Protein stabilization in a highly knotted protein polymer

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.

Elucidating the Role of Optical Activity of Polymers in Protein-Polymer Interactions

Proteins are biomolecules with potential applications in agriculture, food sciences, pharmaceutics, biotechnology, and drug delivery. Interactions of hydrophilic and biocompatible polymers with proteins may impart proteolytic stability, improving the therapeutic effects of biomolecules and also acting as excipients for the prolonged storage of proteins under harsh conditions. The interactions of hydrophilic and stealth polymers such as poly(ethylene glycol), poly(trehalose), and zwitterionic polymers with various proteins are well studied. This study evaluates the molecular interactions of hydrophilic and optically active poly(vitamin B5 analogous methacrylamide) (poly(B5AMA)) with model proteins by fluorescence spectroscopy, nuclear magnetic resonance (NMR) spectroscopy, and circular dichroism (CD) spectroscopy analysis. The optically active hydrophilic polymers prepared using chiral monomers of R-(+)- and S-(-)-B5AMA by the photo-iniferter reversible addition fragmentation chain transfer (RAFT) polymerization showed concentration-dependent weak interactions of the polymers with bovine serum albumin and lysozyme proteins. Poly(B5AMA) also exhibited a concentration-dependent protein stabilizing effect at elevated temperatures, and no effect of the stereoisomers of polymers on protein thermal stability was observed. NMR analysis, however, showed poly(B5AMA) stereoisomer-dependent changes in the secondary structure of proteins.

Folding and functions of knotted proteins

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

Computational analysis of the effect of Gly100Ala mutation on the thermostability of SazCA

Maintaining the protein stability upon mutation is a challenging task in protein engineering. In the present computational study, we induced a single point Gly100Ala mutation in SazCA and examined the factors governing the stability and flexibility of the mutated form, and compared it to that of the wildtype using molecular dynamics simulations. We observed higher structural stability and lesser residual mobility in the mutated SazCA. Improved H-bonding due to Gly100Ala was observed. Ala100 was responsible for the increased helical contents in the mutated SazCA while Gly100 compromised the secondary structure contents in the wildtype. A strong network of salt bridges and high local ordering of the solvent molecules at the protein surface contributed to the enhanced stability of the mutated protein. Our simulations conclusively highlight Gly100Ala mutation as a step towards designing a more robust and thermostable SazCA.Communicated by Ramaswamy H. Sarma.

Knotting Optimization and Folding Pathways of a Go-Model with a Deep Knot

Formation of protein knots is an intriguing offshoot of the protein folding problem. Since experimental resolution on knot formation is limited, theoretical methods currently provide the most detailed insights into the knotting process. While suitable for shallow knots, molecular dynamics simulations have faced challenges capturing the formation of deep knots in proteins such as the minimally tied trefoil α/β methyltransferase from Thermotoga maritima (MTTTM). To improve the efficiency of MTTTM knotting in Cα Go-model simulations, mutant variants of the MTTTM Go-model were investigated. Through a structure-based analysis of knotted and unknotted states, four residues (K71, R72, E75, V76) were identified to increase the knotting efficiency from 2% to 83% when their contact energies were doubled and dihedral strength around the knot loop increased. The key features of this model are (i) a C-terminal slipknot intermediate that threads the knot in a highly unstructured intermediate, (ii) the inability to knot in native-like intermediate states, and (iii) a minor population in a long-lived trap that cannot knot. Examination of residue 71-76 contacts provides a small set of potential mutants that can directly test the model's validity. In addition, the knotting optimization process developed here has broad applicability in generating knotting-efficient models of other knotted proteins.

Mechano-bioconjugation Strategy Empowering Fusion Protein Therapeutics with Aggregation Resistance, Prolonged Circulation, and Enhanced Antitumor Efficacy

Bioconjugation is a powerful protein modification strategy to improve protein properties. Herein, we report mechano-bioconjugation as a novel approach to empower fusion protein therapeutics and demonstrate its utility by a protein heterocatenane (cat-IFN-ABD) containing interferon-α2b (IFN) mechanically interlocked with a consensus albumin-binding domain (ABD). The conjugate was selectively synthesized in cellulo following a cascade of post-translational events using a pair of heterodimerizing p53dim variants and two orthogonal split-intein reactions. The catenane topology was proven by combined techniques of LC-MS, SDS-PAGE, SEC, and controlled proteolytic digestion. Not only did cat-IFN-ABD retain activities comparable to those of the wild-type IFN and ABD, the conjugate also exhibited enhanced aggregation resistance and prolonged circulation time over the simple linear and cyclic fusions. Consequently, cat-IFN-ABD potently inhibited tumor growth in the mouse xenograft model. Therefore, mechano-bioconjugation by catenation accomplishes function integration with additional benefits, providing an alternative pathway for developing advanced protein therapeutics.

Topological Twists in Nature

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

Mechanically tightening, untying and retying a protein trefoil knot by single-molecule force spectroscopy

Knotted conformation is one of the most surprising topological features found in proteins, and understanding the folding mechanism of such knotted proteins remains a challenge. Here, we used optical tweezers (OT) to investigate the mechanical unfolding and folding behavior of a knotted protein Escherichia coli tRNA (guanosine-1) methyltransferase (TrmD). We found that when stretched from its N- and C-termini, TrmD can be mechanically unfolded and stretched into a tightened trefoil knot, which is composed of ca. 17 residues. Stretching of the unfolded TrmD involved a compaction process of the trefoil knot at low forces. The unfolding pathways of the TrmD were bifurcated, involving two-state and three-state pathways. Upon relaxation, the tightened trefoil knot loosened up first, leading to the expansion of the knot, and the unfolded TrmD can then fold back to its native state efficiently. By using an engineered truncation TrmD variant, we stretched TrmD along a pulling direction to allow us to mechanically unfold TrmD and untie the trefoil knot. We found that the folding of TrmD from its unfolded polypeptide without the knot is significantly slower. The knotting is the rate-limiting step of the folding of TrmD. Our results highlighted the critical importance of the knot conformation for the folding and stability of TrmD, offering a new perspective to understand the role of the trefoil knot in the biological function of TrmD.

Optical tweezers are used to stretch a knotted protein along different directions to probe its unfolding–folding behaviors, and the conformational change of its knot structure.

Lasso Proteins: Modular Design, Cellular Synthesis, and Topological Transformation

Entangled proteins have attracted significant research interest. Herein, we report the first rationally designed lasso proteins, or protein [1]rotaxanes, by using a p53dim-entwined dimer for intramolecular entanglement and a SpyTag-SpyCatcher reaction for side-chain ring closure. The lasso structures were confirmed by proteolytic digestion, mutation, NMR spectrometry, and controlled ligation. Their dynamic properties were probed by experiments such as end-capping, proteolytic digestion, and heating/cooling. As a versatile topological intermediate, a lasso protein could be converted to a rotaxane, a heterocatenane, and a "slide-ring" network. Being entirely genetically encoded, this robust and modular lasso-protein motif is a valuable addition to the topological protein repertoire and a promising candidate for protein-based biomaterials.

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.

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.

Atomic insights into the genesis of cellular filaments by globular proteins

Self-assembly of proteins into filaments, such as actin and tubulin filaments, underlies essential cellular processes in all three domains of life. The early emergence of filaments in evolutionary history suggests that filament genesis might be a robust process. Here we describe the fortuitous construction of GFP fusion proteins that self-assemble as fluorescent polar filaments in Escherichia coli. Filament formation is achieved by appending as few as 12 residues. Crystal structures reveal that the protomers each donate an appendage to fill a groove between two following protomers along the filament. This exchange of appendages resembles runaway domain swapping but is distinguished by higher efficiency because monomers cannot competitively bind their own appendages. Ample evidence of this “runaway domain coupling” mechanism in nature suggests it could facilitate the evolutionary pathway from globular protein to polar filament, requiring a minimal extension of protein sequence and no significant refolding.

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

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

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

To Tie or Not to Tie? That Is the Question

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

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.

Geometric Principles for Designing Highly Symmetric Self-Assembling Protein Nanomaterials

Emerging protein design strategies are enabling the creation of diverse, self-assembling supramolecular structures with precision on the atomic scale. The design possibilities include various types of architectures: finite cages or shells, essentially unbounded two-dimensional and three-dimensional arrays (i.e., crystals), and linear or tubular filaments. In nature, structures of those types are generally symmetric, and, accordingly, symmetry provides a powerful guide for developing new design approaches. Recent design studies have produced numerous protein assemblies in close agreement with geometric specifications. For certain design approaches, a complete list of allowable symmetry combinations that can be used for construction has been articulated, opening a path to a rich diversity of geometrically defined protein materials. Future challenges include improving and elaborating on current strategies and endowing designed protein nanomaterials with properties useful in nanomedicine and material science applications.

Protein knotting through concatenation significantly reduces folding stability

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

Thermal Unthreading of the Lasso Peptides Astexin-2 and Astexin-3

Lasso peptides are a class of knot-like polypeptides in which the C-terminal tail of the peptide threads through a ring formed by an isopeptide bond between the N-terminal amine group and a side chain carboxylic acid. The small size (∼20 amino acids) and simple topology of lasso peptides make them a good model system for studying the unthreading of entangled polypeptides, both with experiments and atomistic simulation. Here, we present an in-depth study of the thermal unthreading behavior of two lasso peptides astexin-2 and astexin-3. Quantitative kinetics and energetics of the unthreading process were determined for variants of these peptides using a series of chromatography and mass spectrometry experiments and biased molecular dynamics (MD) simulations. In addition, we show that the Tyr15Phe variant of astexin-3 unthreads via an unprecedented "tail pulling" mechanism. MD simulations on a model ring-thread system coupled with machine learning approaches also led to the discovery of physicochemical descriptors most important for peptide unthreading.

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.

Folding analysis of the most complex Stevedore's protein knot

DehI is a homodimeric haloacid dehalogenase from Pseudomonas putida that contains the most complex 61 Stevedore's protein knot within its folding topology. To examine how DehI attains such an intricate knotted topology we combined far-UV circular dichroism (CD), intrinsic fluorescence spectroscopy and small angle X-ray scattering (SAXS) to investigate its folding mechanism. Equilibrium unfolding of DehI by chemical denaturation indicated the presence of two highly populated folding intermediates, I and I'. While the two intermediates vary in secondary structure contents and tertiary packing according to CD and intrinsic fluorescence, respectively, their overall dimension and compactness are similar according to SAXS. Three single-tryptophan variants (W34, W53, and W196) were generated to probe non-cooperative unfolding events localized around the three fluorophores. Kinetic fluorescence measurements indicated that the transition from the intermediate I' to the unfolded state is rate limiting. Our multiparametric folding analyses suggest that DehI unfolds through a linear folding pathway with two distinct folding intermediates by initial hydrophobic collapse followed by nucleation condensation, and that knotting precedes the formation of secondary structures.

Engineering de novo disulfide bond in bacterial α-type carbonic anhydrase for thermostable carbon sequestration

Exploiting carbonic anhydrase (CA), an enzyme that rapidly catalyzes carbon dioxide hydration, is an attractive biomimetic route for carbon sequestration due to its environmental compatibility and potential economic viability. However, the industrial applications of CA are strongly hampered by the unstable nature of enzymes. In this work, we introduced in silico designed, de novo disulfide bond in a bacterial α-type CA to enhance thermostability. Three variants were selected and expressed in Escherichia coli with an additional disulfide bridge. One of the variants showed great enhancement in terms of both kinetic and thermodynamic stabilities. This improvement could be attributed to the loss of conformational entropy of the unfolded state, showing increased rigidity. The variant showed an upward-shifted optimal temperature and appeared to be thermoactivated, which compensated for the lowered activity at 25 °C. Collectively, the variant constructed by the rapid and effective de novo disulfide engineering can be used as an efficient biocatalyst for carbon sequestration under high temperature conditions.

Designing the structure and folding pathway of modular topological bionanostructures

Polypeptides and polynucleotides are programmable natural polymers whose linear sequence can be easily designed and synthesized by the cellular transcription/translation machinery. Nature primarily uses proteins as the molecular machines and nucleic acids as the medium for the manipulation of heritable information. A protein's tertiary structure and function is defined by multiple cooperative weak long-range interactions that have been optimized through evolution. DNA nanotechnology uses orthogonal pairwise interacting modules of complementary nucleic acids as a strategy to construct defined complex 3D structures. A similar approach has recently been applied to protein design, using orthogonal dimerizing coiled-coil segments as interacting modules. When concatenated into a single polypeptide chain, they self-assemble into the 3D structure defined by the topology of interacting modules within the chain. This approach allows the construction of geometric polypeptide scaffolds, bypassing the folding problem of compact proteins by relying on decoupled pairwise interactions. However, the folding pathway still needs to be optimized in order to allow rapid self-assembly under physiological conditions. Again the modularity of designed topological structures can be used to define the rules that guide the folding pathway of long polymers, such as DNA, based on the stability and topology of connected building modules. This approach opens the way towards incorporation of designed foldamers in biological systems and their functionalization.

Design principles for rapid folding of knotted DNA nanostructures

Knots are some of the most remarkable topological features in nature. Self-assembly of knotted polymers without breaking or forming covalent bonds is challenging, as the chain needs to be threaded through previously formed loops in an exactly defined order. Here we describe principles to guide the folding of highly knotted single-chain DNA nanostructures as demonstrated on a nano-sized square pyramid. Folding of knots is encoded by the arrangement of modules of different stability based on derived topological and kinetic rules. Among DNA designs composed of the same modules and encoding the same topology, only the one with the folding pathway designed according to the ‘free-end' rule folds efficiently into the target structure. Besides high folding yield on slow annealing, this design also folds rapidly on temperature quenching and dilution from chemical denaturant. This strategy could be used to design folding of other knotted programmable polymers such as RNA or proteins.

Driven by complementary base pairing, artificial single-chain DNA is capable of forming complex 3D architectures if an appropriate folding pathway can be realised. Here, the authors describe the design principles for rapidly folding structures, exemplified through fabrication of a nanosized square pyramid.

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.

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.

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.

Effects of knots on protein folding properties

This work explores the impact of knots, knot depth and motif of the threading terminus in protein folding properties (kinetics, thermodynamics and mechanism) via extensive Monte Carlo simulations of lattice models. A knotted backbone has no effect on protein thermodynamic stability but it may affect key aspects of folding kinetics. In this regard, we found clear evidence for a functional advantage of knots: knots enhance kinetic stability because a knotted protein unfolds at a distinctively slower rate than its unknotted counterpart. However, an increase in knot deepness does not necessarily lead to more effective changes in folding properties. In this regard, a terminus with a non-trivial conformation (e.g. hairpin) can have a more dramatic effect in enhancing kinetic stability than knot depth. Nevertheless, our results suggest that the probability of the denatured ensemble to keep knotted is higher for proteins with deeper knots, indicating that knot depth plays a role in determining the topology of the denatured state. Refolding simulations starting from denatured knotted conformations show that not every knot is able to nucleate folding and further indicate that the formation of the knotting loop is a key event in the folding of knotted trefoils. They also show that there are specific native contacts within the knotted core that are crucial to keep a native knotting loop in denatured conformations which otherwise have no detectable structure. The study of the knotting mechanism reveals that the threading of the knotting loop generally occurs towards late folding in conformations that exhibit a significant degree of structural consolidation.

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.

Knot localization in proteins

The backbones of proteins form linear chains. In the case of some proteins, these chains can be characterized as forming linear open knots. The knot type of the full chain reveals only limited information about the entanglement of the chain since, for example, subchains of an unknotted protein can form knots and subchains of a knotted protein can form different types of knots than the entire protein. To understand fully the entanglement within the backbone of a given protein, a complete analysis of the knotting within all of the subchains of that protein is necessary. In the present article, we review efforts to characterize the full knotting complexity within individual proteins and present a matrix that conveys information about various aspects of protein knotting. For a given protein, this matrix identifies the precise localization of knotted regions and shows the knot types formed by all subchains. The pattern in the matrix can be considered as a knotting fingerprint of that protein. We observe that knotting fingerprints of distantly related knotted proteins are strongly conserved during evolution and discuss how some characteristic motifs in the knotting fingerprints are related to the structure of the knotted regions and their possible biological role.

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.

Hysteresis as a Marker for Complex, Overlapping Landscapes in Proteins

Topologically complex proteins fold by multiple routes as a result of hard-to-fold regions of the proteins. Oftentimes these regions are introduced into the protein scaffold for function and increase frustration in the otherwise smooth-funneled landscape. Interestingly, while functional regions add complexity to folding landscapes, they may also contribute to a unique behavior referred to as hysteresis. While hysteresis is predicted to be rare, it is observed in various proteins, including proteins containing a unique peptide cyclization to form a fluorescent chromophore as well as proteins containing a knotted topology in their native fold. Here, hysteresis is demonstrated to be a consequence of the decoupling of unfolding events from the isomerization or hula-twist of a chromophore in one protein and the untying of the knot in a second protein system. The question now is- can hysteresis be a marker for the interplay of landscapes where complex folding and functional regions overlap?

How difficult is it to fold a knotted protein? In silico insights from surface-tethered folding experiments

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

Conservation of complex knotting and slipknotting patterns in proteins

While analyzing all available protein structures for the presence of knots and slipknots, we detected a strict conservation of complex knotting patterns within and between several protein families despite their large sequence divergence. Because protein folding pathways leading to knotted native protein structures are slower and less efficient than those leading to unknotted proteins with similar size and sequence, the strict conservation of the knotting patterns indicates an important physiological role of knots and slipknots in these proteins. Although little is known about the functional role of knots, recent studies have demonstrated a protein-stabilizing ability of knots and slipknots. Some of the conserved knotting patterns occur in proteins forming transmembrane channels where the slipknot loop seems to strap together the transmembrane helices forming the channel.

PyKnot: a PyMOL tool for the discovery and analysis of knots in proteins

SUMMARY

Understanding the differences between knotted and unknotted protein structures may offer insights into how proteins fold. To characterize the type of knot in a protein, we have developed PyKnot, a plugin that works seamlessly within the PyMOL molecular viewer and gives quick results including the knot's invariants, crossing numbers and simplified knot projections and backbones. PyKnot may be useful to researchers interested in classifying knots in macromolecules and provides tools for students of biology and chemistry with which to learn topology and macromolecular visualization.

AVAILABILITY

PyMOL is available at http://www.pymol.org. The PyKnot module and tutorial videos are available at http://youtu.be/p95aif6xqcM.

CONTACT

rhonald.lua@gmail.com.

Rknots: topological analysis of knotted biopolymers with R

MOTIVATION

Rknots is a flexible R package providing tools for the detection and characterization of topological knots in biological polymers. The package is well documented and provides a simple syntax for data import and preprocessing, structure reduction, topological analyses and 2D and 3D visualization. Remarkably, Rknots is not limited to protein knots and allows researchers from interdisciplinary fields to analyze different topological structures and to develop simple yet fully custom pipelines.