Space-filling assembly

All the polyhedra intermediate between the dodecahedron and truncated icosahedron can be realized except /s = 12,/ = 1, and some in more than one form (different arrangements of the 5-gon and 6-gon faces). A number of these polyhedra are of interest in connection with the structures of clathrate hydrates (p. 543), because certain combinations of these solids with dodecahedra form space-filling assemblies in which four edges meet at every vertex. Two of these polyhedra, a tetrakaidecahedron and a hexakaidecahedron, are illustrated in Fig. 3.4. 

In certain 3D nets there are well-defined polyhedral cavities, and the links of the net may alternatively be described as the edges of a space-filling assembly of polyhedra. At least four links must meet at every point of such a net, and the most important nets of this kind are, in fact, 4-connected nets. Space-filling arrangements of polyhedra leading to such nets are therefore described after we have dealt with the simpler 4-connected nets. 

Crystal structures may be described in terms of the coordination polyhedra MX of the atoms or in terms of their duals, that is, the polyhedra enclosed by planes drawn perpendicular to the lines M-X joining each atom to each of its neighbours at the mid-points of these lines. Each atom in the structure is then represented as a polyhedron (polyhedral domain), and the whole structure as a space-filling assembly of polyhedra of one or more kinds. We can visualize these domains as the shapes the atoms (ions) would assume if the structure were uniformly compressed. For example, h.c.p. and c.c.p. spheres would become the polyhedra shown in Fig. 4.29. These polyhedra are the duals of the coordination polyhedra illustrated in Fig. 4.5. These domains provide an alternative way of representing relatively simple c.p. structures (particularly of binary compounds) because the vertices of the domain are the positions of the interstices. The (8) vertices at which three edges meet are the tetrahedral interstices, and those (6) at which four edges meet are the octahedral interstices. Table 4.9 shows the octahedral positions occupied in some simple structures c.p. structures in which tetrahedral or tetrahedral and octahedral sites are occupied may be represented in a similar way. (For examples see JSSC 1970 1 279.)... 

Space-Filling Assembly This is another kind of representation of protein structure of the same three proteins in Figure 18.6. The subunits are assembled looking down the cleft into the active site. The distribution of positive charge and negative charge are often expressed on the surface. Figure 18.7 shows the assemblies of these three proteins. 

Figure 29-6 Some protein-RNA interactions within the ribosome. (A) A space-filling model of the 23S and 5S RNA with associated proteins from the ribosome of Haloarcula marismortui. The CCA ends of bound tRNA molecules in the A, P, and E sites are also included. The view is looking into the active site cleft. The proteins with e after the number are related to eukaryotic ribosomal proteins more closely than to those of E. coli.17 Courtesy of T. A. Steitz. (B) Three-dimensional structure of a 70S ribosome from Thermus thermophilus. The 30S subunit is to the right of the 50S subunit. Courtesy of Yusupov et al.33a (C) Stereoscopic view of the helix 21 to helix 23b region of the 16S RNA with associated proteins S6 (upper left), S18 (upper center, front), and S15 (lower back) from T. thermophilus. Courtesy of Agalarov et at.31 (D) Simplified in vitro assembly map of the central domain of the 30S bacterial ribosome. Courtesy of Gloria Culver. (E) Contacts of proteins with the central (platform) domain of the 16S RNA component. The sequence shown is that of Thermus thermophilus. Courtesy of Agalarov et al. (F) Three drawings showing alternative location of the four copies of protein L7/L12. The N-terminal and C-terminal...

Figure 7.40 Structure of the spherical lanthanide p-sulfonatocalix[4]arene assembly (a) partial space filling view along the pseudo-fivefold axis. Pyridine N oxide and one calixarene are shown in stick mode. S03 groups line the surface of the sphere, aryl rings define the hydrophobic shell and the polar core comprises 30 water molecules and two Na+ ions, (b) cut away view showing an [Na(H20)6] 2 cluster within the core. (Reprinted with permission from AAAS from [52]).

Figure 5.19 Molecular shape of rotaxane 23 (n = 6), a hetero-dimeric assembly of a tetraloop tetra-urea 9 (stick representation) and tetra-tosylurea 4 (space filling), based on MD simulations. Ether groups (OY = OC5Hnn,) areomitted in the formula.

Fig. 7 Organometallic assemblies built with dinuclear ruthenium carbonyl building blocks, Ru2(CO)4 4(OOCCOO)4(PMe3)8 (a) [25] and [CH2Cl2C Ru2(CO)4 3(OOCC6H4COO)3(PMe3)6] (b) (CH2C12 being represented by space-filling model) [23]...

Fig. 8 Organometallic assemblies built from o-bonded ligands, [ 2,9-bis(Pt(PEt3)2)phenanthrene (OOCC4H8COO)]3 (a) [27] and [(CH2Cl2)2cAu8(CCOPh)2(Ph2PC6H4PPh2)4]2+ (b) (CH2C12 being represented by space-filling models) [28]...

Fig. 11 Schematic (left) and space-filling model (right) of the tetrahedral M4L6 assemblies developed by Raymond and coworkers...

Fig. 5.21. Top Self-assembly drives the formation of helical, homochiral dimeric titanium tris-catecholate complexes. Dimerization is only mediated by LC, while Na and K" " do not lead to comparable products. Bottom Crystal structures of the dimers formed from the aldehyde (left, R = H), the ethyl ketone (centre, R = C2H5), and the methyl ester (right, R = OCH3). Shown is a side view in space-filling representation and a ball-and-stick model with a view along the Ti—Ti...

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