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

These Rules are as close as possible to the published version [see Arch. Biochem. Biophys. 1971, 145, 405-421; Biochem. J., 1971, 121, 577-585; Biochemistry, 1971, 9, 3471-3479; Biochim. Biophys. Acta 1971, 229, 1-17; Eur. J. Biochem., 1969, 17, 193-201; J. Biol. Chem., 1970, 245, 6489-6497; J. Mol. Biol., 1970, 52, 1-17; Pure Appl. Chem., 1974, 40, 291-308; and in Biochemical Nomenclature and Related Documents, 2nd edition, Portland Press, 1992, pp 73-81. Copyright IUPAC and IUBMB; reproduced with the permission of IUPAC and IUBMB]. If you need to cite these rules please quote these references as their source.

Any comments should be sent to the current secretary of the Committee, or any other member of the Committee

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• Preamble

• 1. General Principles of Notation
  • 1.1 Designation of atoms
  • 1.2 Amino acid residue numbering
  • 1.3 Peptide units
  • 1.4 Bond lengths
  • 1.5 Bond angles
  • 1.6 Torsion angles

• 2. The Sequence Rule, and Choice of Torsion Angle
  • 2.1. The sequence rule
  • 2.2. Choice of torsion angle and numbering of branches (tetrahedral configurations)
  • 2.3. Choice of torsion angle and numbering of branches (planar trigonal configurations)

• References for this section

4. Side Chains
5. Hydrogen Bonds
6. Helical Segments
Appendix

These rules are based on "A proposal of standard conventions and nomenclature for the description of polypeptide conformation" (Edsall et al., 1966) and have been prepared by a subcommission set up by the IUPAC-IUB Commission on Biochemical Nomenclature in 1966. The original proposals have been modified so as to bring them as far as possible into line with the system of nomenclature current in the fields of organic and polymer chemistry.

Two recommendations are appended to the rules, the first dealing with the terms configuration and conformation and the second with primary, secondary, and tertiary structure. These are formulated as recommendations rather than rules because there is at present no general agreement about their definition.

Note. Two alternative notations are recommended throughout. That with superscripts and subscripts may be used when it is unlikely to cause confusion, e.g., in printed or manuscript material; that without is to be used where superscripts or subscripts may cause confusion or are technically difficult or irnpossible, e.g., in computer outputs. In the latter connection the following Roman equivalents of Greek letters are recommended: , A; , B; , G; , D; , E; , Z; , H; , T; ,U; , F; , X; ,Q; ,W.

Rule 1. General Principles of Notation

1.1. Designation of atoms.

The atoms of the main chain are denoted thus

Amino acid residues, -NH-CHR-CO-, are numbered sequentially from the amino-terminal to the carboxyl-terminal end of the chain, the residue number being denoted i.

Example

C of the i th residue is written C_i or C(i ).

1.3. Peptide units.

For some purposes it is more convenient to group together the atoms -CHR-CO-NH-. These groups are described as "peptide units," and the peptide unit number, like the residue number, is denoted i. It will be noted that the two numbers are identical for all atoms except NH; generally there will be no confusion, because a single document will use either "residues" alone, or "peptide units" alone, but in the latter case explicit reference must be made to this usage at the beginning. If confusion might arise, the symbols N_i* and H_i* are to be used for these atoms in the i th peptide unit, which are N_i and H_i in the i th residue (so that N_i* = N_{i +1}).

Example

(i) Residue notation is used throughout these rules.

(ii) Whether "residues" or "peptide units" are being used, _i and _i, always refer to torsion angles about bonds of the same C_i.

1.4. Bond lengths.

If a bond A-B be denoted Ai-Bj or Ai (see Rules 3.1, 4.5), the bond length is written b(A_i,B_j) (or b(A_i,B_j), or b_i^AA (or bA(i ). An abbreviated notation for use in side chains is indicated in Rule 4.5.

Note. The symbol previously recommended for bond length was l. This symbol is no longer recommended, partly because it is easily confused with 1 in many type fonts and partly because it is also used for vibration amplitude in electron diffraction and spectroscopy.

1.5. Bond angles.

The bond angle included between three atoms is written (A_i,B_j,C_k), which may be abbreviated, if there is no ambiguity, to (B_j) or _j^B or B(j ).

1.6. Torsion angles.

If a system of four atoms is projected onto a plane normal to bond B-C, the angle between the projection of A-B and the projection of C-D is described as the torsion angle of A and D about bond B-C; this angle may also be described as the angle between the plane containing A, B, and C and the plane containing B, C, and D. The torsion angle is written in full as (A_i,B_j,C_k,D_l), which rnay be abbreviated, if there is no ambiguity, to (B_j,C_k), (B_j), or _j^B etc. In the eclipsed conformation in which the projections of A-B and C-D coincide, is given the value 0^o (synplanar conformation). A torsion angle is considered positive (+) or negative (-) according as, when the system is viewed along the central bond in the direction BC (or CB), the bond to the front atom A (or D) requires rotation to the right or to the left, respectively, in order that it may eclipse the bond to the rear atom D (or A); note that it is immaterial whether the system be viewed from one end or the other. These relationships are illustrated in Figure 1.

Figure 1: Newman and perspective projections illustrating positive and negative torsion angles. Note that a right-handed turn of the bond to the front atom about the central bond gives a positive value of from whichever end the system is viewed.

(i) Angles are measured in the range -180 < +180^o, rather than from 0 to 360^o, so that the relationship between enantiomeric configurations or conformations can be readily appreciated.

(ii) The symbols actually used to describe the various torsion angles important in polypeptides are , , , , and (see Rules 3.2, 4.5.2). In the above is used simply as an illustrative generic symbol covering all these.

(iii) The terms dihedral angle and internal rotation angle may be regarded as alternatives to torsion angle though the latter has been used throughout these rules.

Ru1e 2. The Sequence Rule, and Choice of Torsion Angle

2.1. The sequence rule

The rules here enunciated for use in the field of synthetic polypeptides and proteins are in general harmony with the sequence rule of Cahn et al.,[See Cahn et al. (1966), and IUPAC Tentative Rules for the Nomenclature of Organic Chemistry, Section E, IUPAC Information Bulletin (1969). Earlier papers: Cahn and Ingold (1951); Cahn et al. (1956). For a partial, simplified account see Cahn (1964) and Eliel (1962).] with the exceptions of Rules 2.1.1 and 2.2.2 (cases II and III), and later rules dependent upon these. The sequence rule was formulated as a universal and unambiguous means of designating the "handedness" or chirality of an element of asymmetry. It includes subrules for the purpose of arranging atoms or groups in an order of precedence or preference, and this system may conveniently be used in the description of steric relationships across single bonds (see Klyne and Prelog, 1960). Here its function is to determine the priority or precedence of different atoms or groups attached to the same atom. However, Rule 2.1.1 below overrides the precedences of the sequence subrules, providing a new "local" (specialist) system for use with the general sequence rule. [Other local systems are available analogously for steroids, carbohydrates, and cyclitols, where the sequence rule is applied when the local system does not suffice.] After application of Rule 2.1.1, the normal procedure of the sequence rule is applied, but modified by Rule 2.2.2; in this connection the only parts of the sequence rule required are given in Rules 2.1.2-2.1.5.

2.1.1. The main chain is given formal priority over branches, notwithstanding any conflict with the following rules. Thus the main chain has precedence at C over the side chain and at C' over O'.

Note. This rule has not yet been formally accepted except in the present context.

2.1.2. The order of (decreasing) priority is the order of (decreasing) atomic number.

Example

In , the order of priority is Br, Cl, CH₃, H.

2.1.3. If two atoms attached to the central atom are the same, the ligands attached to these two atoms are used to determine the priority.

Examples (i) In , the order is Cl, (CH₂CH₃), CH₃, H. (C^xH₂CH₃ takes precedence over C^yH₃ because C^x is bonded to C, H, H and C^y to H, H, H).

(ii) In , the order is OH, CH₂Cl, CH₂OH, H.

(iii) In , the order is OH, CH(CH₃)₂, CH₂CH₃, H.

2.1.4. A double bond is formally treated as though it were split. Thus >C=O is treated as

Example In CH₃CO-OH the order is =O,-OH, CH₃.

2.1.5. If two ligands are distinguished only by having different masses (e.g., deuterium and hydrogen), the heavier takes precedence.

Example In , the order is Br, CH₃, D, H.

Note. This rule is to be used only if the two previous rules do not give a decision.

2.2. Choice of torsion angle and numbering of branches (tetrahedral configurations).

2.2.1. If, in a compound the sequence rule gives the priorities A > P, Q and D > E > F, then the principal tortion angle is that measured by reference to the atoms A-B-C-D as in Rule 1.6. The branches beginning at C are numbered

2.2.2. If two branches are identical, and the third is different (or nonexistent), they are numbered in a clockwise sense when viewed in the direction BC, as follows (see Figure 2).

Case I: D > E = E. D has the highest priority and is given the smallest number (1).

Case II: D = D > E. E has the lowest priority and is given the largest number (3).

Case III: D = D, numbered 1 and 2 (E nonexistent). In each case the principal torsion angle is measured between A-B and branch 1.

Figure 2; Tetrahedral configurations: case I, D > E = E; case II, D = D > E; case III, D = D (E nonexistent).

Notes.

(i) The rule given in case II differs from conformational selection rule b of the sequence rule (see Cahn et al. 1966 p 406) according to which if an identity among the groups of a set leaves one group unique, the unique group is fiducial. The reason for the difference is that the sequence rule would define principal torsion angle in terms of a hydrogen atom whenever a single such atom formed part of the set; in the X-ray technique, nearly always used to establish structures of the type under discussion, hydrogen atoms are usually unobservable, and even at best not accurately locatable, so that the position of one used to deflne a principal torsion angle could only be established by calculation based on (perhaps unjustified) assumptions about the bond angles concerned. These considerations apply with even more force to case III, where one branch is nonexistent; the "phantom atom" of zero atomic number would be given highest priority because it is unique.

(ii) In case III the clockwise passage from CD¹ to CD² shall be by the shorter of the two possible routes.

2.2.3. If all three branches are identical, that giving the smallest positive or negative value of the principal torsion angle is normally assigned the highest priority and the lowest number (1) (see Figure 3, IV, V); if two brancbes have torsion sngles respectively +60 and -60^o, the former is chosen (see Figure 3, VI). The others are numbered in a clockwise sense when viewed in the direction BC.

Figure 3: Tetrahedral configurations. Three identical branches: IV, general case, positive; V, general case, negative; VI, = 60^o.

(i) The qualification "normally" is added to avoid the need to renumber the branches if by chance the rule would demand this in consequence of a movement during refinement of a structure. In this or similar cases the symbolism should remain unchanged.

(ii) Rule 2.2.3 introduces a new principle, not invoked in 2.2.1 or 2.2.2, that the precedence depends on the conformation. This must necessarily be done since in this case the branches are distinguishable only in this respect. (The same applies to Rule 2.3.2.)

2.3. Choice of torsion anple and numbering of branches (planar trigonal configurations).

2.3.1. If, in a compound such that B, C, D, and E are coplanar, or nearly so, the sequence rule gives the priorities A > P, Q and D > E, then the principal torsion angle is that measured by reference to atoms A-B-C-D as in Rule 1.6 above. The branches beginning at C are numbered

2.3.2. If the branches are identical, that giving the smallest positive or negative value of the principal torsion angle is normally assigned the highest priority and the lowest number (1); if the two branches have torsion angles respectively +90 and -90^o, the former is chosen (see Figure 4).

Figure 4: Planar trigonal configurations. Identical branches: VII, positive; VIII, negative; IX, = 90^o.

Cahn,R.S.(1964), J. Chem. Educ. 41, 116.

Cahn, R. S., and Ingold, C. K. (1951), J. Chem. Soc. 612.

Cahn, R. S., Ingold, C. K., and Prelog, V. (1956), Experientia 12, 81.

Cahn, R. S., Ingold, C. K., and Prelog, V. (1966), Angew. Chem., Int. Ed. Engl. 5, 385, 511; Angew. Chem. 78, 413.

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.

Eliel, E. L. (1962), Stereochemistry of Carbon Compounds, McGraw-Hil1, New York, N. Y., pp 92-94.

IUPAC Information Bulletin (1969), No. 35, 36-80.

Klyne, W., and Prelog, V. (1960), Experientia 16, 521.

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