Helix torsion angles

Many of the polysulfides described above have been investigated by X-ray diffraction on either powders or single crystals. In all cases the more sulfur-rich anions (n>3) form unbranched chains the symmetry of which varies between Ci, C2, and Cs. According to Fig. 1 the symmetry C2 results if all torsion angles have the same sign (right-handed helix + + +... left-handed helix ----...). If the different torsion angles of the anion vary between + and... 

Fig. 2.3 Model of the 2i- and 3i-helical structures proposed for PHB chains with ideal torsion angle values. The 2i-helix was determined by fiber X-ray diffraction of PHB [49-51] while the 3i-helical fold was constructed by using preferred dihedral angles found along the backbone in crystal structures of cyclic oligomers 9 ( oligolides ) [37, 43, 45]...

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°,...

In the cis complexes, the torsion angle is usually smaller than that in trans complexes (Tables 16 and 17), leading to decreased antiferromagnetic coupling. In this case, the chains are helical and the compactness of this helix is a further factor that needs to be considered the more compact the helicoidal structure, the greater the antiferromagnetic coupling. 

Figure 4.1 represents the typical free energy profile or potential of mean force (PMF) along a reaction coordinate. The rc-axis is the reaction coordinate, which could be the distance between two molecules, a torsion angle along the backbone of a protein, or the relative orientation of an a-helix with respect to a membrane. 

Figure 2.14 Maps of conformational energy as function of backbone torsion angles 9i and 02 of a chain of isotactic poly((S)-3-methyl-l-pentene) for (a,b) left-handed helix and (c) right-handed helix.29 For each pair of Oi and 02, reported energy corresponds to minimum obtained by varying torsion angles of lateral group 03 and 04. Curves are reported at intervals of 0.5 kcal/mol of monomeric unit. Values of energies corresponding to minima are also indicated. (Reprinted with permission from Ref. 29. Copyright 1976 by Elsevier Science.)...

For the isotactic polymer, highly extended chains with chain axis of 7.5-7.6 A can be obtained with a helix repeating after two structural units [s(2/l) line repetition group] when 01 02, and 03 are in the range 180° 8, with 8 being 25-30° and 8i + 82 + 83 0.125 The experimental values of the torsion angles found in the crystal structure of i-STCO123 are indeed 0i = —161.5°, 02 = 155.3°, and 03 = -171.4°. Similar values have been found by conformational... 

Balasubramanian et concluded that the Pro ring has two typical puckered conformations (1) conformation A characterized by negative values of %1 (Cq-exo) (found in residues having a-helix-type torsion angles) and (2) conformation B characterized by positive (C7-endo) (found in residues having collagen-type torsion angles). 

Fig. 5 Dependence of the CCR-rates on the peptide backbone torsion angles //(N-Ca-C -N) and 0(C -N-Ca-C ). The thin curve corresponds to the dipole-CSA CCR-rate (/nhc )> the thick curve to the dipole-dipole CCR-rate (Fnhch) [9] and the grey curve to the dipole-dipole CSA-rate (Thnnhnhq ) [47]. The allowed regions for and (j> are indicated a indicates a-helix, ar is left-handed helix, f) is /3-sheet...

Tanaka, Chatani, and Tadokoro improved this model by refining the crystal structure of polyisobutene (182). The resulting structure is a 2/1 helix in which the structural unit contains four nonequivalent monomer units. In the crystal cell there are always eight monomer units arranged in three turns but the 8/3 helical symmetry is no longer retained. This example represents one of the most notable exceptions to the equivalence principle. Displacement from the exact helical conformation is small, however, and all the pairs of torsion angles fall inside the same energy well. 

The general shape of a macromolecule is sometimes referred to as macroconformation—in contrast to microconformation, which concerns the succession of torsion angles about a limited number of consecutive bonds. The random coil, rigid rod, and rigid helix represent examples of macroconformations. The same term is used to specify the molecular shape in semicrystalline polymers, one of the most important and still open problems in the field of polymer morphology. 

Differences between the geometrical structures of helicenes concern mainly the angles between the least square planes of subsequent benzene rings and the torsion angles of the bonds of the inner helix. In Table 24 some X-ray data are given. For heptahelicene two different crystals have been obtained. One of the crystals gave two... 

Figure 2-18 Typical (3 bulges in antiparallel pleated sheets. The residues Rx, R2, and Rx identify the bulges. (A) A "classic" (3 bulge, in which < )[ and /j are nearly those of an a helix while other torsion angles are approximately those of regular (3 structures. (B) The G1 bulge in which the first residue is glycine with = 85°, /j = 0°. It is attached to a type II (3 turn of which the glycine (labeled 1) is the third residue.

A careful stereochemical analysis has led to the conclusion that for all of the different aminoacyl groups to be able to react in the same way at the peptidyltransferase site and to all generate trans amide linkages, the torsion angles < ) and q/ of the resulting peptide must be approximately those of an a helix.388 Thus, the peptide emerging from the ribosome exit tunnel may be largely helical. 

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