Force-clamp spectroscopy of single-protein monomers reveals the individual unfolding and folding pathways of I27 and ubiquitin

Single-protein force experiments have relied on a molecular fingerprint based on tethering multiple single-protein domains in a polyprotein chain. However, correlations between these domains remain an issue in interpreting force spectroscopy data, particularly during protein folding. Here we first show that force-clamp spectroscopy is a sensitive technique that provides a molecular fingerprint based on the unfolding step size of four single-monomer proteins. We then measure the force-dependent unfolding rate kinetics of ubiquitin and I27 monomers and find a good agreement with the data obtained for the respective polyproteins over a wide range of forces, in support of the Markovian hypothesis. Moreover, with a large statistical ensemble at a single force, we show that ubiquitin monomers also exhibit a broad distribution of unfolding times as a signature of disorder in the folded protein landscape. Furthermore, we readily capture the folding trajectories of monomers that exhibit the same stages in folding observed for polyproteins, thus eliminating the possibility of entropic masking by other unfolded modules in the chain or domain-domain interactions. On average, the time to reach the I27 folded length increases with increasing quenching force at a rate similar to that of the polyproteins. Force-clamp spectroscopy at the single-monomer level reproduces the kinetics of unfolding and refolding measured using polyproteins, which proves that there is no mechanical effect of tethering proteins to one another in the case of ubiquitin and I27.     

Dwell-time distribution analysis of polyprotein unfolding using force-clamp spectroscopy

Using the recently developed single molecule force-clamp technique we quantitatively measure the kinetics of conformational changes of polyprotein molecules at a constant force. In response to an applied force of 110 pN, we measure the dwell times of 1647 unfolding events of individual ubiquitin modules within each protein chain. We then establish a rigorous method for analyzing force-clamp data using order statistics. This allows us to test the success of a history-independent, two-state model in describing the kinetics of the unfolding process. We find that the average unfolding trajectory is independent of the number of protein modules N in each trajectory, which varies between 3 and 12 (the engineered protein length), suggesting that the unfolding events in each chain are uncorrelated. We then derive a binomial distribution of dwell times to describe the stochastic dynamics of protein unfolding. This distribution successfully describes 81% of the data with a single rate constant of alpha = 0.6 s(-1) for all N. The remainder of the data that cannot be accounted for suggests alternative unfolding barriers in the energy landscape of the protein. This method investigates the statistical features of unfolding beyond the average measurement of a single rate constant, thus providing an attractive alternative for measuring kinetics by force-clamp spectroscopy.     

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.     

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.     

Single-Molecule Studies on PolySUMO Proteins Reveal Their Mechanical Flexibility

Proteins with β-sandwich and β-grasp topologies are resistant to mechanical unfolding as shown by single-molecule force spectroscopy studies. Their high mechanical stability has generally been associated with the mechanical clamp geometry present at the termini. However, there is also evidence for the importance of interactions other than the mechanical clamp in providing mechanical stability, which needs to be tested thoroughly. Here, we report the mechanical unfolding properties of ubiquitin-like proteins (SUMO1 and SUMO2) and their comparison with those of ubiquitin. Although ubiquitin and SUMOs have similar size and structural topology, they differ in their sequences and structural contacts, making them ideal candidates to understand the variations in the mechanical stability of a given protein topology. We observe a two-state unfolding pathway for SUMO1 and SUMO2, similar to that of ubiquitin. Nevertheless, the unfolding forces of SUMO1 (∼130 pN) and SUMO2 (∼120 pN) are lower than that of ubiquitin (∼190 pN) at a pulling speed of 400 nm/s, indicating their lower mechanical stability. The mechanical stabilities of SUMO proteins and ubiquitin are well correlated with the number of interresidue contacts present in their structures. From pulling speed-dependent mechanical unfolding experiments and Monte Carlo simulations, we find that the unfolding potential widths of SUMO1 (∼0.51 nm) and SUMO2 (∼0.33 nm) are much larger than that of ubiquitin (∼0.19 nm), indicating that SUMO1 is six times and SUMO2 is three times mechanically more flexible than ubiquitin. These findings might also be important in understanding the functional differences between ubiquitin and SUMOs.     

Mechanical unfolding pathway and origin of mechanical stability of proteins of ubiquitin family: An investigation by steered molecular dynamics simulation

Like the muscle protein Titin, proteins of the ubiquitin family exhibit a parallel strand arrangement, but otherwise having a distinctly different fold and not involved in an obvious load‐bearing function, exhibit high resistance to mechanical unfolding. We have applied all‐atom molecular dynamics simulation technique in implicit solvent to present a deep insight into the force‐induced unfolding pathway of three proteins—ubiquitin, NEDD8, and SUMO‐2—all having almost similar structural features. Two intermediates evolve in the unfolding pathway of each of the three proteins. The first intermediate, which has already been identified in case of ubiquitin by earlier simulation results, is similar for ubiquitin and NEDD8, but different in SUMO‐2. We have found a new intermediate with β3–β4 hairpin and some residual α‐helical character; and this intermediate is common for all the three proteins. Thus, proteins of the ubiquitin family pass through a well‐defined conformation in their force‐induced unfolding pathway. Reason behind the higher mechanical stability of the proteins with parallel strand structures like Titin has also been identified. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Direct Quantification of the Attempt Frequency Determining the Mechanical Unfolding of Ubiquitin Protein

Understanding protein dynamics requires a comprehensive knowledge of the underlying potential energy surface that governs the motion of each individual protein molecule. Single molecule mechanical studies have provided the unprecedented opportunity to study the individual unfolding pathways along a well defined coordinate, the end-to-end length of the protein. In these experiments, unfolding requires surmounting an energy barrier that separates the native from the extended state. The calculation of the absolute value of the barrier height has traditionally relied on the assumption of an attempt frequency, υ^‡. Here we used single molecule force-clamp spectroscopy to directly determine the value of υ^‡ for mechanical unfolding by measuring the unfolding rate of the small protein ubiquitin at varying temperatures. Our experiments demonstrate a significant effect of the temperature on the mechanical rate of unfolding. By extrapolating the unfolding rate in the absence of force for different temperatures, varying within the range spanning from 5 to 45 °C, we measured a value for the activation barrier of ΔG^‡ = 71 ± 5 kJ/mol and an exponential prefactor υ^‡ ∼4 × 10⁹ s⁻¹. Although the measured prefactor value is 3 orders of magnitude smaller than the value predicted by the transition state theory (∼6 × 10¹² s⁻¹), it is 400-fold higher than that encountered in analogous experiments studying the effect of temperature on the reactivity of a protein-embedded disulfide bond (∼10⁷ m⁻¹ s⁻¹). This approach will allow quantitative characterization of the complete energy landscape of a folding polypeptide from highly extended states, of capital importance for proteins with elastic function.     

Ligand-modulated parallel mechanical unfolding pathways of maltose-binding proteins

Protein folding and unfolding are complex phenomena, and it is accepted that multidomain proteins generally follow multiple pathways. Maltose-binding protein (MBP) is a large (a two-domain, 370-amino acid residue) bacterial periplasmic protein involved in maltose uptake. Despite the large size, it has been shown to exhibit an apparent two-state equilibrium unfolding in bulk experiments. Single-molecule studies can uncover rare events that are masked by averaging in bulk studies. Here, we use single-molecule force spectroscopy to study the mechanical unfolding pathways of MBP and its precursor protein (preMBP) in the presence and absence of ligands. Our results show that MBP exhibits kinetic partitioning on mechanical stretching and unfolds via two parallel pathways: one of them involves a mechanically stable intermediate (path I) whereas the other is devoid of it (path II). The apoMBP unfolds via path I in 62% of the mechanical unfolding events, and the remaining 38% follow path II. In the case of maltose-bound MBP, the protein unfolds via the intermediate in 79% of the cases, the remaining 21% via path II. Similarly, on binding to maltotriose, a ligand whose binding strength with the polyprotein is similar to that of maltose, the occurrence of the intermediate is comparable (82% via path I) with that of maltose. The precursor protein preMBP also shows a similar behavior upon mechanical unfolding. The percentages of molecules unfolding via path I are 53% in the apo form and 68% and 72% upon binding to maltose and maltotriose, respectively, for preMBP. These observations demonstrate that ligand binding can modulate the mechanical unfolding pathways of proteins by a kinetic partitioning mechanism. This could be a general mechanism in the unfolding of other large two-domain ligand-binding proteins of the bacterial periplasmic space.     

The mechanical stability of ubiquitin is linkage dependent

Ubiquitin chains are formed through the action of a set of enzymes that covalently link ubiquitin either through peptide bonds or through isopeptide bonds between their C terminus and any of four lysine residues. These naturally occurring polyproteins allow one to study the mechanical stability of a protein, when force is applied through different linkages. Here we used single-molecule force spectroscopy techniques to examine the mechanical stability of N-C-linked and Lys48-C-linked ubiquitin chains. We combined these experiments with steered molecular dynamics (SMD) simulations and found that the mechanical stability and unfolding pathway of ubiquitin strongly depend on the linkage through which the mechanical force is applied to the protein. Hence, a protein that is otherwise very stable may be easily unfolded by a relatively weak mechanical force applied through the right linkage. This may be a widespread mechanism in biological systems.     

Titin Domains Progressively Unfolded by Force Are Homogenously Distributed along the Molecule

Titin is a giant filamentous protein of the muscle sarcomere in which stretch induces the unfolding of its globular domains. However, the mechanisms of how domains are progressively selected for unfolding and which domains eventually unfold have for long been elusive. Based on force-clamp optical tweezers experiments we report here that, in a paradoxical violation of mechanically driven activation kinetics, neither the global domain unfolding rate, nor the folded-state lifetime distributions of full-length titin are sensitive to force. This paradox is reconciled by a gradient of mechanical stability so that domains are gradually selected for unfolding as the magnitude of the force field increases. Atomic force microscopic screening of extended titin molecules revealed that the unfolded domains are distributed homogenously along the entire length of titin, and this homogeneity is maintained with increasing overstretch. Although the unfolding of domains with progressively increasing mechanical stability makes titin a variable viscosity damper, the spatially randomized variation of domain stability ensures that the induced structural changes are not localized but are distributed along the molecule''s length. Titin may thereby provide complex safety mechanims for protecting the sarcomere against structural disintegration under excessive mechanical conditions.     

Mechanical anisotropy of ankyrin repeats

Red blood cells are frequently deformed and their cytoskeletal proteins such as spectrin and ankyrin-R are repeatedly subjected to mechanical forces. While the mechanics of spectrin was thoroughly investigated in vitro and in vivo, little is known about the mechanical behavior of ankyrin-R. In this study, we combine coarse-grained steered molecular dynamics simulations and atomic force spectroscopy to examine the mechanical response of ankyrin repeats (ARs) in a model synthetic AR protein NI6C, and in the D34 fragment of native ankyrin-R when these proteins are subjected to various stretching geometry conditions. Our steered molecular dynamics results, supported by AFM measurements, reveal an unusual mechanical anisotropy of ARs: their mechanical stability is greater when their unfolding is forced to propagate from the N-terminus toward the C-terminus (repeats unfold at ~60 pN), as compared to the unfolding in the opposite direction (unfolding force ～ 30 pN). This anisotropy is also reflected in the complex refolding behavior of ARs. The origin of this unfolding and refolding anisotropy is in the various numbers of native contacts that are broken and formed at the interfaces between neighboring repeats depending on the unfolding/refolding propagation directions. Finally, we discuss how these complex mechanical properties of ARs in D34 may affect its behavior in vivo.     

Kinetics of unfolding and folding from amide hydrogen exchange in native ubiquitin

Amide hydrogen (NH) exchange is one of the few experimental techniques with the potential for determining the thermodynamics and kinetics of conformational motions at nearly every residue in native proteins. Quantitative interpretation of NH exchange in terms of molecular motions relies on a simple two-state kinetic model: at any given slowly exchanging NH, a closed or exchange-incompetent conformation is in equilibrium with an open or exchange-competent conformation. Previous studies have demonstrated the accuracy of this model in measuring conformational equilibria by comparing exchange data with the thermodynamics of protein unfolding. We report here a test of the accuracy of the model in determining the kinetics of conformational changes in native proteins. The kinetics of folding and unfolding for ubiquitin have been measured by conventional methods and compared with those derived from a comprehensive analysis of the pH dependence of exchange in native ubiquitin. Rate constants for folding and unfolding from these two very different types of experiments show good agreement. The simple model for NH exchange thus appears to be a robust framework for obtaining quantitative information about molecular motions in native proteins.     

Studying pressure denaturation of a protein by molecular dynamics simulations

Many globular proteins unfold when subjected to several kilobars of hydrostatic pressure. This “unfolding‐up‐on‐squeezing” is counter‐intuitive in that one expects mechanical compression of proteins with increasing pressure. Molecular simulations have the potential to provide fundamental understanding of pressure effects on proteins. However, the slow kinetics of unfolding, especially at high pressures, eliminates the possibility of its direct observation by molecular dynamics (MD) simulations. Motivated by experimental results—that pressure denatured states are water‐swollen, and theoretical results—that water transfer into hydrophobic contacts becomes favorable with increasing pressure, we employ a water insertion method to generate unfolded states of the protein Staphylococcal Nuclease (Snase). Structural characteristics of these unfolded states—their water‐swollen nature, retention of secondary structure, and overall compactness—mimic those observed in experiments. Using conformations of folded and unfolded states, we calculate their partial molar volumes in MD simulations and estimate the pressure‐dependent free energy of unfolding. The volume of unfolding of Snase is negative (approximately ?60 mL/mol at 1 bar) and is relatively insensitive to pressure, leading to its unfolding in the pressure range of 1500–2000 bars. Interestingly, once the protein is sufficiently water swollen, the partial molar volume of the protein appears to be insensitive to further conformational expansion or unfolding. Specifically, water‐swollen structures with relatively low radii of gyration have partial molar volume that are similar to that of significantly more unfolded states. We find that the compressibility change on unfolding is negligible, consistent with experiments. We also analyze hydration shell fluctuations to comment on the hydration contributions to protein compressibility. Our study demonstrates the utility of molecular simulations in estimating volumetric properties and pressure stability of proteins, and can be potentially extended for applications to protein complexes and assemblies. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Mechanically unfolding the small, topologically simple protein L

beta-sheet proteins are generally more able to resist mechanical deformation than alpha-helical proteins. Experiments measuring the mechanical resistance of beta-sheet proteins extended by their termini led to the hypothesis that parallel, directly hydrogen-bonded terminal beta-strands provide the greatest mechanical strength. Here we test this hypothesis by measuring the mechanical properties of protein L, a domain with a topology predicted to be mechanically strong, but with no known mechanical function. A pentamer of this small, topologically simple protein is resistant to mechanical deformation over a wide range of extension rates. Molecular dynamics simulations show the energy landscape for protein L is highly restricted for mechanical unfolding and that this protein unfolds by the shearing apart of two structural units in a mechanism similar to that proposed for ubiquitin, which belongs to the same structural class as protein L, but unfolds at a significantly higher force. These data suggest that the mechanism of mechanical unfolding is conserved in proteins within the same fold family and demonstrate that although the topology and presence of a hydrogen-bonded clamp are of central importance in determining mechanical strength, hydrophobic interactions also play an important role in modulating the mechanical resistance of these similar proteins.     

Dynamic prestress in a globular protein

A protein at equilibrium is commonly thought of as a fully relaxed structure, with the intra-molecular interactions showing fluctuations around their energy minimum. In contrast, here we find direct evidence for a protein as a molecular tensegrity structure, comprising a balance of tensed and compressed interactions, a concept that has been put forward for macroscopic structures. We quantified the distribution of inter-residue prestress in ubiquitin and immunoglobulin from all-atom molecular dynamics simulations. The network of highly fluctuating yet significant inter-residue forces in proteins is a consequence of the intrinsic frustration of a protein when sampling its rugged energy landscape. In beta sheets, this balance of forces is found to compress the intra-strand hydrogen bonds. We estimate that the observed magnitude of this pre-compression is enough to induce significant changes in the hydrogen bond lifetimes; thus, prestress, which can be as high as a few 100 pN, can be considered a key factor in determining the unfolding kinetics and pathway of proteins under force. Strong pre-tension in certain salt bridges on the other hand is connected to the thermodynamic stability of ubiquitin. Effective force profiles between some side-chains reveal the signature of multiple, distinct conformational states, and such static disorder could be one factor explaining the growing body of experiments revealing non-exponential unfolding kinetics of proteins. The design of prestress distributions in engineering proteins promises to be a new tool for tailoring the mechanical properties of made-to-order nanomaterials.     

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.     

Probing force-induced unfolding intermediates of a single staphylococcal nuclease molecule and the effect of ligand binding

Single-molecule manipulation techniques have given experimental access to unfolding intermediates of proteins that are inaccessible in conventional experiments. A detailed characterization of the intermediates is a challenging problem that provides new possibilities for directly probing the energy landscape of proteins. We investigated single-molecule mechanical unfolding of a small globular protein, staphylococcal nuclease (SNase), using atomic force microscopy. The unfolding trajectories of the protein displayed sub-molecular and stochastic behavior with typical lengths corresponding to the size of the unfolded substructures. Our results support the view that the single protein unfolds along multiple pathways as suggested in recent theoretical studies. Moreover, we found the drastic change, caused by the ligand and inhibitor bindings, in the mechanical unfolding dynamics.     

Analyzing forced unfolding of protein tandems by ordered variates, 2: dependent unfolding times

Statistical analyses of forced unfolding data for protein tandems, i.e., unfolding forces (force-ramp) and unfolding times (force-clamp), used in single-molecule dynamic force spectroscopy rely on the assumption that the unfolding transitions of individual protein domains are independent (uncorrelated) and characterized, respectively, by identically distributed unfolding forces and unfolding times. In our previous work, we showed that in the experimentally accessible piconewton force range, this assumption, which holds at a lower constant force, may break at an elevated force level, i.e., the unfolding transitions may become correlated when force is increased. In this work, we develop much needed statistical tests for assessing the independence of the unobserved forced unfolding times for individual protein domains in the tandem and equality of their parent distributions, which are based solely on the observed ordered unfolding times. The use and performance of these tests are illustrated through the analysis of unfolding times for computer models of protein tandems. The proposed tests can be used in force-clamp atomic force microscopy experiments to obtain accurate information on protein forced unfolding and to probe data on the presence of interdomain interactions. The order statistics-based formalism is extended to cover the analysis of correlated unfolding transitions. The use of order statistics leads naturally to the development of new kinetic models, which describe the probabilities of ordered unfolding transitions rather than the populations of chemical species.     

Temperature‐induced unfolding behavior of proteins studied by tensorial elastic network model

Motivated by single molecule experiments and recent molecular dynamics (MD) studies, we propose a simple and computationally efficient method based on a tensorial elastic network model to investigate the unfolding pathways of proteins under temperature variation. The tensorial elastic network model, which relies on the native state topology of a protein, combines the anisotropic network model, the bond bending elasticity, and the backbone twist elasticity to successfully predicts both the isotropic and anisotropic fluctuations in a manner similar to the Gaussian network model and anisotropic network model. The unfolding process is modeled by breaking the native contacts between residues one by one, and by assuming a threshold value for strain fluctuation. Using this method, we simulated the unfolding processes of four well‐characterized proteins: chymotrypsin inhibitor, barnase, ubiquitein, and adenalyate kinase. We found that this step‐wise process leads to two or more cooperative, first‐order‐like transitions between partial denaturation states. The sequence of unfolding events obtained using this method is consistent with experimental and MD studies. The results also imply that the native topology of proteins “encrypts” information regarding their unfolding process. Proteins 2016; 84:1767–1775. © 2016 Wiley Periodicals, Inc.     

The Molecular Mechanism Underlying Mechanical Anisotropy of the Protein GB1

Mechanical responses of elastic proteins are crucial for their biological function and nanotechnological use. Loading direction has been identified as one key determinant for the mechanical responses of proteins. However, it is not clear how a change in pulling direction changes the mechanical unfolding mechanism of the protein. Here, we combine protein engineering, single-molecule force spectroscopy, and steered molecular dynamics simulations to systematically investigate the mechanical response of a small globular protein GB1. Force versus extension profiles from both experiments and simulations reveal marked mechanical anisotropy of GB1. Using native contact analysis, we relate the mechanically robust shearing geometry with concurrent rupture of native contacts. This clearly contrasts the sequential rupture observed in simulations for the mechanically labile peeling geometry. Moreover, we identify multiple distinct mechanical unfolding pathways in two loading directions. Implications of such diverse unfolding mechanisms are discussed. Our results may also provide some insights for designing elastomeric proteins with tailored mechanical properties.