Knotted and topologically complex proteins as models for studying folding and stability

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.

Long-lived metastable knots in polyampholyte chains

Knots in proteins and DNA are known to have significant effect on their equilibrium and dynamic properties as well as on their function. While knot dynamics and thermodynamics in electrically neutral and uniformly charged polymer chains are relatively well understood, proteins are generally polyampholytes, with varied charge distributions along their backbones. Here we use simulations of knotted polymer chains to show that variation in the charge distribution on a polyampholyte chain with zero net charge leads to significant variation in the resulting knot dynamics, with some charge distributions resulting in long-lived metastable knots that escape the (open-ended) chain on a timescale that is much longer than that for knots in electrically neutral chains. The knot dynamics in such systems can be described, quantitatively, using a simple one-dimensional model where the knot undergoes biased Brownian motion along a "reaction coordinate", equal to the knot size, in the presence of a potential of mean force. In this picture, long-lived knots result from charge sequences that create large electrostatic barriers to knot escape. This model allows us to predict knot lifetimes even when those times are not directly accessible by simulations.

A Note on the Effects of Linear Topology Preservation in Monte Carlo Simulations of Knotted Proteins

Monte Carlo simulations are a powerful technique and are widely used in different fields. When applied to complex molecular systems with long chains, such as those in synthetic polymers and proteins, they have the advantage of providing a fast and computationally efficient way to sample equilibrium ensembles and calculate thermodynamic and structural properties under desired conditions. Conformational Monte Carlo techniques employ a move set to perform the transitions in the simulation Markov chain. While accepted conformations must preserve the sequential bonding of the protein chain model and excluded volume among its units, the moves themselves may take the chain across itself. We call this a break in linear topology preservation. In this manuscript, we show, using simple protein models, that there is no difference in equilibrium properties calculated with a move set that preserves linear topology and one that does not. However, for complex structures, such as those of deeply knotted proteins, the preservation of linear topology provides correct equilibrium results but only after long relaxation. In any case, to analyze folding pathways, knotting mechanisms and folding kinetics, the preservation of linear topology may be an unavoidable requirement.

AlphaFold predicts the most complex protein knot and composite protein knots

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

Cell-Free Expression to Probe Co-Translational Insertion of an Alpha Helical Membrane Protein

The majority of alpha helical membrane proteins fold co-translationally during their synthesis on the ribosome. In contrast, most mechanistic folding studies address refolding of full-length proteins from artificially induced denatured states that are far removed from the natural co-translational process. Cell-free translation of membrane proteins is emerging as a useful tool to address folding during translation by a ribosome. We summarise the benefits of this approach and show how it can be successfully extended to a membrane protein with a complex topology. The bacterial leucine transporter, LeuT can be synthesised and inserted into lipid membranes using a variety of in vitro transcription translation systems. Unlike major facilitator superfamily transporters, where changes in lipids can optimise the amount of correctly inserted protein, LeuT insertion yields are much less dependent on the lipid composition. The presence of a bacterial translocon either in native membrane extracts or in reconstituted membranes also has little influence on the yield of LeuT incorporated into the lipid membrane, except at high reconstitution concentrations. LeuT is considered a paradigm for neurotransmitter transporters and possesses a knotted structure that is characteristic of this transporter family. This work provides a method in which to probe the formation of a protein as the polypeptide chain is being synthesised on a ribosome and inserting into lipids. We show that in comparison with the simpler major facilitator transporter structures, LeuT inserts less efficiently into membranes when synthesised cell-free, suggesting that more of the protein aggregates, likely as a result of the challenging formation of the knotted topology in the membrane.

From 4-arm star proteins to diverse stimuli-responsive molecular networks enabled by orthogonal genetically encoded click chemistries

The integrated use of genetically encoded click chemistries and protein topology engineering enabled the creation of various smart protein hydrogels.

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.

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.

Higher Order Protein Catenation Leads to an Artificial Antibody with Enhanced Affinity and In Vivo Stability

The chemical topology is a unique dimension for protein engineering, yet the topological diversity and architectural complexity of proteins remain largely untapped. Herein, we report the biosynthesis of complex topological proteins using a rationally engineered, cross-entwining peptide heterodimer motif derived from p53dim (an entangled homodimeric mutant of the tetramerization domain of the tumor suppressor protein p53). The incorporation of an electrostatic interaction at specific sites converts the p53dim homodimer motif into a pair of heterodimer motifs with high specificity for directing chain entanglement upon folding. Its combination with split-intein-mediated ligation and/or SpyTag/SpyCatcher chemistry facilitates the programmed synthesis of protein heterocatenane or [n]catenanes in cells, leading to a general and modular approach to complex protein catenanes containing various proteins of interest. Concatenation enhances not only the target protein's affinity but also the in vivo stability as shown by its prolonged circulation time in blood. As a proof of concept, artificial antibodies have been developed by embedding a human epidermal growth factor receptor 2-specific affibody onto the [n]catenane scaffolds and shown to exhibit a higher affinity and a better pharmacokinetic profile than the wild-type affibody. These results suggest that topology engineering holds great promise in the development of therapeutic proteins.

Slipknotted and unknotted monovalent cation-proton antiporters evolved from a common ancestor

While the slipknot topology in proteins has been known for over a decade, its evolutionary origin is still a mystery. We have identified a previously overlooked slipknot motif in a family of two-domain membrane transporters. Moreover, we found that these proteins are homologous to several families of unknotted membrane proteins. This allows us to directly investigate the evolution of the slipknot motif. Based on our comprehensive analysis of 17 distantly related protein families, we have found that slipknotted and unknotted proteins share a common structural motif. Furthermore, this motif is conserved on the sequential level as well. Our results suggest that, regardless of topology, the proteins we studied evolved from a common unknotted ancestor single domain protein. Our phylogenetic analysis suggests the presence of at least seven parallel evolutionary scenarios that led to the current diversity of proteins in question. The tools we have developed in the process can now be used to investigate the evolution of other repeated-domain proteins.

In proteins with the slipknot topology, the polypeptide chain forms a slipknot—a structure that is not necessarily manifest to a naked eye, but it can be detected using mathematical methods. Slipknots are conserved motifs often found at catalytic sites and are directly involved in molecular transport. Although the first proteins with slipknots were found in 2007, many questions remain unanswered, e.g. how these proteins appeared, or whether the slipknotted proteins evolved from unknotted ones or vice versa. Here we provide the first analysis of homologous slipknotted and unknotted transmembrane proteins in order to elucidate their evolutionary relationship. We show that two-domain slipknotted and unknotted membrane transporters share the same one-domain unknotted protein as an ancestor. The ancestor gene duplicated and underwent various diversification and fusion events during the evolution, which have led to the appearance of a large superfamily of secondary active transporters. The slipknot motif seems to have been created by chance after a fusion of two single domain genes. Therefore, we show here that the slipknotted transporter evolved from an unknotted one-domain protein and that there are at least seven different evolutionary scenarios that gave rise to this large superfamily of transporters.

819 molecular knot: a theoretical analysis of the electronic structure using an ONIOM approach

The present work analyzes the electronic and molecular properties of the 8₁₉ ([Fe(II)₄]Cℓ) and metal-free knot ligand complexes obtained from X-ray crystal structure of molecular 8₁₉ knot complex [Fe(II)₄(PF₆)₇]Cℓ. The studies were theoretically investigated by means of DFT, TD-DFT, and ONIOM approaches. Basis sets functions from all-electron calculations for bromine, iodine, and iron atoms were adapted to be used along with relativistic effective core potential, while H, C, N, O, and Cℓ atoms were described by Pople basis sets. The diffusion effect of halogen into the 8₁₉ cavity, UV-Vis, and Electronic Circular Dichroism spectra were also analyzed. All calculations were performed using solvent effect through the SCRF/SMD model and dispersion effects by Grimme methodology. The value of mean separation distance between Cℓ and iron atom (7.218 Å) is in good agreement with X-ray experimental result (7.258 Å). Circular dichroism spectrum of metal-free 8₁₉ knot ligand was calculated and the maximum absorption in 262 nm, Δ𝜖 obtained was 67 L mol^- 1 cm^- 1. These results are qualitatively similar to those obtained experimentally, 295 nm and 80 L mol^- 1 cm^- 1, respectively. In this study, we report the electronic and molecular properties of the 8₁₉ ([Fe(II)₄]Cl and metal-free knot ligand complexes and compare with the results obtained from X-ray crystallographic data of 8₁₉ knot complex [Fe(II)₄(PF₆)₇]Cl. The 8₁₉ knot were investigated by means of DFT, TD-DFT, and ONIOM approaches. Basis sets functions from all-electron for Br, I, and Fe atoms were adapted to be used along with relativistic effective core potential, while H, C, N, O, and Cl atoms were described by Pople basis sets. The objective was to understand the stability of the 8₁₉ knot as a function of the substitution of the central halogen atom (Cl), and the signal in the circular dichroism spectra. From the equilibrium geometries, we have obtained good results for values of the bond distance, bond angle, and dihedral angle along the molecular structure when these variables are compared with the results obtained from X-ray data. The diffusion effect of halogen into the 8₁₉ cavity, UV-Vis, and Electronic Circular Dichroism spectra was also analyzed. Circular dichroism spectrum of metal-free 8₁₉ knot ligand was calculated, and the maximum absorption is in good agreement with the experimental value. The ONIOM methodology combined with the relativistic effective core potential and the atomic basis sets provide good results for systems with a complex topology, such as knots.

GLN: a method to reveal unique properties of lasso type topology in proteins

Geometry and topology are the main factors that determine the functional properties of proteins. In this work, we show how to use the Gauss linking integral (GLN) in the form of a matrix diagram-for a pair of a loop and a tail-to study both the geometry and topology of proteins with closed loops e.g. lassos. We show that the GLN method is a significantly faster technique to detect entanglement in lasso proteins in comparison with other methods. Based on the GLN technique, we conduct comprehensive analysis of all proteins deposited in the PDB and compare it to the statistical properties of the polymers. We show how high and low GLN values correlate with the internal exibility of proteins, and how the GLN in the form of a matrix diagram can be used to study folding and unfolding routes. Finally, we discuss how the GLN method can be applied to study entanglement between two structures none of which are closed loops. Since this approach is much faster than other linking invariants, the next step will be evaluation of lassos in much longer molecules such as RNA or loops in a single chromosome.

Crossing complexity of space-filling curves reveals entanglement of S-phase DNA

Space-filling curves have been used for decades to study the folding principles of globular proteins, compact polymers, and chromatin. Formally, space-filling curves trace a single circuit through a set of points (x,y,z); informally, they correspond to a polymer melt. Although not quite a melt, the folding principles of Human chromatin are likened to the Hilbert curve: a type of space-filling curve. Hilbert-like curves in general make biologically compelling models of chromatin; in particular, they lack knots which facilitates chromatin folding, unfolding, and easy access to genes. Knot complexity has been intensely studied with the aid of Alexander polynomials; however, the approach does not generalize well to cases of more than one chromosome. Crossing complexity is an understudied alternative better suited for quantifying entanglement between chromosomes. Do Hilbert-like configurations limit crossing complexity between chromosomes? How does crossing complexity for Hilbert-like configurations compare to equilibrium configurations? To address these questions, we extend the Mansfield algorithm to enable sampling of Hilbert-like space filling curves on a simple cubic lattice. We use the extended algorithm to generate equilibrium, intermediate, and Hilbert-like configurational ensembles and compute crossing complexity between curves (chromosomes) in each configurational snapshot. Our main results are twofold: (a) Hilbert-like configurations limit entanglement between chromosomes and (b) Hilbert-like configurations do not limit entanglement in a model of S-phase DNA. Our second result is particularly surprising yet easily rationalized with a geometric argument. We explore ergodicity of the extended algorithm and discuss our results in the context of more sophisticated models of chromatin.

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.

Revealing Cooperation between Knotted Conformation and Dimerization in Protein Stabilization by Molecular Dynamics Simulations

The topological knot is thought to play a stabilizing role in maintaining the global fold and nature of proteins with the underlying mechanism yet to be elucidated. Given that most proteins containing trefoil knots exist and function as homodimers with a large part of the dimer interface occupied by the knotted region, we reason that the knotted conformation cooperates with dimerization in protein stabilization. Here, we take YbeA from Escherichia coli as the knotted protein model, using molecular dynamics (MD) simulations to compare the stability of two pairs of dimeric proteins having the same sequence and secondary structures but differing in the presence or absence of a trefoil knot in each subunit. The dimer interface of YbeA is identified to involve favorable contacts among three α-helices (α1, α3, and α5), one of which (α5) is threaded through a loop connected with α3 to form the knot. Upon removal of the knot by appropriate change of the knot-making crossing of the polypeptide chain, relevant domains are less constrained and exhibit enhanced fluctuations to decrease contacts at the interface. Unknotted subunits are less compact and undergo structural changes to ease the dimer separation. Such a stabilizing effect is evidenced by steered MD simulations, showing that the mechanical force required for dimer separation is significantly reduced by removing the knot. In addition to the knotted conformation, dimerization further improves the protein stability by restricting the α1-α5 separation, which is defined as a leading step for protein unfolding. These results provide important insights into the structure-function relationship of dimerization in knotted proteins.

Quantum Molecular Dynamics, Topological, Group Theoretical and Graph Theoretical Studies of Protein-Protein Interactions

BACKGROUND

Protein-protein interactions (PPIs) are becoming increasingly important as PPIs form the basis of multiple aggregation-related diseases such as cancer, Creutzfeldt-Jakob, and Alzheimer's diseases. This mini-review presents hybrid quantum molecular dynamics, quantum chemical, topological, group theoretical, graph theoretical, and docking studies of PPIs. We also show how these theoretical studies facilitate the discovery of some PPI inhibitors of therapeutic importance.

OBJECTIVE

The objective of this review is to present hybrid quantum molecular dynamics, quantum chemical, topological, group theoretical, graph theoretical, and docking studies of PPIs. We also show how these theoretical studies enable the discovery of some PPI inhibitors of therapeutic importance.

METHODS

This article presents a detailed survey of hybrid quantum dynamics that combines classical and quantum MD for PPIs. The article also surveys various developments pertinent to topological, graph theoretical, group theoretical and docking studies of PPIs and highlight how the methods facilitate the discovery of some PPI inhibitors of therapeutic importance.

RESULTS

It is shown that it is important to include higher-level quantum chemical computations for accurate computations of free energies and electrostatics of PPIs and Drugs with PPIs, and thus techniques that combine classical MD tools with quantum MD are preferred choices. Topological, graph theoretical and group theoretical techniques are shown to be important in studying large network of PPIs comprised of over 100,000 proteins where quantum chemical and other techniques are not feasible. Hence, multiple techniques are needed for PPIs.

CONCLUSION

Drug discovery and our understanding of complex PPIs require multifaceted techniques that involve several disciplines such as quantum chemistry, topology, graph theory, knot theory and group theory, thus demonstrating a compelling need for a multi-disciplinary approach to the problem.

Metal-peptide rings form highly entangled topologically inequivalent frameworks with the same ring- and crossing-numbers

With increasing ring-crossing number (c), knot theory predicts an exponential increase in the number of topologically different links of these interlocking structures, even for structures with the same ring number (n) and c. Here, we report the selective construction of two topologies of 12-crossing peptide [4]catenanes (n = 4, c = 12) from metal ions and pyridine-appended tripeptide ligands. Two of the 100 possible topologies for this structure are selectively created from related ligands in which only the tripeptide sequence is changed: one catenane has a T₂-tetrahedral link and the other a three-crossed tetrahedral link. Crystallographic studies illustrate that a conformational difference in only one of the three peptide residues in the ligand causes the change in the structure of the final tetrahedral link. Our results thus reveal that peptide-based folding and assembly can be used for the facile bottom-up construction of 3D molecular objects containing polyhedral links.

Proteins' Knotty Problems

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

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

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

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.

Studies of global and local entanglements of individual protein chains using the concept of knotoids

We study here global and local entanglements of open protein chains by implementing the concept of knotoids. Knotoids have been introduced in 2012 by Vladimir Turaev as a generalization of knots in 3-dimensional space. More precisely, knotoids are diagrams representing projections of open curves in 3D space, in contrast to knot diagrams which represent projections of closed curves in 3D space. The intrinsic difference with classical knot theory is that the generalization provided by knotoids admits non-trivial topological entanglement of the open curves provided that their geometry is frozen as it is the case for crystallized proteins. Consequently, our approach doesn’t require the closure of chains into loops which implies that the geometry of analysed chains does not need to be changed by closure in order to characterize their topology. Our study revealed that the knotoid approach detects protein regions that were classified earlier as knotted and also new, topologically interesting regions that we classify as pre-knotted.

Characterization of the Folding of a 52-Knotted Protein Using Engineered Single-Tryptophan Variants

An increasing number of proteins that contain topological knots have been identified over the past two decades; however, their folding mechanisms are still not well understood. UCH-L1 has a 5₂-knotted topology. Here, we constructed a series of variants that contain a single tryptophan at different locations along the polypeptide chain. A study of the thermodynamic properties of the variants shows that the structure of UCH-L1 is remarkably tolerant to incorporation of bulky tryptophan side chains. Comprehensive kinetic studies of the variants reveal that they fold via parallel pathways on which there are two intermediate states very similar to wild-type UCH-L1. The structures of the intermediate states do not change significantly with mutation and therefore occupy local minima on the energy landscape that have relatively narrow basins. The kinetic studies also establish that there are considerably more tertiary interactions in the intermediate states than results from previous NMR studies suggested. The two intermediates differ from each other in the extent to which tertiary interactions between the highly stable central β-sheet and flanking α-helices and loop regions are formed. There is strong evidence that these states are aggregation prone. The transition states from both I₁ and I₂ to the native state are plastic and change with mutation and denaturant concentration. Previous studies indicated that the threading event that creates the 5₂ knot occurs during these steps, suggesting that there is a broad energy barrier consistent with the chain undergoing some searching of conformational space as the threading takes place.

Topology Engineering of Proteins in Vivo Using Genetically Encoded, Mechanically Interlocking SpyX Modules for Enhanced Stability

Recombinant proteins are traditionally limited to linear configuration. Herein, we report in vivo protein topology engineering using highly efficient, mechanically interlocking SpyX modules named AXB and BXA. SpyX modules are protein domains composed of p53dim (X), SpyTag (A), and SpyCatcher (B). The p53dim guides the intertwining of the two nascent protein chains followed by autocatalytic isopeptide bond formation between SpyTag and SpyCatcher to fulfill the interlocking, leading to a variety of backbone topologies. Direct expression of AXB or BXA produces protein catenanes with distinct ring sizes. Recombinant proteins containing SpyX modules are obtained either as mechanically interlocked obligate dimers if the protein of interest is fused to the N- or C-terminus of SpyX modules, or as star proteins if the protein is fused to both N- and C-termini. As examples, cellular syntheses of dimers of (GB1)₂ (where GB1 stands for immunoglobulin-binding domain B1 of streptococcal protein G) and of four-arm elastin-like star proteins were demonstrated. Comparison of the catenation efficiencies in different constructs reveals that BXA is generally much more effective than AXB, which is rationalized by the arrangement of three domains in space. Mechanical interlocking induces considerable stability enhancement. Both AXB and BXA have a melting point ∼20 °C higher than the linear controls and the BXA catenane has a melting point ~2 °C higher than the cyclic control BX'A. Notably, four-arm elastin-like star proteins demonstrate remarkable tolerance against trypsin digestion. The SpyX modules provide a convenient and versatile approach to construct unconventional protein topologies via the "assembly-reaction" synergy, which opens a new horizon in protein science for stability enhancement and function reinforcement via topology engineering.

Untangling the Influence of a Protein Knot on Folding

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

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.

Natural supramolecular protein assemblies

Supramolecular protein assemblies are an emerging area within the chemical sciences, which combine the topological structures of the field of supramolecular chemistry and the state-of-the-art chemical biology approaches to unravel the formation and function of protein assemblies. Recent chemical and biological studies on natural multimeric protein structures, including fibers, rings, tubes, catenanes, knots, and cages, have shown that the quaternary structures of proteins are a prerequisite for their highly specific biological functions. In this review, we illustrate that a striking structural diversity of protein assemblies is present in nature. Furthermore, we describe structure-function relationship studies for selected classes of protein architectures, and we highlight the techniques that enable the characterisation of supramolecular protein structures.

Fold conservation and proteolysis in zebrafish IRBP structure: Clues to possible enzymatic function?

Multiple functions for Interphotoreceptor Retinoid-Binding Protein (IRBP) may explain its localization in the retina, vitreous and pineal gland and association with retinitis pigmentosa and myopia. We have been engaged in uncovering the structure-function relationships of this interesting protein long thought to bind visual-cycle retinoids and fatty acids in the subretinal space. Although hydrophobic domains capable of binding such ligands have now been found, we ask what other structural domains might be present that could predict new functions? Interestingly, IRBP possesses a fold similar to C-terminal processing proteases (CTPases) but is missing the PDZ domain. Here we present structural evidence that this fold may have a role in a recently observed autoproteolytic activity of the two-module zebrafish (z) IRBP (Ghosh et al. Exp. Eye Res., 2015). When the structure of Scenedesmus obliquus D1 CTPase (D1P) is superimposed with the first module of zIRBP (z1), the PDZ domain of D1P occupies roughly the same position in the amino acid sequence as the inter-domain tether in z1, between residues P71 and P85. The catalytic triad K397, S372 and E375 of D1P is located at the inter-domain interfacial cleft, similarly as the tetrad K241, S243, D177 and T179 of z1 residues, presumed to have proteolytic function. Packing of two adjacent symmetry-related molecules within the z1 crystal show that the helix α8 penetrates the interfacial cleft underneath the inter-domain tether, forming a simple intermolecular "knot". The full-length zIRBP is cleaved at or immediately after T309, which is located at the end of α8 and is the ninth residue of the second module z2. We propose that the helix α8 within intact zIRBP bends at P301, away from the improbable knotted fold, and positions the cleavage site T309 near the putative catalytic tetrad of the neighboring zIRBP to be proteolytically cleaved. The conservation of this functional catalytic domain suggests that possible physiological roles of IRBP as a hydrolase needs to be considered.

Thermal and chemical unfolding pathways of PaSdsA1 sulfatase, a homo-dimer with topologically interlinked chains

Understanding the mechanisms as to how interlinked proteins entangle and fold is a challenge. PaSdsA1 sulfatase is a homo-dimer containing two zinc atoms per monomer. The monomer chains are interlinked in a dimerization domain. To study the unfolding pathways denaturation experiments were performed. In the native protein three forms coexist in chemical equilibrium, each with a different number of zinc atoms. In the chemical unfolding of the holo-dimers the entanglement of the chains is preserved and acts as a 'folding seed', allowing the unfolding process to be reversible. Thermal irreversible unfolding of the holo-dimers favours dissociation, producing monomers that are SDS-stabilized. The thermal unfolding of these monomers is reversible. However, it is not possible to form dimers from unfolded monomers.

Artificial domain duplication replicates evolutionary history of ketol-acid reductoisomerases

The duplication of protein structural domains has been proposed as a common mechanism for the generation of new protein folds. A particularly interesting case is the class II ketol-acid reductoisomerase (KARI), which putatively arose from an ancestral class I KARI by duplication of the C-terminal domain and corresponding loss of obligate dimerization. As a result, the class II enzymes acquired a deeply embedded figure-of-eight knot. To test this evolutionary hypothesis we constructed a novel class II KARI by duplicating the C-terminal domain of a hyperthermostable class I KARI. The new protein is monomeric, as confirmed by gel filtration and X-ray crystallography, and has the deeply knotted class II KARI fold. Surprisingly, its catalytic activity is nearly unchanged from the parent KARI. This provides strong evidence in support of domain duplication as the mechanism for the evolution of the class II KARI fold and demonstrates the ability of domain duplication to generate topological novelty in a function-neutral manner.

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.

Knotted proteins: A tangled tale of Structural Biology

Knotted proteins have their native structures arranged in the form of an open knot. In the last ten years researchers have been making significant efforts to reveal their folding mechanism and understand which functional advantage(s) knots convey to their carriers. Molecular simulations have been playing a fundamental role in this endeavor, and early computational predictions about the knotting mechanism have just been confirmed in wet lab experiments. Here we review a collection of simulation results that allow outlining the current status of the field of knotted proteins, and discuss directions for future research.

Transmission electron microscopy enables the reconstruction of the catenane and ring forms of CS2 hydrolase

Transmission electron microscopic studies on CS2 hydrolase provide direct evidence for the existence of the hexadecameric catenane and octameric ring topologies. Reconstructions of both protein assemblies are in good agreement with crystallographic analyses of the catenane and ring forms of CS2 hydrolase.

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.

Pierced Lasso Bundles are a new class of knot-like motifs

A four-helix bundle is a well-characterized motif often used as a target for designed pharmaceutical therapeutics and nutritional supplements. Recently, we discovered a new structural complexity within this motif created by a disulphide bridge in the long-chain helical bundle cytokine leptin. When oxidized, leptin contains a disulphide bridge creating a covalent-loop through which part of the polypeptide chain is threaded (as seen in knotted proteins). We explored whether other proteins contain a similar intriguing knot-like structure as in leptin and discovered 11 structurally homologous proteins in the PDB. We call this new helical family class the Pierced Lasso Bundle (PLB) and the knot-like threaded structural motif a Pierced Lasso (PL). In the current study, we use structure-based simulation to investigate the threading/folding mechanisms for all the PLBs along with three unthreaded homologs as the covalent loop (or lasso) in leptin is important in folding dynamics and activity. We find that the presence of a small covalent loop leads to a mechanism where structural elements slipknot to thread through the covalent loop. Larger loops use a piercing mechanism where the free terminal plugs through the covalent loop. Remarkably, the position of the loop as well as its size influences the native state dynamics, which can impact receptor binding and biological activity. This previously unrecognized complexity of knot-like proteins within the helical bundle family comprises a completely new class within the knot family, and the hidden complexity we unraveled in the PLBs is expected to be found in other protein structures outside the four-helix bundles. The insights gained here provide critical new elements for future investigation of this emerging class of proteins, where function and the energetic landscape can be controlled by hidden topology, and should be take into account in ab initio predictions of newly identified protein targets.

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.