Knots can impair protein degradation by ATP-dependent proteases

The Complex Energy Landscape of miRFP709, a 41-Knotted Protein, Results in Its Irreversible Denaturation

Knotted proteins have a unique topological feature with an open knot, and the physiological significance of these knots remains elusive. In addition, these proteins challenge our understanding of the protein folding process, and whether they retain their native state during unfolding/refolding cycles like other proteins is debated. Most folding studies on knotted proteins have been performed on 31 and 52 knots, monitoring the tryptophan fluorescence. In this study, we probe the unfolding/refolding of a 41-knotted protein, miRFP709, which can be monitored through near-infrared fluorescence in addition to the intrinsic tryptophan emission. miRFP709, upon chemical unfolding and refolding, folds back to a compact, non-native, stable structure that loses its ability to bind to the biliverdin ligand and fluoresce. The refolded protein retains its secondary structure but behaves like a molten-globule state with an exposed hydrophobic surface. The complex folding landscape of these proteins results in hysteresis between the folding and refolding curves. We propose that upon refolding, either an altered knot or an unknotted structure prevents the formation of the native knotted structure.

Activity-driven polymer knotting for macromolecular topology engineering

Macromolecules can gain special properties by adopting knotted conformations, but engineering knotted macromolecules is a challenging task. Here, we unexpectedly find that knots can be efficiently generated in active polymer systems. When one end of an actively reptative polymer is anchored, it undergoes continual self-knotting as a result of intermittent giant conformation fluctuations and the outward reptative motion. Once a knot is formed, it migrates to the anchoring point due to a nonequilibrium ratchet effect. Moreover, when the active polymer is grafted on a passive polymer, it can function as a self-propelling soft needle to either transfer its own knots or directly braid knots on the passive polymer. We further show that these active needles can create intermolecular bridging knots between two passive polymers. Our finding highlights the nonequilibrium effects in modifying the dynamic pathways of polymer systems, which have potential applications in macromolecular topology engineering.

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.

Theta-curves in proteins

We study and characterize the topology of connectivity circuits observed in natively folded protein structures whose coordinates are deposited in the Protein Data Bank (PDB). Polypeptide chains of some proteins naturally fold into unique knotted configurations. Another kind of nontrivial topology of polypeptide chains is observed when, in addition to covalent bonds connecting consecutive amino acids in polypeptide chains, one also considers disulfide and ionic bonds between non-consecutive amino acids. Bonds between non-consecutive amino acids introduce bifurcation points into connectivity circuits defined by bonds between consecutive and nonconsecutive amino acids in analyzed proteins. Circuits with bifurcation points can form θ-curves with various topologies. We catalog here the observed topologies of θ-curves passing through bridges between consecutive and non-consecutive amino acids in studied proteins.

AlphaKnot 2.0: a web server for the visualization of proteins' knotting and a database of knotted AlphaFold-predicted models

The availability of 3D protein models is rapidly increasing with the development of structure prediction algorithms. With the expanding availability of data, new ways of analysis, especially topological analysis, of those predictions are becoming necessary. Here, we present the updated version of the AlphaKnot service that provides a straightforward way of analyzing structure topology. It was designed specifically to determine knot types of the predicted structure models, however, it can be used for all structures, including the ones solved experimentally. AlphaKnot 2.0 provides the user's ability to obtain the knowledge necessary to assess the topological correctness of the model. Both probabilistic and deterministic knot detection methods are available, together with various visualizations (including a trajectory of simplification steps to highlight the topological complexities). Moreover, the web server provides a list of proteins similar to the queried model within AlphaKnot's database and returns their knot types for direct comparison. We pre-calculated the topology of high-quality models from the AlphaFold Database (4th version) and there are now more than 680.000 knotted models available in the AlphaKnot database. AlphaKnot 2.0 is available at https://alphaknot.cent.uw.edu.pl/.

Structure, dynamics, and stability of the smallest and most complex 71 protein knot

Proteins can spontaneously tie a variety of intricate topological knots through twisting and threading of the polypeptide chains. Recently developed artificial intelligence algorithms have predicted several new classes of topological knotted proteins, but the predictions remain to be authenticated experimentally. Here, we showed by X-ray crystallography and solution-state NMR spectroscopy that Q9PR55, an 89-residue protein from Ureaplasma urealyticum, possesses a novel 71 knotted topology that is accurately predicted by AlphaFold 2, except for the flexible N terminus. Q9PR55 is monomeric in solution, making it the smallest and most complex knotted protein known to date. In addition to its exceptional chemical stability against urea-induced unfolding, Q9PR55 is remarkably robust to resist the mechanical unfolding-coupled proteolysis by a bacterial proteasome, ClpXP. Our results suggest that the mechanical resistance against pulling-induced unfolding is determined by the complexity of the knotted topology rather than the size of the molecule.

A Marcus-Type Inverted Region in the Translocation Kinetics of a Knotted Protein

Knotted proteins are rare but important species, yet how their complex topologies affect their physical properties is not fully understood. Here we combine single molecule nanopore experiments and all-atom MD simulations to study the electric-field-driven unfolding during the translocation through a model pore of individual protein knots important for methylating tRNA. One of these knots shows an unusual behavior that resembles the behavior of electrons hopping between two potential surfaces: as the electric potential driving the translocation reaction is increased, the rate eventually plateaus or slows back down in the "Marcus inverted regime". Our results shed light on the influence of topology in knotted proteins on their forced translocation through a pore connecting two electrostatic potential wells.

Stochastic model of translocation of knotted proteins

Knotted proteins, when forced through the pores, can get stuck if the knots in their backbone tighten under force. Alternatively, the knot can slide off the chain, making translocation possible. We construct a simple energy landscape model of this process with a time-periodic potential that mimics the action of a molecular motor. We calculate the translocation time as a function of the period of the pulling force, discuss the asymptotic limits and biological relevance of the results.

The activated ClpP peptidase forcefully grips a protein substrate

ATPases associated with diverse cellular activities (AAA+) proteases power the maintenance of protein homeostasis by coupling ATP hydrolysis to mechanical protein unfolding, translocation, and ultimately degradation. Although ATPase activity drives a large portion of the mechanical work these molecular machines perform, how the peptidase contributes to the forceful denaturation and processive threading of substrates remains unknown. Here, using single-molecule optical trapping, we examine the mechanical activity of the caseinolytic peptidase P (ClpP) from Escherichia coli in the absence of a partner ATPase and in the presence of an activating small-molecule acyldepsipeptide. We demonstrate that ClpP grips protein substrate under mechanical loads exceeding 40 pN, which are greater than those observed for the AAA+ unfoldase ClpX and the AAA+ protease complexes ClpXP and ClpAP. We further characterize substrate-ClpP bond lifetimes and rupture forces under varying loads. We find that the resulting slip bond behavior does not depend on ClpP peptidase activity. In addition, we find that unloaded bond lifetimes between ClpP and protein substrate are on a timescale relevant to unfolding times (up to ∼160 s) for difficult to unfold model substrate proteins. These direct measurements of the substrate-peptidase bond under load define key properties required by AAA+ proteases to mechanically unfold and degrade protein substrates.

Computational Design of Extraordinarily Stable Peptide Structures through Side-Chain-Locked Knots

Extraordinarily stable protein and peptide structures are critically demanded in many applications. Typical approaches to enhance protein and peptide stability are strengthening certain interactions. Here, we develop a very different approach: stabilizing peptide structures through side-chain-locked knots. More specifically, a peptide core consists of a knot, which is prevented from unknotting and unfolding by large side chains of amino acids at knot boundaries. These side chains impose free energy barriers for unknotting. The free energy barriers are quantified using all-atom and coarse-grained simulations. The barriers become infinitely high for large side chains and tight knot cores, resulting in stable peptide structures, which never unfold unless one chemical bond is broken. The extraordinary stability is essentially kinetic stability. Our new approach lifts the thermodynamic restriction in designing peptide structures, provides extra freedom in selecting sequence and structural motifs that are thermodynamically unstable, and should expand the functionality of peptides. This work also provides a bottom-up understanding of how knotting enhances protein stability.

Exploring the Effect of Mechanical Anisotropy of Protein Structures in the Unfoldase Mechanism of AAA+ Molecular Machines

Essential cellular processes of microtubule disassembly and protein degradation, which span lengths from tens of μm to nm, are mediated by specialized molecular machines with similar hexameric structure and function. Our molecular simulations at atomistic and coarse-grained scales show that both the microtubule-severing protein spastin and the caseinolytic protease ClpY, accomplish spectacular unfolding of their diverse substrates, a microtubule lattice and dihydrofolate reductase (DHFR), by taking advantage of mechanical anisotropy in these proteins. Unfolding of wild-type DHFR requires disruption of mechanically strong β-sheet interfaces near each terminal, which yields branched pathways associated with unzipping along soft directions and shearing along strong directions. By contrast, unfolding of circular permutant DHFR variants involves single pathways due to softer mechanical interfaces near terminals, but translocation hindrance can arise from mechanical resistance of partially unfolded intermediates stabilized by β-sheets. For spastin, optimal severing action initiated by pulling on a tubulin subunit is achieved through specific orientation of the machine versus the substrate (microtubule lattice). Moreover, changes in the strength of the interactions between spastin and a microtubule filament, which can be driven by the tubulin code, lead to drastically different outcomes for the integrity of the hexameric structure of the machine.

AAA+ proteins: one motor, multiple ways to work

Numerous ATPases associated with diverse cellular activities (AAA+) proteins form hexameric, ring-shaped complexes that function via ATPase-coupled translocation of substrates across the central channel. Cryo-electron microscopy of AAA+ proteins processing substrate has revealed non-symmetric, staircase-like hexameric structures that indicate a sequential clockwise/2-residue step translocation model for these motors. However, for many of the AAA+ proteins that share similar structural features, their translocation properties have not yet been experimentally determined. In the cases where translocation mechanisms have been determined, a two-residue translocation step-size has not been resolved. In this review, we explore Hsp104, ClpB, ClpA and ClpX as examples to review the experimental methods that have been used to examine, in solution, the translocation mechanisms employed by AAA+ motor proteins. We then ask whether AAA+ motors sharing similar structural features can have different translocation mechanisms. Finally, we discuss whether a single AAA+ motor can adopt multiple translocation mechanisms that are responsive to different challenges imposed by the substrate or the environment. We suggest that AAA+ motors adopt more than one translocation mechanism and are tuned to switch to the most energetically efficient mechanism when constraints are applied.

Structure and function of ClpXP, a AAA+ proteolytic machine powered by probabilistic ATP hydrolysis

ClpXP is an archetypical AAA+ protease, consisting of ClpX and ClpP. ClpX is an ATP-dependent protein unfoldase and polypeptide translocase, whereas ClpP is a self-compartmentalized peptidase. ClpXP is currently the only AAA+ protease for which high-resolution structures exist, the molecular basis of recognition for a protein substrate is understood, extensive biochemical and genetic analysis have been performed, and single-molecule optical trapping has allowed direct visualization of the kinetics of substrate unfolding and translocation. In this review, we discuss our current understanding of ClpXP structure and function, evaluate competing sequential and probabilistic mechanisms of ATP hydrolysis, and highlight open questions for future exploration.

Investigation of the structural dynamics of a knotted protein and its unknotted analog using molecular dynamics

The role of knots in proteins remains elusive. Some studies suggest an impact on stability; the difficulty in comparing systems to assess this effect, however, has been a significant challenge. In this study, we produced and analyzed molecular dynamic trajectories considering three different temperatures of two variants of ornithine transcarbamylase (OTC), only one of which has a 3₁ knot, in order to evaluate the relative stability of the two molecules. RMSD showed equilibrated structures for the produced trajectories, and RMSF showed subtle differences in flexibility. In the knot moiety, the knotted protein did not show a great deal of fluctuation at any temperature. For the unknotted protein, the residue GLY243 showed a high fluctuation in the corresponding moiety. The fraction of native contacts (Q) showed a similar profile at all temperatures, with the greatest decrease by 436 K. The investigation of conformational behavior with principal component analysis (PCA) and dynamic cross-correlation map (DCCM) showed that knotted protein is less likely to undergo changes in its conformation under the conditions employed compared to unknotted. PCA data showed that the unknotted protein had greater dispersion in its conformations, which suggests that it has a greater capacity for conformation transitions in response to thermal changes. DCCM graphs comparing the 310 K and 436 K temperatures showed that the knotted protein had less change in its correlation and anti-correlation movements, indicating stability compared to the unknotted.

Recent structural insights into the mechanism of ClpP protease regulation by AAA+ chaperones and small molecules

ClpP is a highly conserved serine protease that is a critical enzyme in maintaining protein homeostasis and is an important drug target in pathogenic bacteria and various cancers. In its functional form, ClpP is a self-compartmentalizing protease composed of two stacked heptameric rings that allow protein degradation to occur within the catalytic chamber. ATPase chaperones such as ClpX and ClpA are hexameric ATPases that form larger complexes with ClpP and are responsible for the selection and unfolding of protein substrates prior to their degradation by ClpP. Although individual structures of ClpP and ATPase chaperones have offered mechanistic insights into their function and regulation, their structures together as a complex have only been recently determined to high resolution. Here, we discuss the cryoelectron microscopy structures of ClpP-ATPase complexes and describe findings previously inaccessible from individual Clp structures, including how a hexameric ATPase and a tetradecameric ClpP protease work together in a functional complex. We then discuss the consensus mechanism for substrate unfolding and translocation derived from these structures, consider alternative mechanisms, and present their strengths and limitations. Finally, new insights into the allosteric control of ClpP gained from studies using small molecules and gain or loss-of-function mutations are explored. Overall, this review aims to underscore the multilayered regulation of ClpP that may present novel ideas for structure-based drug design.

Quantifying the effects of slit confinement on polymer knots using the tube model

Knots can spontaneously form in DNA, proteins, and other polymers and affect their properties. These knots often experience spatial confinement in biological systems and experiments. While confinement dramatically affects the knot behavior, the physical mechanisms underlying the confinement effects are not fully understood. In this work, we provide a simple physical picture of the polymer knots in slit confinement using the tube model. In the tube model, the polymer segments in the knot core are assumed to be confined in a virtual tube due to the topological restriction. We first perform Monte Carlo simulation of a flexible knotted chain confined in a slit. We find that with the decrease of the slit height from H=+∞ (the 3D case) to H=2a (the 2D case), the most probable knot size L_{knot}^{*} dramatically shrinks from (L_{knot}^{*})_{3D}≈140a to (L_{knot}^{*})_{2D}≈26a, where a is the monomer diameter of the flexible chain. Then we quantitatively explain the confinement-induced knot shrinking and knot deformation using the tube model. Our results for H=2a can be applied to a polymer knot on a surface, which resembles DNA knots measured by atomic force microscopy under the conditions that DNA molecules are weakly absorbed on the surface and reach equilibrium 2D conformations. This work demonstrates the effectiveness of the tube model in understanding polymer knots.

In silico method for identifying the key residues in a knotted protein: with MJ0366 as an example

A simple in silico method for predicting the key residues for knotting and unknotting a knotted protein is put forward, with the residues ranked by the relevance to knotting and unknotting in the annealing molecular dynamics simulations.

Unfolding and Translocation of Knotted Proteins by Clp Biological Nanomachines: Synergistic Contribution of Primary Sequence and Topology Revealed by Molecular Dynamics Simulations

We use Langevin dynamics simulations to model, at an atomistic resolution, how various natively knotted proteins are unfolded in repeated allosteric translocating cycles of the ClpY ATPase. We consider proteins representative of different topologies, from the simplest knot (trefoil 3₁), to the three-twist 5₂ knot, to the most complex stevedore, 6₁, knot. We harness the atomistic detail of the simulations to address aspects that have so far remained largely unexplored, such as sequence-dependent effects on the ruggedness of the landscape traversed during knot sliding. Our simulations reveal the combined effect on translocation of the knotted protein structure, i.e., backbone topology and geometry, and primary sequence, i.e., side chain size and interactions, and show that the latter can dominate translocation hindrance. In addition, we observe that due to the interplay between the knotted topology and intramolecular contacts the transmission of tension along the polypeptide chain occurs very differently from that of homopolymers. Finally, by considering native and non-native interactions, we examine how the disruption or formation of such contacts can affect the translocation processivity and concomitantly create multiple unfolding pathways with very different activation barriers.

Mechanical strength of RNA knot in Zika virus protects against cellular defenses

Unusual knot-like structures recently discovered in viral exoribonuclease-resistant RNAs (xrRNAs) prevent digestion by host RNases to create subgenomic RNAs enhancing infection and pathogenicity. xrRNAs are proposed to prevent digestion through mechanical resistance to unfolding. However, their unfolding force has not been measured, and the factors determining RNase resistance are unclear. Furthermore, how these knots fold remains unknown. Unfolding a Zika virus xrRNA with optical tweezers revealed that it was the most mechanically stable RNA yet observed. The knot formed by threading the 5' end into a three-helix junction before pseudoknot interactions closed a ring around it. The pseudoknot and tertiary contacts stabilizing the threaded 5' end were both required to generate extreme force resistance, whereas removing a 5'-end contact produced a low-force knot lacking RNase resistance. These results indicate mechanical resistance plays a central functional role, with the fraction of molecules forming extremely high-force knots determining the RNase resistance level.

Type III secretion system effector proteins are mechanically labile

Multiple gram-negative bacteria encode type III secretion systems (T3SS) that allow them to inject effector proteins directly into host cells to facilitate colonization. To be secreted, effector proteins must be at least partially unfolded to pass through the narrow needle-like channel (diameter <2 nm) of the T3SS. Fusion of effector proteins to tightly packed proteins-such as GFP, ubiquitin, or dihydrofolate reductase (DHFR)-impairs secretion and results in obstruction of the T3SS. Prior observation that unfolding can become rate-limiting for secretion has led to the model that T3SS effector proteins have low thermodynamic stability, facilitating their secretion. Here, we first show that the unfolding free energy ([Formula: see text]) of two Salmonella effector proteins, SptP and SopE2, are 6.9 and 6.0 kcal/mol, respectively, typical for globular proteins and similar to published [Formula: see text] for GFP, ubiquitin, and DHFR. Next, we mechanically unfolded individual SptP and SopE2 molecules by atomic force microscopy (AFM)-based force spectroscopy. SptP and SopE2 unfolded at low force (F _unfold ≤ 17 pN at 100 nm/s), making them among the most mechanically labile proteins studied to date by AFM. Moreover, their mechanical compliance is large, as measured by the distance to the transition state (Δx ^‡ = 1.6 and 1.5 nm for SptP and SopE2, respectively). In contrast, prior measurements of GFP, ubiquitin, and DHFR show them to be mechanically robust (F _unfold > 80 pN) and brittle (Δx ^‡ < 0.4 nm). These results suggest that effector protein unfolding by T3SS is a mechanical process and that mechanical lability facilitates efficient effector protein secretion.

f -distance of knotoids and protein structure

Recent studies classify the topology of proteins by analysing the distribution of their projections using knotoids. The approximation of this distribution depends on the number of projection directions that are sampled. Here, we investigate the relation between knotoids differing only by small perturbations of the direction of projection. Since such knotoids are connected by at most a single forbidden move, we characterize forbidden moves in terms of equivariant band attachment between strongly invertible knots and of strand passages between θ -curves. This allows for the determination of the optimal sample size needed to produce a well-approximated knotoid distribution. Based on that and on topological properties of the distribution, we probe the depth of knotted proteins with the trefoil as the predominant knot type without using subchain analysis.

RNA Pore Translocation with Static and Periodic Forces: Effect of Secondary and Tertiary Elements on Process Activation and Duration

We use MD simulations to study the pore translocation properties of a pseudoknotted viral RNA. We consider the 71-nucleotide-long xrRNA from the Zika virus and establish how it responds when driven through a narrow pore by static or periodic forces applied to either of the two termini. Unlike the case of fluctuating homopolymers, the onset of translocation is significantly delayed with respect to the application of static driving forces. Because of the peculiar xrRNA architecture, activation times can differ by orders of magnitude at the two ends. Instead, translocation duration is much smaller than activation times and occurs on time scales comparable at the two ends. Periodic forces amplify significantly the differences at the two ends, for both activation times and translocation duration. Finally, we use a waiting-times analysis to examine the systematic slowing downs in xrRNA translocations and associate them to the hindrance of specific secondary and tertiary elements of xrRNA. The findings provide a useful reference to interpret and design future theoretical and experimental studies of RNA translocation.

Progress and prospect of single-molecular ClpX ATPase researching system-a mini-review

ClpXP in Escherichia coli is a proteasome degrading protein substrates. It consists of one hexamer of ATPase (ClpX) and two heptamers of peptidase (ClpP). The ClpX binds ATP and translocates the substrate protein into the ClpP chamber by binding and hydrolysis of ATP. At single molecular level, ClpX harnesses cycles of power stroke (dwell and burst) to unfold the substrates, then releases the ADP and Pi. Based on the construction and function of ClpXP, especially the recent progress on how ClpX unfold protein substrates, in this mini-review, a currently proposed single ClpX molecular model system detected by optical tweezers, and its prospective for the elucidation of the mechanism of force generation of ClpX in its power stroke and the subunit interaction with each other, were discussed in detail.

Topological Twists in Nature

The first entangled protein was observed about 30 years ago, resulting in an increased interest for uncovering the biological functions and biophysical properties of these complex topologies. Recently, the Pierced Lasso Topology (PLT) was discovered in which a covalent bond forms an intramolecular loop, leaving one or both termini free to pierce the loop. This topology is related to knots and other entanglements. PLTs exist in many well-researched systems where the PLTs have previously been unnoticed. PLTs represents 18% of all disulfide containing proteins across all kingdoms of life. In this review, we investigate the biological implications of this specific topology in which the PLT-forming disulfide may act as a molecular switch for protein function and consequently human health.

Directional translocation resistance of Zika xrRNA

xrRNAs from flaviviruses survive in host cells because of their exceptional dichotomic response to the unfolding action of different enzymes. They can be unwound, and hence copied, by replicases, and yet can resist degradation by exonucleases. How the same stretch of xrRNA can encode such diverse responses is an open question. Here, by using atomistic models and translocation simulations, we uncover an elaborate and directional mechanism for how stress propagates when the two xrRNA ends, [Formula: see text] and [Formula: see text], are driven through a pore. Pulling the [Formula: see text] end, as done by replicases, elicits a progressive unfolding; pulling the [Formula: see text] end, as done by exonucleases, triggers a counterintuitive molecular tightening. Thus, in what appears to be a remarkable instance of intra-molecular tensegrity, the very pulling of the [Formula: see text] end is what boosts resistance to translocation and consequently to degradation. The uncovered mechanistic principle might be co-opted to design molecular meta-materials.

Transient knots in intrinsically disordered proteins and neurodegeneration

We provide a brief overview of the topological features found in structured proteins and of the dynamical processes that involve knots. We then discuss the knotted states that arise in the intrinsically disordered polyglutamine and α-synuclein. We argue that the existence of the knotted conformations stalls degradation by proteases and thus enhances aggregation. This mechanism works if the length of a peptide chain exceeds a threshold, as in the Huntington disease. We also study the cavities that form within the conformations of the disordered proteins. The volume of the cavities varies in time in a way that is different than that of the radius of gyration or the end-to-end distance. In addition, we study the traffic between the conformational basins and identify patterns associated with the deep and shallow knots. The results are obtained by molecular dynamics simulations that use coarse-grained and all-atom models (with and without the explicit solvent).

Identifying knot types of polymer conformations by machine learning

We investigate the use of artificial neural networks (NNs) as an alternative tool to current analytical methods for recognizing knots in a given polymer conformation. The motivation is twofold. First, it is of interest to examine whether NNs are effective at learning the global and sequential properties that uniquely define a knot. Second, knot classification is an important and unsolved problem in mathematical and physical sciences, and NNs may provide insights into this problem. Motivated by these points, we generate millions of polymer conformations for five knot types: 0, 3_{1}, 4_{1}, 5_{1}, and 5_{2}, and we design various NN models for classification. Our best model achieves a five-class classification accuracy of above 99% on a polymer of 100 monomers. We find that the sequential modeling ability of recurrent NNs is crucial for this result, as it outperforms feed-forward NNs and successfully generalizes to differently sized conformations as well. We present our methods and suggest that deep learning may be used in specific applications of knot detection where some error is permissible. Hopefully, with further development, NNs can offer an alternative computational method for knot identification and facilitate knot research in mathematical and physical sciences.

Structures of the ATP-fueled ClpXP proteolytic machine bound to protein substrate

ClpXP is an ATP-dependent protease in which the ClpX AAA+ motor binds, unfolds, and translocates specific protein substrates into the degradation chamber of ClpP. We present cryo-EM studies of the E. coli enzyme that show how asymmetric hexameric rings of ClpX bind symmetric heptameric rings of ClpP and interact with protein substrates. Subunits in the ClpX hexamer assume a spiral conformation and interact with two-residue segments of substrate in the axial channel, as observed for other AAA+ proteases and protein-remodeling machines. Strictly sequential models of ATP hydrolysis and a power stroke that moves two residues of the substrate per translocation step have been inferred from these structural features for other AAA+ unfoldases, but biochemical and single-molecule biophysical studies indicate that ClpXP operates by a probabilistic mechanism in which five to eight residues are translocated for each ATP hydrolyzed. We propose structure-based models that could account for the functional results.

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.

Protein droplets in systems of disordered homopeptides and the amyloid glass phase

We study phase diagrams and liquid droplet formation for systems of polyglutamine and polyalanine chains in a coarse-grained model.

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.

Ubiquitin receptors are required for substrate-mediated activation of the proteasome's unfolding ability

The ubiquitin-proteasome system (UPS) is responsible for the bulk of protein degradation in eukaryotic cells, but the factors that cause different substrates to be unfolded and degraded to different extents are still poorly understood. We previously showed that polyubiquitinated substrates were degraded with greater processivity (with a higher tendency to be unfolded and degraded than released) than ubiquitin-independent substrates. Thus, even though ubiquitin chains are removed before unfolding and degradation occur, they affect the unfolding of a protein domain. How do ubiquitin chains activate the proteasome’s unfolding ability? We investigated the roles of the three intrinsic proteasomal ubiquitin receptors - Rpn1, Rpn10 and Rpn13 - in this activation. We find that these receptors are required for substrate-mediated activation of the proteasome’s unfolding ability. Rpn13 plays the largest role, but there is also partial redundancy between receptors. The architecture of substrate ubiquitination determines which receptors are needed for maximal unfolding ability, and, in some cases, simultaneous engagement of ubiquitin by multiple receptors may be required. Our results suggest physical models for how ubiquitin receptors communicate with the proteasomal motor proteins.

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.

Aim for the core: suitability of the ubiquitin-independent 20S proteasome as a drug target in neurodegeneration

Neurodegenerative diseases are a class of age-associated proteopathies characterized by the accumulation of misfolded and/or aggregation-prone proteins. This imbalance has been attributed, in part, to an age-dependent decay in the capacity of protein turnover. Most proteins are degraded by the ubiquitin-proteasome system (UPS), which is composed of ubiquitin ligases and regulatory particles, such as the 19S, that deliver cargo to the proteolytically active 20S proteasome (20S) core. However, a subset of clients, especially intrinsically disordered proteins (IDPs), are also removed by the action of the ubiquitin-independent proteasome system (UIPS). What are the specific contributions of the UPS and UIPS in the context of neurodegeneration? Here, we explore how age-associated changes in the relative contribution of the UPS and UIPS, combined with the IDP-like structure of many neurodegenerative disease-associated proteins, might contribute. Strikingly, the 20S has been shown to predominate in older neurons and to preferentially act on relevant substrates, such as synuclein and tau. Moreover, pharmacological activation of the 20S has been shown to accelerate removal of aggregation-prone proteins in some models. Together, these recent studies are turning attention to the 20S and the UIPS as potential therapeutic targets in neurodegeneration.

Cotranslocational processing of the protein substrate calmodulin by an AAA+ unfoldase occurs via unfolding and refolding intermediates

Protein remodeling by AAA+ enzymes is central for maintaining proteostasis in a living cell. However, a detailed structural description of how this is accomplished at the level of the substrate molecules that are acted upon is lacking. Here, we combine chemical cross-linking and methyl transverse relaxation-optimized NMR spectroscopy to study, at atomic resolution, the stepwise unfolding and subsequent refolding of the two-domain substrate calmodulin by the VAT AAA+ unfoldase from Thermoplasma acidophilum By engineering intermolecular disulphide bridges between the substrate and VAT we trap the substrate at different stages of translocation, allowing structural studies throughout the translocation process. Our results show that VAT initiates substrate translocation by pulling on intrinsically unstructured N or C termini of substrate molecules without showing specificity for a particular amino acid sequence. Although the B1 domain of protein G is shown to unfold cooperatively, translocation of calmodulin leads to the formation of intermediates, and these differ on an individual domain level in a manner that depends on whether pulling is from the N or C terminus. The approach presented generates an atomic resolution picture of substrate unfolding and subsequent refolding by unfoldases that can be quite different from results obtained via in vitro denaturation experiments.

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.

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.