Folding studies on a knotted protein

YibK is a 160 residue homodimeric protein belonging to the SPOUT class of methyltransferases. Proteins in this group all display a unique topological feature; the backbone polypeptide chain folds to form a deep trefoil knot. Such knotted structures were completely unpredicted, it being thought impossible for a protein to fold efficiently in this way. However, they are becoming more common and there are now a growing number of examples in the Protein Data Bank. These intriguing knotted structures represent a new and significant challenge in the field of protein folding. Here, we present an initial characterisation of the folding of YibK, one of the smallest knotted proteins to be identified. This is the first detailed folding study on a knotted protein to be reported. We have established conditions under which the protein can be denatured reversibly in vitro using urea, thereby showing that molecular chaperones are not required for the efficient folding of this protein. A series of equilibrium unfolding experiments were performed over a 400-fold range of protein concentration. Both secondary and tertiary structural probes show a single, protein concentration-dependent unfolding transition, and data are most consistent with a three-state equilibrium denaturation model involving a monomeric intermediate. Thermodynamic parameters obtained from the fit of the data to this model indicate that the intermediate is a stable species with appreciable secondary and tertiary structure; whether the topological knot remains in the intermediate state is still to be shown. Together, these results demonstrate that, despite its complex knotted structure, YibK is able to fold efficiently and behaves remarkably similarly to other dimeric proteins under equilibrium conditions.     

Knot formation in newly translated proteins is spontaneous and accelerated by chaperonins

Topological knots are found in a considerable number of protein structures, but it is not clear how they knot and fold within the cellular environment. We investigated the behavior of knotted protein molecules as they are first synthesized by the ribosome using a cell-free translation system. We found that newly translated knotted proteins can spontaneously self-tie and do not require the assistance of molecular chaperones to fold correctly to their trefoil-knotted structures. This process is slow but efficient, and we found no evidence of misfolded species. A kinetic analysis indicates that the knotting process is rate limiting, occurs post-translationally, and is specifically and significantly (P < 0.001) accelerated by the GroEL-GroES chaperonin complex. This demonstrates a new active mechanism for this molecular chaperone and suggests that chaperonin-catalyzed knotting probably dominates in vivo. These results explain how knotted protein structures have withstood evolutionary pressures despite their topological complexity.     

Proteins' Knotty Problems

Knots in proteins are increasingly being recognized as an important structural concept, and the folding of these peculiar structures still poses considerable challenges. From a functional point of view, most protein knots discovered so far are either enzymes or DNA-binding proteins. Our comprehensive topological analysis of the Protein Data Bank reveals several novel structures including knotted mitochondrial proteins and the most deeply embedded protein knot discovered so far. For the latter, we propose a novel folding pathway based on the idea that a loose knot forms at a terminus and slides to its native position. For the mitochondrial proteins, we discuss the folding problem from the perspective of transport and suggest that they fold inside the mitochondria. We also discuss the evolutionary origin of a novel class of knotted membrane proteins and argue that a novel knotted DNA-binding protein constitutes a new fold. Finally, we have also discovered a knot in an artificially designed protein structure.     

AlphaFold predicts the most complex protein knot and composite protein knots

The computer artificial intelligence system AlphaFold has recently predicted previously unknown three‐dimensional structures of thousands of proteins. Focusing on the subset with high‐confidence scores, we algorithmically analyze these predictions for cases where the protein backbone exhibits rare topological complexity, that is, knotting. Amongst others, we discovered a 7₁‐knot, the most topologically complex knot ever found in a protein, as well several six‐crossing composite knots comprised of two methyltransferase or carbonic anhydrase domains, each containing a simple trefoil knot. These deeply embedded composite knots occur evidently by gene duplication and interconnection of knotted dimers. Finally, we report two new five‐crossing knots including the first 5₁‐knot. Our list of analyzed structures forms the basis for future experimental studies to confirm these novel‐knotted topologies and to explore their complex folding mechanisms.     

A topological framework for the computation of the HOMFLY polynomial and its application to proteins

Polymers can be modeled as open polygonal paths and their closure generates knots. Knotted proteins detection is currently achieved via high-throughput methods based on a common framework insensitive to the handedness of knots. Here we propose a topological framework for the computation of the HOMFLY polynomial, an handedness-sensitive invariant. Our approach couples a multi-component reduction scheme with the polynomial computation. After validation on tabulated knots and links the framework was applied to the entire Protein Data Bank along with a set of selected topological checks that allowed to discard artificially entangled structures. This led to an up-to-date table of knotted proteins that also includes two newly detected right-handed trefoil knots in recently deposited protein structures. The application range of our framework is not limited to proteins and it can be extended to the topological analysis of biological and synthetic polymers and more generally to arbitrary polygonal paths.     

Dynamic and facilitated binding of topoisomerase accelerates topological relaxation

How type 2 Topoisomerase (TopoII) proteins relax and simplify the topology of DNA molecules is one of the most intriguing open questions in genome and DNA biophysics. Most of the existing models neglect the dynamics of TopoII which is expected of proteins searching their targets via facilitated diffusion. Here, we show that dynamic binding of TopoII speeds up the topological relaxation of knotted substrates by enhancing the search of the knotted arc. Intriguingly, this in turn implies that the timescale of topological relaxation is virtually independent of the substrate length. We then discover that considering binding biases due to facilitated diffusion on looped substrates steers the sampling of the topological space closer to the boundaries between different topoisomers yielding an optimally fast topological relaxation. We discuss our findings in the context of topological simplification in vitro and in vivo.     

Knotted fusion proteins reveal unexpected possibilities in protein folding

Proteins that contain a distinct knot in their native structure are impressive examples of biological self-organization. Although this topological complexity does not appear to cause a folding problem, the mechanisms by which such knotted proteins form are unknown. We found that the fusion of an additional protein domain to either the amino terminus, the carboxy terminus, or to both termini of two small knotted proteins did not affect their ability to knot. The multidomain constructs remained able to fold to structures previously thought unfeasible, some representing the deepest protein knots known. By examining the folding kinetics of these fusion proteins, we found evidence to suggest that knotting is not rate limiting during folding, but instead occurs in a denatured-like state. These studies offer experimental insights into when knot formation occurs in natural proteins and demonstrate that early folding events can lead to diverse and sometimes unexpected protein topologies.     

Threading a peptide through a peptide: protein loops, rotaxanes, and knots

Proteins adopt complex folds in nature that typically avoid conformations that are knotted or “threaded” through closed loops. Is this the result of fundamental barriers to folding, or have proteins simply evolved to avoid threaded conformations? Organic synthesis has been used in supramolecular chemistry to install topological links in small molecules. By following these principles, we now show that it is possible to assemble a topologically linked protein complex by threading a linear protein through a cyclic protein to form a [2]pseudo‐rotaxane. Subsequent ring closure using native chemical ligation cyclizes the linear protein, forming a [2]heterocatenane. Although the kinetics of protein threading are slower than the folding kinetics of the native protein, threading appears to be a highly efficient process.     

How topoisomerase IV can efficiently unknot and decatenate negatively supercoiled DNA molecules without causing their torsional relaxation

Freshly replicated DNA molecules initially form multiply interlinked right-handed catenanes. In bacteria, these catenated molecules become supercoiled by DNA gyrase before they undergo a complete decatenation by topoisomerase IV (Topo IV). Topo IV is also involved in the unknotting of supercoiled DNA molecules. Using Metropolis Monte Carlo simulations, we investigate the shapes of supercoiled DNA molecules that are either knotted or catenated. We are especially interested in understanding how Topo IV can unknot right-handed knots and decatenate right-handed catenanes without acting on right-handed plectonemes in negatively supercoiled DNA molecules. To this end, we investigate how the topological consequences of intersegmental passages depend on the geometry of the DNA-DNA juxtapositions at which these passages occur. We observe that there are interesting differences between the geometries of DNA-DNA juxtapositions in the interwound portions and in the knotted or catenated portions of the studied molecules. In particular, in negatively supercoiled, multiply interlinked, right-handed catenanes, we detect specific regions where DNA segments belonging to two freshly replicated sister DNA molecules form left-handed crossings. We propose that, due to its geometrical preference to act on left-handed crossings, Topo IV can specifically unknot supercoiled DNA, as well as decatenate postreplicative catenanes, without causing their torsional relaxation.     

Twists,knots, and rings in proteins. Structural definition of the cyclotide framework

In recent years an increasing number of miniproteins containing an amide-cyclized backbone have been discovered. The cyclotide family is the largest group of such proteins and is characterized by a circular protein backbone and six conserved cysteine residues linked by disulfide bonds in a tight core of the molecule. These form a cystine knot in which an embedded ring formed by two of the disulfide bonds and the connecting backbone segment is threaded by a third disulfide bond. In the current study we have undertaken high resolution structural analysis of two prototypic cyclotides, kalata B1 and cycloviolacin O1, to define the role of the conserved residues in the sequence. We provide the first comprehensive analysis of the topological features in this unique family of proteins, namely rings (a circular backbone), twists (a cis-peptide bond in the M?bius cyclotides) and knots (a knotted arrangement of the disulfide bonds).     

Polymer Uncrossing and Knotting in Protein Folding,and Their Role in Minimal Folding Pathways

We introduce a method for calculating the extent to which chain non-crossing is important in the most efficient, optimal trajectories or pathways for a protein to fold. This involves recording all unphysical crossing events of a ghost chain, and calculating the minimal uncrossing cost that would have been required to avoid such events. A depth-first tree search algorithm is applied to find minimal transformations to fold , , , and knotted proteins. In all cases, the extra uncrossing/non-crossing distance is a small fraction of the total distance travelled by a ghost chain. Different structural classes may be distinguished by the amount of extra uncrossing distance, and the effectiveness of such discrimination is compared with other order parameters. It was seen that non-crossing distance over chain length provided the best discrimination between structural and kinetic classes. The scaling of non-crossing distance with chain length implies an inevitable crossover to entanglement-dominated folding mechanisms for sufficiently long chains. We further quantify the minimal folding pathways by collecting the sequence of uncrossing moves, which generally involve leg, loop, and elbow-like uncrossing moves, and rendering the collection of these moves over the unfolded ensemble as a multiple-transformation “alignment”. The consensus minimal pathway is constructed and shown schematically for representative cases of an , , and knotted protein. An overlap parameter is defined between pathways; we find that proteins have minimal overlap indicating diverse folding pathways, knotted proteins are highly constrained to follow a dominant pathway, and proteins are somewhere in between. Thus we have shown how topological chain constraints can induce dominant pathway mechanisms in protein folding.     

The Energy Landscape,Folding Pathways and the Kinetics of a Knotted Protein

The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling approach, and the resulting potential energy surface is visualized by constructing disconnectivity graphs. Owing to topological constraints, the low-lying portion of the landscape consists of three distinct regions, corresponding to the native knotted state and to configurations where either the N or C terminus is not yet folded into the knot. The fastest folding pathways from denatured states exhibit early formation of the N terminus portion of the knot and a rate-determining step where the C terminus is incorporated. The low-lying minima with the N terminus knotted and the C terminus free therefore constitute an off-pathway intermediate for this model. The insertion of both the N and C termini into the knot occurs late in the folding process, creating large energy barriers that are the rate limiting steps in the folding process. When compared to other protein folding proteins of a similar length, this system folds over six orders of magnitude more slowly.     

Untying a Protein Knot by Circular Permutation

Topologically knotted proteins are tantalizing examples of how polypeptide chains can explore complex free energy landscapes to efficiently attain defined knotted conformations. The evolution trails of protein knots, however, remain elusive. We used circular permutation to change an evolutionally conserved topologically knotted SPOUT RNA methyltransferase into an unknotted form. The unknotted variant adopted the same three-dimensional structure and oligomeric state as its knotted parent, but its folding stability was markedly reduced with accelerated folding kinetics and its ligand binding was abrogated. Our findings support the hypothesis that the universally conserved knotted topology of the SPOUT superfamily evolved from unknotted forms through circular permutation under selection pressure for folding robustness and, more importantly, for functional requirements associated with the knotted structural element.     

In vivo protein complex topologies: sights through a cross-linking lens

Proteins are a remarkable class of molecules that exhibit wide diversity of shapes or topological features that underpin protein interactions and give rise to biological function. In addition to quantitation of abundance levels of proteins in biological systems under a variety of conditions, the field of proteome research has as a primary mission the assignment of function for proteins and if possible, illumination of factors that enable function. For many years, chemical cross-linking methods have been used to provide structural data on single purified proteins and purified protein complexes. However, these methods also offer the alluring possibility to extend capabilities to complex biological samples such as cell lysates or intact living cells where proteins may exhibit native topological features that do not exist in purified form. Recent efforts are beginning to provide glimpses of protein complexes and topologies in cells that suggest continued development will yield novel capabilities to view functional topological features of many proteins and complexes as they exist in cells, tissues, or other complex samples. This review will describe rationale, challenges, and a few success stories along the path of development of cross-linking technologies for measurement of in vivo protein interaction topologies.     

Identification of rare slipknots in proteins and their implications for stability and folding

Among the thousands of known three-dimensional protein folds, only a few have been found whose backbones are in knotted configurations. The rarity of knotted proteins has important implications for how natural proteins reach their natively folded states. Proteins with such unusual features offer unique opportunities for studying the relationships between structure, folding, and stability. Here we report the identification of a unique slipknot feature in the fold of a well-known thermostable protein, alkaline phosphatase. A slipknot is created when a knot is formed by part of a protein chain, after which the backbone doubles back so that the entire structure becomes unknotted in a mathematical sense. Slipknots are therefore not detected by computational tests that look for knots in complete protein structures. A computational survey looking specifically for slipknots in the Protein Data Bank reveals a few other instances in addition to alkaline phosphatase. Unexpected similarities are noted among some of the proteins identified. In addition, two transmembrane proteins are found to contain slipknots. Finally, mutagenesis experiments on alkaline phosphatase are used to probe the contribution the slipknot feature makes to thermal stability. The trends and conserved features observed in these proteins provide new insights into mechanisms of protein folding and stability.     

Topology of globular proteins

This paper inquires whether it is reasonable to expect the native structure of proteins to be “knotted”. To this end, some topological properties of polypeptides containing disulfide bridges are discussed using notions from mathematical knot theory and graph theory. The probability of occurrence of knots in random cyclic polymers is calculated as a function of chain length by elementary Monte Carlo methods. The implications of this for protein renaturation and for determining the tertiary structure of proteins are discussed.     

Protein knots provide mechano-resilience to an AAA+ protease-mediated proteolysis with profound ATP energy expenses

Knotted proteins are some of the most fascinating examples of how linear polypeptide chains can achieve intricate topological arrangements efficiently and spontaneously. The entanglements of polypeptide chains could potentially enhance their folding stabilities. We recently reported the unprecedented mechanostability of the Gordian (5₂) knotted family of human ubiquitin C-terminal hydrolases (UCHs) in the context of withstanding the mechanical unfolding of the bacterial AAA+ proteasome, ClpXP; a green fluorescence protein (GFP) was fused to the N-terminus of various UCHs as a reporter of the unfolding and degradation of these topologically knotted substrates, but it also limited the ability to examine the effect of untying the knotted topology via N-terminal truncation. In this study, we directly monitored the ClpXP-mediated degradation of UCH variants by electrophoresis and quantitative imaging analyses. We demonstrated that untying of the 5₂ knot in UCHL1 via N-terminal truncation (UCHL1_Δ11) significantly reduces its mechanostability. We further quantified the ATP expenditures of degrading different UCH variants by ClpXP. The unknotted UCHL1_Δ11 underwent accelerated ClpXP-dependent proteolysis, with a 30-fold reduction in ATP consumption compared to the knotted wild type. Unlike all other known ClpXP substrates, UCHL5, which is the most resilient substrate known to date, significantly slowed down the ATP turnover rate by ClpXP. Furthermore, UCHL5 required 1000-fold more ATP to be fully degraded by ClpXP compared to GFP. Our results underscored how the complex, knotted folding topology in UCHs may interfere with the mechano-unfolding processes of the AAA+ unfoldase, ClpX.     

Topology of globular proteins. II.

This paper continues the inquiry into the likelihood of occurrence of protein structures which are “knotted”. The probability of knotted con formations is calculated by a simple Monte Carlo method for the proteins lysozyme and ribonuclease and for an elementary bicyclic polymer. Ribonuclease shows no measurable inclination towards tangling, but some 10%. of the lysozyme conformations are knotted. The implications of this result for the role of disulfide bridge formation in protein renaturation are discussed.     

Novel topologically knotted DNA from bacteriophage P4 capsids: studies with DNA topoisomerases.

DNA molecules isolated from bacteriophage P4 are mostly linear with cohesive ends capable of forming circular and concatemeric structures. In contrast, almost all DNA molecules isolated form P4 tailless capsids (heads) are monomeric DNA circles with their cohesive ends hydrogen-bonded. Different form simple DNA circles, such P4 head DNA circles contain topological knots. Gel electrophoretic and electronmicroscopic analyses of P4 head DNA indicate that the topological knots are highly complex and heterogeneous. Resolution of such complex knots has been studied with various DNA topoisomerases. The conversion of highly knotted P4 DNA to its simple circular form is demonstrated by type II DNA topoisomerases which catalyze the topological passing of two crossing double-stranded DNA segments [Liu, L. F., Liu, C. C. & Alberts, B. M. (1980) Cell, 19, 697-707]. The knotted P4 head DNA can be used in a sensitive assay for the detection of a type II DNA topoisomerase even in the presence of excess type I DNA topoisomerases.     

Combination use of protein–protein interaction network topological features improves the predictive scores of deleterious non-synonymous single-nucleotide polymorphisms

Single-nucleotide polymorphisms (SNPs) are the most frequent form of genetic variations. Non-synonymous SNPs (nsSNPs) occurring in coding region result in single amino acid substitutions that associate with human hereditary diseases. Plenty of approaches were designed for distinguishing deleterious from neutral nsSNPs based on sequence level information. Novel in this work, combinations of protein–protein interaction (PPI) network topological features were introduced in predicting disease-related nsSNPs. Based on a dataset that was compiled from Swiss-Prot, a random forest model was constructed with an average accuracy value of 80.43 % and an MCC value of 0.60 in a rigorous tenfold crossvalidation test. For an independent dataset, our model achieved an accuracy of 88.05 % and an MCC of 0.67. Compared with previous studies, our approach presented superior prediction ability. Results showed that the incorporated PPI network topological features outperform conventional features. Our further analysis indicated that disease-related proteins are topologically different from other proteins. This study suggested that nsSNPs may share some topological information of proteins and the change of topological attributes could provide clues in illustrating functional shift due to nsSNPs.