, where the backbone conformation is highly constrained. The conformation of these elements is primarily determined by the interactions between amino acid residues within the secondary structure itself, rather than by the φ and ψ angles of the first and last residues

Therefore, while the Ramachandran angles are crucial for determining the conformation of most amino acids in a protein chain, they are not necessary for the first and last residues since their conformation is predominantly dictated by secondary structure constraints

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