Torsion angles, peptide bond side-chain

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 zero position for is defined with the —N—H group trans to the Ca—C bond, and for l> with the Ca—N bond trans to the —C=0 bond (Fig. 4-4). The peptide-bond torsion angle (ca) is generally 180° (see Example 4.10). A full description of the three-dimensional structure of a protein also requires a knowledge of the side-chain x torsion angles. 

Exhaustive conformational search is a simple and practical way to explore the entire conformational space available to a peptide (or molecular segment) with fewer than a dozen rotatable bonds. A search is performed by systematically varying each rotatable bond in the peptide. Rotations are made about backbone dihedrals (<]) and v) and/or side chain torsions (%). In our work, bond lengths and angles are held rigid. After each rotation, the molecule is checked for steric overlap. If overlap occurs, the conformer is discarded otherwise it is... 

Torsion angles, in addition, may be used to designate the conformation of the side chains. These are denoted by x (x X working along the chain away from Ca). The steric interactions within the side chains in the trans form of the peptide bond (u> = 180°) are much more favorable than those in the cis form (w = 0°), where there may also be steric interference with side chains from residues i- -2. If the residue i+1 is proline, however, the cis and trans forms (Figure 12.25) have similar energies. Proline is the only amino acid taking part in a cis peptide that is normally encountered in proteins. 

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...

Mimicking a p-tum consists in constraining correctly four torsional angles (4>,4>2, P, P2) and four bonds (bonds a-d, cf. Fig. 2.3.3). Bonds a and d direct the entry and the exit of the peptide chain through the turn, respectively, whereas bonds b and c are responsible for the spatial dispositon of the amino acid side chains at position i+1 and i+2 of a turn. The torsional angles determine the backbone geometry of the turn and consequently the shape of the turn hydrogen... 

The physical model of the polypeptide chain we use has been described previously [2] a few minor modifications are introduced as noted below. All bond angles and bond lengths are fixed at ideal values. The variables in the optimization are the torsional angles < ) and [/ of the peptide backbone. Each residue is represented by a C atom and a Cp-like atom. The Cp atom position is given by the average projection of the side-chain center of mass onto the C -Cp bond vector. 

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