Helix projection

Some virus particles have their protein subunits symmetrically packed in a helical array, forming hollow cylinders. The tobacco mosaic virus (TMV) is the classic example. X-ray diffraction data and electron micrographs have revealed that 16 subunits per turn of the helix project from a central axial hole that runs the length of the particle. The nucleic acid does not lie in this hole, but is embedded into ridges on the inside of each subunit and describes its own helix from one end of the particle to the other. 

Figure 5. Molecular drawings of a) one single strand of an amylosic chain in the left-handed conformation, having a six-fold symmetry, repeating in 2.1 nm. b) the double-helix generated by the association of two single strands, through two-fold symmetry operation, c) and d) Space-filling plots of the double helix, projected along and perpendicular to the fiber axis, respectively.

The most decisive support for this contention has proceeded from the X-ray study of crystalline sperm whale myoglobin, which, as Kendrew has demonstrated (Kendrew et al., 1960, 1961), contains 118 of its 153 residues, that is, 77 %, in right-handed a-helices. The side chains of L-amino acids in a right-handed helix project in a direction opposite to that of carbonyl groups hydrogen-bonded into the helix, an orientation that is in fact... 

Fig. 12. Right-handed helicity and its description Geometrical description of a simply crooked, right-handed helix L = inclination of the helix parallel to the z-axis, A = area of the helix projection on to the x,y-plane D length of the helix line...

The screw order, k, is defined as the number of atoms per turn. Here, the repetition of the helix is ten atoms in three turns ( 83) giving k 333. The screw order is connected with the pitch, P, and the atomic repetition length, p, through the relation k=P/p The pitch, P, is the distance along the axis of the helix after one turn The atomic repetition length, p, is defined as the distance of successive atoms in the helix projected to the helical axis The rotation of successive atoms is given by y=360 Ik... 

HELIX project, http //www.projecthelix.eu/. Accessed on March 1, 2014. 

The value 5 is determined by using the outside diameter of the stack in Eq. 3.7, and is obtained by using D + 2 W in place of the same equation. For the most accurate results, you should use Eq. 3.8 because it is the exact radius of curvature of a helix projected on a cylinder [4]. 

Scleroglucan exists in a triple hehcal conformation that is highly stable (314). The D-glucopyranosyl side groups project to the outside of the helix (312) and prevent the aggregation of hehces, which would result in insolubiUty, as in the case of curdlan vide infra). The transition from helix to coil occurs... 

Fhe amino acid side chains project out from the a helix (see Figure 2.2e) and do not interfere with it, except for proline. The last atom of the proline side... 

A convenient way to illustrate the amino acid sequences in helices is the helical wheel or spiral. Since one turn in an a helix is 3.6 residues long, each residue can be plotted every 360/3.6 = 100° around a circle or a spiral, as shown in Figure 2.4. Such a plot shows the projection of the position of the... 

Figure 3.S Schematic diagram of packing side chains In the hydrophobic core of colled-coll structures according to the "knobs In holes" model. The positions of the side chains along the surface of the cylindrical a helix Is pro-jected onto a plane parallel with the heUcal axis for both a helices of the coiled-coil. (a) Projected positions of side chains in helix 1. (b) Projected positions of side chains in helix 2. (c) Superposition of (a) and (b) using the relative orientation of the helices In the coiled-coil structure. The side-chain positions of the first helix, the "knobs," superimpose between the side-chain positions In the second helix, the "holes." The green shading outlines a d-resldue (leucine) from helix 1 surrounded by four side chains from helix 2, and the brown shading outlines an a-resldue (usually hydrophobic) from helix 1 surrounded by four side chains from helix 2.

Figure 3.6 Four-helix bundles frequently occur as domains in a proteins. The arrangement of the a helices is such that adjacent helices in the amino acid sequence are also adjacent in the three-dimensional structure. Some side chains from all four helices are buried in the middle of the bundle, where they form a hydrophobic core, (a) Schematic representation of the path of the polypeptide chain in a four-helrx-bundle domain. Red cylinders are a helices, (b) Schematic view of a projection down the bundle axis. Large circles represent the main chain of the a helices small circles are side chains. Green circles are the buried hydrophobic side chains red circles are side chains that are exposed on the surface of the bundle, which are mainly hydrophilic.

Figure 8.8 The DNA-binding heiix-turn-helix motif in lambda Cro. Ca positions of the amino acids in this motif have been projected onto a plane and the two helices outlined. The second helix (red) is called the recognition helix because it is involved in sequence-specific recognition of DNA.

Figure 18.14 The diffraction pattern of helices in fiber crystallites can be simulated by the diffraction pattern of a single slit with the shape of a sine curve (representing the projection of a helix). Two such simulations are given in (a) and (b), with the helix shown to the left of its diffraction pattern. The spacing between the layer lines is inversely related to the helix pitch, P and the angle of the cross arms in the diffraction pattern is related to the angle of climb of the helix, 6. The helix in (b) has a smaller pitch and angle of climb than the helix in (a). (Courtesy of W. Fuller.)...

FIGURE 19.19 A representation of part of an a helix, one of the secondary structures adopted by polypeptide chains. The cylinder encloses the "backbone" of the polypeptide chain, and the side groups project outward from it. The thin lines represent the hydrogen bonds that maintain the helical shape. 

Fig. 9. — Antiparallel packing arrangement of the 3-fold helices of (1— 4)-(3-D-xylan (7). (a) Stereo view of two unit cells roughly normal to the helix axis and along the short diagonal of the ab-plane. The two helices, distinguished by filled and open bonds, are connected via water (crossed circles) bridges. Cellulose type 3-0H-0-5 hydrogen bonds stabilize each helix, (b) A view of the unit cell projected along the r-axis highlights that the closeness of the water molecules to the helix axis enables them to link adjacent helices.

Fig. 14.—Antiparallel packing arrangement of extended, 4-fold, 2,3,6-tri-O-ethylamylose (12) helices, (a) Stereo view of two unit cells approximately normal to the lie-plane. The helix at the center (filled bonds) is antiparallel to the two helices (open bonds) at the comers in the back. There is no intra- or inter-chain hydrogen bond, and only van der Waals forces stabilize the helices, (b) A e-axis projection of the unit cell shows that the ethyl groups extend into the medium in radial directions. 

Fig. 21.—Structure of the 6-fold anhydrous curdlan III (19) helix, (a) Stereo view of a full turn of the parallel triple helix. The three strands are distinguished by thin bonds, open bonds, and filled bonds, respectively. In addition to intrachain hydrogen bonds, the triplex shows a triad of 2-OH - 0-2 interchain hydrogen bonds around the helix axis (vertical line) at intervals of 2.94 A. (b) A c-axis projection of the unit cell contents illustrates how the 6-0H - 0-4 hydrogen bonds between triple helices stabilize the crystalline lattice.

Fig. 22.—Antiparallel packing arrangement of the 2-fold helices of (1— 3)-a-D-glucan (21). (a) Stereo view of two unit cells approximately normal to the aoplane. The two chains in the back (open bonds) are antiparallel and so are the chains in the front (filled bonds). Each helix is stabilized by 2-OH 0-4 hydrogen bonds across the bridge oxygen atoms. Interchain hydrogen bonds are formed in sheets along the a direction, (b) An axial projection of the unit cell shows that the sheets in the front and back are also joined by hydrogen bonds.

Fig. 24. (continued)—(b) An axial projection of the unit cell contents. The double helix at each corner can be either up- or down-pointing," in terms of the X-ray data. All are, however, up in this diagram so that a calcium ion (crossed circle) is connected to the sulfate groups in three surrounding... 

Fig. 37. (continued)—(b) An axial view projected along the r-axis shows the packing arrangement of three welan double helices in the trigonal unit cell. The helix drawn in solid bonds is antiparallel to the remaining helices (open bonds). Note that calcium ions are positioned between the helices and each water molecule (large open circle) shown here is connected to all three surrounding helices. The interstitial space is occupied by several other ordered water molecules (not shown). 

Fig. 2.39 Schematic representation of the projection of idealized ji- and y-peptide helices in a plane perpendicular to the helix axis and comparison with the helical wheel of the natural a-helix...

It is now almost 50 years since the structure of DNA was elucidated by Watson and Crick (1) (Fig. 1). Since then the double helix has become an icon for modern scientific achievement. With the rapid growth of molecular biology and the consequent success of the human genome project (2) we are now firmly in a post-genomic era. However, in spite of, or perhaps because of this, efforts to understand fundamental aspects of metal-ion interactions with DNA continue to be vigorously pursued. 

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