3 Side Chain Conformation.

The side chain atoms of amino acids are sequentially named according to the Greek alphabet. This naming scheme is commonly translated to latin characters. For example, a lysine side chain is comprised of a β carbon (CB), a γ carbon (CG), a δ carbon (CD), an ε carbon (CE) and a Ζ nitrogen (NZ). Ambiguities, for example in phenylalanine, are resolved with numbers.

**Atom naming in amino acid side chains** Left: Lysine, Right: Phenylalanine

We suggest to consult the protein data bank as a naming reference, e.g. https://www.rcsb.org/ligand/LYS. Due to almost constant bond lengths and bond angles, amino acid side chains can approximately be described with a set of up to 4 dihedral angles (sequentially numbered chi angles, i.e. Χ_1-4). The side chain conformations, so called rotamers, cluster around energetically preferred conformations.

Naming convention in protein side chains — **Side chain dihedrals** Chi (Χ) angles defining side chain conformations in a lysine-tyrosine di-peptide

The Χ₁ angle is subject to restrictions due to steric hindrance between the γ side chain atom(s) and the main chain. The favoured conformations of the side chain torsion angles are referred to as gauche(+), trans and gauche(-). These are indicated in the diagrams below in which the amino acid is viewed along the C_β-C_α bond (Χ₁).

Overview of different chi-angle conformations — **Side chain conformations**. Left: Χ₁-Χ₂ plot for Lysine. The color gradient indicates the frequency of conformations found in experimentally determined protein structures. Right: Schematic view into the C_β (top)-C_α (hidden below) bond. Here the Χ₁ angle can be seen as the angle between the Nitrogen and C_γ atom.

The most frequent Χ₁ conformation is gauche(+) in which the γ side chain atom is opposite to the residue main chain carbonyl group when viewed along the C_β-C_α bond.

The second most frequent Χ₁ conformation is trans in which the side chain γ atom is opposite the main chain nitrogen.

The least frequent Χ₁ conformation is gauche(-) which occurs when the side chain is opposite the hydrogen substituent on the C_α atom. This conformation is unstable because the γ atom is in close contact with the main chain CO and NH groups. The gauche(-) conformation is occasionally adopted by serine or threonine residues in a helix where the steric hindrance is offset by a hydrogen bond between the γ oxygen atom and the main chain.

Aliphatic amino acids which are bifurcated at C_β, i.e. valine and isoleucine, do not adopt the trans conformation for Χ₁ very often as this involves one of the C_γ atoms being in the unfavourable gauche(-) 'position'.

In general, side chains tend to adopt the same three torsion angles (+/-60 and 180 degrees) about Χ₂ since these correspond to staggered conformations. However, for residues with an sp2 hybridised γ atom such as phenylalanine, tyrosine, etc., Χ₂ rarely equals 180 degrees because this would involve an eclipsed conformation. For these side chains the Χ₂ angle is usually close to +/-90 degrees as this minimises close contacts. For residues such as aspartate and asparagine the Χ₂ angles are strongly influenced by the hydrogen bonding capacity of the side chain and its environment. Consequently, these residues adopt a wide range of Χ₂ angles.