Three-dimensional structures projections

Fischer projection A method of representing three-dimensional structures in two-dimensional drawings in which the chiral atom(s) lies in the plane of the paper. The two enantiomeric forms of glyceraldehyde are represented as... 

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.

In the Fischer convention, the ermfigurations of other molecules are described by the descriptors d and L, which are assigned comparison with the reference molecule glyceraldehyde. In ertqrloying the Fischer convention, it is convenient to use projection formulas. These are planar representations defined in such a w as to convey three-dimensional structural information. The molecule is oriented with the major carbon chain aligned vertically in such a marmer that the most oxidized terminal carbon is at the top. The vertical bonds at each carbon are directed back, away fiom the viewer, and the horizontal bonds are directed toward the viewer. The D and L forms of glyceraldehyde are shown below with the equivalent Fischer projection formulas. 

Absolute configuration (Section 9.5) The exact three-dimensional structure of a chiral molecule. Absolute configurations are specified verbally by the Cahn-Ingold-Prelog R,S convention and are represented on paper by Fischer projections. 

Fig. 4. Tentative allocation of probe binding sites within the three-dimensional structure of Ca -ATPase derived from vanadate-induced E2-type crystals. The top picture is the projection view of the Ca -ATPase down the x-axis, revealing the pear-shaped contours of ATPase molecules. The maximum length of the cytoplasmic domain to the tip of the lobe is =r65A. In the middle and bottom pictures the same structure is viewed down the x-axis, revealing the gap between the bridge and the bilayer surface and the connections between ATPase molecules in neighboring dimer chains. The proposed binding sites for lAEDANS and FITC are indicated. The bottom right picture is the same structure viewed down the y-axis. Adapted from Taylor et al. [90].

At the onset of a protein engineering project often only the amino acid sequence of the protein, or fragments thereof, are known. Without access to a three-dimensional structure one has to explore whatever information is available at the sequence level. It is tempting... 

Visualization of conformers There are four conventional methods for visualization of three-dimensional structures on paper. These are the ball and stick method, the sawhorse method, the wedge and broken line method and the Newman projection method. Using these methods, the staggered and eclipsed conformers of ethane can be drawn as follows. 

FIGURE 2.8 The general structure of transfer RNA (tRNA) showing the phosphodiester backbone as a ribbon, with bases or base pairs projecting from the backbone. (Adapted from Rich, A. [1977]. Three-dimensional structure and biological function of transfer RNA Accounts of Chem. Res., 10, 388-396, copyright 1977, American Chemical Society, with permission from Accounts of Chemical Research.)... 

It is called an a-amino acid because the amino group is attached to the a (or number 2) carbon atom. To indicate its three-dimensional structure on a flat piece of paper, the bonds that project out of the plane of the paper and up toward the reader are often drawn as elongated triangles, while bonds that lie behind the plane of the paper are shown as dashed lines. The isomer of alanine having the configuration about the a-carbon atom shown in the following structural formulas is called S-alanine or L-alanine. The isomer which is a mirror image of S-alanine is R-alanine or D-alanine. Pairs of R and S compounds (see Section B for definitions) are known as enantiomorphic forms or enantiomers. 

Other common methods for representing the three-dimensional structures of molecules include Newman projections for showing conformational relationships and sawhorse figures. Newman projections look down a carbon-carbon bond so that the front carbon, designated by a circle, obscures the carbon directly behind it. Valences (bonds) to the front carbon extend to the center of the circle, while bonds to the rear carbon stop at the circle. Sawhorse projections have the carbon-carbon bond at oblique angles, which attempts to represent a perspective drawing of the molecule. Thus for 2-chloro butane, if one chooses to examine the 2,3 bond, then the sawhorse and Newman projections would be... 

As complex as the desulfurization of thiophene might appear, projection of the kinetic picture to benzothiophene and dibenzothiophene, and to their derivatives, is even more complex. As has already been noted for bond energy data, kinetic data derived from model compounds cannot be expected to include contributions from the various steric effects that are a consequence of complex molecules containing three-dimensional structures. Indeed, such steric effects can lead to the requirement of additional catalyst and process parameters for sulfur removal (Isoda et al., 1996a, 1996b). 

Fischer projection formulas show three-dimensional structures in two dimensions. In such formulas, horizontal groups project toward the viewer, and vertical groups project away from the viewer. 

Most of the carbon atoms in sugars have a tetrahedral geometry. Therefore, sugar molecules are not flat, but have a three-dimensional structure. The three-dimensional structure of carbohydrates is commonly depicted using Fischer projections, named in honor of Emile Fischer. Fischer worked out the structures of most of the carbohydrates in the first part of the twentieth century with little... 

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