Folding and Gluing

In this way the adjacency of such a toroidal network can conveniently be represented as a planar rectangular polycyclic structure with opposite sides marked as being identical, i.e., in a labeling, the set of vertices along one side is the same, and in the same sequence, as those of the opposite side (or of a cyclic permutation of them). For toroidal polyhexes this is equivalent to the diagrammatic approach discussed elsewhere. Klein ° uses the Xtxmparity in discussing which identifications are possible. 

Although the simplest shape for this purpose is the rectangle, the technique is by no means confined to this, and it can be any shape where suitable pairs of sides can be identified and joined, and nonrectangular shapes are often necessary for generating some of the possible isomers. Some fairly obvious stipulations are required of the perimeter of this diagram  

Every vertex on the perimeter must be identified with at least one other that is also on the perimeter. On the other hand, an edge may or may not be so identified with another edge. 

A corollary of this is that every vertex label on the perimeter appears at least twice. Two of them (at the comers ) appear three times. 

Identified pairs of vertices cannot both be of degree-3, i.e., a vertex of degree-3 must be matched with one of degree-2 (otherwise the single vertex that they represent will be of more than degree-3). 

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Fig. 60. Chiral tubular units in the structures of the U Mo = 4 5 and 5 7 uranyl molybdate frameworks can be described in terms of tubular units (b and d, respectively). The tubular units can be obtained by folding and gluing tapes shown in (a) and (c), respectively.

Figure 6. "Folding and gluing a polyhex sheet, first to a cylinder, and then to a toroidal polyhex. (The cylinder and the torus are reproduced by kind permission of Dr. Peter John. Technische UoiversitSt Ilmenau, from drawings published by John and WaIther(Ref. I2). ...

Various approaches to the enumeration of connectional isomers have been discussed folding and gluing of a planar lattice section in every possible way, the application of tiling mles,3i,32 the application of hexagon matrix rules, and oth-erg 12,38 appears to have been only one report giving explicit enumeration... 

The results of experiments in which the mutation was made were, however, a complete surprise. The Asp 189-Lys mutant was totally inactive with both Asp and Glu substrates. It was, as expected, also inactive toward Lys and Arg substrates. The mutant was, however, catalytically active with Phe and Tyr substrates, with the same low turnover number as wild-type trypsin. On the other hand, it showed a more than 5000-fold increase in kcat/f m with Leu substrates over wild type. The three-dimensional structure of this interesting mutant has not yet been determined, but the structure of a related mutant Asp 189-His shows the histidine side chain in an unexpected position, buried inside the protein. 

No sequence homologies can be detected. This is, perhaps, not surprising. The X-ray structure analysis of lysozyme by Phillips has shown that the polypeptide chain is folded in a way which puts none of the amino acids in sequential vicinity of the catalytic Asp-52 and Glu-37 that are near to the bound substrate. Comparable folding patterns can probably be realized with widely differing arrangements of amino acids, and thus the apparent lack of homologies. 

It can be assumed that the amino acids following this hinge region (Val 93 to Leu 447) are part of the head domain. The point of papain cleavage is at amino acid 82 27. TTie core part of the polypeptide chain is mainly folded in )3-sheets (34 %) and to a lesser extent (15 %) arranged in alpha-helical structures 7. In contrast with CBH I the core of CBH II possesses only 2 disulfide bridges (176-235 368-415) and four free sulfhydryl groups. Similarly to CBH I carboxyl functions are involved in the active center (Asp 175 and Glu 184) 28. 

The Problem A 9-by-12-inch piece of cardboard is to be made into an open box by cutting slits into square-shaped corners, folding up the sides, and gluing the tabs to the ends. What is the volume of the open box if the corner squares are 2 inches on a side ... 

Fig. 7.5 Folding patterns of the two domains of the / subunit. The core regions of these two domains (shown by diagonal stripes) have very similar folding topologies and are nearly superimposable. The pyridoxal phosphate Lys-87 Schiff base complex, shown in a ball-and-stick model, lies on the surface of each domain. P points to a region that contains several sites that are susceptible to proteolysis in the separate / subunit (see text). The cleavage sites (Lys-272, Arg-275, Lys-283, and Glu-296) are within a stretch of residues (260-310) that contains three long / hairpin loops and apparently lacks any other well-defined secondary structure (modified from Ref. 7). (See also color plates and .)...

Adhesives for Case and Carton Sealing. Once the corrugated board or the solid fiberboard boxes are constructed, they must be glued, filled with product, and the top flaps folded down and glued closed before shipment. The adhesive... 

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