Peptide torsion angle

The Karplus equation (Eq. 3-52) relates / to the torsion angle 0 (so labeled to distinguish it from peptide torsion angle c ) Fig. 2-8). 

Sasisekharan, first performed such an analysis. The Ramachandran plot in Figure 12.27 shows peptide torsion angles for D-xylose isomerase. " ... 

Ramachandran plot, a graphical x/y-repre-sentation of accessible regions of the peptide torsion angles

[Pg.322]

M. Hong, J.D. Gross, R.G. Griffin, Site-resolved determination of peptide torsion angle < ) from the relative orientations of backbone N-H and C-H bonds by sohd-state NMR, J. Phys. Chem. B 101 (1997) 5869-5874. 

In some carefully selected examples, it has been shown how denatured proteins can spontaneously recover their natural folding pattern. The peptide torsion angles, which control the folding, return to the characteristic values of the native protein, known to be independent of chemical factors. Some long-range interaction appears to be at work. 

An interesting correlation has been presented relating peptide torsion angles to spin-lattice relaxation times (Bleich et a/., 1976a,b). The relaxation times relate to the peptide backbone torsion angles (j) and j/. The quaternary values depend on the side-chain torsion angle %. 

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. 

Examination of the backbone torsion angles in a number of crystal stractures of /9-alanine-containing peptides reveals that the conformation around the C(a)-C(/9) bond of /9-alanine residues is essentially gauche or trans (anti) with values close to 60° or 180°, respectively [158]. Populating the gauche conformation of /9-ami-... 

Fig. 2.23 Model of the 2g-helix formed by all-w/i///ce-jff -peptide 109 generated with ideal torsion angle values =-135°, =58°,...

Interestingly, the 28-hehcal fold identified by NMR analysis of /9-peptide 109 compares well with the model of a /9 -peptide consisting of 1-aminomethylcyclo-propanecarboxylic acid residues (Fig. 2.24). This model was generated using ideal torsion angle values ( = + 120°, 9i=-72°, ii/=0°, and < =180°) derived from crystal structures of dimer 110, trimer 111 and tetramer 112 [163] (Fig. 2.25). 

Tab. 2.7 Comparaison of selected backbone torsion angles for strand segments in antiparallel sheet-forming jff-peptides 117-119, 121, 122 [109, 154, 191-194]...

As a consequence of their different turn geometry a 10-membered turn closed by H-bonds between NH and C=0 +i and a 12-membered turn closed by Id-bonds between C=0 and NH +3, antiparallel hairpins formed by y9-peptides 121 and 122 display opposite sheet polarities (see Fig. 2.30A and B). Comparison of backbone torsion angles (X-ray and NMR) for selected y9-amino acids residues within extended strand segments of peptides 117-122 are shown in Tab. 2.7. The observed values are close to ideal values for y9-peptide pleated sheets =-120° (or 120°), 01 = 180°, (/ =120°(or-120°). 

Tab. 2.8 Comparison of selected backbone torsion angles characteristic of the y-peptide 2.5-heli-cal backbone extracted from NMR solution structure of y -hexapeptide 141 and solid-state structure of y -tetrapeptide 146 [200, 205, 207]...

Many of the conformational properties of peptide systems, including protein conformation, can be approximated in terms of the local interactions encountered in dipeptides, where the two torsional angles 4> (N-C(a)) and < i (C(a)-C ) are the main conformational variables. N-acetyl N -methyl alanine amide, shown in Fig. 7.11, is a model dipeptide that has been the subject of numerous computational studies. 

Fig. 16.6 Theoretical curves of the dipole-dipole CCR rate and the di-pole-CSA CCR rate as a function of the peptide backbone torsion angle y/. The sterically allowed regions are indicated by a gray background.

The characteristic properties of peptides result from the presence of a chain of several or many amide bonds. A first problem is that of numbering, and here Fig. 6.1 taken from the IUPAC-IUB rules may help. A second and major aspect of the structure of peptides is their conformational behavior. Three torsion angles exist in the backbone (Fig. 6.2). The dihedral angle co (omega) describes rotation about C-N,

rotation about N-C , and ip (psi) describes rotation about C -C. Fig. 6.2 represents a peptide in a fully extended conformation where these angles have a value of 180°. 

The torsion angle co, which is common to peptides and nonpeptidic amides, always prefers a planar over a nonplanar conformation due to the partial double-bond character of the amide bond (Fig. 6.3, right). Thus, a peptide bond resembles an amide bond in conformational and electronic terms [2] [3], However, peptides differ from amides in that both the carbonyl C-atom and the amido N-atom are nearly always bound to an sp3-hybridized C-atom. As a result, the trans-conformer (a>=180°) is consistently preferred over the cw-conformer, the energy difference usually being ca. 90 kJ mol 1 (Fig. 6.3). The relationship between the partial double-bond character of the amide bond (Fig. 6.3, right) and hydrolysis will be considered in Sect. 6.3. 

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