Three-Dimensional Structure Representation

In principle, extension of the topological graph representations discussed in the preceding sections of this chapter requires little more than the addition of 3D coordinates for the atoms, for example as additional columns in a connection table. Typically these coordinates are generated using a program such 

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Fig. 2. Three-dimensional structural representations for zinc metall-oproteins. Comparison of the zinc ion-protein bonding interactions for zinc requiring enzymes (A—C) with the zinc-insulin hexamer (D, E). (A) Human carbonic anhydrase C, redrawn from Ref. (47) with permission. (B) Bovine carboxypeptidase Ay, redrawn from Ref. 30) with permission. (C) Bacillus thermoprotedyticus thermolysin, redrawn from Ref. 45) with permission. (D) and (E) Porcine Zn-insulin hexamer, taken from Ref. 48) with permission. The composite electron density maps in (D) and (E) show that each of the two zinc atoms present in the hexamer is within inner sphere bonding distance of three solvent molecules and three histidyl imidazolyl groups in an octahedral array about the metal ion. The position of one of the three equivalently positioned solvent molecules is indicated in (D). The electron density map in (E) shows the relative orientations of the three histidyl residues (His-BlO). (The atomic positions of one of the three equivalent histidyl groups are shown)...

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. 

FIGURE 1.11 Three -dimensional spacefilling representation of part of a protein molecule, the antigen-binding domain of immunoglobulin G (IgG). Immunoglobulin G is a major type of circulating antibody. Each of the spheres represents an atom in the structure. 

Fig. 1. Ribbon representation of the three-dimensional structure of D. gigas hydro-genase (32). The large subunit is represented in dark gray. Fe is represented by black spheres, Ni by gray spheres, and inorganic sulfur by white spheres. The C-terminal end of the large subunit is close to the Ni smd completely buried in the structure.

Figure 39-13. A schematic representation of the three-dimensional structure of Cro protein and its binding to DNA by its helix-turn-helix motif. The Cro monomer consists of three antiparallel p sheets (P1-P3) and three a-helices (a,-a3).The helix-turn-helix motif is formed because the aj and U2 helices are held at about 90 degrees to each other by a turn offour amino acids. The helix of Cro is the DNA recognition surface (shaded). Two monomers associate through the antiparallel P3 sheets to form a dimer that has a twofold axis of symmetry (right). A Cro dimer binds to DNA through its helices, each of which contacts about 5 bp on the same surface of the major groove. The distance between comparable points on the two DNA a-helices is 34 A, which is the distance required for one complete turn of the double helix. (Courtesy of B Mathews.)...

Fig. 11.2. Schematic representation of the primary structure of secreted AChE B of N. brasiliensis in comparison with that of Torpedo californica, for which the three-dimensional structure has been resolved. The residues in the catalytic triad (Ser-His-Glu) are depicted with an asterisk, and the position of cysteine residues and the predicted intramolecular disulphide bonding pattern common to cholinesterases is indicated. An insertion of 17 amino acids relative to the Torpedo sequence, which would predict a novel loop at the molecular surface, is marked with a black box. The 14 aromatic residues lining the active-site gorge of the Torpedo enzyme are illustrated. Identical residues in the nematode enzyme are indicated in plain text, conservative substitutions are boxed, and non-conservative substitutions are circled. The amino acid sequence of AChE C is 90% identical to AChE B, and differs only in the features illustrated in that Thr-70 is substituted by Ser.

Our discussion of electronic structure has been in terms of band filling only. Of course, there is a lot more to know about band structures. The density of states represents only a highly simplified representation of the actual electronic structure, which ignores the three-dimensional structure of electron states in the crystal lattice. Angle-dependent photoemission gives information on this property of the electrons. The interested reader is referred to standard books on solid state physics [9,10] and photoemission [16,17]. The interpretation of photoemission and X-ray absorption spectra of catalysis-oriented questions, however, is usually done in terms of the electron density of states only. 

Fig. 2. The P4-P6-domain of the group I intron of Tetrahymena thermophila. A Schematic representation of the secondary structure of the whole self-cleaving intron (modified after Cate et al. [34]). The labels for the paired regions P4 to P6 are indicated. The grey shaded region indicate the phylogenetically conserved catalytic core. The portion of the ribozyme that was crystallized is framed. B Three dimensional structure of the P4-P6 domain. Helices of the PSabc extension are packed against helices of the conserved core due to a bend of approximately 150° at one end of the molecule...

Fig. 2.8 Cleavage in the amphiboles. (A) Schematic representation of the characteristic stacked amphibole I-beams in the three-dimensional structure. A tetrahedral portion of an I-beam is labeled "silica ribbon." The octahedral portion is labeled "cation layer" and represented by solid circles. One of the possible cleavage directions (110) along planes of structural weakness is indicated by the line A-A stepped around the I-beams in the lower part of the diagram. (B) Cross section of the stacked I-beams with the directions of easy cleavage indicated. There is a lower density of bonds between I-beams in the crystallographic directions (110) and (110). These directions, parallel to the c axis and the length of the chains, are the planes of cleavage. The minimum thickness of a rhombic fragment produced through cleavage is 0.84 nm.

Structure 9.1 is most commonly employed as a description of the repeat unit of cellulose but structure 9.2 more nearly represents the actual three-dimensional structure with each D-glucosyl unit rotated 180°. We will employ a combination of these two structural representations. Numbering is shown in structure 9.3 and the type of linkage is written as 1 4 since the units are connected through oxygen atoms contained in carbon 1 and 4 as shown in structure 9.3. 

Fig. 8. Schematic representation of aberrant mFas, which is expected to attenuate the Fas-mediated signaling. Aberrant mFas is functionally and structurally classified into main three types (a) the membrane-binding decoy receptor, (b) the membrane-binding decorative receptor, and (c) the membrane-unstable or soluble receptor. Although both mFas in models (a) and (b) are normally fixed on the membrane, the mFas in the former can bind Fas ligand, but is defective for trimerization, whereas the mFas in the latter would have no ability to bind Fas ligand in vivo because of conformational alteration. Like model (a), the mFas in model (c) can be reactive for Fas ligand, but it cannot transduce the apoptotic signal into the cytoplasmic death cascade because of incomplete trimerization due to an abnormal TM domain or truncation of the 1C domain. The hatched and jagged markings indicate deduced alterations of amino acid sequence or three-dimensional structure, respectively.

Figure 2. Representation of the three dimensional structure of skeletal muscle.

Although not obvious from a two-dimensional representation of its structure, carbamazepine has many similarities to phenytoin. The ureide moiety (-N-CO-NH2) in the heterocyclic ring of most antiseizure drugs is also present in carbamazepine. Three-dimensional structural studies indicate that its spatial conformation is similar to that of phenytoin. 

The first surprise was that these molecules are much longer than seems necessary for the formation of adapters. In addition, 10-20% of their bases are modified greatly from their original form.171 Another surprise was that the anticodons are not all made up of "standard" bases. Thus, hypoxanthine (whose nucleoside is inosine) occurs in some anticodons. Conventional "cloverleaf" representations of tRNA, which display their secondary structures, are shown in Figs. 5-30 and 29-7. However, the molecules usually have an L shape rather than a cloverleaf form (Figs. 5-31 and 29-6),172 and the L form is essential for functioning in protein synthesis as indicated by X-ray and other data.173 Three-dimensional structures, now determined for several different tRNAs,174 175 are all very similar. Structures in solution are also thought to be... 

Figure 31-6 Three-dimensional ribbon representation of the structure of a complex of a soluble Fc fragment of a human IgGl molecule. Pro 329 of the IgG and Trp 87 and Trp 110 of the Fc-receptor fragment form a "proline sandwich/ which is shown in ball-and-stick form. The oligosaccharide attached to the Fc fragment of the antibody and the disulfide bridge between the two Cys 229 residues (at the N termini of the C2 domains of the heavy y chains) are also shown. The small spheres on the Fc receptor fragment are potential sites for N-glycosylation. From Sondermann et al.107 Courtesy of Uwe Jacob.

Every branched or unbranched alkane chain is built as a zigzag chain. When a chain contains three or more C atoms a part of the molecule can turn freely around a single bond in relation to the rest of the molecule. In a spontaneous process the molecule converts from one three-dimensional structure to another. According to a chemists the molecule changes from one conformation into another . Figure 3.15 is a representation of an alkane chain and two conformations of the same molecule. 

FIGURE 6 Graphical representation of the guest-host diastereoisomeric complex formation (a) in the presence of acid in the mobile phase and (b) in the absence of acid in the mobile phase, (c) Three-dimensional structures of the guest-host complexes formed between R- and 5-enantiomers of a-phenylethylamine and chiral 18-crown-6 ether CSP. 

Figure 7-2. A representation of the cobalt(m) complex 7.1 formed from the reaction of tris(di-methylglyoximato)cobaltate(in) with BF3 Et20. The three-dimensional structure observed in the crystal lattice of the tetrafluoroborate salt is also shown. The final view emphasises that the co-ordination geometry about the metal centre is distorted towards trigonal prismatic in these complexes.

Figure 7-4. Two representations of the fullerene C60. The upper representation shows the normal three-dimensional structure, whilst the lower one emphasises that this molecule is topologically planar. The fact that the various rings appear deformed is immaterial in this topological representation.

Even a molecule with as defined a three-dimensional structure as the fullerene C60 is topologically planar (Fig. 7-4). This type of representation is known as a Schlegel diagram. 

Fig. 2. Mapping of conserved features onto three-dimensional structure. The sequence differences between chymotrypsin and its closest homologs are mapped onto a surface representation of the structure of chymotrypsin (PDB lab9). Apeptide ligand (TPGVY) is show in stick format.

Figure 8.3 Stereo representation of a computer-aided modeling of the three-dimensional structure of the triazine-binding niche, according to Tietjen et al. (1991). (See Color Plate Section)...

Figure 15.1 Structure of the BmPBP-bombykol complex highlighting the three disulfide bridges that play a pivotal role in the rigidity of the three-dimensional structure of PBPs. Helices are shown as ribbons and loop regions as thin tubes. Bombykol is displayed in space-filling representation with all atoms. This figure was prepared by Fred Damberger by using the program molmol (Koradi et al., 1996).

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