Non-helical

The only doublets consistent with this inequality, with the necessity of identical parity for p and q, and with values of r close to 0.34 nm, are given in Table 1 (from which the doublet (10,0) can be excluded since it is characteristic of a symmetrical, non-helical sheet). Hence, if br — 0, the necessary conditions for two successive helical cylindrical sheets to have strictly identical pitch angles are ... 

The tubes (a, a) and (a, 0) are generated from hexagons with 0 = jt/6 and 0, respectively. These tubes become non-helical and are called, respectively, armchair and zigzag structures. Other condition (0 < 0 < Jt/6) generates the tube (a, b) of helical structures (see Fig. 2). 

The case of isotactic polypropylene (iPP) presents some differences with respect to those just discussed. While both sPP and PET adopt in their mesophases disordered, extended, essentially non-helical conformations, iPP is characterized by a unique, relatively well ordered, stable chain structure with three-fold helical symmetry [18,19,36]. More accurately we can state that an iPP chain segment can exist in the mesophase either as a left handed or as the enantiomeric right-handed three-fold helix. The two are isoener-getic and will be able to interconvert only through a rather complex, cooperative process. From a morphological point of view Geil has reported that thin films of mesomorphic iPP quenched from the melt to 0 °C consist of... 

IV [79] which present respectively chains in trans-planar and in a non-helical (T6G2T2G2)n conformation. In form I (see Table 2), i.e., the stable form of sPP obtained under most crystallization conditions, the chains are packed with an alternation of right-handed and left-handed helices. On the contrary, in the somewhat less stable form II [80], all the helical chains share the same chirality. 

The intrinsic viscosity of the collagen preparation supports the notion that a significant fraction of the adsorbed collagen is present in the form of the dimer, i.e. of two triple helical, 3000 A long cylinders, flexibly joined together. Whereas at 7.7°C these dimers may mainly be folded and have two of the non-helical ends on the surface. It is conceivable that one end is permitted to lift off at the higher temperature and that the doubling in thickness is thus produced by a mechanism not related to a BET-like multilayer formation. 

Fig. 9 (a) Constant-time frequency-selective pulse sequence used for indirect measurement of 13C -13C distances in MB(i + 4)EK with uniformly 15N,13C-labeled L-alanine at Ala9 and AlalO. The 2D spectra in (b) and (c) and the extracted data points in (d) show that the dephasing is more rapid, with hence a shorter intemuclear distance, for 13C nuclei in the helical conformation (represented by squares) than for those in the non-helical conformation (represented by circles) (reproduced from [149] with permission)... 

Collagens from different tissues do not necessarily contain the same cross-links. In dentin, cross-links occur between two collagen molecules with two or three peptide chains involved. The difunctional didehydro-hydroxylysinonorleucine and didehydro-dihydroxylysinonorleucine, and the trifunctional hydroxylysylpyridinoline and lysylpyridinoline have been demonstrated in human and animal dentin (fig. 1). Fredentin, on the other hand, contains more difunctional and fewer trifunctional cross-links than dentin (Linde and Robins, 1988 Walters and Eyre, 1983 Yamauchi et al., 1992). These cross-links connect the non-helical extension... 

Finally, it is noted that suitable enantiomers of helicenes have been applied as selector for non-helical compounds. The disodium salt of P-( +)-7,10-dicarboxy hexahelicene coated on silicagel was successfully used in resolving the N-(2,4-dinitro-phenyl)-a-amino acid esters. Good resolutions were found for alanine, isoleucine, valine, phenylalanine and phenylglycine 94). 

Besides the knot, the major cyclization product (24%) obtained in the latter reaction could be identified as a dicopper complex consisting of two 43-membered rings arranged around the metallic centers in an approximate face-to-face geometry [94]. This unknotted compound originates from a non-helical precursor which is in equilibrium with the expected double helix. Figure 18 describes in a schematic way the alternative cyclization reaction leading to the unknotted face-to-face complex and the equilibrium which interconverts the helical and the non-helical precursors. 

Orgel, J. P., Wess, T. J., and Miller, A. (2000). The in situ conformation and axial location of the intermolecular cross-linked non-helical telopeptides of type I collagen. Struct. Fold. Des. 8, 137-142. 

Several points of non-helicity occur, corresponding to the combinations y, y= 0°, 0° y, y— 0°, 180° y, y = 180°, 180°. In real systems of atoms and bonds the first point is forbidden by steric bulk effects and the second (5) is disfavored by the strain associated with a cis conformation (y=0°).The last point is the conformationally favored oll-trans planar zig-zag chain (6) with symmetry 1/1 as seen end on. 

There is also a line of non-helicity for the case where ya = — yx>- In real systems the points along this line where u/t is an integer are occupied by even-membered rings in their most regular puckered conformations [e.g., 7). This line divides the largest region of helicity, that of the ring helices (8), into dextroverse and sinistroverse domains. 

Different orientations of the directional amino acid-bridged ligands (parallel or anti-parallel helical or non-helical, Figure 6) can, however, lead to up to seven isomers I-VII of complexes with the composition [ (OCHs T ]2- (Figure 1.3.6) [20, 21]. 

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