Principles of Protein Structure - H. Schultz 1982

The structural role of the peptide bond
Peptide bond parameters

Rotation around the peptide bond is hindered. The geometric parameters of the peptide bond are shown in Fig. 2.1, a. These data were obtained by Pauling and Corey [25] from the crystal structures of molecules containing one or more peptide bonds. The most unexpected finding was the short distance between the C' and N atoms, which is 0.15 Å, or 10%, shorter than usual. In addition, the C'—O double bond is 0.02 Å longer than in aldehydes and ketones [26]. Pauling et al. explained this effect by the Resonance of two limiting structures shown in Fig. 2.1, b. In Structure I, the C'—N bond involves only σ-electrons, whose axial Symmetry allows free rotation, whereas in structure II, the σ- and π-electrons of the C'—N bond result in a large dipole moment and hindered rotation.

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Fig. 2.1. Amide or peptide bond [29]. a — Bond Angles and distances for the trans-peptide bond according to Pauling and Corey [25]. The C' and N atoms lie in a plane; b — two limiting electronic structures of the bond; form I allows free rotation, whereas form II, which has a large dipole moment, exhibits hindered rotation. The hybrid structure consists of 60% form I and 40% form II, as inferred from the C'—N bond length; the resonance energy is about 20 kcal/mol. c — bond angles and interatomic distances in the rarely occurring cis-peptide bond.

Fig. 2.2. Definition of dihedral angles in a polypeptide chain; the chain direction is indicated. A Ser residue is used to illustrate the definition of side-chain dihedral angles.

The notation follows the 1969 IUPAC—IUB Commission recommendations [21]. For the designation of other dihedral angles in side chains, these recommendations should be consulted. Zero values for the dihedral angles are defined as follows:

In the main chain shown, the angles are φ_і = 180° and ψ_і = 180°. As indicated by the shading, the six atoms C^а_і, С'_і, O_і, N_і+1, C^а_і+1, H_і+1 generally lie in the same plane, i.e., the ω angle is equal to 180°. H_і and H_і+1 are the amide group hydrogen atoms. The indicated directions of rotation for ω, ψ, and φ are positive when viewed from the N-terminal atom of the given peptide bond and rotating the C-terminal end of this bond in the direction indicated by the arrows (clockwise). The same definition applies to χ when viewed from the atom closest to the C_а atom.

Judging by the difference in Bond Lengths, the resulting hybrid structure comprises forms I and II in a 3 : 2 ratio, with π-electrons delocalized over the C'—O and C'—N bonds. Thermodynamic data indicate that the resonance energy is about 20 kcal/mol [23]. Since structure II is planar, the hybrid structure is also planar, meaning that the six atoms C^а_і, С_і, О_і, N_і+1, H_і+1, C^а_і+1 (Fig. 2.2) lie in a single plane.

Each residue in the polypeptide main chain is described by two dihedral angles. Given a rigid peptide bond and fairly constant bond lengths and valence angles, the conformation of the polypeptide chain is essentially described by the dihedral angles φ and ψ at the C_а atoms, as shown in Fig. 2.2. This description conforms to the 1969 IUPAC—IUB nomenclature [21]. The torsional angle ω is also introduced, although rotation around the C'—N bond is hindered. All dihedral angles in side chains are denoted by the letter χ with a subscript that can range from one to five. The Ser side chain shown in Fig. 2.2 is unbranched, and therefore only a single subscript is required. A comprehensive Description of the notation can be found in the IUPAC—IUB recommendations [21].

It should be mentioned that earlier, in 1966, a different reference point was semi-officially introduced for the main-chain dihedral angles φ and ψ [27]:

Since quite A number of publications on Cell/13.html">Protein Structure determination appeared between these two dates, the older notation can still occasionally be found in the literature.