Protein knots and fold complexity: Some new twists

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.

Folding a Molecular Strand into a Trefoil Knot of Single Handedness with Co(II)/Co(III) Chaperones

We report the synthesis of a right-handed (Δ-stereochemistry of strand crossings) trefoil knot from a single molecular strand containing three pyrazine-2,5-dicarboxamide units adjacent to point-chiral centers and six pyridine moieties. The oligomeric ligand strand folds into an overhand (open-trefoil) knot through the assistance of coordinatively dynamic Co(II) "chaperones" that drive the formation of a three-metal-ion circular helicate. The entangled structure is kinetically locked by oxidation to Co(III) and covalently captured by ring-closing olefin metathesis to generate a trefoil knot of single topological handedness. The stereochemistry of the strand crossings in the metal-coordinated overhand knot is governed by the stereochemistry of the point-chiral carbon centers in the ligand strand. The overhand and trefoil knots were characterized by NMR spectroscopy, mass spectrometry, and X-ray crystallography. Removal of the metal ions from the knot, followed by hydrogenation of the alkene, yielded the wholly organic trefoil knot. The metal-free knot and parent ligand were investigated by circular dichroism (CD) spectroscopy. The CD spectra indicate that the topological stereochemistry of the knot has a greater effect on the asymmetry of the chromophore environment than do the point-chiral centers of the strand.

Are there double knots in proteins? Prediction and in vitro verification based on TrmD-Tm1570 fusion from C. nitroreducens

We have been aware of the existence of knotted proteins for over 30 years-but it is hard to predict what is the most complicated knot that can be formed in proteins. Here, we show new and the most complex knotted topologies recorded to date-double trefoil knots (31 #31). We found five domain arrangements (architectures) that result in a doubly knotted structure in almost a thousand proteins. The double knot topology is found in knotted membrane proteins from the CaCA family, that function as ion transporters, in the group of carbonic anhydrases that catalyze the hydration of carbon dioxide, and in the proteins from the SPOUT superfamily that gathers 31 knotted methyltransferases with the active site-forming knot. For each family, we predict the presence of a double knot using AlphaFold and RoseTTaFold structure prediction. In the case of the TrmD-Tm1570 protein, which is a member of SPOUT superfamily, we show that it folds in vitro and is biologically active. Our results show that this protein forms a homodimeric structure and retains the ability to modify tRNA, which is the function of the single-domain TrmD protein. However, how the protein folds and is degraded remains unknown.

AlphaFold Blindness to Topological Barriers Affects Its Ability to Correctly Predict Proteins' Topology

AlphaFold is a groundbreaking deep learning tool for protein structure prediction. It achieved remarkable accuracy in modeling many 3D structures while taking as the user input only the known amino acid sequence of proteins in question. Intriguingly though, in the early steps of each individual structure prediction procedure, AlphaFold does not respect topological barriers that, in real proteins, result from the reciprocal impermeability of polypeptide chains. This study aims to investigate how this failure to respect topological barriers affects AlphaFold predictions with respect to the topology of protein chains. We focus on such classes of proteins that, during their natural folding, reproducibly form the same knot type on their linear polypeptide chain, as revealed by their crystallographic analysis. We use partially artificial test constructs in which the mutual non-permeability of polypeptide chains should not permit the formation of complex composite knots during natural protein folding. We find that despite the formal impossibility that the protein folding process could produce such knots, AlphaFold predicts these proteins to form complex composite knots. Our study underscores the necessity for cautious interpretation and further validation of topological features in protein structures predicted by AlphaFold.

Streamlining N-terminally anchored yeast surface display via structural insights into S. cerevisiae Pir proteins

Surface display co-opts yeast's innate ability to embellish its cell wall with mannoproteins, thus converting the yeast's outer surface into a growing and self-sustaining catalyst. However, the efficient toolbox for converting the enzyme of interest into its surface-displayed isoform is currently lacking, especially if the isoform needs to be anchored to the cell wall near the isoform's N-terminus, e.g., through a short GPI-independent protein anchor. Aiming to advance such N-terminally anchored surface display, we employed in silico and machine-learning strategies to study the 3D structure, function, genomic organisation, and evolution of the Pir protein family, whose members evolved to covalently attach themselves near their N-terminus to the β-1,3-glucan of the cell wall. Through the newly-gained insights, we rationally engineered 14 S. cerevisiae Hsp150 (Pir2)-based fusion proteins. We quantified their performance, uncovering guidelines for efficient yeast surface display while developing a construct that promoted a 2.5-fold more efficient display of a reporter protein than the full-length Hsp150. Moreover, we developed a Pir-tag, i.e., a peptide spanning only 4.5 kDa but promoting as efficient surface display of a reporter protein as the full-length Hsp150. These constructs fortify the existing surface display toolbox, allowing for a prompt and routine refitting of intracellular proteins into their N-terminally anchored isoforms.

Solvent-Controlled Quadruple Catenation of Giant Chiral [8+12] Salicylimine Cubes Driven by Weak Hydrogen Bonding

Mechanically interlocked structures are fascinating synthetic targets and the topological complexity achieved through catenation offers numerous possibilities for the construction of new molecules with exciting properties. In the structural space of catenated organic cage molecules, only few examples have been realized so far, and control over the catenation process in solution is still barely achieved. Herein, we describe the formation of a quadruply interlocked catenane of giant chiral [8+12] salicylimine cubes. The formation could be controlled by the choice of solvent used in the reaction. The interlocked structure was unambiguously characterized by single crystal X-ray diffraction and weak hydrogen bonding was identified as a central driving force for the catenation. Furthermore, scrambling experiments using partially deuterated cages were performed, revealing that the catenane formation occurs through mechanical interlocking of preformed single cages.

Self-Assembly of Molecular Trefoil Knots Featuring Pentadecanuclear Homoleptic AuI -, AuI /AgI -, or AuI /CuI -Alkynyl Coordination

Metal-free and metal-containing molecular trefoil knots are fascinating ensembles that are usually covalently assembled, the latter requiring the rational design of di- or multidentate/multipodal ligands as connectors. In this work, we describe the self-assembly of pentadecanuclear Au^I trefoil knots [Au₁₅ (C≡CR)₁₅ ] from monoalkynes HC≡CR (R=9,9-X₂ -fluorenyl with X=nBu, n-hexyl) and [Au^I (THT)Cl]. Hetero-bimetallic counterparts [Au₉ M₆ (C≡CR)₁₅ ] (M=Cu/Ag) were self-assembled by reactions of [Au₁₅ (C≡CR)₁₅ ] with [Cu(MeCN)₄ ]⁺ /AgNO₃ and HC≡CR. The type of pentadecanuclear trefoil knots described herein is characterized by X-ray crystallography, 2D NMR and HR-ESI-MS. [Au₉ Cu₆ (C≡CR)₁₅ ] is relatively stable in hexane; its excited state properties were investigated. DFT calculations revealed that non-covalent metal-metal and metal-ligand interactions, together with longer alkyl chain-strengthened inter-ligand dispersion interactions, govern the stability of the trefoil knot structures.

Circuit Topology for Bottom-Up Engineering of Molecular Knots

The art of tying knots is exploited in nature and occurs in multiple applications ranging from being an essential part of scouting programs to engineering molecular knots. Biomolecular knots, such as knotted proteins, bear various cellular functions, and their entanglement is believed to provide them with thermal and kinetic stability. Yet, little is known about the design principles of naturally evolved molecular knots. Intra-chain contacts and chain entanglement contribute to the folding of knotted proteins. Circuit topology, a theory that describes intra-chain contacts, was recently generalized to account for chain entanglement. This generalization is unique to circuit topology and not motivated by other theories. In this conceptual paper, we systematically analyze the circuit topology approach to a description of linear chain entanglement. We utilize a bottom-up approach, i.e., we express entanglement by a set of four fundamental structural units subjected to three (or five) binary topological operations. All knots found in proteins form a well-defined, distinct group which naturally appears if expressed in terms of these basic structural units. We believe that such a detailed, bottom-up understanding of the structure of molecular knots should be beneficial for molecular engineering.

Lasso Proteins-Unifying Cysteine Knots and Miniproteins

Complex lasso proteins are a recently identified class of biological compounds that are present in considerable fraction of proteins with disulfide bridges. In this work, we look at complex lasso proteins as a generalization of well-known cysteine knots and miniproteins (lasso peptides). In particular, we show that complex lasso proteins with the same crucial topological features-cysteine knots and lasso peptides-are antimicrobial proteins, which suggests that they act as a molecular plug. Based on an analysis of the stability of the lasso piercing residue, we also introduce a method to determine which lasso motif is potentially functional. Using this method, we show that the lasso motif in antimicrobial proteins, as well in that in cytokines, is functionally relevant. We also study the evolution of lasso motifs, their conservation, and the usefulness of the lasso fingerprint, which extracts all topologically non-triviality concerning covalent loops. The work is completed by the presentation of extensive statistics on complex lasso proteins to analyze, in particular, the strange propensity for "negative" piercings. We also identify 21 previously unknown complex lasso proteins with an ester and a thioester bridge.

Revealing Topological Barriers against Knot Untying in Thermal and Mechanical Protein Unfolding by Molecular Dynamics Simulations

The knot is one of the most remarkable topological features identified in an increasing number of proteins with important functions. However, little is known about how the knot is formed during protein folding, and untied or maintained in protein unfolding. By means of all-atom molecular dynamics simulation, here we employ methyltransferase YbeA as the knotted protein model to analyze changes of the knotted conformation coupled with protein unfolding under thermal and mechanical denaturing conditions. Our results show that the trefoil knot in YbeA is occasionally untied via knot loosening rather than sliding under enhanced thermal fluctuations. Through correlating protein unfolding with changes in the knot position and size, several aspects of barriers that jointly suppress knot untying are revealed. In particular, protein unfolding is always prior to knot untying and starts preferentially from separation of two α-helices (α1 and α5), which protect the hydrophobic core consisting of β-sheets (β1-β4) from exposure to water. These β-sheets form a loop through which α5 is threaded to form the knot. Hydrophobic and hydrogen bonding interactions inside the core stabilize the loop against loosening. In addition, residues at N-terminal of α5 define a rigid turning to impede α5 from sliding out of the loop. Site mutations are designed to specifically eliminate these barriers, and easier knot untying is achieved under the same denaturing conditions. These results provide new molecular level insights into the folding/unfolding of knotted proteins.

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.

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).

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.

Self-Sorting Assembly of Molecular Trefoil Knots of Single Handedness

We report on the stereoselective synthesis of trefoil knots of single topological handedness in up to 90% yield (over two steps) through the formation of trimeric circular helicates from ligand strands containing either imine or, unexpectedly, amide chelating units and metal ion templates of the appropriate coordination character (zinc(II) for imines; cobalt(III) for amides). The coordination stereochemistry of the octahedral metal complexes is determined by asymmetric carbon centers in the strands, ultimately translating into trefoil knots that are a single enantiomer, both physically and in terms of their fundamental topology. Both the imine-zinc and amide-cobalt systems display self-sorting behavior, with racemic ligands forming knots that individually contain only building blocks of the same chirality. The knots and the corresponding trimeric circular helicate intermediates (Zn(II)₃ complex for the imine ligands; Co(III)₃ complex for the amide ligands) were characterized by nuclear magnetic resonance spectroscopy, mass spectrometry, and X-ray crystallography. The latter confirms the trefoil knots as 84-membered macrocycles, with each of the metal ions sited at a crossing point for three regions of the strand. The stereochemistry of the octahedral coordination centers imparts alternating crossings of the same handedness within each circular helicate. The expression of chirality of the knotted molecules was probed by circular dichroism: The topological handedness of the demetalated knots was found to have a greater effect on the CD response than the Euclidean chirality of an individual chiral center.

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.

Stabilizing Effect of Inherent Knots on Proteins Revealed by Molecular Dynamics Simulations

A growing number of proteins have been identified as knotted in their native structures, with such entangled topological features being expected to play stabilizing roles maintaining both the global fold and the nature of proteins. However, the molecular mechanism underlying the stabilizing effect is ambiguous. Here, we combine unbiased and mechanical atomistic molecular dynamics simulations to investigate how a protein is stabilized by an inherent knot by directly comparing chemical, thermal, and mechanical denaturing properties of two proteins having the same sequence and secondary structures but differing in the presence or absence of an inherent knot. One protein is YbeA from Escherichia coli, containing a deep trefoil knot within the sequence, and the other is the modified protein with the knot of YbeA being removed. Under certain chemical denaturing conditions, the unknotted protein fully unfolds whereas the knotted protein does not, suggesting a higher intrinsic stability for the protein having a knot. Both proteins unfold under enhanced thermal fluctuations but at different rates and with distinct pathways. Opening the hydrophobic core via separation between two α-helices is identified as a crucial step initiating the protein unfolding, which, however, is restrained for the knotted protein by topological and geometrical frustrations. Energy barriers for denaturing the protein are reduced by removing the knot, as evidenced by mechanical unfolding simulations. Finally, yet importantly, no obvious change in size or location of the knot was observed during denaturing processes, indicating that YbeA may remain knotted for a relatively long time during and after denaturation.

Periodic Motion of Sedimenting Flexible Knots

We study the dynamics of knotted deformable closed chains sedimenting in a viscous fluid. We show experimentally that trefoil and other torus knots often attain a remarkably regular horizontal toroidal structure while sedimenting, with a number of intertwined loops, oscillating periodically around each other. We then recover this motion numerically and find out that it is accompanied by a very slow rotation around the vertical symmetry axis. We analyze the dependence of the characteristic timescales on the chain flexibility and aspect ratio. It is observed in the experiments that this oscillating mode of the dynamics can spontaneously form even when starting from a qualitatively different initial configuration. In numerical simulations, the oscillating modes are usually present as transients or final stages of the evolution, depending on chain aspect ratio and flexibility, and the number of loops.

A nanofluidic knot factory based on compression of single DNA in nanochannels

Knots form when polymers self-entangle, a process enhanced by compaction with important implications in biological and artificial systems involving chain confinement. In particular, new experimental tools are needed to assess the impact of multiple variables influencing knotting probability. Here, we introduce a nanofluidic knot factory for efficient knot formation and detection. Knots are produced during hydrodynamic compression of single DNA molecules against barriers in a nanochannel; subsequent extension of the chain enables direct assessment of the number of independently evolving knots. Knotting probability increases with chain compression as well as with waiting time in the compressed state. Using a free energy derived from scaling arguments, we develop a knot-formation model that can quantify the effect of interactions and the breakdown of Poisson statistics at high compression. Our model suggests that highly compressed knotted states are stabilized by a decreased free energy as knotted contour contributes a lower self-exclusion derived free energy.

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.

Molecular Knots

The first synthetic molecular trefoil knot was prepared in the late 1980s. However, it is only in the last few years that more complex small-molecule knot topologies have been realized through chemical synthesis. The steric restrictions imposed on molecular strands by knotting can impart significant physical and chemical properties, including chirality, strong and selective ion binding, and catalytic activity. As the number and complexity of accessible molecular knot topologies increases, it will become increasingly useful for chemists to adopt the knot terminology employed by other disciplines. Here we give an overview of synthetic strategies towards molecular knots and outline the principles of knot, braid, and tangle theory appropriate to chemistry and molecular structure.

Are There Knots in Chromosomes?

Recent developments have for the first time allowed the determination of three-dimensional structures of individual chromosomes and genomes in nuclei of single haploid mouse embryonic stem (ES) cells based on Hi⁻C chromosome conformation contact data. Although these first structures have a relatively low resolution, they provide the first experimental data that can be used to study chromosome and intact genome folding. Here we further analyze these structures and provide the first evidence that G1 phase chromosomes are knotted, consistent with the fact that plots of contact probability vs sequence separation show a power law dependence that is intermediate between that of a fractal globule and an equilibrium structure.

Pierced Lasso Topology Controls Function in Leptin

Protein engineering is a powerful tool in drug design and therapeutics, where disulphide bridges are commonly introduced to stabilize proteins. However, these bonds also introduce covalent loops, which are often neglected. These loops may entrap the protein backbone on opposite sides, leading to a "knotted" topology, forming a so-called Pierced Lasso (PL). In this elegant system, the "knot" is held together with a single disulphide bridge where part of the polypeptide chain is threaded through. The size and position of these covalent loops can be manipulated through protein design in vitro, whereas nature uses polymorphism to switch the PL topology. The PL protein leptin shows genetic modification of an N-terminal residue, adding a third cysteine to the same sequence. In an effort to understand the mechanism of threading of these diverse topologies, we designed three loop variants to mimic the polymorphic sequence. This adds elegance to the system under study, as it allows the generation of three possible covalent loops; they are the original wild-type C-terminal loop protein, the fully circularized unthreaded protein, and the N-terminal loop protein, responsible for different lasso topologies. The size of the loop changes the threading mechanism from a slipknotting to a plugging mechanism, with increasing loop size. Interestingly, the ground state of the native protein structure is largely unaffected, but biological assays show that the activity is maximized by properly controlled dynamics in the threaded state. A threaded topology with proper conformational dynamics is important for receptor interaction and activation of the signaling pathways in vivo.

The elusive quest for RNA knots

Physical entanglement, and particularly knots arise spontaneously in equilibrated polymers that are sufficiently long and densely packed. Biopolymers are no exceptions: knots have long been known to occur in proteins as well as in encapsidated viral DNA. The rapidly growing number of RNA structures has recently made it possible to investigate the incidence of physical knots in this type of biomolecule, too. Strikingly, no knots have been found to date in the known RNA structures. In this Point of View Article we discuss the absence of knots in currently available RNAs and consider the reasons why knots in RNA have not yet been found, despite the expectation that they should exist in Nature. We conclude by singling out a number of RNA sequences that, based on the properties of their predicted secondary structures, are good candidates for knotted RNAs.

In Search of Functional Advantages of Knots in Proteins

We analysed the structure of deeply knotted proteins representing three unrelated families of knotted proteins. We looked at the correlation between positions of knotted cores in these proteins and such local structural characteristics as the number of intra-chain contacts, structural stability and solvent accessibility. We observed that the knotted cores and especially their borders showed strong enrichment in the number of contacts. These regions showed also increased thermal stability, whereas their solvent accessibility was decreased. Interestingly, the active sites within these knotted proteins preferentially located in the regions with increased number of contacts that also have increased thermal stability and decreased solvent accessibility. Our results suggest that knotting of polypeptide chains provides a favourable environment for the active sites observed in knotted proteins. Some knotted proteins have homologues without a knot. Interestingly, these unknotted homologues form local entanglements that retain structural characteristics of the knotted cores.

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.

Knotting and unknotting of a protein in single molecule experiments

Spontaneous folding of a polypeptide chain into a knotted structure remains one of the most puzzling and fascinating features of protein folding. The folding of knotted proteins is on the timescale of minutes and thus hard to reproduce with atomistic simulations that have been able to reproduce features of ultrafast folding in great detail. Furthermore, it is generally not possible to control the topology of the unfolded state. Single-molecule force spectroscopy is an ideal tool for overcoming this problem: by variation of pulling directions, we controlled the knotting topology of the unfolded state of the 52-knotted protein ubiquitin C-terminal hydrolase isoenzyme L1 (UCH-L1) and have therefore been able to quantify the influence of knotting on its folding rate. Here, we provide direct evidence that a threading event associated with formation of either a 31 or 52 knot, or a step closely associated with it, significantly slows down the folding of UCH-L1. The results of the optical tweezers experiments highlight the complex nature of the folding pathway, many additional intermediate structures being detected that cannot be resolved by intrinsic fluorescence. Mechanical stretching of knotted proteins is also of importance for understanding the possible implications of knots in proteins for cellular degradation. Compared with a simple 31 knot, we measure a significantly larger size for the 52 knot in the unfolded state that can be further tightened with higher forces. Our results highlight the potential difficulties in degrading a 52 knot compared with a 31 knot.

Molecular knots in biology and chemistry

Knots and entanglements are ubiquitous. Beyond their aesthetic appeal, these fascinating topological entities can be either useful or cumbersome. In recent decades, the importance and prevalence of molecular knots have been increasingly recognised by scientists from different disciplines. In this review, we provide an overview on the various molecular knots found in naturally occurring biological systems (DNA, RNA and proteins), and those created by synthetic chemists. We discuss the current knowledge in these fields, including recent developments in experimental and, in some cases, computational studies which are beginning to shed light into the complex interplay between the structure, formation and properties of these topologically intricate molecules.

Lanthanide Template Synthesis of Trefoil Knots of Single Handedness

We report on the assembly of 2,6-pyridinedicarboxamide ligands (1) with point chirality about lanthanide metal ion (Ln(3+)) templates, in which the helical chirality of the resulting entwined 3:1 ligand:metal complexes is covalently captured by ring-closing olefin metathesis to form topologically chiral molecular trefoil knots of single handedness. The ligands do not self-sort (racemic ligands form a near-statistical mixture of homoleptic and heteroleptic lanthanide complexes), but the use of only (R,R)-1 leads solely to a trefoil knot of Λ-handedness, whereas (S,S)-1 forms the Δ-trefoil knot with complete stereoselectivity. The knots and their isomeric unknot macrocycles were characterized by NMR spectroscopy, mass spectrometry, and X-ray crystallography and the expression of the chirality that results from the topology of the knots studied by circular dichroism.

Catenanes: fifty years of molecular links

Half a century after Schill and Lüttringhaus carried out the first directed synthesis of a [2]catenane, a plethora of strategies now exist for the construction of molecular Hopf links (singly interlocked rings), the simplest type of catenane. The precision and effectiveness with which suitable templates and/or noncovalent interactions can arrange building blocks has also enabled the synthesis of intricate and often beautiful higher order interlocked systems, including Solomon links, Borromean rings, and a Star of David catenane. This Review outlines the diverse strategies that exist for synthesizing catenanes in the 21st century and examines their emerging applications and the challenges that still exist for the synthesis of more complex topologies.

Folding mechanisms of Trefoil Knot proteins studied by molecular dynamics simulations and Go-model

Most proteins need to avoid the complex topologies when folding into the native structures, but some proteins with nontrivial topologies have been found in nature. Here we used protein unfolding simulations under high temperature and all-atom Gō-model to investigate the folding mechanisms for two trefoil knot proteins. Results show that, the contacts in β-sheet are important to the formation of knot protein, and if these contacts disappeared, the knot protein would be easy to untie. In the Gō-model simulations, the folding processes of the two knot proteins are similar. The compact structures of the two knot proteins with the native contacts in β-sheet are formed in transition state, and the intermediate state has loose C-terminal. This model also reveals the detailed folding mechanisms for the two proteins.

An intramolecular lock facilitates folding and stabilizes the tertiary structure of Streptococcus mutans adhesin P1

The cariogenic bacterium Streptococcus mutans uses adhesin P1 to adhere to tooth surfaces, extracellular matrix components, and other bacteria. A composite model of P1 based on partial crystal structures revealed an unusual complex architecture in which the protein forms an elongated hybrid alpha/polyproline type II helical stalk by folding back on itself to display a globular head at the apex and a globular C-terminal region at the base. The structure of P1's N terminus and the nature of its critical interaction with the C-terminal region remained unknown, however. We have cocrystallized a stable complex of recombinant N- and C-terminal fragments and here describe a previously unidentified topological fold in which these widely discontinuous domains are intimately associated. The structure reveals that the N terminus forms a stabilizing scaffold by wrapping behind the base of P1's elongated stalk and physically "locking" it into place. The structure is stabilized through a highly favorable ΔG(solvation) on complex formation, along with extensive hydrogen bonding. We confirm the functional relevance of this intramolecular interaction using differential scanning calorimetry and circular dichroism to show that disruption of the proper spacing of residues 989-1001 impedes folding and diminishes stability of the full-length molecule, including the stalk. Our findings clarify previously unexplained functional and antigenic properties of P1.

Mechanistic insights into the folding of knotted proteins in vitro and in vivo

The importance of knots and entanglements in biological systems is increasingly being realized and the number of proteins with topologically complex knotted structures has risen. However, the mechanism as to how these proteins knot and fold efficiently remains unclear. Using a cell-free expression system and pulse-proteolysis experiments, we have investigated the mechanism of knotting and folding for two bacterial trefoil-knotted methyltransferases. This study provides the first experimental evidence for a knotting mechanism. Results on fusions of stable protein domains to N-terminus, C-terminus or both termini of the knotted proteins clearly demonstrate that threading of the nascent chain through a knotting loop occurs via the C-terminus. Our results strongly suggest that this mechanism occurs even when the C-terminus is severely hindered by the addition of a large stable structure, in contrast to some simulations indicating that even the folding pathways of knotted proteins have some plasticity. The same strategy was employed to probe the effects of GroEL-GroES. In this case, results suggest active mechanisms for the molecular chaperonin. We demonstrate that a simple model in which GroEL-GroES sterically confines the unknotted polypeptide chain thereby promoting knotting is unlikely, and we propose two alternatives: (a) the chaperonin facilitates unfolding of kinetically and topologically trapped intermediates or (b) the chaperonin stabilizes interactions that promote knotting. These findings provide mechanistic insights into the folding of knotted proteins both in vitro and in vivo, thus elucidating how they have withstood evolutionary pressures regardless of their complex topologies and intrinsically slow folding rates.

A knot in the protein structure - probing the near-infrared fluorescent protein iRFP designed from a bacterial phytochrome

The possibility of engineering near-infrared fluorescent proteins and biosensors from bacterial phytochrome photoreceptors (BphPs) has led to substantial interest in this family of proteins. The near-infrared fluorescent proteins have allowed non-invasive bio-imaging of deep tissues and whole organs in living animals. BphPs and derived near-infrared fluorescent proteins contain a structural element, called a knot, in their polypeptide chains. The formation of knot structures in proteins was refuted for a long time. Here, we studied the denaturation and renaturation processes of the near-infrared fluorescent probe iRFP, engineered from RpBphP2, which utilizes a heme-derived tetrapyrrole compound biliverdin as a chromophore. iRFP contains a unique figure-of-eight knot. The denaturation and renaturation curves of the iRFP apoform coincided well, suggesting efficient refolding. However, the iRFP holoform exhibited irreversible unfolding and aggregation associated with the bound chromophore. The knot structure in the apoform did not prevent subsequent binding of biliverdin, resulting in the functional iRFP holoform. We suggest that the irreversibility of protein unfolding is caused by post-translational protein modifications, such as chromophore binding, rather than the presence of the knot. These results are essential for future design of BphP-based near-infrared probes, and add important features to our knowledge of protein folding.

The role of non-native interactions in the folding of knotted proteins: insights from molecular dynamics simulations

For several decades, the presence of knots in naturally-occurring proteins was largely ruled out a priori for its supposed incompatibility with the efficiency and robustness of folding processes. For this very same reason, the later discovery of several unrelated families of knotted proteins motivated researchers to look into the physico-chemical mechanisms governing the concerted sequence of folding steps leading to the consistent formation of the same knot type in the same protein location. Besides experiments, computational studies are providing considerable insight into these mechanisms. Here, we revisit a number of such recent investigations within a common conceptual and methodological framework. By considering studies employing protein models with different structural resolution (coarse-grained or atomistic) and various force fields (from pure native-centric to realistic atomistic ones), we focus on the role of native and non-native interactions. For various unrelated instances of knotted proteins, non-native interactions are shown to be very important for favoring the emergence of conformations primed for successful self-knotting events.

Knotting pathways in proteins

Most proteins, in order to perform their biological function, have to fold to a compact native state. The increasing number of knotted and slipknotted proteins identified suggests that proteins are able to manoeuvre around topological barriers during folding. In the present article, we review the current progress in elucidating the knotting process in proteins. Although we concentrate on theoretical approaches, where a knotted topology can be unambiguously detected, comparison with experiments is also reviewed. Numerical simulations suggest that the folding process for small knotted proteins is composed of twisted loop formation and then threading by either slipknot geometries or flipping. As the size of the knotted proteins increases, particularly for more deeply threaded termini, the prevalence of traps in the free energy landscape also increases. Thus, in the case of longer knotted and slipknotted proteins, the folding mechanism is probably supported by chaperones. Overall, results imply that knotted proteins can be folded efficiently and survive evolutionary pressure in order to perform their biological functions.

Tightening and Untying the Knot in Human Carbonic Anhydrase III

The forced mechanical unfolding of the knotted protein Human Carbonic Anhydrase (HCA) III is examined by steered, explicit-water molecular dynamics computer simulations. In agreement with previous indications from experiments and coarse-grained simulations, knot tightening by pulling near-terminal amino acids (4 and 267) leads to a much higher resistance to unfolding than for knot untying, where pulling amino acids 4 and 253 untangles the knot by threading the C-terminal end out of the knotting loop. In particular, the resistance during knot tightening is observed to diverge due to a tightly tied-up enzymatic core of the HCA if it is coordinated by the catalytically important zinc ion. The underlying structural pictures are presented and discussed.

Tight knots in proteins: can they block the mitochondrial pores?

Proteins need to be unfolded when translocated through the pores in mitochondrial and other cellular membranes. Knotted proteins, however, might get stuck during this process since the diameter of the pore is smaller than the size of maximally tightened knot. In the present article, I briefly review the experimental and numerical studies of tight knots in proteins, with a particular emphasis on the estimates of the size of these knots. Next, I discuss the process of protein translocation through the mitochondrial pores and report the results of molecular dynamics simulations of knotted protein translocation, which show how the knot can indeed block the pore.

Folding pathways of a knotted protein with a realistic atomistic force field

We report on atomistic simulation of the folding of a natively-knotted protein, MJ0366, based on a realistic force field. To the best of our knowledge this is the first reported effort where a realistic force field is used to investigate the folding pathways of a protein with complex native topology. By using the dominant-reaction pathway scheme we collected about 30 successful folding trajectories for the 82-amino acid long trefoil-knotted protein. Despite the dissimilarity of their initial unfolded configuration, these trajectories reach the natively-knotted state through a remarkably similar succession of steps. In particular it is found that knotting occurs essentially through a threading mechanism, involving the passage of the C-terminal through an open region created by the formation of the native -sheet at an earlier stage. The dominance of the knotting by threading mechanism is not observed in MJ0366 folding simulations using simplified, native-centric models. This points to a previously underappreciated role of concerted amino acid interactions, including non-native ones, in aiding the appropriate order of contact formation to achieve knotting.

It has been recently observed that the native structure of proteins can contain knots. These are formed during the folding process and are tightened in a specific (i.e. native) location, along the poly-peptide chain. The existence of knots hence implies a high degree coordination of local and global conformational changes, during the folding reaction. In this work we investigate how the knot is formed and what are the dynamical mechanisms which drive the self-entanglement process. To this end, we report on the first atomistically detailed numerical simulation of the folding of a knotted protein, based on a realistic description of the inter-atomic forces. These simulations show that the knot is formed by following a specific sequence of contacts. The comparison of the findings with those based on simplified folding models suggest that the productive succession of contacts is aided by a concerted interplay of amino acid interactions, arguably including non-native ones.