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.     

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.     

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.     

Pulling geometry defines the mechanical resistance of a beta-sheet protein

Proteins show diverse responses when placed under mechanical stress. The molecular origins of their differing mechanical resistance are still unclear, although the orientation of secondary structural elements relative to the applied force vector is thought to have an important function. Here, by using a method of protein immobilization that allows force to be applied to the same all-beta protein, E2lip3, in two different directions, we show that the energy landscape for mechanical unfolding is markedly anisotropic. These results, in combination with molecular dynamics (MD) simulations, reveal that the unfolding pathway depends on the pulling geometry and is associated with unfolding forces that differ by an order of magnitude. Thus, the mechanical resistance of a protein is not dictated solely by amino acid sequence, topology or unfolding rate constant, but depends critically on the direction of the applied extension.     

Stabilization provided by neighboring strands is critical for the mechanical stability of proteins

Single-molecule force spectroscopy studies and steered molecular dynamics simulations have revealed that protein topology and pulling geometry play important roles in determining the mechanical stability of proteins. Most studies have focused on local interactions that are associated with the force-bearing β-strands. Interactions mediated by neighboring strands are often overlooked. Here we use Top7 and barstar as model systems to illustrate the critical importance of the stabilization effect provided by neighboring β-strands on the mechanical stability. Using single-molecule atomic force microscopy, we showed that Top7 and barstar, which have similar topology in their force-bearing region, exhibit vastly different mechanical-stability characteristics. Top7 is mechanically stable and unfolds at ∼150 pN, whereas barstar is mechanically labile and unfolds largely below 50 pN. Steered molecular dynamics simulations revealed that stretching force peels one force-bearing strand away from barstar to trigger unfolding, whereas Top7 unfolds via a substructure-sliding mechanism. This previously overlooked stabilization effect from neighboring β-strands is likely to be a general mechanism in protein mechanics and can serve as a guideline for the de novo design of proteins with significant mechanical stability and novel protein topology.     

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.     

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.     

The nanomechanics of polycystin-1 extracellular region

Recent evidence suggests that polycystin-1 (PC1) acts as a mechanosensor, receiving signals from the primary cilia, neighboring cells, and extracellular matrix and transduces them into cellular responses that regulate proliferation, adhesion, and differentiation that are essential for the control of renal tubules and kidney morphogenesis. PC1 has an unusually long extracellular region ( approximately 3000 amino acids) with a multimodular structure. Proteins with a similar architecture have structural and mechanical roles. Based on the structural similarities between PC1 and other modular proteins that have elastic properties we hypothesized that PC1 functions mechanically by providing a flexible and elastic linkage between cells. Here we directly tested this hypothesis by analyzing the mechanical properties of the entire PC1 extracellular region by using single molecule force spectroscopy. We show that the PC1 extracellular region is highly extensible and that this extensibility is mainly caused by the unfolding of its Ig-like domains. Stretching the native PC1 extracellular region results in a sawtooth pattern with equally spaced force peaks that have a wide range of unfolding forces (50-200 pN). By combining single-molecule force spectroscopy and protein engineering techniques, we demonstrate that the sawtooth pattern in native PC1 extracellular region corresponds to the sequential unfolding of individual Ig-like domains. We found that Ig-like domains refold after mechanical unfolding. Hence, the PC1 extracellular region displays a dynamic extensibility whereby the resting length might be regulated through unfolding/refolding of its Ig-like domains. These force-driven reactions may be important for cell elasticity and the regulation of cell signaling events mediated by PC1.     

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.     

Protein-protein interaction regulates proteins' mechanical stability

Elastomeric proteins are molecular springs found not only in a variety of biological machines and tissues, but also in biomaterials of superb mechanical properties. Regulating the mechanical stability of elastomeric proteins is not only important for a range of biological processes, but also critical for the use of engineered elastomeric proteins as building blocks to construct nanomechanical devices and novel materials of well-defined mechanical properties. Here we demonstrate that protein-protein interactions can potentially serve as an effective means to regulate the mechanical properties of elastomeric proteins. We show that the binding of fragments of IgG antibody to a small protein, GB1, can significantly enhance the mechanical stability of GB1. The regulation of the mechanical stability of GB1 by IgG fragments is not through direct modification of the interactions in the mechanically key region of GB1; instead, it is accomplished via the long-range coupling between the IgG binding site and the mechanically key region of GB1. Although Fc and Fab bind GB1 at different regions of GB1, their binding to GB1 can increase the mechanical stability of GB1 significantly. Using alanine point mutants of GB1, we show that the amplitude of mechanical stability enhancement of GB1 by Fc does not correlate with the binding affinity, suggesting that binding affinity only affects the population of GB1/human Fc (hFc) complex at a given concentration of hFc, but does not affect the intrinsic mechanical stability of the GB1/hFc complex. Furthermore, our results indicate that the mechanical stability enhancement by IgG fragments is robust and can tolerate sequence/structural perturbation to GB1. Our results demonstrate that the protein-protein interaction is an efficient approach to regulate the mechanical stability of GB1-like proteins and we anticipate that this new methodology will help to develop novel elastomeric proteins with tunable mechanical stability and compliance.     

Mechanically induced titin kinase activation studied by force-probe molecular dynamics simulations

The conversion of mechanical stress into a biochemical signal in a muscle cell requires a force sensor. Titin kinase, the catalytic domain of the elastic muscle protein titin, has been suggested as a candidate. Its activation requires major conformational changes resulting in the exposure of its active site. Here, force-probe molecular dynamics simulations were used to obtain insight into the tension-induced activation mechanism. We find evidence for a sequential mechanically induced opening of the catalytic site without complete domain unfolding. Our results suggest the rupture of two terminal beta-sheets as the primary unfolding steps. The low force resistance of the C-terminal relative to the N-terminal beta-sheet is attributed to their different geometry. A subsequent rearrangement of the autoinhibitory tail is seen to lead to the exposure of the active site, as is required for titin kinase activity. These results support the hypothesis of titin kinase as a force sensor.     

Unfolding mechanics of multiple OspA substructures investigated with single molecule force spectroscopy

We investigated mechanical unfolding of Borrelia burgdorferi outer surface protein A (OspA), a Lyme disease antigen containing a unique single-layer beta-sheet, with atomic force microscopy (AFM). We mechanically stretched a monomeric unit, rather than a tandem repeat, by pulling it from its N and C-terminal residues without using intervening polymer as a spacer. We detected two peaks in the force-extension profile before the final rupture of a fully extended polypeptide, which we interpreted as unfolding of multiple substructures in OspA. The double-peaked unfolding curves are consistent with results of previous thermodynamic studies showing two cooperative units in OspA. The mechanical unfolding processes were reversible, and the two substructures refolded within one second. Mutations near the boundary of the two thermodynamic cooperative units reduced the height of the first unfolding peak to undetectable levels and marginally affected the second one, indicating that the boundary between the two mechanical substructures is related to that previously assigned between the thermodynamic cooperative units. Based on a "worm-like chain" analysis of our AFM data, we propose a model for mechanical unfolding of OspA, where nearly a half of the chain is stretched with minimal resistive force, followed by sequential breakdown of C-terminal and N-terminal substructures. Based on these results, we discuss similarities and differences between mechanical and thermodynamic unfolding reactions of OspA. This work demonstrates that AFM study of monomeric proteins can elucidate details of the intramolecular mechanics of protein substructures.     

Ca2+ Binding Enhanced Mechanical Stability of an Archaeal Crystallin

Structural topology plays an important role in protein mechanical stability. Proteins with β-sandwich topology consisting of Greek key structural motifs, for example, I27 of muscle titin and ¹⁰FNIII of fibronectin, are mechanically resistant as shown by single-molecule force spectroscopy (SMFS). In proteins with β-sandwich topology, if the terminal strands are directly connected by backbone H-bonding then this geometry can serve as a “mechanical clamp”. Proteins with this geometry are shown to have very high unfolding forces. Here, we set out to explore the mechanical properties of a protein, M-crystallin, which belongs to β-sandwich topology consisting of Greek key motifs but its overall structure lacks the “mechanical clamp” geometry at the termini. M-crystallin is a Ca²⁺ binding protein from Methanosarcina acetivorans that is evolutionarily related to the vertebrate eye lens β and γ-crystallins. We constructed an octamer of crystallin, (M-crystallin)₈, and using SMFS, we show that M-crystallin unfolds in a two-state manner with an unfolding force ∼90 pN (at a pulling speed of 1000 nm/sec), which is much lower than that of I27. Our study highlights that the β-sandwich topology proteins with a different strand-connectivity than that of I27 and ¹⁰FNIII, as well as lacking “mechanical clamp” geometry, can be mechanically resistant. Furthermore, Ca²⁺ binding not only stabilizes M-crystallin by 11.4 kcal/mol but also increases its unfolding force by ∼35 pN at the same pulling speed. The differences in the mechanical properties of apo and holo M-crystallins are further characterized using pulling speed dependent measurements and they show that Ca²⁺ binding reduces the unfolding potential width from 0.55 nm to 0.38 nm. These results are explained using a simple two-state unfolding energy landscape.     

A Comprehensive Multidimensional-Embedded, One-Dimensional Reaction Coordinate for Protein Unfolding/Folding

The goal of the Dynameomics project is to perform, store, and analyze molecular dynamics simulations of representative proteins, of all known globular folds, in their native state and along their unfolding pathways. To analyze unfolding simulations, the location of the protein along the unfolding reaction coordinate (RXN) must be determined. Properties such as the fraction of native contacts and radius of gyration are often used; however, there is an issue regarding degeneracy with these properties, as native and nonnative species can overlap. Here, we used 15 physical properties of the protein to construct a multidimensional-embedded, one-dimensional RXN coordinate that faithfully captures the complex nature of unfolding. The unfolding RXN coordinates for 188 proteins (1534 simulations and 22.9 μs in explicit water) were calculated. Native, transition, intermediate, and denatured states were readily identified with the use of this RXN coordinate. A global native ensemble based on the native-state properties of the 188 proteins was created. This ensemble was shown to be effective for calculating RXN coordinates for folds outside the initial 188 targets. These RXN coordinates enable, high-throughput assignment of conformational states, which represents an important step in comparing protein properties across fold space as well as characterizing the unfolding of individual proteins.     

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.     

Simulated refolding of stretched titin immunoglobulin domains

Steered molecular dynamics (SMD) is used to investigate forced unfolding and spontaneous refolding of immunoglobulin I27, a domain of the muscle protein titin. Previous SMD simulations revealed the events leading to stretch-induced unfolding of I27, the rupture of hydrogen bonds bridging beta-strands A and B, and those bridging beta-strands A' and G, the latter rupture occurring at an extension of approximately 15 A and preceding the complete unfolding. Simulations are now used to study the refolding of partially unfolded I27 domains. The results reveal that stretched domains with ruptured interstrand hydrogen bonds shrink along the extension direction. Two types of refolding patterns are recognized: for separated beta-strands A' and G, in most simulations five of the six hydrogen bonds between A' and G stably reformed in 2 ns, whereas for separated beta-strands A and B hydrogen bonds seldom reformed in eight 2-ns simulations. The mechanical stability of the partially refolded intermediates has been tested by re-stretching.     

Single molecule force spectroscopy reveals that electrostatic interactions affect the mechanical stability of proteins

It is well known that electrostatic interactions play important roles in determining the thermodynamic stability of proteins. However, the investigation into the role of electrostatic interactions in mechanical unfolding of proteins has just begun. Here we used single molecule atomic force microscopy techniques to directly evaluate the effect of electrostatic interactions on the mechanical stability of a small protein GB1. We engineered a bi-histidine motif into the force-bearing region of GB1. By varying the pH, histidine residues can switch between protonated and deprotonated states, leading to the change of the electrostatic interactions between the two histidine residues. We found that the mechanical unfolding force of the engineered protein decreased by ∼34% (from 115 pN to 76 pN) on changing the pH from 8.5 to 3, due to the increased electrostatic repulsion between the two positively charged histidines at acidic pH. Our results demonstrated that electrostatic interactions can significantly affect the mechanical stability of elastomeric proteins, and modulating the electrostatic interactions of key charged residues can become a promising method for regulating the mechanical stability of elastomeric proteins.     

Direct observation of markovian behavior of the mechanical unfolding of individual proteins

Single-molecule force-clamp spectroscopy is a valuable tool to analyze unfolding kinetics of proteins. Previous force-clamp spectroscopy experiments have demonstrated that the mechanical unfolding of ubiquitin deviates from the generally assumed Markovian behavior and involves the features of glassy dynamics. Here we use single molecule force-clamp spectroscopy to study the unfolding kinetics of a computationally designed fast-folding mutant of the small protein GB1, which shares a similar β-grasp fold as ubiquitin. By treating the mechanical unfolding of polyproteins as the superposition of multiple identical Poisson processes, we developed a simple stochastic analysis approach to analyze the dwell time distribution of individual unfolding events in polyprotein unfolding trajectories. Our results unambiguously demonstrate that the mechanical unfolding of NuG2 fulfills all criteria of a memoryless Markovian process. This result, in contrast with the complex mechanical unfolding behaviors observed for ubiquitin, serves as a direct experimental demonstration of the Markovian behavior for the mechanical unfolding of a protein and reveals the complexity of the unfolding dynamics among structurally similar proteins. Furthermore, we extended our method into a robust and efficient pseudo-dwell-time analysis method, which allows one to make full use of all the unfolding events obtained in force-clamp experiments without categorizing the unfolding events. This method enabled us to measure the key parameters characterizing the mechanical unfolding energy landscape of NuG2 with improved precision. We anticipate that the methods demonstrated here will find broad applications in single-molecule force-clamp spectroscopy studies for a wide range of proteins.     

Probing the energy landscape of the membrane protein bacteriorhodopsin

The folding and stability of transmembrane proteins is a fundamental and unsolved biological problem. Here, single bacteriorhodopsin molecules were mechanically unfolded from native purple membranes using atomic force microscopy and force spectroscopy. The energy landscape of individual transmembrane alpha helices and polypeptide loops was mapped by monitoring the pulling speed dependence of the unfolding forces and applying Monte Carlo simulations. Single helices formed independently stable units stabilized by a single potential barrier. Mechanical unfolding of the helices was triggered by 3.9-7.7 A extension, while natural unfolding rates were of the order of 10(-3) s(-1). Besides acting as individually stable units, helices associated pairwise, establishing a collective potential barrier. The unfolding pathways of individual proteins reflect distinct pulling speed-dependent unfolding routes in their energy landscapes. These observations support the two-stage model of membrane protein folding in which alpha helices insert into the membrane as stable units and then assemble into the functional protein.