Three Torsion Angles

FIGURE 11-1 Structure of acetylcholine. (A) The three torsion angles, ly T2 and T3. (B) Newman projection of the gauche conformation. (C) Newman projection of the trans conformation. The molecule is viewed in the plane of the paper from the left side, and the bond angles around t2 are compared. 

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°. 

Histamine (1) is a flexible molecule that can adopt numerous conformations (Figure 2). These can be described in terms of three torsional angles Xj, X2 and x3. Quantum mechanical calculations on conformations for histamine [15,17-19] reveal that with respect to t2, the histamine monocation is found basically in the trans and gauche conformation. The values for X] and x3 are less restricted. 

Conventions have been established for the conformational analysis of protein structures. Three torsion angles, main chain of a protein, as shown in Figure 12.25(a). The angle w describes rotation about the peptide bond, Ci(=0)-N. Since this group is nearly planar (Figure 12.24). 

FIGURE 12.25. The three torsion angles that describe a peptide group, and the representation of the planarity of the peptide group. 

From a variety of X-ray crystal studies (e.g., didehydro-QCI/QCD and didehydro-quinidine), we have established that alkyne quinuclidines are twisted consistently less than the vinyl and ethyl analogues. Overall torsion angles, that is, the sum of the three torsion angles, vary from 26 to 49° compared with up to 65° for ethyl and 60° for ethenyl derivatives, respectively (Figure 12.3). Fine-tuning of nitrogen polarity (and basicity), which may be important for catalysis and perhaps pharmacological activity, is thus possible ([28] R. Wartchow, personal communication). 

Fig. 2.14. Left An arbitrary conformation of a Ph3PX molecule is specified by three torsion angles 0, 02>03> f°r the phenyl groups labeled A,B,C in a clockwise sequence when viewed down the X-P direction. Right Definition of torsion angle 0...

Next, we have examined the relationship between the chemical shifts and the molecular chain conformation. The versatility of chain conformation of cellulose molecules is expressed in three torsion angles as shown in Fig. 14 (j> and xp, rotations around the /3-l,4-glycosidic linkages and the rotation of methylol side groups around the C5-C6 bonds. In order to find out the relationship between the chemical shifts of cellulose samples and the torsion angles, the... 

Figure 12.2 Partitioning of generic molecule in branched chain of four fragments and three torsional angles MF is set on central fragment.

---