Helices asymmetry

More recently, Smith et al. have developed another model based on spontaneous curvature.163 Their analysis is motivated by a remarkable experimental study of the elastic properties of individual helical ribbons formed in model biles. As mentioned in Section 5.2, they measure the change in pitch angle and radius for helical ribbons stretched between a rigid rod and a movable cantilever. They find that the results are inconsistent with the following set of three assumptions (a) The helix is in equilibrium, so that the number of helical turns between the contacts is free to relax, (b) The tilt direction is uniform, as will be discussed below in Section 6.3. (c) The free energy is given by the chiral model of Eq. (5). For that reason, they eliminate assumption (c) and consider an alternative model in which the curvature is favored not by a chiral asymmetry but by an asymmetry between the two sides of the bilayer membrane, that is, by a spontaneous curvature of the bilayer. With this assumption, they are able to explain the measurements of elastic properties. 

Finally, in a recent paper, Yeganeh et al. suggest that the large asymmetries seen in polarized electron transmission are partly due to a combination of the presence of a molecule with axial chirality, surface orientation, and cooperative effects in the monolayer [129]. They use scattering theory to show that differences in transmitted intensity arise from the preferential transmission of electrons whose polarization is oriented in the same direction as the sense of advance of the helix. 

If a mesomeric group is attached to the cyclopropane skeleton the helix contribution is considerably larger than the atomic asymmetry term The resulting rotation... 

Only the methoxy- and chloro-compounds (38, 3 ) exhibit large deviations between calculated and observed rotations. In general, the 1,1-diphenylcyclopropanes XVIII have rather large optical rotations ( [ ]d > 90°). Inspection of Table 3 reveals that the molar rotations of XVIII are almost entirely due to helix optical activity ( 0 q > 0 d ). This is in contrast to an earlier assumption which has attributed optical rotations of XVIII to atomic asymmetry. Further comparisons between calculated and observed optical rotations of complex cyclopropanes I are presented in Table 4. 

If one analyzes the rotation of D-a-(methylenecyclopropyl)glycine (82) the optical activity must come from (at least) four sources. One rotation contribution is associated with the atomic asymmetry of the open-chain moiety (methylenecyclopropane being viewed as a ligand). On the other hand, optical activity will also be induced by the asymmetric carbon atom of the ring and the asymmetry in the electron density distribution of the exocyclic double bond system (with diastereotopic faces). Finally also helix optical activity may be operative. The example of 82 demonstrates the complexity of the optical rotation of an apparently simple cyclopropane derivative. Further discussions of optical rotations of similar compounds, therefore, will cling to only the qualitative level. 

Optical rotation can be used to identify unknown compounds, to determine concentrations of known compounds, and to follow the course of a reaction where the substrate and product have different specific rotations. Optical rotary dispersion measurements (i.e., the optical rotation at several different wavelengths) can provide information concerning the structure and asymmetry of a compound (e.g., percent a-helix content of a protein),... 

Table 4. Isotropic 15N shielding (asymmetry parameter (t/) of solid polypeptides [Ala, X] containing 15N-labelled L-alanine residue in the a-helix, aL-helix, and /3-sheet forms. 

In a similar manner, the coalescence temperature for the methyl groups of the tetramer was determined as 4°C. AG was calculated as 12.7 kcal/mol which was 3.7 kcal/mol smaller than that for the pentamer. The hexamer showed a total of seven signals with narrow linewidth due to two methyl groups and six methine protons even at 70°C, indicating that the rate of helix sense reversal is much slower than the rate for the pentamer. This suggests the possibility that the symmetrical oligomers over the pentamer level may be optically resolved at room temperature based entirely on conformational asymmetry. This was confirmed by the chiral HPLC technique using (+)poly(triphenylmethyl methacrylate) as a stationary phase.282... 

Finally, there is a pressing need for more-detailed information on the molecular fine-structure, or conformation, of polysaccharides in solution. The potential of small-angle x-ray diffraction for distinguishing between a random coil and a broken or partial helix in solution has been established. A better definition of the helical conformation of dissolved polysaccharides, which, because of basic chemical asymmetry, have a favored chirality ( handedness ), is awaited. This area of x-ray study is only beginning to be developed. ... 

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