Folding analysis of the most complex Stevedore's protein knot

Conformational and Structural Characterization of Knotted Proteins

Knotted proteins are fascinating natural biomolecules whose backbones entangle themselves in a knot. Their particular knotted configurations provide them with a wide range of topological features. However, their folding/unfolding mechanisms, stability, and function are poorly understood. In the present work, native trapped ion mobility spectrometry-mass spectrometry (TIMS-MS) was used for characterizing structural features of two model knotted proteins: a Gordian 52 knot ubiquitin C-terminal hydrolase (UCH) and a Stevedore 61 knot (α-haloacid dehalogenase, DehI). Experimental results showed structural transitions of UCH and DehI as a function of solution composition (0-50% MeOH) and temperature (T ∼20-95 °C). An increase in the protein charge states and collision cross sections (∼2750-8750 Å2 and ∼3250-15,385 Å2 for UCH and DehI, respectively) with the solution organic content (OC) and temperature suggested a three-step unfolding pathway with at least four structural transitions. Results also showed that the integrity of the UCH knot core was more resistant to thermal unfolding when compared to DehI; however, both knot cores can be disrupted with the increase in the solution OC. Additional enzymatic digestion experiments using carboxypeptidase Y combined with molecular dynamics simulations showed that the knot core was preserved between Glu20 and Glu188 and Arg89 and His304 residues for UCH and DehI, respectively, where disruption of the knot core led to structural collapse followed by unfolding events. This work highlights the potential of solution OC and temperature studies combined with native TIMS-MS for the comprehensive characterization of knotted proteins to gain a better understanding of their structural transitions.

Is There a Functional Role for the Knotted Topology in Protein UCH-L1?

Knotted proteins are present in nature, but there is still an open issue regarding the existence of a universal role for these remarkable structures. To address this question, we used classical molecular dynamics (MD) simulations combined with in vitro experiments to investigate the role of the Gordian knot in the catalytic activity of UCH-L1. To create an unknotted form of UCH-L1, we modified its amino acid sequence by truncating several residues from its N-terminus. Remarkably, we find that deleting the first two N-terminal residues leads to a partial loss of enzyme activity with conservation of secondary structural content and knotted topological state. This happens because the integrity of the N-terminus is critical to ensure the correct alignment of the catalytic triad. However, the removal of five residues from the N-terminus, which significantly disrupts the native structure and the topological state, leads to a complete loss of enzymatic activity. Overall, our findings indicate that UCH-L1's catalytic activity depends critically on the integrity of the N-terminus and the secondary structure content, with the latter being strongly coupled with the knotted topological state.

Application of singular value decomposition analysis: Insights into the complex mechanisms of amyloidogenesis

Amyloidogenesis, with its multifaceted nature spanning from peptide self-assembly to membrane-mediated structural transitions, presents a significant challenge for the interdisciplinary scientific community. Here, we emphasize on how Singular Value Decomposition (SVD) can be employed to reveal hidden patterns and dominant modes of interaction that govern the complex process of amyloidogenesis. We first utilize SVD analysis on Circular Dichroism (CD) spectral datasets to identify the intermediate structural species emerging during peptide-membrane interactions and to determine binding constants more precisely than conventional methods. We investigate the monomer loss kinetics associated with peptide self-assembly using Nuclear Magnetic Resonance (NMR) dataset and determine the global kinetic parameters through SVD. Furthermore, we explore the seeded growth of amyloid fibrils by analyzing a time-dependent NMR dataset, shedding light on the kinetic intricacies of this process. Our analysis uncovers two distinct states in the aggregation of Aβ40 and pinpoints key residues responsible for this seeded growth. To strengthen our findings and enhance their robustness, we validate those using simulated data, thereby highlighting the physical interpretations derived from SVD. Overall, SVD analysis offers a model-free, global kinetic perspective, enabling the selection of optimal kinetic models. This study not only contributes valuable insights into the dynamics but also highlights the versatility of SVD in unravelling complex processes of amyloidogenesis.

Folding and functions of knotted proteins

Topologically knotted proteins have entangled structural elements within their native structures that cannot be disentangled simply by pulling from the N- and C-termini. Systematic surveys have identified different types of knotted protein structures, constituting as much as 1% of the total entries within the Protein Data Bank. Many knotted proteins rely on their knotted structural elements to carry out evolutionarily conserved biological functions. Being knotted may also provide mechanical stability to withstand unfolding-coupled proteolysis. Reconfiguring a knotted protein topology by circular permutation or cyclization provides insights into the importance of being knotted in the context of folding and functions. With the explosion of predicted protein structures by artificial intelligence, we are now entering a new era of exploring the entangled protein universe.

CalFitter 2.0: Leveraging the power of singular value decomposition to analyse protein thermostability

The importance of the quantitative description of protein unfolding and aggregation for the rational design of stability or understanding the molecular basis of protein misfolding diseases is well established. Protein thermostability is typically assessed by calorimetric or spectroscopic techniques that monitor different complementary signals during unfolding. The CalFitter webserver has already proved integral to deriving invaluable energy parameters by global data analysis. Here, we introduce CalFitter 2.0, which newly incorporates singular value decomposition (SVD) of multi-wavelength spectral datasets into the global fitting pipeline. Processed time- or temperature-evolved SVD components can now be fitted together with other experimental data types. Moreover, deconvoluted basis spectra provide spectral fingerprints of relevant macrostates populated during unfolding, which greatly enriches the information gains of the CalFitter output. The SVD analysis is fully automated in a highly interactive module, providing access to the results to users without any prior knowledge of the underlying mathematics. Additionally, a novel data uploading wizard has been implemented to facilitate rapid and easy uploading of multiple datasets. Together, the newly introduced changes significantly improve the user experience, making this software a unique, robust, and interactive platform for the analysis of protein thermal denaturation data. The webserver is freely accessible at https://loschmidt.chemi.muni.cz/calfitter.

A Topological Selection of Folding Pathways from Native States of Knotted Proteins

Understanding how knotted proteins fold is a challenging problem in biology. Researchers have proposed several models for their folding pathways, based on theory, simulations and experiments. The geometry of proteins with the same knot type can vary substantially and recent simulations reveal different folding behaviour for deeply and shallow knotted proteins. We analyse proteins forming open-ended trefoil knots by introducing a topologically inspired statistical metric that measures their entanglement. By looking directly at the geometry and topology of their native states, we are able to probe different folding pathways for such proteins. In particular, the folding pathway of shallow knotted carbonic anhydrases involves the creation of a double-looped structure, contrary to what has been observed for other knotted trefoil proteins. We validate this with Molecular Dynamics simulations. By leveraging the geometry and local symmetries of knotted proteins’ native states, we provide the first numerical evidence of a double-loop folding mechanism in trefoil proteins.

A Specific Set of Heterogeneous Native Interactions Yields Efficient Knotting in Protein Folding

Native interactions are crucial for folding, and non-native interactions appear to be critical for efficiently knotting proteins. Therefore, it is important to understand both their roles in the folding of knotted proteins. It has been proposed that non-native interactions drive the correct order of contact formation, which is essential to avoid backtracking and efficiently self-tie. In this study, we ask if non-native interactions are strictly necessary to tangle a protein or if the correct order of contact formation can be assured by a specific set of native, but otherwise heterogeneous (i.e., having distinct energies), interactions. In order to address this problem, we conducted extensive Monte Carlo simulations of lattice models of protein-like sequences designed to fold into a preselected knotted conformation embedding a trefoil knot. We were able to identify a specific set of heterogeneous native interactions that drives efficient knotting and is able to fold the protein when combined with the remaining native interactions modeled as homogeneous. This specific set of heterogeneous native interactions is strictly enough to efficiently self-tie. A distinctive feature of these native interactions is that they do not backtrack because their energies ensure the correct order of contact formation. Furthermore, they stabilize a knotted intermediate state, which is en route to the native structure. Our results thus show that-at least in the context of the adopted model-non-native interactions are not necessary to knot a protein. However, when they are taken into account in protein energetics, it is possible to find specific, nonlocal non-native interactions that operate as a scaffold that assists the knotting step.

Tying up the Loose Ends: A Mathematically Knotted Protein

Knots have attracted scientists in mathematics, physics, biology, and engineering. Long flexible thin strings easily knot and tangle as experienced in our daily life. Similarly, long polymer chains inevitably tend to get trapped into knots. Little is known about their formation or function in proteins despite >1,000 knotted proteins identified in nature. However, these protein knots are not mathematical knots with their backbone polypeptide chains because of their open termini, and the presence of a “knot” depends on the algorithm used to create path closure. Furthermore, it is generally not possible to control the topology of the unfolded states of proteins, therefore making it challenging to characterize functional and physicochemical properties of knotting in any polymer. Covalently linking the amino and carboxyl termini of the deeply trefoil-knotted YibK from Pseudomonas aeruginosa allowed us to create the truly backbone knotted protein by enzymatic peptide ligation. Moreover, we produced and investigated backbone cyclized YibK without any knotted structure. Thus, we could directly probe the effect of the backbone knot and the decrease in conformational entropy on protein folding. The backbone cyclization did not perturb the native structure and its cofactor binding affinity, but it substantially increased the thermal stability and reduced the aggregation propensity. The enhanced stability of a backbone knotted YibK could be mainly originated from an increased ruggedness of its free energy landscape and the destabilization of the denatured state by backbone cyclization with little contribution from a knot structure. Despite the heterogeneity in the side-chain compositions, the chemically unfolded cyclized YibK exhibited several macroscopic physico-chemical attributes that agree with theoretical predictions derived from polymer physics.

Converging experimental and computational views of the knotting mechanism of a small knotted protein

MJ0366 from Methanocaldococcus jannaschii is the smallest topologically knotted protein known to date. 92 residues in length, MJ0366 ties a trefoil (31) knot by threading its C-terminal helix through a buttonhole formed by the remainder of the secondary structure elements. By generating a library of point mutations at positions pertinent to the knot formation, we systematically evaluated the contributions of individual residues to the folding stability and kinetics of MJ0366. The experimental Φ-values were used as restraints to computationally generate an ensemble of conformations that correspond to the transition state of MJ0366, which revealed several nonnative contacts. The importance of these nonnative contacts in stabilizing the transition state of MJ0366 was confirmed by a second round of mutagenesis, which also established the pivotal role of F15 in stapling the network of hydrophobic interactions around the threading C-terminal helix. Our converging experimental and computational results show that, despite the small size, the transition state of MJ0366 is formed at a very late stage of the folding reaction coordinate, following a polarized pathway. Eventually, the formation of extensive native contacts, as well as a number of nonnative ones, leads to the threading of the C-terminal helix that defines the topological knot.

Cross-over Loop Cysteine C152 Acts as an Antioxidant to Maintain the Folding Stability and Deubiquitinase Activity of UCH-L1 Under Oxidative Stress

Redox-dependent inactivation of deubiquitinases (DUBs) is a critical factor for attenuating their DUB activity in response to cellular oxidative stress. Ubiquitin C-terminal hydrolase isoform (UCH-L1) is an important DUB that is highly expressed in human neuronal cells and is implicated in a myriad of human diseases such as neurodegenerative diseases and cancer. Increasing evidence suggests an important role of UCH-L1 in redox regulation and the protection of neuronal cells from oxidative stress. In this study, we examined the molecular basis of how UCH-L1 responds to oxidation in a reversible manner. Using H₂O₂ as a model oxidant, we showed by mass spectrometry that a subset of methionine and cysteine residues, namely (M1, M6, M12, C90, and C152) were more susceptible to oxidation. Spectroscopic analysis showed that oxidation of C90 can lead to profound structural changes in addition to the loss of function. Importantly, we further demonstrated that C152, which is located at the substrate recognition cross-over loop, serves as a reactive oxygen species (ROS) scavenger to protect catalytic C90 from oxidation under moderate oxidative conditions. Hydrogen-deuterium exchange mass spectrometry analysis provided detailed structural mapping of the destabilizing effect of H₂O₂-mediated oxidation, which resulted in global destabilization far beyond the oxidation sites. These perturbations may be responsible for irreversible aggregation when subject to prolonged oxidative stress.

Mechanical unfolding of a knotted protein unveils the kinetic and thermodynamic consequences of threading a polypeptide chain

Knots are remarkable topological features in nature. The presence of knots in crystallographic structures of proteins have stimulated considerable research to determine the kinetic and thermodynamic consequences of threading a polypeptide chain. By mechanically manipulating MJ0366, a small single domain protein harboring a shallow trefoil knot, we allow the protein to refold from either the knotted or the unknotted denatured state to characterize the free energy profile associated to both folding pathways. By comparing the stability of the native state with reference to the knotted and unknotted denatured state we find that knotting the polypeptide chain of MJ0366 increase the folding energy barrier in a magnitude close to the energy cost of forming a knot randomly in the denatured state. These results support that a protein knot can be formed during a single cooperative step of folding but occurs at the expenses of a large increment on the free energy barrier.

Restriction of S-adenosylmethionine conformational freedom by knotted protein binding sites

S-adenosylmethionine (SAM) is one of the most important enzyme substrates. It is vital for the function of various proteins, including large group of methyltransferases (MTs). Intriguingly, some bacterial and eukaryotic MTs, while catalysing the same reaction, possess significantly different topologies, with the former being a knotted one. Here, we conducted a comprehensive analysis of SAM conformational space and factors that affect its vastness. We investigated SAM in two forms: free in water (via NMR studies and explicit solvent simulations) and bound to proteins (based on all data available in the PDB and on all-atom molecular dynamics simulations in water). We identified structural descriptors—angles which show the major differences in SAM conformation between unknotted and knotted methyltransferases. Moreover, we report that this is caused mainly by a characteristic for knotted MTs compact binding site formed by the knot and the presence of adenine-binding loop. Additionally, we elucidate conformational restrictions imposed on SAM molecules by other protein groups in comparison to conformational space in water.

The topology of a folded polypeptide chain has great impact on the resulting protein function and its interaction with ligands. Interestingly, topological constraints appear to affect binding of one of the most ubiquitous substrates in the cell, S-adenosylmethionine (SAM), to its target proteins. Here, we demonstrate how binding sites of specific proteins restrict SAM conformational freedom in comparison to its unbound state, with a special interest in proteins with non-trivial topology, including an exciting group of knotted methyltransferases. Using a vast array of computational methods combined with NMR experiments, we identify key structural features of knotted methyltransferases that impose unorthodox SAM conformations. We compare them with the characteristics of standard, unknotted SAM binding proteins. These results are significant for understanding differences between analogous, yet topologically different enzymes, as well as for future rational drug design.

On folding of entangled proteins: knots, lassos, links and θ-curves

Around 6% of protein structures deposited in the PDB are entangled, forming knots, slipknots, lassos, links, and θ-curves. In each of these cases, the protein backbone weaves through itself in a complex way, and at some point passes through a closed loop, formed by other regions of the protein structure. Such a passing can be interpreted as crossing a topological barrier. How proteins overcome such barriers, and therefore different degrees of frustration, challenged scientists and has shed new light on the field of protein folding. In this review, we summarize the current knowledge about the free energy landscape of proteins with non-trivial topology. We describe identified mechanisms which lead proteins to self-tying. We discuss the influence of excluded volume, such as crowding and chaperones, on tying, based on available data. We briefly discuss the diversity of topological complexity of proteins and their evolution. We also list available tools to investigate non-trivial topology. Finally, we formulate intriguing and challenging questions at the boundary of biophysics, bioinformatics, biology, and mathematics, which arise from the discovery of entangled proteins.

Computational methods in the study of self-entangled proteins: a critical appraisal

The existence of self-entangled proteins, the native structure of which features a complex topology, unveils puzzling, and thus fascinating, aspects of protein biology and evolution. The discovery that a polypeptide chain can encode the capability to self-entangle in an efficient and reproducible way during folding, has raised many questions, regarding the possible function of these knots, their conservation along evolution, and their role in the folding paradigm. Understanding the function and origin of these entanglements would lead to deep implications in protein science, and this has stimulated the scientific community to investigate self-entangled proteins for decades by now. In this endeavour, advanced experimental techniques are more and more supported by computational approaches, that can provide theoretical guidelines for the interpretation of experimental results, and for the effective design of new experiments. In this review we provide an introduction to the computational study of self-entangled proteins, focusing in particular on the methodological developments related to this research field. A comprehensive collection of techniques is gathered, ranging from knot theory algorithms, that allow detection and classification of protein topology, to Monte Carlo or molecular dynamics strategies, that constitute crucial instruments for investigating thermodynamics and kinetics of this class of proteins.

Hydrophobic confinement modulates thermal stability and assists knotting in the folding of tangled proteins

There is growing support for the idea that the in vivo folding process of knotted proteins is assisted by chaperonins, but the mechanism of chaperonin assisted folding remains elusive. Here, we conduct extensive Monte Carlo simulations of lattice and off-lattice models to explore the effects of confinement and hydrophobic intermolecular interactions with the chaperonin cage in the folding and knotting processes. We find that moderate to high protein-cavity interactions (which are likely to be established in the beginning of the chaperonin working cycle) cause an energetic destabilization of the protein that overcomes the entropic stabilization driven by excluded volume, and leads to a decrease of the melting temperature relative to bulk conditions. Moreover, mild-to-moderate hydrophobic interactions with the cavity (which would be established later in the cycle) lead to a significant enhancement of knotting probability in relation to bulk conditions while simultaneously moderating the effect of steric confinement in the enhancement of thermal stability. Our results thus indicate that the chaperonin may be able to assist knotting without simultaneously thermally stabilizing potential misfolded states to a point that would hamper productive folding thus compromising its functional role.

Topological descriptions of protein folding

How knotted proteins fold has remained controversial since the identification of deeply knotted proteins nearly two decades ago. Both computational and experimental approaches have been used to investigate protein knot formation. Motivated by the computer simulations of Bölinger et al. [Bölinger D, et al. (2010) PLoS Comput Biol 6:e1000731] for the folding of the [Formula: see text]-knotted α-haloacid dehalogenase (DehI) protein, we introduce a topological description of knot folding that could describe pathways for the formation of all currently known protein knot types and predicts knot types that might be identified in the future. We analyze fingerprint data from crystal structures of protein knots as evidence that particular protein knots may fold according to specific pathways from our theory. Our results confirm Taylor's twisted hairpin theory of knot folding for the [Formula: see text]-knotted proteins and the [Formula: see text]-knotted ketol-acid reductoisomerases and present alternative folding mechanisms for the [Formula: see text]-knotted phytochromes and the [Formula: see text]- and [Formula: see text]-knotted proteins.

Direct observation of the fast and robust folding of a slipknotted protein by optical tweezers

Understanding the folding mechanism of knotted and slipknotted proteins has attracted considerable interest. Due to their topological complexity, knotted and slipknotted proteins are predicted to fold slowly and involve large topological barriers. Molecular dynamics simulation studies suggest that a slipknotted conformation can serve as an important intermediate to help greatly reduce the topological difficulty during the folding of some knotted proteins. Here we use a single molecule optical tweezers technique to directly probe the folding of a small slipknotted protein AFV3-109. We found that stretching AFV3-109 can lead to the untying of the slipknot and complete unfolding of AFV3-109. Upon relaxation, AFV3-109 can readily refold back to its native slipknot conformation with high fidelity when the stretching force is lower than 6 pN. The refolding of AFV3-109 occurs in a sharp two-state like transition. Our results indicate that, different from knotted proteins, the folding of a slipknotted protein like AFV3-109 can be fast, and may not necessarily involve a high topological barrier.

The AAA+ protease ClpXP can easily degrade a 31 and a 52-knotted protein

Knots in proteins are hypothesized to make them resistant to enzymatic degradation by ATP-dependent proteases and recent studies have shown that whereas ClpXP can easily degrade a protein with a shallow 3₁ knot, it cannot degrade 5₂-knotted proteins if degradation is initiated at the C-terminus. Here, we present detailed studies of the degradation of both 3₁- and 5₂-knotted proteins by ClpXP using numerous constructs where proteins are tagged for degradation at both N- and C-termini. Our results confirm and extend earlier work and show that ClpXP can easily degrade a deeply 3₁-knotted protein. In contrast to recently published work on the degradation of 5₂-knotted proteins, our results show that the ClpXP machinery can also easily degrade these proteins. However, the degradation depends critically on the location of the degradation tag and the local stability near the tag. Our results are consistent with mechanisms in which either the knot simply slips along the polypeptide chain and falls off the free terminus, or one in which the tightened knot enters the translocation pore of ClpXP. Results of experiments on knotted protein fusions with a highly stable domain show partial degradation and the formation of degradation intermediates.

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.

Protein Knotting by Active Threading of Nascent Polypeptide Chain Exiting from the Ribosome Exit Channel

The mechanism of folding of deeply knotted proteins into their native structure is still not understood. Current thinking about protein folding is dominated by the Anfinsen dogma, stating that the structure of the folded proteins is uniquely dictated by the amino acid sequence of a given protein and that the folding is driven uniquely by the energy gained from interactions between amino acids that contact each other in the native structure of the protein. The role of ribosomes in protein folding was only seen as permitting the folding to progress from the N-terminal part of nascent protein chains. We propose here that ribosomes can participate actively in the folding of knotted proteins by actively threading nascent chains emerging from the ribosome exit channels through loops formed by a synthesized earlier portion of the same protein. Our simulations of folding of deeply knotted protein Tp0624 positively verify the proposed ribosome-driven active threading mechanism leading to the formation of deeply knotted proteins.

Topologically knotted deubiquitinases exhibit unprecedented mechanostability to withstand the proteolysis by an AAA+ protease

More than one thousand knotted protein structures have been identified so far, but the functional roles of these knots remain elusive. It has been postulated that backbone entanglement may provide additional mechanostability. Here, we employed a bacterial proteasome, ClpXP, to mechanically unfold 5₂-knotted human ubiquitin C-terminal hydrolase (UCH) paralogs from their C-termini, followed by processive translocation into the proteolytic chamber for degradation. Our results revealed unprecedentedly slow kinetics of ClpXP-mediated proteolysis for the proteasome-associated UCHL5: ten thousand times slower than that of a green fluorescence protein (GFP), which has a comparable size to the UCH domain but much higher chemical and thermal stabilities. The ClpXP-dependent mechanostability positively correlates with the intrinsic unfolding rates of the substrates, spanning over several orders of magnitude for the UCHs. The broad range of mechanostability within the same protein family may be associated with the functional requirements for their differential malleabilities.

The exclusive effects of chaperonin on the behavior of proteins with 52 knot

The folding of proteins with a complex knot is still an unresolved question. Based on representative members of Ubiquitin C-terminal Hydrolases (UCHs) that contain the 5₂ knot in the native state, we explain how UCHs are able to unfold and refold in vitro reversibly within the structure-based model. In particular, we identify two, topologically different folding/unfolding pathways and corroborate our results with experiment, recreating the chevron plot. We show that confinement effect of chaperonin or weak crowding greatly facilitates folding, simultaneously slowing down the unfolding process of UCHs, compared with bulk conditions. Finally, we analyze the existence of knots in the denaturated state of UCHs. The results of the work show that the crowded environment of the cell should have a positive effect on the kinetics of complex knotted proteins, especially when proteins with deeper knots are found in this family.

Self-tying of knotted proteins remains a challenge both for theoreticians and experimentalist. In this work, we study the proteins with complex, the 5₂ knot, in a bulk and confined within a chaperonin box. We show that in our model we recreate the experimental results, identify two topologically distinct folding pathways and explain the beneficial role of confinement for complex knotted proteins. Encapsulation provides a possibility to fold via alternative pathway—folding via trefoil intermediate knot (N-terminal pathway) from entropic reason while folding via the C-terminal (direct tying) appears with the same probability. The results of this work show, how crowded environment in the real cell may enhance self-tying of proteins. The results are also the first step to the identification of possible oligomerization-prone forms of UCHs, which may cause neurodegenerative diseases.

To Tie or Not to Tie? That Is the Question

In this review, we provide an overview of entangled proteins. Around 6% of protein structures deposited in the PBD are entangled, forming knots, slipknots, lassos and links. We present theoretical methods and tools that enabled discovering and classifying such structures. We discuss the advantages and disadvantages of the non-trivial topology in proteins, based on available data about folding, stability, biological properties and evolutionary conservation. We also formulate intriguing and challenging questions on the border of biophysics, bioinformatics, biology and mathematics, which arise from the discovery of an entanglement in proteins. Finally, we discuss possible applications of entangled proteins in medicine and nanotechnology, such as the chance to design super stable proteins, whose stability could be controlled by chemical potential.

Entropic stabilization of a deubiquitinase provides conformational plasticity and slow unfolding kinetics beneficial for functioning on the proteasome

Human ubiquitin C-terminal hydrolyase UCH-L5 is a topologically knotted deubiquitinase that is activated upon binding to the proteasome subunit Rpn13. The length of its intrinsically disordered cross-over loop is essential for substrate recognition. Here, we showed that the catalytic domain of UCH-L5 exhibits higher equilibrium folding stability with an unfolding rate on the scale of 10⁻⁸ s⁻¹, over four orders of magnitudes slower than its paralogs, namely UCH-L1 and -L3, which have shorter cross-over loops. NMR relaxation dynamics analysis confirmed the intrinsic disorder of the cross-over loop. Hydrogen deuterium exchange analysis further revealed a positive correlation between the length of the cross-over loop and the degree of local fluctuations, despite UCH-L5 being thermodynamically and kinetically more stable than the shorter UCHs. Considering the role of UCH-L5 in removing K48-linked ubiquitin to prevent proteasomal degradation of ubiquitinated substrates, our findings offered mechanistic insights into the evolution of UCH-L5. Compared to its paralogs, it is entropically stabilized to withstand mechanical unfolding by the proteasome while maintaining structural plasticity. It can therefore accommodate a broad range of substrate geometries at the cost of unfavourable entropic loss.

Protein knotting through concatenation significantly reduces folding stability

Concatenation by covalent linkage of two protomers of an intertwined all-helical HP0242 homodimer from Helicobacter pylori results in the first example of an engineered knotted protein. While concatenation does not affect the native structure according to X-ray crystallography, the folding kinetics is substantially slower compared to the parent homodimer. Using NMR hydrogen-deuterium exchange analysis, we showed here that concatenation destabilises significantly the knotted structure in solution, with some regions close to the covalent linkage being destabilised by as much as 5 kcal mol^-1. Structural mapping of chemical shift perturbations induced by concatenation revealed a pattern that is similar to the effect induced by concentrated chaotrophic agent. Our results suggested that the design strategy of protein knotting by concatenation may be thermodynamically unfavourable due to covalent constrains imposed on the flexible fraying ends of the template structure, leading to rugged free energy landscape with increased propensity to form off-pathway folding intermediates.

How to fold intricately: using theory and experiments to unravel the properties of knotted proteins

Over the years, advances in experimental and computational methods have helped us to understand the role of thermodynamic, kinetic and active (chaperone-aided) effects in coordinating the folding steps required to achieving a knotted native state. Here, we review such developments by paying particular attention to the complementarity of experimental and computational studies. Key open issues that could be tackled with either or both approaches are finally pointed out.