Knotted conformations

Figure 13 Possible collagen type III C-terminal cystine knot conformations.

Figure 14 Possible FACIT cystine knot conformations based on NMR data of type XIV collagen cystine knot-containing peptide.

As their name implies, these molecules are characterised by their distinctive topology in which the macrocycle is intertwined to form a knot [170, 171]. The simplest form of knot is the so-called trefoil knot - trefoil as in tracery or heraldry, in turn derived from tripartite leaves, as in clover (which of course is not knotted ). More complex forms are found throughout chemistry and physics [318] and in Nature - in proteins [319], metalloproteins [320] and DNA (both natural [321], and in synthetic derivatives [322]). However not all structures claimed to be knots conform to the strict mathematical definition of a knot (Section 4.2.1). 

For a monograph, see Schill, G. Catenanes, Rotaxanes, and Knots Academic Press NY, 1971. For a review, see Schill, G. in Chiurdoglu Conformational Analysis Academic Press NY, 1971, p. 229. 

P conformation of 60 knotted chains 74 torsion angles 60 Peptide deformylase 627 Peptide hormone(s). See also Chapter 30 amidationof 522 Peptide linkage 51,55s cis 56s... 

Another example of a quantal repeat—but with considerable variation in sequence—is seen in the keratin-associated proteins (KAPs). In sheep, these display pentapeptide and decapeptide consensus repeats of the form G—G—Q—P—S/T and C-C-Q/R—P—S/T—C/S/T—C—Q—P/T—S, respectively (Parry et al., 1979). Some of the positions, as indicated by the presence of a consensus sequence, contain residues that occur much more frequently than others, but the absolute conservation of a residue in any position is not observed. The decapeptide consists of a pair of five-residue repeats closely related, but different to that displayed by the pentapeptide. Although the repeats have an undetermined structure, the similarity of the repeat to a sequence in snake neurotoxin suggests that the pentapeptides will adopt a closed loop conformation stabilized by a disulphide bond between cysteine residues four apart (Fig. 5 Fraser et al., 1988 Parry et al, 1979). Relative freedom of rotation about the single bond connecting disulphide-bonded knots would give rise to the concept of a linear array of knots that can fold up to form a variety of tertiary structures. The KAPS display imperfect disulphide stabilization of knots and have interacting... 

Lukin, O., Muller, W.M., Muller, U., Kaufmann, A., Schmidt, C., Leszczynski, J., Vogtle, F. Covalent chemistry and conformational dynamics of topologically chiral amide-based molecular knots, Chem. Eur. J. 9 (2003), 3507-3517. 

Figure 7. a) The lowest energy conformation of the intermediate 14 which promotes knot formation, b) The reversed sequence of adding the diacyl chlorides 2 and 6 into the reaction does not produce the helical intermediate knot formation does not occur. 

Every knot connects four chains by chemical bonds. At T > Tg, both chains and knots take part in thermal motion as Brownian particles, at T < Tg, the network is in a glassy state, large-scale conformations of the chains are frozen, the motion of the knots is negligible. 

Although a network is not present in a concentrated solution, there exists a characteristic length, which had earlier been assumed the distance between neighbouring network sites. The characteristic length is a dynamic one. There are no temporary knots in a polymer system, though there is a characteristic time, which is the lifetime of the frozen large-scale conformation of a macromolecule in the system. So, the conceptions of intermediate length and characteristic time are based on deeper ideas and are reflected in the theory. 

Christmann, A., Walter, K., Wentzel, A., Kratzner, R., and Kolmar, H. (1999). The cystine knot of a squash-type protease inhibitor as a structural scaffold for Escherichia coli cell surface display of conformationally constrained peptides. Prot. Eng. 12, 797-806. 

The synthetic chemist can see beauty in an approach to a chemical object, be it in the form of the perceived elegance, efficiency, directness, or combination of approaches. Covalent bond forming, coordination chemistry and purely non-covalent possibilities are all important of course, but each one on its own is weak. Take the statistical approach to link formation A flexible linear molecule in random motion is not likely to form a knot, and it is even less likely that we could separate and characterise it even if it did. There is no direction in the reactivity. Covalent bonds can be used to hold fragments together, and then those bonds used to orient the fragments are removed to leave the linked molecule. With today s control over molecular conformation and covalent bond making and breaking, this has to be considered a viable approach. But, those approaches based on coordination chemistry and non-covalent bonds are more direct and efficient for the moment. 

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