Conservation of complex knotting and slipknotting patterns in proteins

Abstract

While analyzing all available protein structures for the presence of knots and slipknots, we detected a strict conservation of complex knotting patterns within and between several protein families despite their large sequence divergence. Because protein folding pathways leading to knotted native protein structures are slower and less efficient than those leading to unknotted proteins with similar size and sequence, the strict conservation of the knotting patterns indicates an important physiological role of knots and slipknots in these proteins. Although little is known about the functional role of knots, recent studies have demonstrated a proteinstabilizing ability of knots and slipknots. Some of the conserved knotting patterns occur in proteins forming transmembrane channels where the slipknot loop seems to strap together the transmembrane helices forming the channel.protein knots | knot theory | topology T here are increasing numbers of known proteins that form linear open knots in their native folded structure (1, 2). In general, knots in proteins are orders of magnitude less frequent than would be expected for random polymers with similar length, compactness, and flexibility (3). In principle, the polypeptide chains folding into knotted native protein structures encounter more kinetic difficulties than unknotted proteins (4-12). Therefore, it is believed that knotted protein structures were, in part, eliminated during evolution because proteins that fold slowly and/or nonreproducibly should be evolutionarily disadvantageous for the hosting organisms. Nevertheless, there are several families of proteins that reproducibly form simple knots, complex knots, and slipknots (1, 2). In these proteins, the disadvantage of less efficient folding may be balanced by a functional advantage connected with the presence of these knots. Numerous experimental (13-16) and theoretical (17-27) studies have been devoted to understanding the precise nature of the structural and functional advantages created by the presence of these knots in protein backbones. It has been proposed that in some cases the protein knots and slipknots provide a stabilizing function that can act by holding together certain protein domains (4). In the majority of cases, however, one is unable to determine the precise structural and functional advantages provided by the presence of knots.To shed light on the function and formation of protein knots, we performed a thorough characterization of knotting within protein structures deposited in the Protein Data Bank (PDB) (28) by creating a precise mapping of the position and size of the knotted and slipknotted domains and knot tails (1, 2). We identified the types of knots that are formed by the backbone of the entire polypeptide chain and also by all continuous backbone portions of a given protein (1, 2). To characterize the knotting of proteins with linear backbones, one needs to set aside the orthodox rule of knot theory that states that all linear chains are unknotted because, by a continuous deformation,...

Characterization of the Folding of a 5 2 -Knotted Protein Using Engineered Single-Tryptophan Variants

“…Previous investigations on the folding mechanisms of a few knotted proteins established that these proteins have complex multistep folding pathways with slow kinetics rather than the simple two-state mechanisms that are commonly seen for small, fast-folding, single-domain proteins (6)(7)(8)(9)(10)(11). Despite experimental and computational work over the last 10 years (12)(13)(14)(15)(16)(17), the folding mechanisms of knotted proteins remain poorly understood compared with those described for small model systems that have been studied in great detail (18)(19)(20)(21)(22)(23).…”

Knots in knots: A study of classical knot diagrams

“…Subsequent to these discussions, Rawdon, Stasiak and I studied the presence of subknots, using the spatial closure method discussed earlier, in ideal and random knots [4], the knotting fingerprint, in a generalization of the earlier protein structural analysis [2,6] in which we used another version of a knotting fingerprint. Here, each cell in the circular fingerprint expresses the strength of the knotting of …”

Effects of topological constraints on globular polymers

“…We found that loops of the knotted globule were highly knotted, with the knot complexity rising sharply with s. Loops of the unknotted globule, on the contrary, were weakly knotted, and their complexity increased slowly with length. Their knotting complexity was also very variable, indicating the abundance of slip knots [32] (Fig. S5).…”