Interlocked knots

There are also a number of other fairly obvious stereoisomeric possibilities (i.e., ones transparent to graph theory) that have as yet received no attention, e.g., multiple toroidal rings (or Klein bottles) with a catenane type of interlocking knots tied in the torus tube concentric multilayered toroidal tubes. 

A useful summary of the various and numerous types of rotaxanes, catenanes, and knots can be found in a review of template routes to interlocked molecular structures 468). Inorganic chemistry is centrally involved in the templating involved in self-assembly and in controlled synthesis of such species. 

Our definitions of the stereoisomeric center, line, and plane all stipulate the existence of bonds between the ligating element and its ligands. The exclusive use of these elements limits our analysis to classical stereochemistry and thus does not encompass the so-called topological isomerism (47) of interlocked rings—catenanes (48)—or of knots. As there is no bond between the rings of the catenanes we cannot expect to handle such compounds with a system based on connectedness. At the present stage of development, this limitation in scope... 

You turn back to Sally. Zollner devised three rests for Slade to see if Slade could use the fourth dimension to perform miracles. One He gave Slade two oak rings that were to be interlocked without breaking them. Two He gave Slade a snail shell and watched to see if a right spiral could be turned into a left spiral, and vice versa. Three He gave Slade a rubber band and asked him to place a knot in one strand of the band. Actually it was band made from dried gut, but you get the idea. ... 

The synthesis of interlocking ring molecular systems and knots combines both sets of motivation but it also adds an aesthetic dimension to the chemical problem. Indeed the search for aesthetically attractive molecules has been a goal since the very origin of chemistry. 

The discovery that DNA forms catenanes and knots, some of them extremely complex, initiated a new field of research which has been called Biochemical Topology [21]. In 1967, Vinograd and co-workers detected in HeLa cell mitochondria isolable DNA molecules that consist of independent, double-stranded, closed circles that are topologically interlocked or catenated like the links in a chain [22, 23]. A few years later, catenanes had been observed everywhere that circular DNA molecules were known [24] and the first knot was found by Liu and coworkers in single-stranded circular phage fd DNA treated with Escherichia coli co-protein [25]. In 1980, knots could also be generated in double-stranded circular DNA [26]. 

After numerous answers were brought to the synthetic challenge itself, there arose ever more insistently the quest for functions and properties of such special compounds. Already, even if still far from real applications, one can imagine, based on interlocked, threaded or knotted multi-component molecules, new organic materials, specific polymers, molecular devices or machines able to process and transfer energy, electrons or information. 

While a DNA molecule may exist as a straight rod, the two ends are often covalently joined. Thus, the chromosomes of E. coli and of other bacteria are single closed circles. Circular DNA molecules are also found in mitochondria, chloroplasts, and many viruses. Further complexity arises from the fact that the circles of DNA are sometimes interlocked in chainlike fashion (catenated). An unusual example of this phenomenon is the presence of thousands of small catenated DNA circles in the single mitochondrion of a trypanosome (Fig. 5-16).183 Sometimes circular DNA is knotted as in Fig. 5-17.184-186 Knots and catenanes often appear as intermediate forms during replication and recombination, especially involving circular DNA.187 188... 

Figure 10.54 Topological isomerism, diastereoisomerism and chirality as related to a [2] catenane, a trefoil knot and a doubly interlocked [2] catenane.

Figure 10.89 Conceptual production of increasingly interlocked species through the use of multime-tallic helicates. (a) Doubly interlocked [2]catenane from three metal centres, (b) Pentafoil knot from four metal ions, (c) Triply interlocked [2]catenane. (Reproduced with permission from [98]).

The functionalisation also allows extending the complexity of intertwined molecular assemblies involving molecular catenanes, rotaxanes and knots. Elaborate interlocked assemblies constructed by means of metal-templation techniques and ji-ji-stacking preorganisation were reviewed [3, 11], Our last survey was devoted to the hydrogen bond templated synthesis of amide-based catenanes and rotaxanes [32], Since then a considerable advancement in elucidation of mechanisms of templation and derivatisation of the amide-based interlocked structures has been reached. Moreover, in 2000 we reported a one pot synthesis of amide-based knots such as 8 [21], which is so far the easiest preparation of molecular knots. In the following, specific possibilities of functionalisation of amide-based catenanes, rotaxanes and knots will be discussed. 

In the introduction we mentioned extravagant interlocked structures of higher complexity such as doubly intertwined catenane and molecular composite knots of Sauvage et al. and multicatenanes made up of 4 to 7 interlocked rings obtained by Stoddart et al. In this section, we will discuss assemblies made up of amide-based catenanes, rotaxanes and knots. Here we use the term assembly to describe covalent or... 

Figure 27(c)]. It remains to be noted that Borromean links composed of metric circles are impossible,108 that Borromean links composed of three triangles or three squares have inspired sculptures by John Robinson,109 and that this link, in the form of three interlocked triangles, was known to the ancient Scandinavians as Odin s triangle or the Walknot (meaning knot of the slain ).110... 

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