Untying knots in proteins

Topological Reaction Coordinate Captures the Folding Transition State Ensemble in a Pierced Lasso Protein

Proteins with a pierced lasso topology (PLT) have a covalent loop created by a disulfide bond, and the backbone circles back to thread the loop. This threaded topology has unique features compared to knotted topologies; notably, the topology is controlled by the chemical environment and the covalent loop remains intact even when denatured. In this work, we use the hormone leptin as our model PLT system and study its folding using molecular dynamics simulations that employ a structure-based (Go̅-like) model. We find that the reduced protein has a two-state folding mechanism with a transition state ensemble (TSE) that can be characterized by the reaction coordinate Q, the fraction of native contacts formed. In contrast, the oxidized protein, which must thread part of the polypeptide chain through a covalent loop, has a folding process that is poorly characterized by Q. Instead, we find that a topological coordinate that monitors the residue crossing the loop can identify the TSE of oxidized leptin. By precisely identifying the predicted TSE, one may now reliably calculate theoretical phi-values for the PLT protein, thereby enabling a comparison with experimental measurements. We find the loop-threading constraint leads to noncanonical phi-values that are uniformly small because this PLT protein has a flat energy landscape through the TSE.

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.

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.

Theory and Practice of Coarse-Grained Molecular Dynamics of Biologically Important Systems

Molecular dynamics with coarse-grained models is nowadays extensively used to simulate biomolecular systems at large time and size scales, compared to those accessible to all-atom molecular dynamics. In this review article, we describe the physical basis of coarse-grained molecular dynamics, the coarse-grained force fields, the equations of motion and the respective numerical integration algorithms, and selected practical applications of coarse-grained molecular dynamics. We demonstrate that the motion of coarse-grained sites is governed by the potential of mean force and the friction and stochastic forces, resulting from integrating out the secondary degrees of freedom. Consequently, Langevin dynamics is a natural means of describing the motion of a system at the coarse-grained level and the potential of mean force is the physical basis of the coarse-grained force fields. Moreover, the choice of coarse-grained variables and the fact that coarse-grained sites often do not have spherical symmetry implies a non-diagonal inertia tensor. We describe selected coarse-grained models used in molecular dynamics simulations, including the most popular MARTINI model developed by Marrink's group and the UNICORN model of biological macromolecules developed in our laboratory. We conclude by discussing examples of the application of coarse-grained molecular dynamics to study biologically important processes.

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.

Transient knots in intrinsically disordered proteins and neurodegeneration

We provide a brief overview of the topological features found in structured proteins and of the dynamical processes that involve knots. We then discuss the knotted states that arise in the intrinsically disordered polyglutamine and α-synuclein. We argue that the existence of the knotted conformations stalls degradation by proteases and thus enhances aggregation. This mechanism works if the length of a peptide chain exceeds a threshold, as in the Huntington disease. We also study the cavities that form within the conformations of the disordered proteins. The volume of the cavities varies in time in a way that is different than that of the radius of gyration or the end-to-end distance. In addition, we study the traffic between the conformational basins and identify patterns associated with the deep and shallow knots. The results are obtained by molecular dynamics simulations that use coarse-grained and all-atom models (with and without the explicit solvent).

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.

Computational methods in the study of self-entangled proteins: a critical appraisal

The existence of self-entangled proteins, the native structure of which features a complex topology, unveils puzzling, and thus fascinating, aspects of protein biology and evolution. The discovery that a polypeptide chain can encode the capability to self-entangle in an efficient and reproducible way during folding, has raised many questions, regarding the possible function of these knots, their conservation along evolution, and their role in the folding paradigm. Understanding the function and origin of these entanglements would lead to deep implications in protein science, and this has stimulated the scientific community to investigate self-entangled proteins for decades by now. In this endeavour, advanced experimental techniques are more and more supported by computational approaches, that can provide theoretical guidelines for the interpretation of experimental results, and for the effective design of new experiments. In this review we provide an introduction to the computational study of self-entangled proteins, focusing in particular on the methodological developments related to this research field. A comprehensive collection of techniques is gathered, ranging from knot theory algorithms, that allow detection and classification of protein topology, to Monte Carlo or molecular dynamics strategies, that constitute crucial instruments for investigating thermodynamics and kinetics of this class of proteins.

The AAA+ protease ClpXP can easily degrade a 31 and a 52-knotted protein

Knots in proteins are hypothesized to make them resistant to enzymatic degradation by ATP-dependent proteases and recent studies have shown that whereas ClpXP can easily degrade a protein with a shallow 3₁ knot, it cannot degrade 5₂-knotted proteins if degradation is initiated at the C-terminus. Here, we present detailed studies of the degradation of both 3₁- and 5₂-knotted proteins by ClpXP using numerous constructs where proteins are tagged for degradation at both N- and C-termini. Our results confirm and extend earlier work and show that ClpXP can easily degrade a deeply 3₁-knotted protein. In contrast to recently published work on the degradation of 5₂-knotted proteins, our results show that the ClpXP machinery can also easily degrade these proteins. However, the degradation depends critically on the location of the degradation tag and the local stability near the tag. Our results are consistent with mechanisms in which either the knot simply slips along the polypeptide chain and falls off the free terminus, or one in which the tightened knot enters the translocation pore of ClpXP. Results of experiments on knotted protein fusions with a highly stable domain show partial degradation and the formation of degradation intermediates.

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

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

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.

Multiple folding pathways of proteins with shallow knots and co-translational folding

We study the folding process in the shallowly knotted protein MJ0366 within two variants of a structure-based model. We observe that the resulting topological pathways are much richer than identified in previous studies. In addition to the single knot-loop events, we find novel, and dominant, two-loop mechanisms. We demonstrate that folding takes place in a range of temperatures and the conditions of most successful folding are at temperatures which are higher than those required for the fastest folding. We also demonstrate that nascent conditions are more favorable to knotting than off-ribosome folding.

Connecting thermal and mechanical protein (un)folding landscapes

Molecular dynamics simulations supplement single-molecule pulling experiments by providing the possibility of examining the full free energy landscape using many coordinates. Here, we use an all-atom structure-based model to study the force and temperature dependence of the unfolding of the protein filamin by applying force at both termini. The unfolding time-force relation τ(F) indicates that the force-induced unfolding behavior of filamin can be characterized into three regimes: barrier-limited low- and intermediate-force regimes, and a barrierless high-force regime. Slope changes of τ(F) separate the three regimes. We show that the behavior of τ(F) can be understood from a two-dimensional free energy landscape projected onto the extension X and the fraction of native contacts Q. In the low-force regime, the unfolding rate is roughly force-independent due to the small (even negative) separation in X between the native ensemble and transition state ensemble (TSE). In the intermediate-force regime, force sufficiently separates the TSE from the native ensemble such that τ(F) roughly follows an exponential relation. This regime is typically explored by pulling experiments. While X may fail to resolve the TSE due to overlap with the unfolded ensemble just below the folding temperature, the overlap is minimal at lower temperatures where experiments are likely to be conducted. The TSE becomes increasingly structured with force, whereas the average order of structural events during unfolding remains roughly unchanged. The high-force regime is characterized by barrierless unfolding, and the unfolding time approaches a limit of ∼10 μs for the highest forces we studied. Finally, a combination of X and Q is shown to be a good reaction coordinate for almost the entire force range.

Prediction of the optimal set of contacts to fold the smallest knotted protein

Knotted protein chains represent a new motif in protein folds. They have been linked to various diseases, and recent extensive analysis of the Protein Data Bank shows that they constitute 1.5% of all deposited protein structures. Despite thorough theoretical and experimental investigations, the role of knots in proteins still remains elusive. Nonetheless, it is believed that knots play an important role in mechanical and thermal stability of proteins. Here, we perform a comprehensive analysis of native, shadow-specific and non-native interactions which describe free energy landscape of the smallest knotted protein (PDB id 2efv). We show that the addition of shadow-specific contacts in the loop region greatly enhances folding kinetics, while the addition of shadow-specific contacts along the C-terminal region (H3 or H4) results in a new folding route with slower kinetics. By means of direct coupling analysis (DCA) we predict non-native contacts which also can accelerate kinetics. Next, we show that the length of the C-terminal knot tail is responsible for the shape of the free energy barrier, while the influence of the elongation of the N-terminus is not significant. Finally, we develop a concept of a minimal contact map sufficient for 2efv protein to fold and analyze properties of this protein using this map.

Cotranslational folding of deeply knotted proteins

Proper folding of deeply knotted proteins has a very low success rate even in structure-based models which favor formation of the native contacts but have no topological bias. By employing a structure-based model, we demonstrate that cotranslational folding on a model ribosome may enhance the odds to form trefoil knots for protein YibK without any need to introduce any non-native contacts. The ribosome is represented by a repulsive wall that keeps elongating the protein. On-ribosome folding proceeds through a a slipknot conformation. We elucidate the mechanics and energetics of its formation. We show that the knotting probability in on-ribosome folding is a function of temperature and that there is an optimal temperature for the process. Our model often leads to the establishment of the native contacts without formation of the knot.

Molecular knots in biology and chemistry

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

Engineering covalent loops in proteins can serve as an on/off switch to regulate threaded topologies

Knots in proteins are under active investigation motivating refinements of current techniques and the development of tools to better understand the knotted topology. A strong focus is to identify new knots and expand upon the current understanding of their complex topology. Previous work has shown that the knotted topology, even in the simplest case of knots, encompasses a variety of unique challenges in folding and tying a chain. To bypass many of the in vitro experimental complications involved in working with knots, it is useful to apply methodologies to a more simplified system. The pierced lasso bundles (PLB), we discovered where a single disulphide bridge holds the threaded topology together, presents a simpler system to study knots in vitro. Having a disulphide bridge as an on/off switch between the threaded/unthreaded topology is advantageous because a covalent loop allows manipulation of the knot without directly altering affecting secondary and tertiary structure. Because disulphide bridges are commonly used in protein engineering, a pierced lasso (PL) topology can be easily introduced into a protein of interest to form a knotted topology within a given secondary structure. It is also important to take into account that if formed, disulphides can inadvertently introduce an unwanted PL. This was found upon determination of the crystal structure (PDB code 2YHG) of the recently de novo designed nucleoside hydrolase. Our detailed investigations of the PL presented here will allow researchers to look at the introduction of disulphide bridges in a larger context with respect to potential geometrical consequences on the structure and functional properties of proteins.

Heterogeneous side chain conformation highlights a network of interactions implicated in hysteresis of the knotted protein, minimal tied trefoil

Hysteresis is a signature for a bistability in the native landscape of a protein with significant transition state barriers for the interconversion of stable species. Large global stability, as in GFP, contributes to the observation of this rare hysteretic phenomenon in folding. The signature for such behavior is non-coincidence in the unfolding and refolding transitions, despite waiting significantly longer than the time necessary for complete denaturation. Our work indicates that hysteresis in the knotted protein, the minimal tied trefoil from Thermotoga maritma (MTTTm), is mediated by a network of side chain interactions within a tightly packed core. These initially identified interactions include proline 62 from a tight β-like turn, phenylalanine 65 at the beginning of the knotting loop, and histidine 114 that initiates the threading element. It is this tightly packed region and the knotting element that we propose is disrupted with prolonged incubation in the denatured state, and is involved in the observed hysteresis. Interestingly, the disruption is not linked to backbone interactions, but rather to the packing of side chains in this critical region.

KnotProt: a database of proteins with knots and slipknots

The protein topology database KnotProt, http://knotprot.cent.uw.edu.pl/, collects information about protein structures with open polypeptide chains forming knots or slipknots. The knotting complexity of the cataloged proteins is presented in the form of a matrix diagram that shows users the knot type of the entire polypeptide chain and of each of its subchains. The pattern visible in the matrix gives the knotting fingerprint of a given protein and permits users to determine, for example, the minimal length of the knotted regions (knot's core size) or the depth of a knot, i.e. how many amino acids can be removed from either end of the cataloged protein structure before converting it from a knot to a different type of knot. In addition, the database presents extensive information about the biological functions, families and fold types of proteins with non-trivial knotting. As an additional feature, the KnotProt database enables users to submit protein or polymer chains and generate their knotting fingerprints.

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

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

Knotting pathways in proteins

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

Tightening and Untying the Knot in Human Carbonic Anhydrase III

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

Topological features in stretching of proteins

In the present article, we highlight the diversity of mechanical clamps, some of them topological in nature, that have been found by making surveys of mechanostability of approximately 18000 proteins within structure-based models. The existence of superstable proteins (with the characteristic unfolding force in the region of 1000 pN) is predicted.

Single-molecule detection reveals knot sliding in TrmD denaturation

An increasing number of proteins are found to contain a knot in their polypeptide chain. Although some studies have looked into the folding mechanism of knotted proteins, why and how these complex topologies form are still far from being fully answered. Moreover, no experimental information about how the knot moves during the protein-folding process is available. Herein, by combining single-molecule fluorescence resonance energy transfer (smFRET) experiments with molecular dynamics (MD) simulations, we performed a detailed study to characterize the knot in the denatured state of TrmD, a knotted tRNA (guanosine-1) methyltransferase from Escherichia coli, as a model system. We found that the knot still existed in the unfolded state of TrmD, consistent with the results for two other knotted proteins, YibK and YbeA. More interestingly, both smFRET experiments and MD simulations revealed that the knot slid towards the C-terminal during the unfolding process, which could be explained by the relatively strong interactions between the β-sheet core at the N terminal of the native knot region. The size of the knot in the unfolded state is not larger than that in the native state. In addition, the knot slid in a "downhill" mode with simultaneous chain collapse in the denatured state.

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.

Mechanically untying a protein slipknot: multiple pathways revealed by force spectroscopy and steered molecular dynamics simulations

Protein structure is highly diverse when considering a wide range of protein types, helping to give rise to the multitude of functions that proteins perform. In particular, certain proteins are known to adopt a knotted or slipknotted fold. How such proteins undergo mechanical unfolding was investigated utilizing a combination of single molecule atomic force microscopy (AFM), protein engineering, and steered molecular dynamics (SMD) simulations to show the mechanical unfolding mechanism of the slipknotted protein AFV3-109. Our results reveal that the mechanical unfolding of AFV3-109 can proceed via multiple parallel unfolding pathways that all cause the protein slipknot to untie and the polypeptide chain to completely extend. These distinct unfolding pathways proceed via either a two- or three-state unfolding process involving the formation of a well-defined, stable intermediate state. SMD simulations predict the same contour length increments for different unfolding pathways as single molecule AFM results, thus providing a plausible molecular mechanism for the mechanical unfolding of AFV3-109. These SMD simulations also reveal that two-state unfolding is initiated from both the N- and C-termini, while three-state unfolding is initiated only from the C-terminus. In both pathways, the protein slipknot was untied during unfolding, and no tightened slipknot conformation was observed. Detailed analysis revealed that interactions between key structural elements lock the knotting loop in place, preventing it from shrinking and the formation of a tightened slipknot conformation. Our results demonstrate the bifurcation of the mechanical unfolding pathway of AFV3-109 and point to the generality of a kinetic partitioning mechanism for protein folding/unfolding.

Engineering proteins with enhanced mechanical stability by force-specific sequence motifs

Use of atomic force microscopy (AFM) has recently led to a better understanding of the molecular mechanisms of the unfolding process by mechanical forces; however, the rational design of novel proteins with specific mechanical strength remains challenging. We have approached this problem from a new perspective that generates linear physical-chemical properties (PCP) motifs from a limited AFM data set. Guided by our linear sequence analysis, we designed and analyzed four new mutants of the titin I1 domain with the goal of increasing the domain's mechanical strength. All four mutants could be cloned and expressed as soluble proteins. AFM data indicate that at least two of the mutants have increased molecular mechanical strength. This observation suggests that the PCP method is useful to graft sequences specific for high mechanical stability to weak proteins to increase their mechanical stability, and represents an additional tool in the design of novel proteins besides steered molecular dynamics calculations, coarse grained simulations, and ϕ-value analysis of the transition state.

Knot formation in newly translated proteins is spontaneous and accelerated by chaperonins

Topological knots are found in a considerable number of protein structures, but it is not clear how they knot and fold within the cellular environment. We investigated the behavior of knotted protein molecules as they are first synthesized by the ribosome using a cell-free translation system. We found that newly translated knotted proteins can spontaneously self-tie and do not require the assistance of molecular chaperones to fold correctly to their trefoil-knotted structures. This process is slow but efficient, and we found no evidence of misfolded species. A kinetic analysis indicates that the knotting process is rate limiting, occurs post-translationally, and is specifically and significantly (P < 0.001) accelerated by the GroEL-GroES chaperonin complex. This demonstrates a new active mechanism for this molecular chaperone and suggests that chaperonin-catalyzed knotting probably dominates in vivo. These results explain how knotted protein structures have withstood evolutionary pressures despite their topological complexity.