The energy cost of polypeptide knot formation and its folding consequences

Knot or not? Identifying unknotted proteins in knotted families with sequence-based Machine Learning model

Knotted proteins, although scarce, are crucial structural components of certain protein families, and their roles continue to be a topic of intense research. Capitalizing on the vast collection of protein structure predictions offered by AlphaFold (AF), this study computationally examines the entire UniProt database to create a robust dataset of knotted and unknotted proteins. Utilizing this dataset, we develop a machine learning (ML) model capable of accurately predicting the presence of knots in protein structures solely from their amino acid sequences. We tested the model's capabilities on 100 proteins whose structures had not yet been predicted by AF and found agreement with our local prediction in 92% cases. From the point of view of structural biology, we found that all potentially knotted proteins predicted by AF can be classified only into 17 families. This allows us to discover the presence of unknotted proteins in families with a highly conserved knot. We found only three new protein families: UCH, DUF4253, and DUF2254, that contain both knotted and unknotted proteins, and demonstrate that deletions within the knot core could potentially account for the observed unknotted (trivial) topology. Finally, we have shown that in the majority of knotted families (11 out of 15), the knotted topology is strictly conserved in functional proteins with very low sequence similarity. We have conclusively demonstrated that proteins AF predicts as unknotted are structurally accurate in their unknotted configurations. However, these proteins often represent nonfunctional fragments, lacking significant portions of the knot core (amino acid sequence).

A new method to experimentally quantify dynamics of initial protein-protein interactions

Cells run on initiation of protein-protein interactions, which are dynamically tuned spatially and temporally to modulate cellular events. This tuning can be physical, such as attaching the protein to a cargo or protein complex, thereby altering its diffusive properties, or modulating the distance between protein pairs, or chemical, by altering the proteins' conformations (e.g., nucleotide binding state of an enzyme, post-translational modification of a protein, etc.). Because a dynamic and changing subset of proteins in the cell could be in any specific state, ensemble measurements are not ideal-to untangle which of the factors are important, and how, we need single-molecule measurements. Experimentally, until now we have not had good tools to precisely measure initiation of such protein-protein interactions at the single-molecule level. Here, we develop a new method to measure dynamics of initial protein-protein interactions, allowing measurement of how properties such as the distance between proteins, and their tethered length can modulate the rate of interactions. In addition to precise measurement distance dependent motor-MT rebinding dynamics, we demonstrate the use of a dithered optical trap to measure dynamic motor-MT interactions and further discuss the possibilities of this technique being applicable to other systems.

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.

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.

Pincus blob elasticity in an intrinsically disordered protein

Understanding the dynamic structure of intrinsically disordered proteins (IDPs) is important to deciphering their biological functions. Here, we exploit precision entropic elasticity measurements to infer the conformational behavior of a model IDP construct formed from the disordered tail of the neurofilament low molecular weight protein. The IDP construct notably displays a low-force power-law elastic regime, consistent with the Pincus blob model, which allows direct extraction of the Flory exponent, [Formula: see text], from the force-extension relationship. We find [Formula: see text] increases with added denaturant, transitioning from a nearly ideal chain to a swollen chain in a manner quantitatively consistent with measurements of IDP dimensions from other experimental techniques. We suggest that measurements of entropic elasticity could be broadly useful in the study of IDP structure.

Ligand-switchable nanoparticles resembling viral surface for sequential drug delivery and improved oral insulin therapy

Mutual interference between surface ligands on multifunctional nanoparticles remains a significant obstacle to achieving optimal drug-delivery efficacy. Here, we develop ligand-switchable nanoparticles which resemble viral unique surfaces, enabling them to fully display diverse functions. The nanoparticles are modified with a pH-responsive stretchable cell-penetrating peptide (Pep) and a liver-targeting moiety (Gal) (Pep/Gal-PNPs). Once orally administered, the acidic environments trigger the extension of Pep from surface in a virus-like manner, enabling Pep/Gal-PNPs to traverse intestinal barriers efficiently. Subsequently, Gal is exposed by Pep folding at physiological pH, thereby allowing the specific targeting of Pep/Gal-PNPs to the liver. As a proof-of-concept, insulin-loaded Pep/Gal-PNPs are fabricated which exhibit effective intestinal absorption and excellent hepatic deposition of insulin. Crucially, Pep/Gal-PNPs increase hepatic glycogen production by 7.2-fold, contributing to the maintenance of glucose homeostasis for effective diabetes management. Overall, this study provides a promising approach to achieving full potential of diverse ligands on multifunctional nanoparticles.

Knotting matters: orderly molecular entanglements

Entangling strands in a well-ordered manner can produce useful effects, from shoelaces and fishing nets to brown paper packages tied up with strings. At the nanoscale, non-crystalline polymer chains of sufficient length and flexibility randomly form tangled mixtures containing open knots of different sizes, shapes and complexity. However, discrete molecular knots of precise topology can also be obtained by controlling the number, sequence and stereochemistry of strand crossings: orderly molecular entanglements. During the last decade, substantial progress in the nascent field of molecular nanotopology has been made, with general synthetic strategies and new knotting motifs introduced, along with insights into the properties and functions of ordered tangle sequences. Conformational restrictions imparted by knotting can induce allostery, strong and selective anion binding, catalytic activity, lead to effective chiral expression across length scales, binding modes in conformations efficacious for drug delivery, and facilitate mechanical function at the molecular level. As complex molecular topologies become increasingly synthetically accessible they have the potential to play a significant role in molecular and materials design strategies. We highlight particular examples of molecular knots to illustrate why these are a few of our favourite things.

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.

Determination of protein-protein interactions at the single-molecule level using optical tweezers

Biomolecular interactions are at the base of all physical processes within living organisms; the study of these interactions has led to the development of a plethora of different methods. Among these, single-molecule (in singulo) experiments have become relevant in recent years because these studies can give insight into mechanisms and interactions that are hidden for ensemble-based (in multiplo) methods. The focus of this review is on optical tweezer (OT) experiments, which can be used to apply and measure mechanical forces in molecular systems. OTs are based on optical trapping, where a laser is used to exert a force on a dielectric bead; and optically trap the bead at a controllable position in all three dimensions. Different experimental approaches have been developed to study protein–protein interactions using OTs, such as: (1) refolding and unfolding in trans interaction where one protein is tethered between the beads and the other protein is in the solution; (2) constant force in cis interaction where each protein is bound to a bead, and the tension is suddenly increased. The interaction may break after some time, giving information about the lifetime of the binding at that tension. And (3) force ramp in cis interaction where each protein is attached to a bead and a ramp force is applied until the interaction breaks. With these experiments, parameters such as kinetic constants (k_off, k_on), affinity values (K_D), energy to the transition state ΔG^≠, distance to the transition state Δx^≠ can be obtained. These parameters characterize the energy landscape of the interaction. Some parameters such as distance to the transition state can only be obtained from force spectroscopy experiments such as those described here.

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.

Single-molecule optical tweezers reveals folding steps of the domain swapping mechanism of a protein

Domain swapping is a mechanism of protein oligomerization by which two or more subunits exchange structural elements to generate an intertwined complex. Numerous studies support a diversity of swapping mechanisms in which structural elements can be exchanged at different stages of the folding pathway of a subunit. Here, we used single-molecule optical tweezers technique to analyze the swapping mechanism of the forkhead DNA-binding domain of human transcription factor FoxP1. FoxP1 populates folded monomers in equilibrium with a swapped dimer. We generated a fusion protein linking two FoxP1 domains in tandem to obtain repetitive mechanical folding and unfolding trajectories. Thus, by stretching the same molecule several times, we detected either the independent folding of each domain or the elusive swapping step between domains. We found that a swapped dimer can be formed directly from fully or mostly folded monomer. In this situation, the interaction between the monomers in route to the domain-swapped dimer is the rate-limiting step. This approach is a useful strategy to test the different proposed domain swapping mechanisms for proteins with relevant physiological functions.

Metal-Peptide Nonafoil Knots and Decafoil Supercoils

Despite the frequent occurrence of knotted frameworks in protein structures, the latent potential of peptide strands to form entangled structures is rarely discussed in peptide chemistry. Here we report the construction of highly entangled molecular topologies from Ag(I) ions and tripeptide ligands. The efficient entanglement of metal-peptide strands and the wide scope for design of the amino acid side chains in these ligands enabled the construction of metal-peptide 9₁ torus knots and 10₁² torus links. Moreover, steric control of the peptide side chain induced ring opening and twisting of the torus framework, which resulted in an infinite toroidal supercoil nanostructure.

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

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

A Specific Set of Heterogeneous Native Interactions Yields Efficient Knotting in Protein Folding

Native interactions are crucial for folding, and non-native interactions appear to be critical for efficiently knotting proteins. Therefore, it is important to understand both their roles in the folding of knotted proteins. It has been proposed that non-native interactions drive the correct order of contact formation, which is essential to avoid backtracking and efficiently self-tie. In this study, we ask if non-native interactions are strictly necessary to tangle a protein or if the correct order of contact formation can be assured by a specific set of native, but otherwise heterogeneous (i.e., having distinct energies), interactions. In order to address this problem, we conducted extensive Monte Carlo simulations of lattice models of protein-like sequences designed to fold into a preselected knotted conformation embedding a trefoil knot. We were able to identify a specific set of heterogeneous native interactions that drives efficient knotting and is able to fold the protein when combined with the remaining native interactions modeled as homogeneous. This specific set of heterogeneous native interactions is strictly enough to efficiently self-tie. A distinctive feature of these native interactions is that they do not backtrack because their energies ensure the correct order of contact formation. Furthermore, they stabilize a knotted intermediate state, which is en route to the native structure. Our results thus show that-at least in the context of the adopted model-non-native interactions are not necessary to knot a protein. However, when they are taken into account in protein energetics, it is possible to find specific, nonlocal non-native interactions that operate as a scaffold that assists the knotting step.

Circuit Topology Analysis of Polymer Folding Reactions

Circuit topology is emerging as a versatile measure to classify the internal structures of folded linear polymers such as proteins and nucleic acids. The topology framework can be applied to a wide range of problems, most notably molecular folding reactions that are central to biology and molecular engineering. In this Outlook, we discuss the state-of-the art of the technology and elaborate on the opportunities and challenges that lie ahead.

Mechanical unfolding of a knotted protein unveils the kinetic and thermodynamic consequences of threading a polypeptide chain

Knots are remarkable topological features in nature. The presence of knots in crystallographic structures of proteins have stimulated considerable research to determine the kinetic and thermodynamic consequences of threading a polypeptide chain. By mechanically manipulating MJ0366, a small single domain protein harboring a shallow trefoil knot, we allow the protein to refold from either the knotted or the unknotted denatured state to characterize the free energy profile associated to both folding pathways. By comparing the stability of the native state with reference to the knotted and unknotted denatured state we find that knotting the polypeptide chain of MJ0366 increase the folding energy barrier in a magnitude close to the energy cost of forming a knot randomly in the denatured state. These results support that a protein knot can be formed during a single cooperative step of folding but occurs at the expenses of a large increment on the free energy barrier.

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.

Hydrophobic confinement modulates thermal stability and assists knotting in the folding of tangled proteins

There is growing support for the idea that the in vivo folding process of knotted proteins is assisted by chaperonins, but the mechanism of chaperonin assisted folding remains elusive. Here, we conduct extensive Monte Carlo simulations of lattice and off-lattice models to explore the effects of confinement and hydrophobic intermolecular interactions with the chaperonin cage in the folding and knotting processes. We find that moderate to high protein-cavity interactions (which are likely to be established in the beginning of the chaperonin working cycle) cause an energetic destabilization of the protein that overcomes the entropic stabilization driven by excluded volume, and leads to a decrease of the melting temperature relative to bulk conditions. Moreover, mild-to-moderate hydrophobic interactions with the cavity (which would be established later in the cycle) lead to a significant enhancement of knotting probability in relation to bulk conditions while simultaneously moderating the effect of steric confinement in the enhancement of thermal stability. Our results thus indicate that the chaperonin may be able to assist knotting without simultaneously thermally stabilizing potential misfolded states to a point that would hamper productive folding thus compromising its functional role.

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.