Refolding upon force quench and pathways of mechanical and thermal unfolding of ubiquitin

The refolding from stretched initial conformations of ubiquitin (PDB ID: 1ubq) under the quenched force is studied using the C(alpha)-Gō model and the Langevin dynamics. It is shown that the refolding decouples the collapse and folding kinetics. The force-quench refolding-times scale as tau(F) approximately exp(f(q)Deltax(F)/k(B)T), where f(q) is the quench force and Deltax(F) approximately 0.96 nm is the location of the average transition state along the reaction coordinate given by the end-to-end distance. This value is close to Deltax(F) approximately 0.8 nm obtained from the force-clamp experiments. The mechanical and thermal unfolding pathways are studied and compared with the experimental and all-atom simulation results in detail. The sequencing of thermal unfolding was found to be markedly different from the mechanical one. It is found that fixing the N-terminus of ubiquitin changes its mechanical unfolding pathways much more drastically compared to the case when the C-end is anchored. We obtained the distance between the native state and the transition state Deltax(UF) approximately 0.24 nm, which is in reasonable agreement with the experimental data.     

Thermal effects in stretching of Go-like models of titin and secondary structures

The effect of temperature on mechanical unfolding of proteins is studied using a Go-like model with a realistic contact map and Lennard-Jones contact interactions. The behavior of the I27 domain of titin and its serial repeats is contrasted to that of simple secondary structures. In all cases, thermal fluctuations accelerate the unraveling process, decreasing the unfolding force nearly linearly at low temperatures. However, differences in bonding geometry lead to different sensitivity to temperature and different changes in the unfolding pattern. Due to its special native-state geometry, titin is much more thermally and elastically stable than the secondary structures. At low temperatures, serial repeats of titin show a parallel unfolding of all domains to an intermediate state, followed by serial unfolding of the domains. At high temperatures, all domains unfold simultaneously, and the unfolding distance decreases monotonically with the contact order, that is, the sequence distance between the amino acids that form the native contact.     

Configurational entropy modulates the mechanical stability of protein GB1

Configurational entropy plays important roles in defining the thermodynamic stability as well as the folding/unfolding kinetics of proteins. Here we combine single-molecule atomic force microscopy and protein engineering techniques to directly examine the role of configurational entropy in the mechanical unfolding kinetics and mechanical stability of proteins. We used a small protein, GB1, as a model system and constructed four mutants that elongate loop 2 of GB1 by 2, 5, 24 and 46 flexible residues, respectively. These loop elongation mutants fold properly as determined by far-UV circular dichroism spectroscopy, suggesting that loop 2 is well tolerant of loop insertions without affecting GB1′s native structure. Our single-molecule atomic force microscopy results reveal that loop elongation decreases the mechanical stability of GB1 and accelerates the mechanical unfolding kinetics. These results can be explained by the loss of configurational entropy upon closing an unstructured flexible loop using classical polymer theory, highlighting the important role of loop regions in the mechanical unfolding of proteins. This study not only demonstrates a general approach to investigating the structural deformation of the loop regions in mechanical unfolding transition state, but also provides the foundation to use configurational entropy as an effective means to modulate the mechanical stability of proteins, which is of critical importance towards engineering artificial elastomeric proteins with tailored nanomechanical properties.     

Stability of bacteriorhodopsin alpha-helices and loops analyzed by single-molecule force spectroscopy

The combination of high-resolution atomic force microscopy imaging and single-molecule force spectroscopy allows the identification, selection, and mechanical investigation of individual proteins. In a recent paper we had used this technique to unfold and extract single bacteriorhodopsins (BRs) from native purple membrane patches. We show that subsets of the unfolding spectra can be classified and grouped to reveal detailed insight into the individualism of the unfolding pathways. We have further developed this technique and analysis to report here on the influence of pH effects and local mutations on the stability of individual structural elements of BR against mechanical unfolding. We found that, although the seven transmembrane alpha-helices predominantly unfold in pairs, each of the helices may also unfold individually and in some cases even only partially. Additionally, intermittent states in the unfolding process were found, which are associated with the stretching of the extracellular loops connecting the alpha-helices. This suggests that polypeptide loops potentially act as a barrier to unfolding and contribute significantly to the structural stability of BR. Chemical removal of the Schiff base, the covalent linkage of the photoactive retinal to the helix G, resulted in a predominantly two-step unfolding of this helix. It is concluded that the covalent linkage of the retinal to helix G stabilizes the structure of BR. Trapping mutant D96N in the M state of the proton pumping photocycle did not affect the unfolding barriers of BR.     

Complex Stability of Single Proteins Explored by Forced Unfolding Experiments

In the last decade atomic force microscopy has been used to measure the mechanical stability of single proteins. These force spectroscopy experiments have shown that many water-soluble and membrane proteins unfold via one or more intermediates. Recently, Li and co-workers found a linear correlation between the unfolding force of the native state and the intermediate in fibronectin, which they suggested indicated the presence of a molecular memory or multiple unfolding pathways (1). Here, we apply two independent methods in combination with Monte Carlo simulations to analyze the unfolding of α-helices E and D of bacteriorhodopsin (BR). We show that correlation analysis of unfolding forces is very sensitive to errors in force calibration of the instrument. In contrast, a comparison of relative forces provides a robust measure for the stability of unfolding intermediates. The proposed approach detects three energetically different states of α-helices E and D in trimeric BR. These states are not observed for monomeric BR and indicate that substantial information is hidden in forced unfolding experiments of single proteins.     

Mutational analysis of acylphosphatase suggests the importance of topology and contact order in protein folding.

Muscle acylphosphatase (AcP) is a small protein that folds very slowly with two-state behavior. The conformational stability and the rates of folding and unfolding have been determined for a number of mutants of AcP in order to characterize the structure of the folding transition state. The results show that the transition state is an expanded version of the native protein, where most of the native interactions are partially established. The transition state of AcP turns out to be remarkably similar in structure to that of the activation domain of procarboxypeptidase A2 (ADA2h), a protein having the same overall topology but sharing only 13% sequence identity with AcP. This suggests that transition states are conserved between proteins with the same native fold. Comparison of the rates of folding of AcP and four other proteins with the same topology, including ADA2h, supports the concept that the average distance in sequence between interacting residues (that is, the contact order) is an important determinant of the rate of protein folding.     

D/H amide kinetic isotope effects reveal when hydrogen bonds form during protein folding

We have exploited a procedure to identify when hydrogen bonds (H-bonds) form under two-state folding conditions using equilibrium and kinetic deuterium/hydrogen amide isotope effects. Deuteration decreases the stability of equine cytochrome c and the dimeric and crosslinked versions of the GCN4-p1 coiled coil by approximately 0. 5 kcal mol-1. For all three systems, the decrease in equilibrium stability is reflected by a decrease in refolding rates and a near equivalent increase in unfolding rates. This apportionment indicates that approximately 50% of the native H-bonds are formed in the transition state of these helical proteins. In contrast, an alpha/beta protein, mammalian ubiquitin, exhibits a small isotope effect only on unfolding rates, suggesting its folding pathway may be different. These four proteins recapitulate the general trend that approximately 50% of the surface buried in the native state is buried in the transition state, leading to the hypothesis that H-bond formation in the transition state is cooperative, with alpha-helical proteins forming a number of H-bonds proportional to the amount of surface buried in the transition state.     

Observing the osmophobic effect in action at the single molecule level

Protecting osmolytes are widespread small organic molecules able to stabilize the folded state of most proteins against various denaturing stresses in vivo. The osmophobic model explains thermodynamically their action through a preferential exclusion of the osmolyte molecules from the protein surface, thus favoring the formation of intrapeptide hydrogen bonds. Few works addressed the influence of protecting osmolytes on the protein unfolding transition state and kinetics. Among those, previous single molecule force spectroscopy experiments evidenced a complexation of the protecting osmolyte molecules at the unfolding transition state of the protein, in apparent contradiction with the osmophobic nature of the protein backbone. We present single-molecule evidence that glycerol, which is a ubiquitous protecting osmolyte, stabilizes a globular protein against mechanical unfolding without binding into its unfolding transition state structure. We show experimentally that glycerol does not change the position of the unfolding transition state as projected onto the mechanical reaction coordinate. Moreover, we compute theoretically the projection of the unfolding transition state onto two other common reaction coordinates, that is, the number of native peptide bonds and the weighted number of native contacts. To that end, we augment an analytic Ising-like protein model with support for group-transfer free energies. Using this model, we find again that the position of the unfolding transition state does not change in the presence of glycerol, giving further support to the conclusions based on the single-molecule experiments.     

Complex stability of single proteins explored by forced unfolding experiments

In the last decade atomic force microscopy has been used to measure the mechanical stability of single proteins. These force spectroscopy experiments have shown that many water-soluble and membrane proteins unfold via one or more intermediates. Recently, Li and co-workers found a linear correlation between the unfolding force of the native state and the intermediate in fibronectin, which they suggested indicated the presence of a molecular memory or multiple unfolding pathways (1). Here, we apply two independent methods in combination with Monte Carlo simulations to analyze the unfolding of alpha-helices E and D of bacteriorhodopsin (BR). We show that correlation analysis of unfolding forces is very sensitive to errors in force calibration of the instrument. In contrast, a comparison of relative forces provides a robust measure for the stability of unfolding intermediates. The proposed approach detects three energetically different states of alpha-helices E and D in trimeric BR. These states are not observed for monomeric BR and indicate that substantial information is hidden in forced unfolding experiments of single proteins.     

How do chemical denaturants affect the mechanical folding and unfolding of proteins?

We present the first single-molecule atomic force microscopy study on the effect of chemical denaturants on the mechanical folding/unfolding kinetics of a small protein GB1 (the B1 immunoglobulin-binding domain of protein G from Streptococcus). Upon increasing the concentration of the chemical denaturant guanidinium chloride (GdmCl), we observed a systematic decrease in the mechanical stability of GB1, indicating the softening effect of the chemical denaturant on the mechanical stability of proteins. This mechanical softening effect originates from the reduced free-energy barrier between the folded state and the unfolding transition state, which decreases linearly as a function of the denaturant concentration. Chemical denaturants, however, do not alter the mechanical unfolding pathway or shift the position of the transition state for mechanical unfolding. We also found that the folding rate constant of GB1 is slowed down by GdmCl in mechanical folding experiments. By combining the mechanical folding/unfolding kinetics of GB1 in GdmCl solution, we developed the “mechanical chevron plot” as a general tool to understand how chemical denaturants influence the mechanical folding/unfolding kinetics and free-energy diagram in a quantitative fashion. This study demonstrates great potential in combining chemical denaturation with single-molecule atomic force microscopy techniques to reveal invaluable information on the energy landscape underlying protein folding/unfolding reactions.     

Mechanical unfolding of a titin Ig domain: structure of transition state revealed by combining atomic force microscopy,protein engineering and molecular dynamics simulations

Titin I27 shows a high resistance to unfolding when subject to external force. To investigate the molecular basis of this mechanical stability, protein engineering Phi-value analysis has been combined with atomic force microscopy to investigate the structure of the barrier to forced unfolding. The results indicate that the transition state for forced unfolding is significantly structured, since highly destabilising mutations in the core do not affect the force required to unfold the protein. As has been shown before, mechanical strength lies in the region of the A' and G-strands but, contrary to previous suggestions, the results indicate clearly that side-chain interactions play a significant role in maintaining mechanical stability. Since Phi-values calculated from molecular dynamics simulations are the same as those determined experimentally, we can, with confidence, use the molecular dynamics simulations to analyse the structure of the transition state in detail, and are able to show loss of interactions between the A' and G-strands with associated A-B and E-F loops in the transition state. The key event is not a simple case of loss of hydrogen bonding interactions between the A' and G-strands alone. Comparison with Phi-values from traditional folding studies shows differences between the force and "no-force" transition states but, nevertheless, the region important for kinetic stability is the same in both cases. This explains the correspondence between hierarchy of kinetic stability (measured in stopped-flow denaturant studies) and mechanical strength in these titin domains.     

Modulation of contact order effects in the two-state folding of stefins A and B

It is well established that contact order and folding rates are correlated for small proteins. The folding rates of stefins A and B differ by nearly two orders of magnitude despite sharing an identical native fold and hence contact order. We break down the determinants of this behavior and demonstrate that the modulation of contact order effects can be accounted for by the combined contributions of a framework-like mechanism, characterized by intrinsic helix stabilities, together with nonnative helical backbone conformation and nonnative hydrophobic interactions within the folding transition state. These contributions result in the formation of nonnative interactions in the transition state as evidenced by the opposing effects on folding rate and stability of these proteins.     

Worm-like Ising model for protein mechanical unfolding under the effect of osmolytes

We show via single-molecule mechanical unfolding experiments that the osmolyte glycerol stabilizes the native state of the human cardiac I27 titin module against unfolding without shifting its unfolding transition state on the mechanical reaction coordinate. Taken together with similar findings on the immunoglobulin-binding domain of streptococcal protein G (GB1), these experimental results suggest that osmolytes act on proteins through a common mechanism that does not entail a shift of their unfolding transition state. We investigate the above common mechanism via an Ising-like model for protein mechanical unfolding that adds worm-like-chain behavior to a recent generalization of the Wako-Saitô-Muñoz-Eaton model with support for group-transfer free energies. The thermodynamics of the model are exactly solvable, while protein kinetics under mechanical tension can be simulated via Monte Carlo algorithms. Notably, our force-clamp and velocity-clamp simulations exhibit no shift in the position of the unfolding transition state of GB1 and I27 under the effect of various osmolytes. The excellent agreement between experiment and simulation strongly suggests that osmolytes do not assume a structural role at the mechanical unfolding transition state of proteins, acting instead by adjusting the solvent quality for the protein chain analyte.     

On the role of some conserved and nonconserved amino acid residues in the transitional state and intermediate of apomyoglobin folding

The contributions of some amino acid residues in the A, B, G, and H helices to the formation of the folding nucleus and folding intermediate of apomyoglobin were estimated. The effects of point substitutions of Ala for hydrophobic amino acid residues on the structural stability of the native (N) protein and its folding intermediate (I), as well as on the folding/unfolding rates for four mutant apomyoglobin forms, were studied. The equilibrium and kinetic studies of the folding/unfolding rates of these mutant proteins in a wide range of urea concentrations demonstrated that their native state was considerably destabilized as compared with the wild-type protein, whereas the stability of the intermediate state changed moderately. It was shown that the amino acid residues in the A, G, and H helices contributed insignificantly to the stabilization of the apomyoglobin folding nucleus in the rate-limiting I ? N transition, taking place after the formation of the intermediate, whereas the residue of the B helix was of great importance in the formation of the folding nucleus in this transition.     

Single molecule force spectroscopy reveals a weakly populated microstate of the FnIII domains of tenascin

The native states of proteins exist as an ensemble of conformationally similar microstates. The fluctuations among different microstates are of great importance for the functions and structural stability of proteins. Here, we demonstrate that single molecule atomic force microscopy (AFM) can be used to directly probe the existence of multiple folded microstates. We used the AFM to repeatedly stretch and relax a recombinant tenascin fragment TNfnALL to allow the fibronectin type III (FnIII) domains to undergo repeated unfolding/refolding cycles. In addition to the native state, we discovered that some FnIII domains can refold from the unfolded state into a previously unrecognized microstate, N* state. This novel state is conformationally similar to the native state, but mechanically less stable. The native state unfolds at approximately 120 pN, while the N* state unfolds at approximately 50 pN. These two distinct populations of microstates constitute the ensemble of the folded states for some FnIII domains. An unfolded FnIII domain can fold into either one of the two microstates via two distinct folding routes. These results reveal the dynamic and heterogeneous picture of the folded ensemble for some FnIII domains of tenascin, which may carry important implications for the mechanical functions of tenascins in vivo.     

Reversible mechanical unfolding of single ubiquitin molecules

Single-molecule manipulation techniques have enabled the characterization of the unfolding and refolding process of individual protein molecules, using mechanical forces to initiate the unfolding transition. Experimental and computational results following this approach have shed new light on the mechanisms of the mechanical functions of proteins involved in several cellular processes, as well as revealed new information on the protein folding/unfolding free-energy landscapes. To investigate how protein molecules of different folds respond to a stretching force, and to elucidate the effects of solution conditions on the mechanical stability of a protein, we synthesized polymers of the protein ubiquitin and characterized the force-induced unfolding and refolding of individual ubiquitin molecules using an atomic-force-microscope-based single-molecule manipulation technique. The ubiquitin molecule was highly resistant to a stretching force, and the mechanical unfolding process was reversible. A model calculation based on the hydrogen-bonding pattern in the native structure was performed to explain the origin of this high mechanical stability. Furthermore, pH effects were studied and it was found that the forces required to unfold the protein remained constant within a pH range around the neutral value, and forces decreased as the solution pH was lowered to more acidic values.     

Small proteins fold through transition states with native-like topologies

The folding pathway of common-type acyl phosphatase (ctAcP) is characterized using psi-analysis, which identifies specific chain-chain contacts using bi-histidine (biHis) metal-ion binding sites. In the transition state ensemble (TSE), the majority of the protein is structured with a near-native topology, only lacking one beta-strand and an alpha-helix. psi-Values are zero or unity for all sites except one at the amino terminus of helix H2. This fractional psi-value remains unchanged when three metal ions of differing coordination geometries are used, indicating this end of the helix experiences microscopic heterogeneity through fraying in the TSE. Ubiquitin, the other globular protein characterized using psi-analysis, also exhibits a single consensus TSE structure. Hence, the TSE of both proteins have converged to a single configuration, albeit one that contains some fraying at the periphery. Models of the TSE of both proteins are created using all-atom Langevin dynamics simulations using distance constraints derived from the experimental psi-values. For both proteins, the relative contact order of the TS models is approximately 80% of the native value. This shared value viewed in the context of the known correlation between contact order and folding rates, suggests that other proteins will have a similarly high fraction of the native contact order. This constraint greatly limits the range of possible configurations at the rate-limiting step.     

Unfolding a linker between helical repeats

In many multi-repeat proteins, linkers between repeats have little secondary structure and place few constraints on folding or unfolding. However, the large family of spectrin-like proteins, including alpha-actinin, spectrin, and dystrophin, share three-helix bundle, spectrin repeats that appear in crystal structures to be linked by long helices. All of these proteins are regularly subjected to mechanical stress. Recent single molecule atomic force microscopy (AFM) experiments demonstrate not only forced unfolding but also simultaneous unfolding of tandem repeats at finite frequency, which suggests that the contiguous helix between spectrin repeats can propagate a cooperative helix-to-coil transition. Here, we address what happens atomistically to the linker under stress by steered molecular dynamics simulations of tandem spectrin repeats in explicit water. The results for alpha-actinin repeats reveal rate-dependent pathways, with one pathway showing that the linker between repeats unfolds, which may explain the single-repeat unfolding pathway observed in AFM experiments. A second pathway preserves the structural integrity of the linker, which explains the tandem-repeat unfolding event. Unfolding of the linker begins with a splay distortion of proximal loops away from hydrophobic contacts with the linker. This is followed by linker destabilization and unwinding with increased hydration of the backbone. The end result is an unfolded helix that mechanically decouples tandem repeats. Molecularly detailed insights obtained here aid in understanding the mechanical coupling of domain stability in spectrin family proteins.     

Similarity of force-induced unfolding of apomyoglobin to its chemical-induced unfolding: an atomistic molecular dynamics simulation approach

We have compared force-induced unfolding with traditional unfolding methods using apomyoglobin as a model protein. Using molecular dynamics simulation, we have investigated the structural stability as a function of the degree of mechanical perturbation. Both anisotropic perturbation by stretching two terminal atoms and isotropic perturbation by increasing the radius of gyration of the protein show the same key event of force-induced unfolding. Our primary results show that the native structure of apomyoglobin becomes destabilized against the mechanical perturbation as soon as the interhelical packing between the G and H helices is broken, suggesting that our simulation results share a common feature with the experimental observation that the interhelical contact is more important for the folding of apomyoglobin than the stability of individual helices. This finding is further confirmed by simulating both helix destabilizing and interhelical packing destabilizing mutants.     

Sequential Unfolding of Beta Helical Protein by Single-Molecule Atomic Force Microscopy

The parallel βhelix is a common fold among extracellular proteins, however its mechanical properties remain unexplored. In Gram-negative bacteria, extracellular proteins of diverse functions of the large ‘TpsA’ family all fold into long βhelices. Here, single-molecule atomic force microscopy and steered molecular dynamics simulations were combined to investigate the mechanical properties of a prototypic TpsA protein, FHA, the major adhesin of Bordetella pertussis. Strong extension forces were required to fully unfold this highly repetitive protein, and unfolding occurred along a stepwise, hierarchical process. Our analyses showed that the extremities of the βhelix unfold early, while central regions of the helix are more resistant to mechanical unfolding. In particular, a mechanically resistant subdomain conserved among TpsA proteins and critical for secretion was identified. This nucleus harbors structural elements packed against the βhelix that might contribute to stabilizing the N-terminal region of FHA. Hierarchical unfolding of the βhelix in response to a mechanical stress may maintain β-helical portions that can serve as templates for regaining the native structure after stress. The mechanical properties uncovered here might apply to many proteins with β-helical or related folds, both in prokaryotes and in eukaryotes, and play key roles in their structural integrity and functions.