Untangling the Influence of a Protein Knot on Folding

Entanglement and knots occur across all aspects of the physical world. Despite the common belief that knots are too complicated for incorporation into proteins, knots have been identified in the native fold of a growing number of proteins. The discovery of proteins with this unique backbone characteristic has challenged the preconceptions about the complexity of biological structures, as well as current folding theories. Given the intricacies of the knotted geometry, the interplay between a protein’s fold, structure, and function is of particular interest. Interestingly, for most of these proteins, the knotted region appears critical both in folding and function, although full understanding of these contributions is still incomplete. Here, we experimentally reveal the impact of the knot on the landscape, the origin of the bistable nature of the knotted protein, and broaden the view of knot formation as uniquely decoupled from folding.     

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.     

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.     

The folding mechanics of a knotted protein

An increasing number of proteins are being discovered with a remarkable and somewhat surprising feature, a knot in their native structures. How the polypeptide chain is able to "knot" itself during the folding process to form these highly intricate protein topologies is not known. Here we perform a computational study on the 160-amino-acid homodimeric protein YibK, which, like other proteins in the SpoU family of MTases, contains a deep trefoil knot in its C-terminal region. In this study, we use a coarse-grained C(alpha)-chain representation and Langevin dynamics to study folding kinetics. We find that specific, attractive nonnative interactions are critical for knot formation. In the absence of these interactions, i.e., in an energetics driven entirely by native interactions, knot formation is exceedingly unlikely. Further, we find, in concert with recent experimental data on YibK, two parallel folding pathways that we attribute to an early and a late formation of the trefoil knot, respectively. For both pathways, knot formation occurs before dimerization. A bioinformatics analysis of the SpoU family of proteins reveals further that the critical nonnative interactions may originate from evolutionary conserved hydrophobic segments around the knotted region.     

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.     

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.     

Intricate knots in proteins: Function and evolution

Our investigation of knotted structures in the Protein Data Bank reveals the most complicated knot discovered to date. We suggest that the occurrence of this knot in a human ubiquitin hydrolase might be related to the role of the enzyme in protein degradation. While knots are usually preserved among homologues, we also identify an exception in a transcarbamylase. This allows us to exemplify the function of knots in proteins and to suggest how they may have been created.     

A Stevedore's Protein Knot

Protein knots, mostly regarded as intriguing oddities, are gradually being recognized as significant structural motifs. Seven distinctly knotted folds have already been identified. It is by and large unclear how these exceptional structures actually fold, and only recently, experiments and simulations have begun to shed some light on this issue. In checking the new protein structures submitted to the Protein Data Bank, we encountered the most complex and the smallest knots to date: A recently uncovered α-haloacid dehalogenase structure contains a knot with six crossings, a so-called Stevedore knot, in a projection onto a plane. The smallest protein knot is present in an as yet unclassified protein fragment that consists of only 92 amino acids. The topological complexity of the Stevedore knot presents a puzzle as to how it could possibly fold. To unravel this enigma, we performed folding simulations with a structure-based coarse-grained model and uncovered a possible mechanism by which the knot forms in a single loop flip.     

Knots in rings. The circular knotted protein Momordica cochinchinensis trypsin inhibitor-II folds via a stable two-disulfide intermediate

The aim of this work was to elucidate the oxidative folding mechanism of the macrocyclic cystine knot protein MCoTI-II. We aimed to investigate how the six-cysteine residues distributed on the circular backbone of the reduced unfolded peptide recognize their correct partner and join up to form a complex cystine-knotted topology. To answer this question, we studied the oxidative folding of the naturally occurring peptide using a range of spectroscopic methods. For both oxidative folding and reductive unfolding, the same disulfide intermediate species was prevalent and was characterized to be a native-like two-disulfide intermediate in which the Cys1-Cys18 disulfide bond was absent. Overall, the folding pathway of this head-to-tail cyclized protein was found to be similar to that of linear cystine knot proteins from the squash family of trypsin inhibitors. However, the pathway differs in an important way from that of the cyclotide kalata B1, in that the equivalent two-disulfide intermediate in that case is not a direct precursor of the native protein. The size of the embedded ring within the cystine knot motif appears to play a crucial role in the folding pathway. Larger rings contribute to the independence of disulfides and favor an on-pathway native-like intermediate that has a smaller energy barrier to cross to form the native fold. The fact that macrocyclic proteins are readily able to fold to a complex knotted structure in vitro in the absence of chaperones makes them suitable as protein engineering scaffolds that have remarkable stability.     

A comparison of the folding of two knotted proteins: YbeA and YibK

The extraordinary topology of proteins belonging to the alpha/beta-knot superfamily of proteins is unexpected, due to the apparent complexities involved in the formation of a deep trefoil knot in a polypeptide backbone. Despite this, an increasing number of knotted structures are being identified; how such proteins fold remains a mystery. Studies on the dimeric protein YibK from Haemophilus influenzae have led to the characterisation of its folding pathway in some detail. To complement research into the folding of YibK, and to address whether folding pathways are conserved for members of the alpha/beta-knot superfamily, the structurally similar knotted protein YbeA from Escherichia coli has been studied. A comprehensive thermodynamic and kinetic analysis of the folding of YbeA is presented here, and compared to that of YibK. Both fold via an intermediate state populated under equilibrium conditions that is monomeric and considerably structured. The unfolding/refolding kinetics of YbeA are simpler than those found for YibK and involve two phases attributed to the formation of a monomeric intermediate state and a dimerisation step. In contrast to YibK, a change in the rate-determining step on the unfolding pathway for YbeA is observed with a changing concentration of urea. Despite this difference, both proteins fold by a mechanism involving at least one sequential monomeric intermediate that has properties similar to that observed during the equilibrium unfolding. The rate of dimerisation observed for YbeA and YibK is very similar, as is the rate constant for formation of the kinetic monomeric intermediate that precedes dimerisation. The findings suggest that relatively slow folding and dimerisation may be common attributes of knotted proteins.     

How Difficult Is It to Fold a Knotted Protein? In Silico Insights from Surface-Tethered Folding Experiments

We explore the effect of surface tethering on the folding process of a lattice protein that contains a trefoil knot in its native structure via Monte Carlo simulations. We show that the outcome of the tethering experiment depends critically on which terminus is used to link the protein to a chemically inert plane. In particular, if surface tethering occurs at the bead that is closer to the knotted core the folding rate becomes exceedingly slow and the protein is not able to find the native structure in all the attempted folding trajectories. Such low folding efficiency is also apparent from the analysis of the probability of knot formation, p_knot, as a function of nativeness. Indeed, p_knot increases abruptly from ∼0 to ∼1 only when the protein has more than 80% of its native contacts formed, showing that a highly compact conformation must undergo substantial structural re-arrangement in order to get effectively knotted. When the protein is surface tethered by the bead that is placed more far away from the knotted core p_knot is higher than in the other folding setups (including folding in the bulk), especially if conformations are highly native-like. These results show that the mobility of the terminus closest to the knotted core is critical for successful folding of trefoil proteins, which, in turn, highlights the importance of a knotting mechanism that is based on a threading movement of this terminus through a knotting loop. The results reported here predict that if this movement is blocked, knotting occurs via an alternative mechanism, the so-called spindle mechanism, which is prone to misfolding. Our simulations show that in the three considered folding setups the formation of the knot is typically a late event in the folding process. We discuss the implications of our findings for co-translational folding of knotted trefoils.     

Diversity in the disulfide folding pathways of cystine knot peptides

Summary The plant cyclotides are a fascinating family of circular proteins that contain a cyclic cystine knot motif (CCK). This unique family was discovered only recently but contains over 50 known sequences to date. Various biological activities are associated with these peptides including antimicrobial and insecticidal activity. The knotted topology and cyclic nature of the cyclotides poses interesting questions about the folding mechanisms and how the knotted arrangement of disulfide bonds is formed. Some studies have been performed on related inhibitor cystine knot (ICK) containing peptides, but little is known about the folding mechanisms of CCK molecules. We have examined the oxidative refolding and reductive unfolding of the prototypic member of the cyclotide family, kalata B1. Analysis of the rates of formation of the intermediates along the reductive unfolding pathway highlights the stability conferred by the cystine knot motif. Significant differences are observed between the folding of kalata B1 and an acyclic cystine knot protein, EETI-II, suggesting that the circular backbone has a significant influence in directing the folding pathway.     

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.     

Probing nature's knots: the folding pathway of a knotted homodimeric protein

The homodimeric protein YibK from Haemophilus influenzae belongs to a recently discovered superfamily of knotted proteins that has brought about a new protein-folding conundrum. Members of the alpha/beta-knot clan form deep trefoil knots in their native backbone structure, a topological feature that is currently unexplained in the protein-folding field. To help solve the puzzle of how a polypeptide chain can efficiently knot itself, the folding kinetics of YibK have been studied extensively and the results are reported here. Folding was monitored using probes for changes in both secondary and tertiary structure, and the monomer-dimer equilibrium was perturbed with a variety of solution conditions to allow characterisation of otherwise inaccessible states. Multiphasic kinetics were observed in the unfolding and refolding reactions of YibK, and under conditions where the dimer is favoured, dissociation and association were rate-limiting, respectively. A folding model consistent with all kinetic data is proposed: YibK appears to fold via two parallel pathways, partitioned by proline isomerisation events, to two distinct monomeric intermediates. These form a common third intermediate that is able to fold to native dimer. Kinetic simulations suggest that all intermediates are on-pathway. These results provide the valuable groundwork required to further understand how Nature codes for knot formation.     

Oxidative folding of the cystine knot motif in cyclotide proteins

The cyclotides are a large family of plant proteins that have a cyclic backbone and a knotted arrangement of three conserved disulfide bonds. Despite the apparent complexity of their cystine knot motif it is possible to efficiently fold these proteins, as exemplified by oxidative folding studies on the prototypic cyclotide, kalata B1. This mini-review reports on the current understanding of the folding process in cyclotides. The synthesis and folding of these molecules paves the way for their application as stable molecular templates.     

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.     

Predicting Atomic Details of the Unfolding Pathway for YibK,a Knotted Protein from the SPOUT Superfamily

Abstract

Several protein structures have been reported to contain intricate knots of the polypeptide backbone but the mechanism of the (un)folding process of knotted proteins remains unknown. The members of the SPOUT superfamily of RNA methyltransferases are some of the most intensely studied systems for investigation of the knot formation and function. YibK (whose biochemical function remains unknown) is the representative protein of the SPOUT superfamily. This protein exhibits a deep trefoil knot at the C-terminus.

We conducted an extensive computational analysis of the unfolding process for the monomeric form of YibK. In order to predict the (un)folding pathway of YibK, we have calculated the order of secondary structure disassembly using UNFOLD, and performed thermal unfolding simulations using classical Molecular Dynamics (MD), as well as simulations employing reduced representation of the peptide chain using either MD with the UNRES method or the Monte Carlo (MC) unfolding with the REFINER method.

Results obtained from all methods used in this work are in qualitative agreement. We found that YibK unfolds through four intermediate states. The trefoil knot in YibK disappears at the end of the unfolding process, long after the protein loses its native topology. We observed that the C-terminus leaves the knotting loop folded into a hairpin-like structure, in agreement with the results of coarse-grained simulation reported earlier. We propose that the folding pathway of YibK corresponds to the reversed sequence of events observed in the unfolding pathway elucidated in this study. Thus, we predict that the knot formation is the slowest part of the YibK folding process.     

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.     

Backbone NMR assignments of a topologically knotted protein in urea-denatured state

YbeA is a 3-methylpseudoridine methyltransferase from Escherichia coli that forms a stable homodimer in solution. It is one of the deeply trefoil 3₁ knotted proteins, of which the knot encompasses the C-terminal helix that threads through a long loop. Recent studies on the knotted protein folding pathways using YbeA have suggested that the protein knot remains present under chemically denaturing conditions. Here, we report ¹H, ¹³C and ¹⁵N chemical shift assignments for urea-denatured YbeA, which will serve as the basis for further structural characterisations using solution state NMR spectroscopy with paramagnetic spin labeled and partial alignment media.     

Universally conserved positions in protein folds: reading evolutionary signals about stability, folding kinetics and function.

Here, we provide an analysis of molecular evolution of five of the most populated protein folds: immunoglobulin fold, oligonucleotide-binding fold, Rossman fold, alpha/beta plait, and TIM barrels. In order to distinguish between "historic", functional and structural reasons for amino acid conservations, we consider proteins that acquire the same fold and have no evident sequence homology. For each fold we identify positions that are conserved within each individual family and coincide when non-homologous proteins are structurally superimposed. As a baseline for statistical assessment we use the conservatism expected based on the solvent accessibility. The analysis is based on a new concept of "conservatism-of-conservatism". This approach allows us to identify the structural features that are stabilized in all proteins having a given fold, despite the fact that actual interactions that provide such stabilization may vary from protein to protein. Comparison with experimental data on thermodynamics, folding kinetics and function of the proteins reveals that such universally conserved clusters correspond to either: (i) super-sites (common location of active site in proteins having common tertiary structures but not function) or (ii) folding nuclei whose stability is an important determinant of folding rate, or both (in the case of Rossman fold). The analysis also helps to clarify the relation between folding and function that is apparent for some folds.