Helicates left-handed

Figure 10.1 Basic polypeptide geometry. The upper panel shows a short peptide sequence of three amino acids joined by two peptide bonds. A relatively rigid planar structure, indicated by dashed lines, is formed by each peptide bond. The relative positions of two adjacent peptide bond planes is determined by the rotational dihedral angles

An a helix can in theory be either right-handed or left-handed depending on the screw direction of the chain. A left-handed a helix is not, however, allowed for L-amino acids due to the close approach of the side chains and the CO group. Thus the a helix that is observed in proteins is almost always right-handed. Short regions of left-handed a helices (3-5 residues) occur only occasionally. 

Collagen is a superhelix formed by three parallel, very extended left-handed helices... 

D- or L-amino acids, but a given helix must be composed entirely of amino acids of one configuration. a-Helices cannot be formed from a mixed copolymer of D- and L-amino acids. An a-helix composed of D-amino acids is left-handed. 

FIGURE 6.18 Poly(Gly-Pro-Pro), a collagen-like right-handed triple helix composed of three left-handed helical chains. (Adaptedfrom Miller Scheraga, H. A., 1976, Calculation of the... 

Antiparallel tt-helix proteins are structures heavily dominated by a-helices. The simplest way to pack helices is in an antiparallel manner, and most of the proteins in this class consist of bundles of antiparallel helices. Many of these exhibit a slight (15°) left-handed twist of the helix bundle. Figure 6.29 shows a representative sample of antiparallel a-helix proteins. Many of these are regular, uniform structures, but in a few cases (uteroglobin, for example) one of the helices is tilted away from the bundle. Tobacco mosaic virus protein has small, highly... 

FIGURE 10.41 (a) Gramicidin forms a double helix in organic solvents a helical dimer is the preferred strnctnre in lipid bilayers. The strnctnre is a head-to-head, left-handed helix, with the carboxy-termini of the two monomers at the ends of the strnctnre. (b) The hydrogen-bonding pattern resembles that of a parallel /3-sheet. 

Figure 15.9 The structure of right-handed and left-handed Sot helices in fibrous sulfur (see...

A. Side view of channel spanning the lipid layer of a planar lipid bilayer, The structure is comprised of two monomers, each in a left-handed, single stranded p -helical conformation, and joined together at the head or formyl end by means of six, intermolecular hydrogen bonds. The two formyl protons are seen at the center of the structure in this view. Replacement of these protons by methyls destabilizes the conducting dimer as shown with N-acetyl desformyl Gramicidin A (Fig. 3D). 

Collagen, the principal fibrous protein in mammalian tissue, has a tertiary structure made up of twisted a-helices. Three polypeptide chains, each of which is a left-handed helix, are twisted into a right-handed super helix to form an extremely strong tertiary structure. It has remarkable tensile strength, which makes it important in the structure of bones, tendons, teeth, and cartilage. 

In other words that a negaton initially in a state of momentum p, energy Vp2 + m2 helicity s, would remain forever in that state (since it does not interact with anything). Let us, however, compute the left-hand side of Eq. (11-123) with the -matrix given in terms of the interaction hamiltonian (11-121). To lowest order the diagrams indicated in Fig. 11-6 contribute and give rise to the following contribution to the matrix element of S between one-particle states... 

Fig. 9. The right-handed (R) and left-handed (L) three-fold helices of i-PP. For each handedness, the two different orientations (up or down) with respect to the reference axis are shown. The heights of the methyl groups are expressed ic c/6 units...

Fig. 10. Mode of packing of right- (/ ) and left-handed (L) helices in the a form of i-PP, viewed along the c axis. The triangles are schematic representations of the three-fold helices, with the methyl groups projecting at the vertices.

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