Helical structure, geometry

Addition of 5% ganglioside Gmi into the L-Glu-Bis-3 resulted in the appearance of vesicles along with twisted ribbons, while addition of nonchiral 10,12-docosadiynedioic acid caused the formation of platelets.97 These results affirm the importance of packing geometry, along with head group chirality, for the formation of helical structures. 

It is important to realize that polymer configuration and conformation are related. Thus, there is a great tendency for isotactic polymers (configuration) to form helical structures (conformation) in an effort to minimize steric constrains brought about because of the isotactic geometry. 

Early studies of peptides isolated from microbial sources and possessing antibiotic activity led to the discovery of some a-amino acids not normally found in proteins. The peptides containing these nonproteinogenic, but natural a-amino acids exhibit helical structures which act as channels for transmembrane ion transport 32 Formation of a- or 310-helices in these peptides was ascribed to the unique geometry of these residues and their present use in the induction of these conformations is now widely established. 

Naturally, it is not necessary to limit the procedure to the use of tetrahedral metal centres. For example, it is possible to build double-helical structures from the interaction of molecular threads containing tridentate domains with metal ions possessing a preference for a six-co-ordinate octahedral geometry. An example of such a process is shown in Figu-... 

Fig. 7. Geometry of a helical structure (A) and the form of its diffraction pattern (B). In (A), the pitch (P) of the helix is like the wavelength of a sine wave. The radius (r) of the helix is like the amplitude of the sinewave. The subunit axial translation (h) is the rise along the helix axis from one monomer to the next. If there is not a whole number of monomers in one turn of the helix (said to be a non-integral helix), then there may be a longer repeat (C). In the case illustrated C = 2P. Dimensions in the helix in (A) have their counterparts in the diffraction pattern illustrated in (B), but dimensions in (B) are reciprocal to those in (A). Meridional reflections occur at positions m/h from the equator, where m is an integer. Each of these positions is the center of a so-called helix cross consisting of layer lines, which are n/P up or down from the meridional peaks, where n is another integer. All of the resulting layers of intensity can be related to orders of 1/C, where C is the repeat of the helix and l is the layer line number.

Figure 1.30 The double helical structure of B -DNA. Interchanging of either the bases of a base pair and/or base pair with base pair does not affect the geometry of this structure. Reproduced by permission of Prentice Hall from Chemistry for Pharmacists and the Life Sciences by G Thomas...

There are many examples of compounds, usually short polymers, that spontaneously form double helical structures. A classic example involves a number of bipyridyl ligands joined by short, flexible spacers. In the presence of Cu(I), which has both an affinity for nitrogen-containing ligands and a preference for a tetrahedral disposition of donor atoms, discrete double helical complexes are formed [23], A similar phenomenon gives rise to a triple helical motif when a metal that preferentially adopts an octahedral coordination geometry is used [24],... 

Interestingly, for these molecules the most common a-helical structural motive is not stable in the gas phase. It converts into a 3io helix for small polypeptides with n<8 upon geometry optimization with DFT methods. Only for n > 8, a conformations start to form in the middle of the helix. However, these helices are energetically less stable than the pure 3io helices [34],... 

Based on the geometry of the central A-tract, a double helix was constructed. Compared with normal B-DNA, it displays a very narrow, deep minor groove and a wide, shallow major groove and has a pitch of 34 A with 10.0 base pairs per turn. The three-center hydrogen bonding which links all the base pairs of the double helix in axial direction confers extra stabilization to this double helical structure, which explains several experimental findings not understood previously [702, 703]. 

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