Polypeptide torsion angles

To understand the function of a protein at the molecular level, it is important to know its three-dimensional stmcture. The diversity in protein stmcture, as in many other macromolecules, results from the flexibiUty of rotation about single bonds between atoms. Each peptide unit is planar, ie, oJ = 180°, and has two rotational degrees of freedom, specified by the torsion angles ( ) and /, along the polypeptide backbone. The number of torsion angles associated with the side chains, R, varies from residue to residue. The allowed conformations of a protein are those that avoid atomic coUisions between nonbonded atoms. 

The conformational distance does not have to be defined in Cartesian coordinates. Eor comparing polypeptide chains it is likely that similarity in dihedral angle space is more important than similarity in Cartesian space. Two conformations of a linear molecule separated by a single low barrier dihedral torsion in the middle of the molecule would still be considered similar on the basis of dihedral space distance but will probably be considered very different on the basis of their distance in Cartesian space. The RMS distance is dihedral angle space differs from Eq. (12) because it has to take into account the 2n periodicity of the torsion angle. 

Note The formal lUPAC-IUB Commission on Biochemical Nomenclature convention for the definition of the torsion angles polypeptide chain (Biochemistry 9 3471-3479, 1970) is different from that used here, where the atom serves as the point of reference for both rotations, but the result is the same. (Irving Gas)... 

Fig. 2.31 Comparison of the turn segment found in hairpin 122 with a naturally-occuring type II / -turn of a-polypeptides together with backbone dihedral angles in degrees. In the case of 122, the angles were extracted from one low energy conformer derived from NMR data and shown in Fig. 2.30. Torsion angles with comparable values are shown in bold [191, 195]...

Schaumann T, Braun W, Wilthrich K. The program FANTOM for energy refinement of polypeptides and proteins using a Newton-Raphson minimizer in torsion angle space. Biopolymers 1990 29 679-694. 

Polypeptide(s) 56 - 59. See also Proteins antibiotics 66 chemical synthesis 85 conformation of 59 - 61, 78 definition of 51 torsion angles 59-62 Polypeptides. See also Peptides Polyphosphates 302, 303 Polyprenyl compounds... 

Table 1.2 Torsion angles for regular polypeptide conformations...

Figure 1.10 Definitions of the torsional angles fa ip, and w. These are all equal to 180° for a fully extended polypeptide chain (top left). to, defines rotation about the C,—Nl+1 bond. The normal tram planar peptide bond has = i/r = 180°, bottom) left, fa viewed along N —C bond (N >C) right, fa viewed along the C —C(C , — C j).

Fig. 2. A segment of a polypeptide chain showing the torsion angles about the Ca-N bond (if)) and Ca-C bond (y).

Figure 5.1. Notation for torsion angles of biopolymer chains. Torsion angles ( and ift) that affect the main chain conformations of biopolymers are shown for polysaccharide (a), polypeptide (b), and polynucleotide (c) chains according to the IUBMB notation. The two torsion angles, and ij>, specified around the phosphodiesteric bonds of nucleic acids correspond to a and respectively. Reproduced from IUBMB at http //www.chem.gmw. ac.uk/iubmb.

If the backbone torsion angles of a polypeptide are kept constant from one residue to the next, a regular repeating structure will result. While all possible structures of this type might be considered to be helices from a mathematical viewpoint, they are more commonly described by their appearance hence a helices and /3 pleated sheets. 

FANTOM for Energy Refinement of Polypeptides and Proteins Using a Newton—Raphson Minimizer in Torsion Angle Space. 

Fig. 15c. Since the polypeptide backbone of the silk structure is expected to show variations in the torsion angles, normal iterative fitting of the torsion angles to model the experimental spectrum will probably fail since it does not include a distribution of the parameters. To handle this problem, Meier and co-workersused an alternative approach and modeled the experimental spectrum m2) as...

Schwalbe and co-workers have measured /c ca and VnNHa couplings in unfolded ubiquitin. The authors have found that the measured carbon-carbon couplings which are related to the torsion angles are small with a mean value of 0.85 0.2 Hz, This means that individual amino acids of the unfolded ubiquitin sample have both positive and negative torsion angles. The authors also observed that the measured proton-proton couplings fit in well with the predicted values, which supports the model of local conformational preferences in the denatured polypeptide chain. 

Fig. 7.1 Protein building blocks. (A) The polypeptide chain, with a closeup showing the chemical form of the backbone , to which the side chains R , R +i,..., are attached. The (C=0) and (N-H) groups are linked by the peptide bond, which has a partial double bond character, making the (C=0)-(N-H) peptide group stiff and approximately planar. The torsion angles tj) and tfr, around single bonds, are soft. (B) The side chains R , R +i,..., can be any of the twenty common amino acid side chains, shown here labeled by their conventionial three-letter abbreviations (see also text). The horizontal axis corresponds roughly to the polarity of the sidechain the vertical axis corresponds to size. Reprinted from Thomas Simonson (2003) Electrostatics and dynamics of proteins. Reports on progresses in physics, vol 66, pp 737-787 with kind permission of lOP Pubhshing...

Ramachandran and Sasisekharan (1968) established early that most combinations of the cp, 4 torsion angles in a polypeptide are conformationally inaccessible because of steric hindrance between the van der Waals radii of the atoms in the successive amino acids. In a plot of all possible combinations of the torsion angles -the so-called Ramachandran plot - there are only two small regions of sterically allowed cp, rp combinations that together define what might be considered the first... 

Torsion angles for the polypeptide chain and hydrogen bonds can be established with precision. 

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