Untangling the Influence of a Protein Knot on Folding

A Marcus-Type Inverted Region in the Translocation Kinetics of a Knotted Protein

Knotted proteins are rare but important species, yet how their complex topologies affect their physical properties is not fully understood. Here we combine single molecule nanopore experiments and all-atom MD simulations to study the electric-field-driven unfolding during the translocation through a model pore of individual protein knots important for methylating tRNA. One of these knots shows an unusual behavior that resembles the behavior of electrons hopping between two potential surfaces: as the electric potential driving the translocation reaction is increased, the rate eventually plateaus or slows back down in the "Marcus inverted regime". Our results shed light on the influence of topology in knotted proteins on their forced translocation through a pore connecting two electrostatic potential wells.

Hysteresis behavior in the unfolding/refolding processes of a protein trapped in metallo-cages

Confinement of molecules in a synthetic host can physically isolate even their unstable temporary structures, which has potential for application to protein transient structure analysis. Here we report the NMR snapshot observation of protein unfolding and refolding processes by confining a target protein in a self-assembled coordination cage. With increasing acetonitrile content in CD₃CN/H₂O media (50 to 90 vol%), the folding structure of a protein sharply denatured at 83 vol%, clearly revealing the regions of initial unfolding. Unfavorable aggregation of the protein leading to irreversible precipitation is completely prevented because of the spatial isolation of the single protein molecule in the cage. When the acetonitrile content reversed (84 to 70 vol%), the once-denatured protein started to regain its original folded structure at 80 vol%, showing that the protein folding/unfolding process can be referred to as a phase transition with hysteresis behavior.

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

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

Transcription factors and chaperone proteins play a role in launching a faster response to heat stress and aggregation

Proteins, under conditions of cellular stress, typically tend to unfold and form lethal aggregates leading to neurological diseases like Parkinson's and Alzheimer's. A clear understanding of the conditions that favor dis-aggregation and restore the cell to its healthy state after they have been stressed is therefore important in dealing with these diseases. The heat shock response (HSR) mechanism is a signaling network that deals with these undue protein aggregates and aids in the maintenance of homeostasis within a cell. This framework, on its own, is a mathematically well studied mechanism. However, not much is known about how the various intermediate mis-folded protein states of the aggregation process interact with some of the key components of the HSR pathway such as the Heat Shock Protein (HSP), the Heat Shock Transcription Factor (HSF) and the HSP-HSF complex. In this article, using kinetic parameters from the literature, we propose and analyze two mathematical models for HSR that also include explicit reactions for the formation of protein aggregates. Deterministic analysis and stochastic simulations of these models show that the folded proteins and the misfolded aggregates exhibit bistability in a certain region of the parameter space. Further, the models also highlight the role of HSF and the HSF-HSP complex in reducing the time lag of response to stress and in re-folding all the mis-folded proteins back to their native state. These models, therefore, call attention to the significance of studying related pathways such as the HSR and the protein aggregation and re-folding process in conjunction with each other.

Tying up the Loose Ends: A Mathematically Knotted Protein

Knots have attracted scientists in mathematics, physics, biology, and engineering. Long flexible thin strings easily knot and tangle as experienced in our daily life. Similarly, long polymer chains inevitably tend to get trapped into knots. Little is known about their formation or function in proteins despite >1,000 knotted proteins identified in nature. However, these protein knots are not mathematical knots with their backbone polypeptide chains because of their open termini, and the presence of a “knot” depends on the algorithm used to create path closure. Furthermore, it is generally not possible to control the topology of the unfolded states of proteins, therefore making it challenging to characterize functional and physicochemical properties of knotting in any polymer. Covalently linking the amino and carboxyl termini of the deeply trefoil-knotted YibK from Pseudomonas aeruginosa allowed us to create the truly backbone knotted protein by enzymatic peptide ligation. Moreover, we produced and investigated backbone cyclized YibK without any knotted structure. Thus, we could directly probe the effect of the backbone knot and the decrease in conformational entropy on protein folding. The backbone cyclization did not perturb the native structure and its cofactor binding affinity, but it substantially increased the thermal stability and reduced the aggregation propensity. The enhanced stability of a backbone knotted YibK could be mainly originated from an increased ruggedness of its free energy landscape and the destabilization of the denatured state by backbone cyclization with little contribution from a knot structure. Despite the heterogeneity in the side-chain compositions, the chemically unfolded cyclized YibK exhibited several macroscopic physico-chemical attributes that agree with theoretical predictions derived from polymer physics.

Converging experimental and computational views of the knotting mechanism of a small knotted protein

MJ0366 from Methanocaldococcus jannaschii is the smallest topologically knotted protein known to date. 92 residues in length, MJ0366 ties a trefoil (31) knot by threading its C-terminal helix through a buttonhole formed by the remainder of the secondary structure elements. By generating a library of point mutations at positions pertinent to the knot formation, we systematically evaluated the contributions of individual residues to the folding stability and kinetics of MJ0366. The experimental Φ-values were used as restraints to computationally generate an ensemble of conformations that correspond to the transition state of MJ0366, which revealed several nonnative contacts. The importance of these nonnative contacts in stabilizing the transition state of MJ0366 was confirmed by a second round of mutagenesis, which also established the pivotal role of F15 in stapling the network of hydrophobic interactions around the threading C-terminal helix. Our converging experimental and computational results show that, despite the small size, the transition state of MJ0366 is formed at a very late stage of the folding reaction coordinate, following a polarized pathway. Eventually, the formation of extensive native contacts, as well as a number of nonnative ones, leads to the threading of the C-terminal helix that defines the topological knot.

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.

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

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

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

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

Topological descriptions of protein folding

How knotted proteins fold has remained controversial since the identification of deeply knotted proteins nearly two decades ago. Both computational and experimental approaches have been used to investigate protein knot formation. Motivated by the computer simulations of Bölinger et al. [Bölinger D, et al. (2010) PLoS Comput Biol 6:e1000731] for the folding of the [Formula: see text]-knotted α-haloacid dehalogenase (DehI) protein, we introduce a topological description of knot folding that could describe pathways for the formation of all currently known protein knot types and predicts knot types that might be identified in the future. We analyze fingerprint data from crystal structures of protein knots as evidence that particular protein knots may fold according to specific pathways from our theory. Our results confirm Taylor's twisted hairpin theory of knot folding for the [Formula: see text]-knotted proteins and the [Formula: see text]-knotted ketol-acid reductoisomerases and present alternative folding mechanisms for the [Formula: see text]-knotted phytochromes and the [Formula: see text]- and [Formula: see text]-knotted proteins.

Direct observation of the fast and robust folding of a slipknotted protein by optical tweezers

Understanding the folding mechanism of knotted and slipknotted proteins has attracted considerable interest. Due to their topological complexity, knotted and slipknotted proteins are predicted to fold slowly and involve large topological barriers. Molecular dynamics simulation studies suggest that a slipknotted conformation can serve as an important intermediate to help greatly reduce the topological difficulty during the folding of some knotted proteins. Here we use a single molecule optical tweezers technique to directly probe the folding of a small slipknotted protein AFV3-109. We found that stretching AFV3-109 can lead to the untying of the slipknot and complete unfolding of AFV3-109. Upon relaxation, AFV3-109 can readily refold back to its native slipknot conformation with high fidelity when the stretching force is lower than 6 pN. The refolding of AFV3-109 occurs in a sharp two-state like transition. Our results indicate that, different from knotted proteins, the folding of a slipknotted protein like AFV3-109 can be fast, and may not necessarily involve a high topological barrier.

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.

The energy cost of polypeptide knot formation and its folding consequences

Knots are natural topologies of chains. Yet, little is known about spontaneous knot formation in a polypeptide chain—an event that can potentially impair its folding—and about the effect of a knot on the stability and folding kinetics of a protein. Here we used optical tweezers to show that the free energy cost to form a trefoil knot in the denatured state of a polypeptide chain of 120 residues is 5.8 ± 1 kcal mol⁻¹. Monte Carlo dynamics of random chains predict this value, indicating that the free energy cost of knot formation is of entropic origin. This cost is predicted to remain above 3 kcal mol⁻¹ for denatured proteins as large as 900 residues. Therefore, we conclude that naturally knotted proteins cannot attain their knot randomly in the unfolded state but must pay the cost of knotting through contacts along their folding landscape.

The effect of knots on protein stability and folding kinetics is not well understood. Here the authors combine optical tweezer experiments and calculations to experimentally determine the energy cost for knot formation, which indicates that knotted proteins evolved specific folding pathways because knot formation in unfolded chains is unfavorable.

Backbone assignments for the SPOUT methyltransferase MTT Tm , a knotted protein from Thermotoga maritima

The SPOUT family of methyltransferase proteins is noted for containing a deep trefoil knot in their defining backbone fold. This unique fold is of high interest for furthering the understanding of knots in proteins. Here, we report the 1H, 13C, 15N assignments for MTT Tm , a canonical member of the SPOUT family. This protein is unique, as it is one of the smallest members of the family, making it an ideal system for probing the unique properties of the knot. Our present work represents the foundation for further studies into the topology of MTT Tm , and understanding how its structure affects both its folding and function.

How to fold intricately: using theory and experiments to unravel the properties of knotted proteins

Over the years, advances in experimental and computational methods have helped us to understand the role of thermodynamic, kinetic and active (chaperone-aided) effects in coordinating the folding steps required to achieving a knotted native state. Here, we review such developments by paying particular attention to the complementarity of experimental and computational studies. Key open issues that could be tackled with either or both approaches are finally pointed out.

Folding analysis of the most complex Stevedore's protein knot

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