Structure, three-dimensional topological diagrams

Figure S.2 Schematic and topological diagrams of an up-and-down fi barrel. The eight p strands are all antiparallel to each other and are connected by hairpin loops. Beta strands that are adjacent in the amino acid sequence are also adjacent in the three-dimensional structure of up-and-down barrels.

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. 20. Top stereogram of the three-dimensional structure of spinach Fd NADP reductase (FNR) with the p-strands shown as arrows, the o-helices as spirals, and FAD and 2 -phospho-5 -AMP as ball-and-stick models Bottom topological diagram for FNR, with the p-strands shown as arrows, and the a-helices as rectangles. Figure source Karplus and Bruns (1994) Structure-function relations for ferredoxin reductase. J Bioenerg Biomembr 26 92 and Karplus, Daniels and Herriotf (1991) Atomic structure of ferredoxin-NADP reductase Prototype for a structurally novel flavoenzyme family. Science 251 62.

Fig. 16.4. Phylogenetic trees or cladograms based on the sequence differences (SEQ) and three-dimensional structural differences (STR) of immunoglobulin fragments. The structural distance metric is a function of both the rms distance difference between superposed structures and the number of topologically equivalent positions in each pairwise comparison (taken from [11]). The lower part of the diagram shows a multidimensional scaling analysis based on structural differences. The constant (C) and variable (V) domains cluster together for the light (L) and heavy (H) chains of the immunoglobulin fragments...

A third difference lies in the way the structures are represented graphically. Organic molecules can be represented by a two-dimensional bond diagram which shows the topology of the molecule, i.e. the way in which the atoms are connected together. If carefully drawn, this diagram can be made to look like a projection of the three-dimensional structure of the molecule (Fig. 2.1). 

Topologically, it turns out that the helical structure of the cholesteric cannot be deformed continuously to produce a cubic lattice without creating defects. Thus BP I and BP II are unique examples in nature of a regular three-dimensional lattice composed of disclination lines. Possible unit cells of such a disclination network, arrived at by minimizing the Oseen-Frank free energy, are shown in fig. 4.8.3. The tubes in the diagram represent disclination lines, whose cores are supposed to consist of isotropic (liquid) material. Precisely which of these configurations represents the true situation is a matter for further study. 

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