Principles of Protein Structure - H. Schultz 1982

The structural role of the peptide bond
Steric hindrances

The values of the backbone dihedral angles are restricted. The conformational flexibility of the polypeptide chain is limited. The rigid peptide bond significantly constrains polypeptide chain mobility. Furthermore, the peptide unit is quite bulky and introduces substantial steric hindrances. While working on Collagen Structure models, Ramachandran et al. [28] investigated how long-range steric interactions restrict the freedom of rotation around the N—C_a and C_a—C' chain bonds, i.e., the range of allowable angles — and ψ. To this end, using known crystal structures, they determined the Van der Waals Contact distances between the atoms of interest and obtained values characterizing the so-called lower normal limit (Table 2.1). In addition, they determined the "lower limit o boundary", which was 0.10 Å smaller than the "lower normal" limit [29]. It turned out that, with an error of 0.05 Å, the distances corresponding to the contacts were equal to the sums of the contact radii, meaning that THE CONTRIBUTION OF a given atom to the contact distance did not depend on its partner. Consequently, the atoms of chosen sizes used in the calculations probed space essentially in the same way as space-filling models employing rigid spheres of contact radius do.

Class="center">Table 2.1 Empirical lower limits of non-bonded contact distances [29]

The conformational space, represented by the range of angles — and ψ allowed for a residue lacking a side chain (Gly), is shown in Fig. 2.3a. This ∅ψ-map was constructed for a rigid peptide bond with the parameters given in Fig. 2.1a, taking into account both the lower normal and lower limiting boundaries of contact distances (Table 2.1). The map coordinates are labeled According to the old nomenclature [27]. When plotting the new values of ∅, ψ [21], the origin shifts to the center of the map. The Gly residue possesses a large and continuous allowed region occupying about 50% of the space. Explicitly forbidden contacts arise between the H_i+1 and O_i-1 atoms in the center, as well as between the O_i-1 and O_i atoms. Less prominent hindrances are found between the H_i and H_i+1, O_i-1, and C'_i atoms, as well as O_i-1 and N_i+1. The steric interaction between the N_i and H_i+1 atoms is the least significant.

For all residues except Gly and Pro, essentially the same regions are sterically allowed. In the presence of a C_ß atom, i.e., for all residues except Gly, the space of allowed Conformations is sharply restricted to the regions shown in Fig. 2.3b. In the rigid-sphere model with radii corresponding to the normal and lower limiting boundaries, only 8% and 22% of the space remain allowed, respectively. The map shows the contacts of C_β atoms that restrict the three large regions of Gly space. The two fully allowed regions encompass the conformations of the right-handed a-helix and of parallel and antiparallel ß-structures, respectively. The conditionally allowed region (—, ψ)=(+ 60°, + 60°) contains the left-handed a_L-helix. Aside from Gly, Fig. 2.3b fails to describe only the Pro residue. Pro behaves differently because its side chain, bonded to the peptide nitrogen, fixes — = — 60° ± 20°. The allowed variation of the ф angles in the case of Pro reflects The flexibility of the pyrrolidine ring geometry.

Fig. 2.3. Allowed regions for backbone dihedral angles. The Pauling and Corey Peptide bond parameters shown in Fig. 2.1 are adopted [29].

These maps are often referred to as "Ramachandran maps". a — map for Glycine, which lacks a side chain, using the rigid-sphere model with normal and lower boundary (———) contact distances given in Table 2.1. Forbidden contacts are indicated in certain regions. Atom designations are given in Fig. 2.2. b — map for Amino Acids containing C_β atoms, constructed using the same rigid-sphere model. The conformations of the right-handed a-helix, ß-pleated sheet, and collagen are indicated. Steric hindrances caused by the C_β atom are marked, which reduce the large glycine region to the smaller region shown in the figure. The three allowed regions are sometimes designated as a_R — right-handed a-helix, the region around symbol a; a_L — left-handed a-helix, the region (∅, ψ) ≈ (+60°, +60°); ε — extended chain, the region around symbol ß. Assuming the rigid-sphere model (- - - normal radii; — — — radii corresponding to lower limits), the regions allowed for poly-L-cis-Alanine are indicated. The conformation shown in Fig. 2.6 is denoted by x, and the conformation corresponding to poly-L-Proline I (fully cis) is denoted by a circled x.