Knots in Proteins

The logic of a biologist is unlikely to make parallels between DNA and proteins, for they are of completely different roles in the cell. By contrast, the logic of polymer physics makes such comparison quite natural. Thus, are there knots in proteins Proteins are, of course, much shorter, but they are globular, so the question is delicate. 

The answer is positive yes, there are proteins with knots. Sometimes, these are simple trefoil knots, but a few cases are known with rather complex 

So he started to climb out of the hole. He pulled with his front paws, and pushed with his back paws, and in a little while his nose was out in the open again... and then his ears.. .and then his front paws... and then his shoulders.. and then... 

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Fig. C11.5 Three examples of knots in proteins, including the very complex knot 5i in a protein called human ubiquitin hydrolase (the rightmost image). In each case, a simple model of sticks shows the same knot as in the protein. To help the eye, each chain is colored in rainbow colors from one end to the other. The figure is reproduced, with kind permission by the authors, from the paper P. Virnau, L. Mirny and M. Kardar, Intricate Knots in Proteins Function and Evolution, PLoS Computational Biology, v. 2, pp. 1074-1079, 2006.

The seeds of squash plants are rich in a family of trypsin and chymotrypsin inhibitors that are approximately 35 amino acids in size and have been extensively investigated not only for their enzyme inhibitory activity, but also because they are very stable mini-protein scaffolds with applications in protein engineering. The best studied examples are Ecballium elaterium trypsin inhibitor (EETI-II) and Cucurbita maxima trypsin inhibitor (CMTI). Both X-ray and NMR have been used to characterise their structures, which incorporate a cystine-knot motif formed by three conserved disulphide bonds.93 We will describe this motif in more detail in a later section describing the plant cyclotides. 

Resuspend the precipitated protein obtained from step 10-31 in a second 10 ml cold water. Remove the undissolved protein by centrifugation and combine this supernatant solution with that obtained in step 10-31. This is supernatant V. Note its volume and remove a 0.5 ml sample for assay purposes. The insoluble protein precipitate may be discarded. 10-33. Cut a convenient length (15 to 18 in.) of cellulose dialysis tubing (jin. diameter). Wet the tubing with distilled water and tie two knots in one end of it, as shown in Figure 10-7. 

All these chiral structural standards and the corresponding families around them in proteins and nucleic acids represent, however, only the main building blocks upon which evolution has been operating. The colored loop- and knot-stretches and all the more disordered parts of protein and nucleic acid structural designs are of primary importance for the evolutionary aspects of informational and functional processings in our evolving life patterns. 

Fig. 11.6 A slip knot. It is not really a knot, because you can untie it if you just pull the ends. Nevertheless, it is an interesting long lived feature of some proteins. Some data on slip knots in real proteins can be found in the paper J. Sulkowska, P. Sulkowski and J. Onuchic, Proceedings of the National Academy of Sciences, USA, v. 106, p. 3119, 2009.

Is there anything similar in the physics of biopolymers, any general laws that are not affected by the random choices There certainly are They control the formation of knots in DNA (see Section 2.6), the hydrophobic-hydrophilic separation of a globular protein (Section 5.7), and many other properties most of these laws may still be unknown. 

In the next sections we present a brief discussion of the derivation of knots from the molecular space curves representing the protein backbone, using projections to a sphere. The knots are characterized by topological invariants. As in ref. 14, we use the Jones polynomials [15]. The occurrence of basic structural patterns can be recognized in terms of the knots we discuss briefly some of the results derived in ref. 16. Finally, we comment on the application of this procedure to study conformational motions in proteins, and to recognize the occurrence of essential changes in the shape or folding patterns. 

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). 

Conformational studies on knots may be relevant to polymer chemistry (interpenetrating network polymers[43]) as well as to biology (motions in proteins or DNA). 

Rosengren KJ, Daly NL, Plan MR, Waine C, Craik DJ (2003) Twists, knots, and rings in proteins - structural definition of the cycloride framework. J Biol Chem 278 8606-8616... 

In a recent paper, Krasnow and co-workers (120) applied a Rec A protein coating to DNA knots and catenanes to enhance visualization of the helical DNA segments and, in particular, to determine the absolute handedness of the knots. The Rec A protein is known to bind cooperatively to duplex DNA, forming a stiffened complex about 100 A in diameter in the presence of ATPase (121). 

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