Methyl transfer by substrate signaling from a knotted protein fold

Discovery of a trefoil knot in the RydC RNA: Challenging previous notions of RNA topology

Knots are very common in polymers, including DNA and protein molecules. Yet, no genuine knot has been identified in natural RNA molecules to date. Upon re-examining experimentally determined RNA 3D structures, we discovered a trefoil knot 31, the most basic non-trivial knot, in the RydC RNA. This knotted RNA is a member of a small family of short bacterial RNAs, whose secondary structure is characterized by an H-type pseudoknot. Molecular dynamics simulations suggest a folding pathway of the RydC RNA that starts with a native twisted loop. Based on sequence analyses and computational RNA 3D structure predictions, we postulate that this trefoil knot is a conserved feature of all RydC-related RNAs. The first discovery of a knot in a natural RNA molecule introduces a novel perspective on RNA 3D structure formation and on fundamental research on the relationship between function and spatial structure of biopolymers.

Tying a true topological protein knot by cyclization

Knotted proteins are fascinating to biophysicists because of their robust ability to fold into intricately defined three-dimensional structures with complex and topologically knotted arrangements. Exploring the biophysical properties of the knotted proteins is of significant interest, as they could offer enhanced chemical, thermal, and mechanostabilities. A true mathematical knot requires a closed path; in contrast, knotted protein structures have open N- and C-termini. To address the question of how a truly knotted protein differs from the naturally occurring counterpart, we enzymatically cyclized a 31 knotted YibK protein from Haemophilus influenza (HiYibK) to investigate the impact of path closure on its structure-function relationship and folding stability. Through the use of a multitude of structural and biophysical tools, including X-ray crystallography, NMR spectroscopy, small angle X-ray scattering, differential scanning calorimetry, and isothermal calorimetry, we showed that the path closure minimally perturbs the native structure and ligand binding of HiYibK. Nevertheless, the cyclization did alter the folding stability and mechanism according to chemical and thermal unfolding analysis. These molecular insights contribute to our fundamental understanding of protein folding and knotting that could have implications in the protein design with higher stabilities.

Conservation of knotted and slipknotted topology in transmembrane transporters

The existence of nontrivial topology is well accepted in globular proteins but not in membrane proteins. Our comprehensive topological analysis of the Protein Data Bank structures reveals 18 families of transmembrane proteins with nontrivial topology, showing that they constitute a significant number of membrane proteins. Moreover, we found that they comprise one of the largest groups of secondary active transporters. We classified them based on their knotted fingerprint into four groups: three slipknotted and one knotted. Unexpectedly, we found that the same protein can possess two distinct slipknot motifs that correspond to its outward- and inward-open conformational state. Based on the analysis of structures and knotted fingerprints, we show that slipknot topology is directly involved in the conformational transition and substrate transfer. Therefore, entanglement can be used to classify proteins and to find their structure-function relationship. Furthermore, based on the topological analysis of the transmembrane protein structures predicted by AlphaFold, we identified new potentially slipknotted protein families.

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.

Nucleolar Essential Protein 1 (Nep1): Elucidation of enzymatic catalysis mechanism by molecular dynamics simulation and quantum mechanics study

The Nep1 protein is essential for the formation of eukaryotic and archaeal small ribosomal subunits, and it catalyzes the site-directed SAM-dependent methylation of pseudouridine (Ψ) during pre-rRNA processing. It possesses a non-trivial topology, namely, a 31 knot in the active site. Here, we address the issue of seemingly unfeasible deprotonation of Ψ in Nep1 active site by a distant aspartate residue (D101 in S. cerevisiae), using a combination of bioinformatics, computational, and experimental methods. We identified a conserved hydroxyl-containing amino acid (S233 in S. cerevisiae, T198 in A. fulgidus) that may act as a proton-transfer mediator. Molecular dynamics simulations, based on the crystal structure of S. cerevisiae, and on a complex generated by molecular docking in A. fulgidus, confirmed that this amino acid can shuttle protons, however, a water molecule in the active site may also serve this role. Quantum-chemical calculations based on density functional theory and the cluster approach showed that the water-mediated pathway is the most favorable for catalysis. Experimental kinetic and mutational studies reinforce the requirement for the aspartate D101, but not S233. These findings provide insight into the catalytic mechanisms underlying proton transfer over extended distances and comprehensively elucidate the mode of action of Nep1.

Stochastic model of translocation of knotted proteins

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

Tied up in knots: Untangling substrate recognition by the SPOUT methyltransferases

The SpoU-TrmD (SPOUT) methyltransferase superfamily was designated when structural similarity was identified between the transfer RNA-modifying enzymes TrmH (SpoU) and TrmD. SPOUT methyltransferases are found in all domains of life and predominantly modify transfer RNA or ribosomal RNA substrates, though one instance of an enzyme with a protein substrate has been reported. Modifications placed by SPOUT methyltransferases play diverse roles in regulating cellular processes such as ensuring translational fidelity, altering RNA stability, and conferring bacterial resistance to antibiotics. This large collection of S-adenosyl-L-methionine-dependent methyltransferases is defined by a unique α/β fold with a deep trefoil knot in their catalytic (SPOUT) domain. Herein, we describe current knowledge of SPOUT enzyme structure, domain architecture, and key elements of catalytic function, including S-adenosyl-L-methionine co-substrate binding, beginning with a new sequence alignment that divides the SPOUT methyltransferase superfamily into four major clades. Finally, a major focus of this review will be on our growing understanding of how these diverse enzymes accomplish the molecular feat of specific substrate recognition and modification, as highlighted by recent advances in our knowledge of protein-RNA complex structures and the discovery of the dependence of one SPOUT methyltransferase on metal ion binding for catalysis. Considering the broad biological roles of RNA modifications, developing a deeper understanding of the process of substrate recognition by the SPOUT enzymes will be critical for defining many facets of fundamental RNA biology with implications for human disease.

tRNA methylation resolves codon usage bias at the limit of cell viability

Codon usage of each genome is closely correlated with the abundance of tRNA isoacceptors. How codon usage bias is resolved by tRNA post-transcriptional modifications is largely unknown. Here we demonstrate that the N¹-methylation of guanosine at position 37 (m¹G37) on the 3′-side of the anticodon, while not directly responsible for reading of codons, is a neutralizer that resolves differential decoding of proline codons. A genome-wide suppressor screen of a non-viable Escherichia coli strain, lacking m¹G37, identifies proS suppressor mutations, indicating a coupling of methylation with tRNA prolyl-aminoacylation that sets the limit of cell viability. Using these suppressors, where prolyl-aminoacylation is decoupled from tRNA methylation, we show that m¹G37 neutralizes differential translation of proline codons by the major isoacceptor. Lack of m¹G37 inactivates this neutralization and exposes the need for a minor isoacceptor for cell viability. This work has medical implications for bacterial species that exclusively use the major isoacceptor for survival.

Masuda et al. show that loss of m¹G37 from the 3′ side of the tRNA anticodon renders a modified wobble nucleotide of the anticodon insufficient to decode a set of rare codons, providing a functional underpinning for the “modification circuit” between position 37 and the wobble position of the tRNA anticodon.

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

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

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

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

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

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

Evolutionary repair reveals an unexpected role of the tRNA modification m1G37 in aminoacylation

The tRNA modification m¹G37, introduced by the tRNA methyltransferase TrmD, is thought to be essential for growth in bacteria because it suppresses translational frameshift errors at proline codons. However, because bacteria can tolerate high levels of mistranslation, it is unclear why loss of m¹G37 is not tolerated. Here, we addressed this question through experimental evolution of trmD mutant strains of Escherichia coli. Surprisingly, trmD mutant strains were viable even if the m¹G37 modification was completely abolished, and showed rapid recovery of growth rate, mainly via duplication or mutation of the proline-tRNA ligase gene proS. Growth assays and in vitro aminoacylation assays showed that G37-unmodified tRNA^Pro is aminoacylated less efficiently than m¹G37-modified tRNA^Pro, and that growth of trmD mutant strains can be largely restored by single mutations in proS that restore aminoacylation of G37-unmodified tRNA^Pro. These results show that inefficient aminoacylation of tRNA^Pro is the main reason for growth defects observed in trmD mutant strains and that proS may act as a gatekeeper of translational accuracy, preventing the use of error-prone unmodified tRNA^Pro in translation. Our work shows the utility of experimental evolution for uncovering the hidden functions of essential genes and has implications for the development of antibiotics targeting TrmD.

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.

Theoretical Study of O-CH3 Bond Dissociation Enthalpy in Anisole Systems

Understanding ubiquitous methyl transfer reactions requires a systematic study of thermodynamical parameters that could reveal valuable information about the nature of the chemical bond and the feasibility of those processes. In the present study, the O-CH₃ bond dissociation enthalpies (BDEs) of 67 compounds belonging to phenol/anisole systems were calculated employing the Gaussian-4 (G4) method. Those compounds contain different substituents including alkyl groups, electron-donating groups (EDGs), and electron-withdrawing groups (EWGs). The results show that the bigger branched alkyl groups and EDGs will destabilize the O-CH₃ bond, while EWGs have the opposite effect. A combination of different effects including steric effects, hydrogen bonds, and substituents and their position can achieve around 20 kcal/mol difference compared to the basic phenyl frame. Also, the linear correlation between σ_p ⁺ and O-CH₃ BDE can provide a reference for the O-CH₃ BDE prediction. The present study represents a step forward to establish a comprehensive O-CH₃ BDE database to understand the substituent effect and make its contribution to the rational design of inhibitors and drugs.

Loss of N1-methylation of G37 in tRNA induces ribosome stalling and reprograms gene expression

N¹-methylation of G37 is required for a subset of tRNAs to maintain the translational reading-frame. While loss of m¹G37 increases ribosomal +1 frameshifting, whether it incurs additional translational defects is unknown. Here, we address this question by applying ribosome profiling to gain a genome-wide view of the effects of m¹G37 deficiency on protein synthesis. Using E coli as a model, we show that m¹G37 deficiency induces ribosome stalling at codons that are normally translated by m¹G37-containing tRNAs. Stalling occurs during decoding of affected codons at the ribosomal A site, indicating a distinct mechanism than that of +1 frameshifting, which occurs after the affected codons leave the A site. Enzyme- and cell-based assays show that m¹G37 deficiency reduces tRNA aminoacylation and in some cases peptide-bond formation. We observe changes of gene expression in m¹G37 deficiency similar to those in the stringent response that is typically induced by deficiency of amino acids. This work demonstrates a previously unrecognized function of m¹G37 that emphasizes its role throughout the entire elongation cycle of protein synthesis, providing new insight into its essentiality for bacterial growth and survival.

DNA Knot Malleability in Single-Digit Nanopores

Knots in long DNA molecules are prevalent in biological systems and serve as a model system for investigating static and dynamic properties of biopolymers. We explore the dynamics of knots in double-stranded DNA in a new regime of nanometer-scale confinement, large forces, and short time scales, using solid-state nanopores. We show that DNA knots undergo isomorphic translocation through a nanopore, retaining their equilibrium morphology by swiftly compressing in a lateral direction to fit the constriction. We observe no evidence of knot tightening or jamming, even for single-digit nanopores. We explain the observations as the malleability of DNA, characterized by sharp buckling of the DNA in nanopores, driven by the transient disruption of base pairing. Our molecular dynamics simulations support the model. These results are relevant not only for the understanding of DNA packing and manipulation in living cells but also for the polymer physics of DNA and the development of nanopore-based sequencing technologies.

f -distance of knotoids and protein structure

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

Fragment-based discovery of a new class of inhibitors targeting mycobacterial tRNA modification

Translational frameshift errors are often deleterious to the synthesis of functional proteins and could therefore be promoted therapeutically to kill bacteria. TrmD (tRNA-(N(1)G37) methyltransferase) is an essential tRNA modification enzyme in bacteria that prevents +1 errors in the reading frame during protein translation and represents an attractive potential target for the development of new antibiotics. Here, we describe the application of a structure-guided fragment-based drug discovery approach to the design of a new class of inhibitors against TrmD in Mycobacterium abscessus. Fragment library screening, followed by structure-guided chemical elaboration of hits, led to the rapid development of drug-like molecules with potent in vitro TrmD inhibitory activity. Several of these compounds exhibit activity against planktonic M. abscessus and M. tuberculosis as well as against intracellular M. abscessus and M. leprae, indicating their potential as the basis for a novel class of broad-spectrum mycobacterial drugs.

Mg2+-Dependent Methyl Transfer by a Knotted Protein: A Molecular Dynamics Simulation and Quantum Mechanics Study

Mg²⁺ is required for the catalytic activity of TrmD, a bacteria-specific methyltransferase that is made up of a protein topological knot-fold, to synthesize methylated m¹G37-tRNA to support life. However, neither the location of Mg²⁺ in the structure of TrmD nor its role in the catalytic mechanism is known. Using molecular dynamics (MD) simulations, we identify a plausible Mg²⁺ binding pocket within the active site of the enzyme, wherein the ion is coordinated by two aspartates and a glutamate. In this position, Mg²⁺ additionally interacts with the carboxylate of a methyl donor cofactor S-adenosylmethionine (SAM). The computational results are validated by experimental mutation studies, which demonstrate the importance of the Mg²⁺-binding residues for the catalytic activity. The presence of Mg²⁺ in the binding pocket induces SAM to adopt a unique bent shape required for the methyl transfer activity and causes a structural reorganization of the active site. Quantum mechanical calculations show that the methyl transfer is energetically feasible only when Mg²⁺ is bound in the position revealed by the MD simulations, demonstrating that its function is to align the active site residues within the topological knot-fold in a geometry optimal for catalysis. The obtained insights provide the opportunity for developing a strategy of antibacterial drug discovery based on targeting of Mg²⁺-binding to TrmD.

A Supersymmetry and Quantum Cryptosystem with Path Integral Approach in Biology

The source of cancerous mutations and the relationship to telomeres is explained in an alternative way. We define the smallest subunit in the genetic code as a loop braid group element. The loop braid group is suitable to be defined as a configuration space in the process of converting the information written in the DNA into the structure of a folded protein. This smallest subunit, or a flying ring in our definition, is a representation of 8-spinor field in the supermanifold of the genetic code. The image of spectral analysis from the tensor correlation of mutation genes as our biological system is produced. We apply the loop braid group for biology and authentication in quantum cryptography to understand the cell cocycle and division mechanism of telomerase aging. A quantum biological cryptosystem is used to detect cancer signatures in 36 genotypes of the bone ALX1 cancer gene. The loop braid group with the RSA algorithm is applied for the calculation of public and private keys as cancer signatures in genes. The key role of this approach is the use of the Chern–Simons current and then the fiber bundle representation of the genetic code that allows a quantization procedure.

tRNA methylation: An unexpected link to bacterial resistance and persistence to antibiotics and beyond

A major threat to public health is the resistance and persistence of Gram-negative bacteria to multiple drugs during antibiotic treatment. The resistance is due to the ability of these bacteria to block antibiotics from permeating into and accumulating inside the cell, while the persistence is due to the ability of these bacteria to enter into a nonreplicating state that shuts down major metabolic pathways but remains active in drug efflux. Resistance and persistence are permitted by the unique cell envelope structure of Gram-negative bacteria, which consists of both an outer and an inner membrane (OM and IM, respectively) that lay above and below the cell wall. Unexpectedly, recent work reveals that m¹ G37 methylation of tRNA, at the N¹ of guanosine at position 37 on the 3'-side of the tRNA anticodon, controls biosynthesis of both membranes and determines the integrity of cell envelope structure, thus providing a novel link to the development of bacterial resistance and persistence to antibiotics. The impact of m¹ G37-tRNA methylation on Gram-negative bacteria can reach further, by determining the ability of these bacteria to exit from the persistence state when the antibiotic treatment is removed. These conceptual advances raise the possibility that successful targeting of m¹ G37-tRNA methylation can provide new approaches for treating acute and chronic infections caused by Gram-negative bacteria. This article is categorized under: Translation > Translation Regulation RNA Processing > RNA Editing and Modification RNA Structure and Dynamics > Influence of RNA Structure in Biological Systems.

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

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

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

Unraveling Allostery in a Knotted Minimal Methyltransferase by NMR Spectroscopy

The methyltransferases that belong to the SpoU-TrmD family contain trefoil knots in their backbone fold. Recent structural dynamic and binding analyses of both free and bound homologs indicate that the knot within the polypeptide backbone plays a significant role in the biological activity of the molecule. The knot loops form the S-adenosyl-methionine (SAM)-binding pocket as well as participate in SAM binding and catalysis. Knots contain both at once a stable core as well as moving parts that modulate long-range motions. Here, we sought to understand allosteric effects modulated by the knotted topology. Uncovering the residues that contribute to these changes and the functional aspects of these protein motions are essential to understanding the interplay between the knot, activation of the methyltransferase, and the implications in RNA interactions. The question we sought to address is as follows: How does the knot, which constricts the backbone as well as forms the SAM-binding pocket with its three distinctive loops, affect the binding mechanism? Using a minimally tied trefoil protein as the framework for understanding the structure-function roles, we offer an unprecedented view of the conformational mechanics of the knot and its relationship to the activation of the ligand molecule. Focusing on the biophysical characterization of the knot region by NMR spectroscopy, we identify the SAM-binding region and observe changes in the dynamics of the loops that form the knot. Importantly, we also observe long-range allosteric changes in flanking helices consistent with winding/unwinding in helical propensity as the knot tightens to secure the SAM cofactor.

Identifying knot types of polymer conformations by machine learning

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

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

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

How to Untie a Protein Knot

The origin of protein backbone threading through a topological knot remains elusive. To understand the evolutionary origin of protein knots, in this issue of StructureKo et al. (2019) used circular permutation to untie a knotted protein. They showed that a domain-swapped dimer releases the knot and the associated high-energy state for substrate binding.

Protein knots provide mechano-resilience to an AAA+ protease-mediated proteolysis with profound ATP energy expenses

Knotted proteins are some of the most fascinating examples of how linear polypeptide chains can achieve intricate topological arrangements efficiently and spontaneously. The entanglements of polypeptide chains could potentially enhance their folding stabilities. We recently reported the unprecedented mechanostability of the Gordian (5₂) knotted family of human ubiquitin C-terminal hydrolases (UCHs) in the context of withstanding the mechanical unfolding of the bacterial AAA+ proteasome, ClpXP; a green fluorescence protein (GFP) was fused to the N-terminus of various UCHs as a reporter of the unfolding and degradation of these topologically knotted substrates, but it also limited the ability to examine the effect of untying the knotted topology via N-terminal truncation. In this study, we directly monitored the ClpXP-mediated degradation of UCH variants by electrophoresis and quantitative imaging analyses. We demonstrated that untying of the 5₂ knot in UCHL1 via N-terminal truncation (UCHL1_Δ11) significantly reduces its mechanostability. We further quantified the ATP expenditures of degrading different UCH variants by ClpXP. The unknotted UCHL1_Δ11 underwent accelerated ClpXP-dependent proteolysis, with a 30-fold reduction in ATP consumption compared to the knotted wild type. Unlike all other known ClpXP substrates, UCHL5, which is the most resilient substrate known to date, significantly slowed down the ATP turnover rate by ClpXP. Furthermore, UCHL5 required 1000-fold more ATP to be fully degraded by ClpXP compared to GFP. Our results underscored how the complex, knotted folding topology in UCHs may interfere with the mechano-unfolding processes of the AAA+ unfoldase, ClpX.

Crystal structure and catalytic mechanism of the essential m1G37 tRNA methyltransferase TrmD from Pseudomonas aeruginosa

The tRNA (m¹G37) methyltransferase TrmD catalyzes m¹G formation at position 37 in many tRNA isoacceptors and is essential in most bacteria, which positions it as a target for antibiotic development. In spite of its crucial role, little is known about TrmD in Pseudomonas aeruginosa (PaTrmD), an important human pathogen. Here we present detailed structural, substrate, and kinetic properties of PaTrmD. The mass spectrometric analysis confirmed the G36G37-containing tRNAs Leu(GAG), Leu(CAG), Leu(UAG), Pro(GGG), Pro(UGG), Pro(CGG), and His(GUG) as PaTrmD substrates. Analysis of steady-state kinetics with S-adenosyl-l-methionine (SAM) and tRNA^Leu(GAG) showed that PaTrmD catalyzes the two-substrate reaction by way of a ternary complex, while isothermal titration calorimetry revealed that SAM and tRNA^Leu(GAG) bind to PaTrmD independently, each with a dissociation constant of 14 ± 3 µM. Inhibition by the SAM analog sinefungin was competitive with respect to SAM (K_i = 0.41 ± 0.07 µM) and uncompetitive for tRNA (K_i = 6.4 ± 0.8 µM). A set of crystal structures of the homodimeric PaTrmD protein bound to SAM and sinefungin provide the molecular basis for enzyme competitive inhibition and identify the location of the bound divalent ion. These results provide insights into PaTrmD as a potential target for the development of antibiotics.

Complex DNA knots detected with a nanopore sensor

Equilibrium knots are common in biological polymers-their prevalence, size distribution, structure, and dynamics have been extensively studied, with implications to fundamental biological processes and DNA sequencing technologies. Nanopore microscopy is a high-throughput single-molecule technique capable of detecting the shape of biopolymers, including DNA knots. Here we demonstrate nanopore sensors that map the equilibrium structure of DNA knots, without spurious knot tightening and sliding. We show the occurrence of both tight and loose knots, reconciling previous contradictory results from different experimental techniques. We evidence the occurrence of two quantitatively different modes of knot translocation through the nanopores, involving very different tension forces. With large statistics, we explore the complex knots and, for the first time, reveal the existence of rare composite knots. We use parametrized complexity, in concert with simulations, to test the theoretical assumptions of the models, further asserting the relevance of nanopores in future investigation of knots.

Defining and detecting links in chromosomes

Sophisticated methods for mapping chromatin contacts enable to generate data of the genome structure that provide deep insights into the formation of chromatin interactions within cell nuclei. Due to the recent progress in this field, three-dimensional genomic structures of individual haploid mouse embryonic stem cells have been determined. Here, we analyze these data (8 cells) and determine comprehensive landscape of entanglements between interphase chromosomes. We find a significant number of stable links formed by chromosome pairs. Some links are even conserved between cells. Moreover, examples of stable multiple links, with at least three chromosomes engaged, are also identified. Types of links and their location along chromosomes are determined based on computations of HOMFLY-PT polynomials and Gauss Linking Numbers. Furthermore, stability of links is studied between different models, cells, and based on relaxation simulations of the genomic structure in a simplified structure-based representation. Identified links suggest that small fraction of chromosomes are entangled not only locally. How topoisomerases engineer such configurations remains an open question. Furthermore, presented methods can be used as a quantitative assessment - descriptor - to distinguish the quality of modeled data.

Selective terminal methylation of a tRNA wobble base

Active tRNAs are extensively post-transcriptionally modified, particularly at the wobble position 34 and the position 37 on the 3′-side of the anticodon. The 5-carboxy-methoxy modification of U34 (cmo⁵U34) is present in Gram-negative tRNAs for six amino acids (Ala, Ser, Pro, Thr, Leu and Val), four of which (Ala, Ser, Pro and Thr) have a terminal methyl group to form 5-methoxy-carbonyl-methoxy-uridine (mcmo⁵U34) for higher reading-frame accuracy. The molecular basis for the selective terminal methylation is not understood. Many cmo⁵U34-tRNAs are essential for growth and cannot be substituted for mutational analysis. We show here that, with a novel genetic approach, we have created and isolated mutants of Escherichia coli tRNA^Pro and tRNA^Val for analysis of the selective terminal methylation. We show that substitution of G35 in the anticodon of tRNA^Pro inactivates the terminal methylation, whereas introduction of G35 to tRNA^Val confers it, indicating that G35 is a major determinant for the selectivity. We also show that, in tRNA^Pro, the terminal methylation at U34 is dependent on the primary m¹G methylation at position 37 but not vice versa, indicating a hierarchical ranking of modifications between positions 34 and 37. We suggest that this hierarchy provides a mechanism to ensure top performance of a tRNA inside of cells.

Searching the Optimal Folding Routes of a Complex Lasso Protein

Understanding how polypeptides can efficiently and reproducibly attain a self-entangled conformation is a compelling biophysical challenge that might shed new light on our general knowledge of protein folding. Complex lassos, namely self-entangled protein structures characterized by a covalent loop sealed by a cysteine bridge, represent an ideal test system in the framework of entangled folding. Indeed, because cysteine bridges form in oxidizing conditions, they can be used as on/off switches of the structure topology to investigate the role played by the backbone entanglement in the process. In this work, we have used molecular dynamics to simulate the folding of a complex lasso glycoprotein, granulocyte-macrophage colony-stimulating factor, modeling both reducing and oxidizing conditions. Together with a well-established Gō-like description, we have employed the elastic folder model, a coarse-grained, minimalistic representation of the polypeptide chain driven by a structure-based angular potential. The purpose of this study is to assess the kinetically optimal pathways in relation to the formation of the native topology. To this end, we have implemented an evolutionary strategy that tunes the elastic folder model potentials to maximize the folding probability within the early stages of the dynamics. The resulting protein model is capable of folding with high success rate, avoiding the kinetic traps that hamper the efficient folding in the other tested models. Employing specifically designed topological descriptors, we could observe that the selected folding routes avoid the topological bottleneck by locking the cysteine bridge after the topology is formed. These results provide valuable insights on the selection of mechanisms in self-entangled protein folding while, at the same time, the proposed methodology can complement the usage of established minimalistic models and draw useful guidelines for more detailed simulations.

tRNA Methylation Is a Global Determinant of Bacterial Multi-drug Resistance

Gram-negative bacteria are intrinsically resistant to drugs because of their double-membrane envelope structure that acts as a permeability barrier and as an anchor for efflux pumps. Antibiotics are blocked and expelled from cells and cannot reach high-enough intracellular concentrations to exert a therapeutic effect. Efforts to target one membrane protein at a time have been ineffective. Here, we show that m¹G37-tRNA methylation determines the synthesis of a multitude of membrane proteins via its control of translation at proline codons near the start of open reading frames. Decreases in m¹G37 levels in Escherichia coli and Salmonella impair membrane structure and sensitize these bacteria to multiple classes of antibiotics, rendering them incapable of developing resistance or persistence. Codon engineering of membrane-associated genes reduces their translational dependence on m¹G37 and confers resistance. These findings highlight the potential of tRNA methylation in codon-specific translation to control the development of multi-drug resistance in Gram-negative bacteria.

Codon-Specific Translation by m1G37 Methylation of tRNA

Although the genetic code is degenerate, synonymous codons for the same amino acid are not translated equally. Codon-specific translation is important for controlling gene expression and determining the proteome of a cell. At the molecular level, codon-specific translation is regulated by post-transcriptional epigenetic modifications of tRNA primarily at the wobble position 34 and at position 37 on the 3'-side of the anticodon. Modifications at these positions determine the quality of codon-anticodon pairing and the speed of translation on the ribosome. Different modifications operate in distinct mechanisms of codon-specific translation, generating a diversity of regulation that is previously unanticipated. Here we summarize recent work that demonstrates codon-specific translation mediated by the m1G37 methylation of tRNA at CCC and CCU codons for proline, an amino acid that has unique features in translation.

KnotProt 2.0: a database of proteins with knots and other entangled structures

The KnotProt 2.0 database (the updated version of the KnotProt database) collects information about proteins which form knots and other entangled structures. New features in KnotProt 2.0 include the characterization of both probabilistic and deterministic entanglements which can be formed by disulfide bonds and interactions via ions, a refined characterization of entanglement in terms of knotoids, the identification of the so-called cysteine knots, the possibility to analyze all or a non-redundant set of proteins, and various technical updates. The KnotProt 2.0 database classifies all entangled proteins, represents their complexity in the form of a knotting fingerprint, and presents many biological and geometrical statistics based on these results. Currently the database contains >2000 entangled structures, and it regularly self-updates based on proteins deposited in the Protein Data Bank (PDB).

A Family Divided: Distinct Structural and Mechanistic Features of the SpoU-TrmD (SPOUT) Methyltransferase Superfamily

The SPOUT family of enzymes makes up the second largest of seven structurally distinct groups of methyltransferases and is named after two evolutionarily related RNA methyltransferases, SpoU and TrmD. A deep trefoil knotted domain in the tertiary structures of member enzymes defines the SPOUT family. For many years, formation of a homodimeric quaternary structure was thought to be a strict requirement for all SPOUT enzymes, critical for substrate binding and formation of the active site. However, recent structural characterization of two SPOUT members, Trm10 and Sfm1, revealed that they function as monomers without the requirement of this critical dimerization. This unusual monomeric form implies that these enzymes must exhibit a nontraditional substrate binding mode and active site architecture and may represent a new division in the SPOUT family with distinct properties removed from the dimeric enzymes. Here we discuss the mechanistic features of SPOUT enzymes with an emphasis on the monomeric members and implications of this "novel" monomeric structure on cofactor and substrate binding.

Proteins' Knotty Problems

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

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

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

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

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