Abbreviations and Symbols for the Description of the Conformation of Polypeptide Chains

Continued from 2. The Sequence Rules and Choice of Torsion Angle

Contents

• 3. The Main Chain (or Polypeptide Backbone)
  • 3.1. Designation of bonds
  • 3.2. Torsion angles
  • 3.3. Chain terminations

• References for this section

3.1. Designation of bonds.

Bonds between main-chain atoms are denoted by the symbols of the two atoms terminating them, e.g., N_i-C_i, C_i-C_i, C_i-N_i+1, C_i-O_i, N_i-H_i. Abbreviated symbols should not be used. Bond lengths are written b(C_i,N_i+l), etc.

3.2. Torsion angles.

3.2.1. The principal torsion angle describing rotation about N-C is denoted by , that describing rotation about C-C is denoted by , and that describing rotation about C-N is denoted by . The symbols _i, _i, and _i are used to denote torsion angles of bonds within the i th residue in the case of and and between the i th and (i +1)th residues in the case of ; specifically, i refers to the torsion angle of the sequence of atoms C_i-1, N_i, C_i, C_i; _ito the sequence Ni, Ci, C_i, Ni+l; and i to the sequence Ci, C_i, N_i+1, C_i+1 (see Figure 5). In accordance with Rules 1.6 and 2.1.1, these torsion angles are ascribed zero values for eclipsed conformations of the main-chain atoms N, C, and C, that is, for the so-called cis conformations (see Table I).

Figure 5: Perspective drawing of a section of polypeptide chain representing two peptide units. The limits of a residue are indicated by dashed lines, and recommended notations for atoms and torsion angles are indicated. The chain is shown in a fully extended conformation (_i = _i = _i = 180^o), and the residue illustrated is L.

(i) This convention differs from that proposed by Edsall et al. (1966). The new designation of angles may be derived from the old by adding 180^o to, or subtracting 180^o from, the latter. (This statement is precisely correct only if the peptide bond is exactly planar, which is not generally the case in experimentally determined structures).

(ii) Owing to the partial double-bond character of , it is normally possible for to assume values only in the A neighborhood of 0 or 180^o. ~ 180^o is the value which is generally found (i.e., the trans conformation),

(iii) A "fully extended" polypeptide chain is characterized by = = = +180^o. The case of = = 0^o would involve the relations indicated in Table I.

(iv) Table II gives values of and for various well-known regular structures. It is noteworthy that a right-handed helix has negative torsion angles.

(v) Figure 6 is a typical conformational map ( - plot) using the rules enunciated above.

Table I Main-Chain Torsion Angles for Various Conformations in Peptides of L-Amino Acids.^a,b

(deg)	Rotation about N-C (to N-H)	(deg)	Rotation about C-C (to C-O)
0	C-C trans	0	C-N trans
+60	C-H cis	+60	C-R cis
+120	C-R trans	+120	C-H trans
+180	C-C cis	+180	C-N cis
-120	C-H trans	-120	C-R trans
-60	C-R cis	-60	C-H cis

b For the description of D-amino acids, interchange C-H and C-R in the table.

Table II: Approximate Torsion Angles for Some Regular Structures.^a

	(deg)	(deg)	(deg)	Reference
Right handed helix (-poly(L-alanine))	-57	-47	+180	Arnott and Dover (1967)
Left-handed helix	+57	+47	+180	Arnott and Dover (1967)
Parallel-chain pleated sheet	-119	+113	+180	Schellman and Schellman (1964)
Antiparallel-chain pleated sheet (-poly(L-alanine))	-139	+135	-178	Arnott et al. (1967)
Polyglycine II	-80	+150	+180	Ramachandran et al. (1966)
Collagen	-51, -76, -45	+153, +127, +148	+180	Yonath and Traub (1969)
Poly(L-proline) I	-83	+158	0	Ramachandran and Sasisekharan (1968), calculated from Traub and Schmueli (1963)
Poly(L-proline) II	-78	+149	+180	Arnott and Dover (1968)

Figure 6: Typical conformatial map (Ramachandran et al., 1963) transposed into the standard conventions. Note: this diagram is identical with that of Edsall et al. (1966) except that the origin is now at the center, instead of at the lower left hand corner. The solid lines enclose the freely allowed values of and for an alanyl residue in a polypeptide; the dotted lines enclose "outer limit" values based on the shortest known van der Waals radii in related structures. Analogous diagrams for other residues, and for slightly different assumptions, are given by Ramachandran and Sasisekharan (1968; note that these authors used the earlier convention with the origin at the corner).

3.3. Chain terminations.

3.3.1. If the terminal amino group of the chain is protonated the three hydrogen atoms are denoted H₁¹, H₁², and H₁³; the hydrogen atom giving the smallest (positive or negative) value of the principal torsion angle H-N-C-C is denoted H₁¹ and the others are numbered in a clockwise sense when viewed in the direction CN. The corresponding torsion angles are denoted ₁¹, ₁² and ₁³. If the terminal amino group is not protonated the hydrogen atoms are denoted H₁¹ and H₁² in accordance with Rule 2.2.2, and the corresponding torsion angles, ₁¹ and ₁².

3.3.2. At the carboxyl terminus of the chain (i = T) the double-bonded oxygen is written as O' and the other oxygen as O", thus

The torsion angles about the C-C bond are written _T¹ and _T² (or 1(T), 2(T)); the torsion angle about the C-O" bond, defining the orientation of the hydrogen atom of the hydroxyl group relative to C, is written _T^C (or C(T)). If the terminal carboxyl group is ionized the oxygen atoms are denoted O' and O", the precedence being determined by Rule 2.3.2, and the torsion angles are written as before.

Note. Instead of O' and O" the alternative notations O¹ and O² may be used. _T may be used instead of _T¹, in conformity with the convention for the middle of the chain, so long as confusion does not arise.

3.3.3. Substituted terminal groups. Natural extensions of the above rules may be devised, e.g.

(i) N-formyl group H₀-C₀O₀-N₁H₁-C₁H₁-

(ii) N-acetyl group C₀(H₀¹,H₀²,H₀³)-C₀O₀-N₁H₁-C₁H₁-

(iii) C-amido group

Arnott, S., and Dover, S. D. (1967), J. Mol. Biol. 30, 209.

Arnott, S., and Dover, S. D. (1968), Acta Cryst. B24, 599.

Arnott, S., Dover, S. D., and Elliott, A. (1967), J. Mol. Biol. 30, 201.

Edsall, J. T., Flory, P. J., Kendrew, J. C., Liquori, A. M., Némethy, G., Ramachandran, G. N., and Scheraga, H. A. (1966), J. Biol. Chem. 241, 1004; Biopolymers 4, 130; J. Mol. Biol. 15, 339.

Ramachandran, G. N., Ramakrishnan, C., and Sasisekharan, V. (1963), J. Mol. Biol. 7, 95.

Ramachandran, G. N., and Sasisekharan, V. (1968), Advan. Protein Chem. 23, 283.

Ramachandran, G. N., Sasisekharan, V., and Ramakrishnan, C. (1966), Biochim. Biophys. Acta 112, 168.

Schellman, J. A., and Schellman, C. (1964), Proteins 2, 1.

Traub, W., and Schmueli, U. (1963), in Aspects of Protein Structure, Ramachandran, G. N., Ed., Academic Press, London, p 81.

Yonath, A.,and Traub, W. (1969), J. Mol. Biol. 43, 461.

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