Ubiquitin-like Protein Domains Show High Resistance to Mechanical Unfolding Similar to That of the I27 Domain in Titin: Evidence from Simulations

Atomic Force Microscopy for Protein Detection and Their Physicoсhemical Characterization

This review is focused on the atomic force microscopy (AFM) capabilities to study the properties of protein biomolecules and to detect the proteins in solution. The possibilities of application of a wide range of measuring techniques and modes for visualization of proteins, determination of their stoichiometric characteristics and physicochemical properties, are analyzed. Particular attention is paid to the use of AFM as a molecular detector for detection of proteins in solutions at low concentrations, and also for determination of functional properties of single biomolecules, including the activity of individual molecules of enzymes. Prospects for the development of AFM in combination with other methods for studying biomacromolecules are discussed.

Kinetic Ductility and Force-Spike Resistance of Proteins from Single-Molecule Force Spectroscopy

Ductile materials can absorb spikes in mechanical force, whereas brittle ones fail catastrophically. Here we develop a theory to quantify the kinetic ductility of single molecules from force spectroscopy experiments, relating force-spike resistance to the differential responses of the intact protein and the unfolding transition state to an applied mechanical force. We introduce a class of unistable one-dimensional potential surfaces that encompass previous models as special cases and continuously cover the entire range from ductile to brittle. Compact analytic expressions for force-dependent rates and rupture-force distributions allow us to analyze force-clamp and force-ramp pulling experiments. We find that the force-transmitting protein domains of filamin and titin are kinetically ductile when pulled from their two termini, making them resistant to force spikes. For the mechanostable muscle protein titin, a highly ductile model reconciles data over 10 orders of magnitude in force loading rate from experiment and simulation.

Staphylokinase Displays Surprisingly Low Mechanical Stability

Single-molecule force spectroscopy (SMFS) and molecular dynamics (MD) simulations have revealed that shear topology is an important structural feature for mechanically stable proteins. Proteins containing a β-grasp fold display the typical shear topology and are generally of significant mechanical stability. In an effort to experimentally identify mechanically strong proteins using single-molecule atomic force microscopy, we found that staphylokinase (SAK), which has a typical β-grasp fold and was predicted to be mechanically stable in coarse-grained MD simulations, displays surprisingly low mechanical stability. At a pulling speed of 400 nm/s, SAK unfolds at ∼60 pN, making it the mechanically weakest protein among the β-grasp fold proteins that have been characterized experimentally. In contrast, its structural homologous protein streptokinase β domain displays significant mechanical stability under the same experimental condition. Our results showed that the large malleability of native-state SAK is largely responsible for its low mechanical stability. The molecular origin of this large malleability of SAK remains unknown. Our results reveal a hidden complexity in protein mechanics and call for a detailed investigation into the molecular determinants of the protein mechanical malleability.

Perspective: Mechanochemistry of biological and synthetic molecules

Coupling of mechanical forces and chemical transformations is central to the biophysics of molecular machines, polymer chemistry, fracture mechanics, tribology, and other disciplines. As a consequence, the same physical principles and theoretical models should be applicable in all of those fields; in fact, similar models have been invoked (and often repeatedly reinvented) to describe, for example, cell adhesion, dry and wet friction, propagation of cracks, and action of molecular motors. This perspective offers a unified view of these phenomena, described in terms of chemical kinetics with rates of elementary steps that are force dependent. The central question is then to describe how the rate of a chemical transformation (and its other measurable properties such as the transition path) depends on the applied force. I will describe physical models used to answer this question and compare them with experimental measurements, which employ single-molecule force spectroscopy and which become increasingly common. Multidimensionality of the underlying molecular energy landscapes and the ensuing frequent misalignment between chemical and mechanical coordinates result in a number of distinct scenarios, each showing a nontrivial force dependence of the reaction rate. I will discuss these scenarios, their commonness (or its lack), and the prospects for their experimental validation. Finally, I will discuss open issues in the field.

Reaction Coordinates and Pathways of Mechanochemical Transformations

The notions of a reaction path and a reaction coordinate are central to chemistry as they provide low-dimensional descriptions of complex molecular processes. Here we discuss how to define, compute, and use the reaction paths for chemical transformations in molecules that are subjected to mechanical stress and thus driven toward regions of conformational space that are otherwise inaccessible both in computational studies and in reality. We further show that the circuitous nature of mechanochemical pathways often makes their one-dimensional description impossible and describe how multidimensional effects can be detected experimentally.

Surface activity of octanoic acid in ethanol-water solutions from molecular simulation and experiment

The surface activity of a typical surfactant, octanoic acid (OA), in ethanol-water solutions is investigated with a combined experimental and molecular simulation approach. The experiments show that OA reduces the surface tension of ethanol-water solutions at low ethanol concentration, but the effectiveness decreases with increasing ethanol concentration and vanishes for ethanol concentrations above 60%. Molecular dynamics simulations are used to obtain free energy landscapes for OA as a function of the distance from the surface. The free energy driving force pushing OA to the surface decreases with increasing ethanol concentration, and becomes insignificant (i.e., less than kT) for ethanol concentrations above 70%. Thus, the decrease in the effectiveness of OA in reducing the surface tension at higher ethanol concentrations can be attributed to the decrease in the free energy driving force keeping OA at the surface. We expect these results to apply generally to hydrocarbon-based surfactants.

Engineered bi-histidine metal chelation sites map the structure of the mechanical unfolding transition state of an elastomeric protein domain GB1

Determining the structure of the transition state is critical for elucidating the mechanism behind how proteins fold and unfold. Due to its high free energy, however, the transition state generally cannot be trapped and studied directly using traditional structural biology methods. Thus, characterizing the structure of the transition state that occurs as proteins fold and unfold remains a major challenge. Here, we report a novel (to our knowledge) method that uses engineered bi-histidine (bi-His) metal-binding sites to directly map the structure of the mechanical unfolding transition state of proteins. This method is adapted from the traditional ψ-value analysis, which uses engineered bi-His metal chelation sites to probe chemical (un)folding transition-state structure. The φ(M2+)(U)-value is defined as ΔΔG(‡-N)/ΔΔG(U-N), which is the energetic effects of metal chelation by the bi-His site on the unfolding energy barrier (ΔG(‡-N)) relative to its thermodynamic stability (ΔG(U-N)) and can be used to obtain information about the transition state in the mutational site. As a proof of principle, we used the small protein GB1 as a model system and set out to map its mechanical unfolding transition-state structure. Using single-molecule atomic force microscopy and spectrofluorimetry, we directly quantified the effect of divalent metal ion binding on the mechanical unfolding free energy and thermodynamic stability of GB1, which allowed us to quantify φ(M2+)(U)-values for different sites in GB1. Our results enabled us to map the structure of the mechanical unfolding transition state of GB1. Within GB1's mechanical unfolding transition state, the interface between force-bearing β-strands 1 and 4 is largely disrupted, and the first β-hairpin is partially disordered while the second β-hairpin and the α-helix remain structured. Our results demonstrate the unique application of ψ-value analysis in elucidating the structure of the transition state that occurs during the mechanical unfolding process, offering a potentially powerful new method for investigating the design of novel elastomeric proteins.

Evolution of the potential energy landscape with static pulling force for two model proteins

The energy landscape is analyzed for off-lattice bead models of protein L and protein G as a function of a static pulling force. Two different pairs of attachment points (pulling directions) are compared in each case, namely, residues 1/56 and 10/32. For the terminal residue pulling direction 1/56, the distinct global minimum structures are all extended, aside from the compact geometry that correlates with zero force. The helical turns finally disappear at the highest pulling forces considered. For the 10/32 pulling direction, the changes are more complicated, with a variety of competing arrangements for beads outside the region where the force is directly applied. These alternatives produce frustrated energy landscapes, with low-lying minima separated by high barriers. The calculated folding pathways in the absence of force are in good agreement with previous work. The N-terminal hairpin folds first for protein L and the C-terminal hairpin for protein G, which exhibits an intermediate. However, for a relatively low static force, where the global minimum retains its structure, the folding mechanisms change, sometimes dramatically, depending on the protein and the attachment points. The scaling relations predicted by catastrophe theory are found to hold in the limit of short path lengths.

Protein high-force pulling simulations yield low-force results

All-atom explicit-solvent molecular dynamics simulations are used to pull with extremely large constant force (750–3000 pN) on three small proteins. The introduction of a nondimensional timescale permits direct comparison of unfolding across all forces. A crossover force of approximately 1100 pN divides unfolding dynamics into two regimes. At higher forces, residues sequentially unfold from the pulling end while maintaining the remainder of the protein force-free. Measurements of hydrodynamic viscous stresses are made easy by the high speeds of unfolding. Using an exact low-Reynolds-number scaling, these measurements can be extrapolated to provide, for the first time, an estimate of the hydrodynamic force on low-force unfolding. Below 1100 pN, but surprisingly still at extremely large applied force, intermediate states and cooperative unfoldings as seen at much lower forces are observed. The force-insensitive persistence of these structures indicates that decomposition into unfolded fragments requires a large fluctuation. This finding suggests how proteins are constructed to resist transient high force. The progression of helix and sheet unfolding is also found to be insensitive to force. The force-insensitivity of key aspects of unfolding opens the possibility that numerical simulations can be accelerated by high applied force while still maintaining critical features of unfolding.

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

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

Enhancing the mechanical stability of proteins through a cocktail approach

Rationally enhancing the mechanical stability of proteins remains a challenge in the field of single molecule force spectroscopy. Here we demonstrate that it is feasible to use a "cocktail" approach for combining more than one approach to enhance significantly the mechanical stability of proteins in an additive fashion. As a proof of principle, we show that metal chelation and protein-protein interaction can be combined to enhance the unfolding force of a protein to ∼450 pN, which is >3 times of its original value. This is also higher than the mechanical stability of most of proteins studied so far. We also extend such a cocktail concept to combine two different metal chelation sites to enhance protein mechanical stability. This approach opens new avenues to efficiently regulating the mechanical properties of proteins, and should be applicable to a wide range of elastomeric proteins.

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.

Water's role in the force-induced unfolding of ubiquitin

In atomic force spectroscopic studies of the elastomeric protein ubiquitin, the β-strands 1-5 serve as the force clamp. Simulations show how the rupture force in the force-induced unfolding depends on the kinetics of water molecule insertion into positions where they can eventually form hydrogen bonding bridges with the backbone hydrogen bonds in the force-clamp region. The intrusion of water into this region is slowed down by the hydrophobic shielding effect of carbonaceous groups on the surface residues of β-strands 1-5, which thereby regulates water insertion prior to hydrogen bond breakage. The experiments show that the unfolding of the mechanically stressed protein is nonexponential due to static disorder. Our simulations show that different numbers and/or locations of bridging water molecules give rise to a long-lived distribution of transition states and static disorder. We find that slowing down the translational (not rotational) motions of the water molecules by increasing the mass of their oxygen atoms, which leaves the force field and thereby the equilibrium structure of the solvent unchanged, increases the average rupture force; however, the early stages of the force versus time behavior are very similar for our "normal" and fictitious "heavy" water models. Finally, we construct six mutant systems to regulate the hydrophobic shielding effect of the surface residues in the force-clamp region. The mutations in the two termini of β-sheets 1-5 are found to determine a preference for different unfolding pathways and change mutant's average rupture force.

Protein mechanics: from single molecules to functional biomaterials

Elastomeric proteins act as the essential functional units in a wide variety of biomechanical machinery and serve as the basic building blocks for biological materials that exhibit superb mechanical properties. These proteins provide the desired elasticity, mechanical strength, resilience, and toughness within these materials. Understanding the mechanical properties of elastomeric protein-based biomaterials is a multiscale problem spanning from the atomistic/molecular level to the macroscopic level. Uncovering the design principles of individual elastomeric building blocks is critical both for the scientific understanding of multiscale mechanics of biomaterials and for the rational engineering of novel biomaterials with desirable mechanical properties. The development of single-molecule force spectroscopy techniques has provided methods for characterizing mechanical properties of elastomeric proteins one molecule at a time. Single-molecule atomic force microscopy (AFM) is uniquely suited to this purpose. Molecular dynamic simulations, protein engineering techniques, and single-molecule AFM study have collectively revealed tremendous insights into the molecular design of single elastomeric proteins, which can guide the design and engineering of elastomeric proteins with tailored mechanical properties. Researchers are focusing experimental efforts toward engineering artificial elastomeric proteins with mechanical properties that mimic or even surpass those of natural elastomeric proteins. In this Account, we summarize our recent experimental efforts to engineer novel artificial elastomeric proteins and develop general and rational methodologies to tune the nanomechanical properties of elastomeric proteins at the single-molecule level. We focus on general design principles used for enhancing the mechanical stability of proteins. These principles include the development of metal-chelation-based general methodology, strategies to control the unfolding hierarchy of multidomain elastomeric proteins, and the design of novel elastomeric proteins that exhibit stimuli-responsive mechanical properties. Moving forward, we are now exploring the use of these artificial elastomeric proteins as building blocks of protein-based biomaterials. Ultimately, we would like to rationally tailor mechanical properties of elastomeric protein-based materials by programming the molecular sequence, and thus nanomechanical properties, of elastomeric proteins at the single-molecule level. This step would help bridge the gap between single protein mechanics and material biomechanics, revealing how the mechanical properties of individual elastomeric proteins are translated into the properties of macroscopic materials.

Periodic forces trigger a complex mechanical response in ubiquitin

Mechanical forces govern physiological processes in all living organisms. Many cellular forces, for example, those generated in cyclic conformational changes of biological machines, have repetitive components. In apparent contrast, little is known about how dynamic protein structures respond to periodic mechanical information. Ubiquitin is a small protein found in all eukaryotes. We developed molecular dynamics simulations to unfold single and multimeric ubiquitins with periodic forces. By using a coarse-grained representation, we were able to model forces with periods about 2 orders of magnitude longer than the protein's relaxation time. We found that even a moderate periodic force weakened the protein and shifted its unfolding pathways in a frequency- and amplitude-dependent manner. A complex dynamic response with secondary structure refolding and an increasing importance of local interactions was revealed. Importantly, repetitive forces with broadly distributed frequencies elicited very similar molecular responses compared to fixed-frequency forces. When testing the influence of pulling geometry on ubiquitin's mechanical stability, it was found that the linkage involved in the mechanical degradation of cellular proteins renders the protein remarkably insensitive to periodic forces. We also devised a complementary kinetic energy landscape model that traces these observations and explains periodic-force, single-molecule measurements. In turn, this analytical model is capable of predicting dynamic protein responses. These results provide new insights into ubiquitin mechanics and a potential mechanical role during protein degradation, as well as first frameworks for dynamic protein stability and the modeling of repetitive mechanical processes.

Single molecule force spectroscopy reveals engineered metal chelation is a general approach to enhance mechanical stability of proteins

Significant mechanical stability is an essential feature shared by many elastomeric proteins, which function as molecular springs in a wide variety of biological machinery and biomaterials of superb mechanical properties. Despite the progress in understanding molecular determinants of mechanical stability, it remains challenging to rationally enhance the mechanical stability of proteins. Using single molecule force spectroscopy and protein engineering techniques, we demonstrate that engineered bi-histidine metal chelation can enhance the mechanical stability of proteins significantly and reversibly. Based on simple thermodynamic cycle analysis, we engineered a bi-histidine metal chelation site into various locations of the small protein, GB1, to achieve preferential stabilization of the native state over the mechanical unfolding transition state of GB1 through the binding of metal ions. Our results demonstrate that the metal chelation can enhance the mechanical stability of GB1 by as much as 100 pN. Since bi-histidine metal chelation sites can be easily implemented, engineered metal chelation provides a general methodology to enhance the mechanical stability of a wide variety of proteins. This general approach in protein mechanics will enable the rational tuning of the mechanical stability of proteins. It will not only open new avenues toward engineering proteins of tailored nanomechanical properties, but also provide new approaches to systematically map the mechanical unfolding pathway of proteins.

Engineered elastomeric proteins with dual elasticity can be controlled by a molecular regulator

Elastomeric proteins are molecular springs that confer excellent mechanical properties to many biological tissues and biomaterials. Depending on the role performed by the tissue or biomaterial, elastomeric proteins can behave as molecular springs or shock absorbers. Here we combine single-molecule atomic force microscopy and protein engineering techniques to create elastomeric proteins that can switch between two distinct types of mechanical behaviour in response to the binding of a molecular regulator. The proteins are mechanically labile by design and behave as entropic springs with an elasticity that is governed by their configurational entropy. However, when a molecular regulator binds to the protein, it switches into a mechanically stable state and can act as a shock absorber. These engineered proteins effectively mimic and combine the two extreme forms of elastic behaviour found in natural elastomeric proteins, and thus represent a new type of smart nanomaterial that will find potential applications in nanomechanics and material sciences.

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 beta-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 beta-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 approximately 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 beta-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.

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.

A functional single-molecule binding assay via force spectroscopy

Protein-ligand interactions, including protein-protein interactions, are ubiquitously essential in biological processes and also have important applications in biotechnology. A wide range of methodologies have been developed for quantitative analysis of protein-ligand interactions. However, most of them do not report direct functional/structural consequence of ligand binding. Instead they only detect the change of physical properties, such as fluorescence and refractive index, because of the colocalization of protein and ligand, and are susceptible to false positives. Thus, important information about the functional state of protein-ligand complexes cannot be obtained directly. Here we report a functional single-molecule binding assay that uses force spectroscopy to directly probe the functional consequence of ligand binding and report the functional state of protein-ligand complexes. As a proof of principle, we used protein G and the Fc fragment of IgG as a model system in this study. Binding of Fc to protein G does not induce major structural changes in protein G but results in significant enhancement of its mechanical stability. Using mechanical stability of protein G as an intrinsic functional reporter, we directly distinguished and quantified Fc-bound and Fc-free forms of protein G on a single-molecule basis and accurately determined their dissociation constant. This single-molecule functional binding assay is label-free, nearly background-free, and can detect functional heterogeneity, if any, among protein-ligand interactions. This methodology opens up avenues for studying protein-ligand interactions in a functional context, and we anticipate that it will find broad application in diverse protein-ligand systems.

Mechanical unbinding of abeta peptides from amyloid fibrils

Using the experimental structures of Abeta amyloid fibrils and all-atom molecular dynamics, we study the force-induced unbinding of Abeta peptides from the fibril. We show that the mechanical dissociation of Abeta peptides is highly anisotropic and proceeds via different pathways when force is applied in parallel or perpendicular direction with respect to the fibril axis. The threshold forces associated with lateral unbinding of Abeta peptides exceed those observed during the mechanical dissociation along the fibril axis. In addition, Abeta fibrils are found to be brittle in the lateral direction of unbinding and soft along the fibril axis. Lateral mechanical unbinding and the unbinding along the fibril axis load different types of fibril interactions. Lateral unbinding is primarily determined by the cooperative rupture of fibril backbone hydrogen bonds. The unbinding along the fibril axis largely depends on the interpeptide Lys-Asp electrostatic contacts and the hydrophobic interactions formed by the Abeta C terminal. Due to universality of the amyloid beta structure, the anisotropic mechanical dissociation observed for Abeta fibrils is likely to be applicable to other amyloid assemblies. The estimates of equilibrium forces required to dissociate Abeta peptide from the amyloid fibril suggest that these supramolecular structures are mechanically stronger than most protein domains.

Computer simulations of the translocation and unfolding of a protein pulled mechanically through a pore

Protein degradation by ATP-dependent proteases and protein import into the mitochondrial matrix involve the unfolding of proteins upon their passing through narrow constrictions. It has been hypothesized that the cellular machinery accomplishes protein unfolding by pulling mechanically at one end of the polypeptide chain. Here, we use Langevin dynamics simulations of a minimalist off-lattice model to examine this hypothesis and to study the unfolding of a protein domain pulled mechanically through a long narrow pore. We compute the potential of mean force (PMF) experienced by the domain as a function of its displacement along the pore and identify the unfolding intermediates corresponding to the local minima of the PMF. The observed unfolding mechanism is different from that found when the two termini are pulled apart, as in single-molecule mechanical unfolding experiments. It depends on the pore diameter, the magnitude of the pulling force, and on whether the force is applied at the N- or the C-terminus of the chain. Consequently, the translocation time exhibits a pulling force dependence that is more complex than a simple exponential function expected on the basis of simple phenomenological models of translocation.

The mechanical unfolding of ubiquitin through all-atom Monte Carlo simulation with a Go-type potential

The mechanical unfolding of proteins under a stretching force has an important role in living systems and is a logical extension of the more general protein folding problem. Recent advances in experimental methodology have allowed the stretching of single molecules, thus rendering this process ripe for computational study. We use all-atom Monte Carlo simulation with a Gō-type potential to study the mechanical unfolding pathway of ubiquitin. A detailed, robust, well-defined pathway is found, confirming existing results in this vein though using a different model. Additionally, we identify the protein's fundamental stabilizing secondary structure interactions in the presence of a stretching force and show that this fundamental stabilizing role does not persist in the absence of mechanical stress. The apparent success of simulation methods in studying ubiquitin's mechanical unfolding pathway indicates their potential usefulness for future study of the stretching of other proteins and the relationship between protein structure and the response to mechanical deformation.

Polyprotein of GB1 is an ideal artificial elastomeric protein

Naturally occurring elastomeric proteins function as molecular springs in their biological settings and show mechanical properties that underlie the elasticity of natural adhesives, cell adhesion proteins and muscle proteins. Constantly subject to repeated stretching-relaxation cycles, many elastomeric proteins demonstrate remarkable consistency and reliability in their mechanical performance. Such properties had hitherto been observed only in naturally evolved elastomeric proteins. Here we use single-molecule atomic force microscopy techniques to demonstrate that an artificial polyprotein made of tandem repeats of non-mechanical protein GB1 has mechanical properties that are comparable or superior to those of known elastomeric proteins. In addition to its mechanical stability, we show that GB1 polyprotein shows a unique combination of mechanical features, including the fastest folding kinetics measured so far for a tethered protein, high folding fidelity, low mechanical fatigue during repeated stretching-relaxation cycles and ability to fold against residual forces. These fine features make GB1 polyprotein an ideal artificial protein-based molecular spring that could function in a challenging working environment requiring repeated stretching-relaxation. This study represents a key step towards engineering artificial molecular springs with tailored nanomechanical properties for bottom-up construction of new devices and materials.

Fluctuations of primary ubiquitin folding intermediates in a force clamp

Folding experiments of single ubiquitin molecules under force clamp using an atomic force microscope revealed a dynamic long-lived intermediate with nanometer scale end-to-end distance fluctuations along an unexpectedly complex folding pathway. To examine the nature of this intermediate at the atomic level as well as the driving forces that give rise to the observed fluctuations, we performed molecular dynamics refolding simulations of unfolded ubiquitin under constant force. After an initial fast collapse, we find a highly dynamic, broad ensemble of conformations with partial and continuously changing secondary structure and side chain interactions. This ensemble resembles a molten-globule-like state, similar in nature to the previously described non-native state of ubiquitin in solution, but stretched by the external force. The scale of the end-to-end distance fluctuations derived from the simulations compares well with experiment. Transient formation of unspecific and metastable hydrophobic clusters along the chain are found to give rise to the observed end-to-end distance fluctuations. These distinct collapses, interpreted as folding attempts, imply an upper limit for the folding attempt frequency of approximately 10 ns. Our results suggest possible relations between force-induced unfolding and temperature or chemically induced denaturation.

Repetitive pulling catalyzes co-translocational unfolding of barnase during import through a mitochondrial pore

We present a computational study of barnase unfolding during import into mitochondria through a model translocon. In contrast to thermal (or chemical) unfolding, the major intermediates of co-translocational unfolding are mainly mediated by non-native interactions accompanying the protein configurations induced by pulling forces. These energy contributions, combined with backbone topological constraints imposed by the model pore, result in milestones along the unfolding pathways which are significantly different not only from those experienced during thermal (or chemical) denaturation, but also from those observed in single-molecule pulling by both ends without pore constraints. Two on-pathway major translocation intermediates trapped in long-lived states by significantly high unfolding barriers are identified. A fraction of these pathways can, however, skip such local kinetic traps and result in extremely fast translocations, leading to a dramatic kinetic partitioning spanning approximately four orders of magnitude. The fraction of fast translocation events is shown to increase upon switching the pull off and on, when compared to pulling at constant force. This suggests a "catalytic" mechanism by which the mitochondrial import machinery regulates this partitioning by repetitively pulling in cycles. A number of mutation sites that alter the kinetic "flow" of the unfolding trajectories are suggested and tested.

How well can simulation predict protein folding kinetics and thermodynamics?

Simulation of protein folding has come a long way in five years. Notably, new quantitative comparisons with experiments for small, rapidly folding proteins have become possible. As the only way to validate simulation methodology, this achievement marks a significant advance. Here, we detail these recent achievements and ask whether simulations have indeed rendered quantitative predictions in several areas, including protein folding kinetics, thermodynamics, and physics-based methods for structure prediction. We conclude by looking to the future of such comparisons between simulations and experiments.

Topography of the free-energy landscape probed via mechanical unfolding of proteins

Single-molecule experiments in which proteins are unfolded by applying mechanical stretching forces generally force unfolding to proceed along a reaction coordinate that is different from that in chemical or thermal denaturation. Here we simulate the mechanical unfolding and refolding of a minimalist off-lattice model of the protein ubiquitin to explore in detail the slice of the multidimensional free-energy landscape that is accessible via mechanical pulling experiments. We find that while the free-energy profile along typical "chemical" reaction coordinates may exhibit two minima, corresponding to the native and denatured states, the free energy G(z) is typically a monotonic function of the mechanical coordinate z equal to the protein extension. Application of a stretching force along z tilts the free-energy landscape resulting in a bistable (or multistable) free energy G(z)-fz probed in mechanical unfolding experiments. We construct a two-dimensional free-energy surface as a function of both chemical and mechanical reaction coordinates and examine the coupling between the two. We further study the refolding trajectories after the protein has been prestretched by a large force, as well as the mechanical unfolding trajectories in the presence of a large stretching force. We demonstrate that the stretching forces required to destabilize the native state thermodynamically are larger than those expected on the basis of previous experimental estimates of G(z). This finding is consistent with the recent experimental studies, indicating that proteins may refold even in the presence of a substantial stretching force. Finally, we show that for certain temperatures the free energy of a polyprotein chain consisting of multiple domains is a linear function of the chain extension. We propose that the recently observed "slow phase" in the refolding of proteins under mechanical tension may be viewed as downhill diffusion in such a linear potential.

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.

Theoretical studies of the kinetics of mechanical unfolding of cross-linked polymer chains and their implications for single-molecule pulling experiments

We have used kinetic Monte Carlo simulations to study the kinetics of unfolding of cross-linked polymer chains under mechanical loading. As the ends of a chain are pulled apart, the force transmitted by each cross-link increases until it ruptures. The stochastic cross-link rupture process is assumed to be governed by first order kinetics with a rate that depends exponentially on the transmitted force. We have performed random searches to identify optimal cross-link configurations whose unfolding requires a large applied force (measure of strength) and/or large dissipated energy (measure of toughness). We found that such optimal chains always involve cross-links arranged to form parallel strands. The location of those optimal strands generally depends on the loading rate. Optimal chains with a small number of cross-links were found to be almost as strong and tough as optimal chains with a large number of cross-links. Furthermore, optimality of chains with a small number of cross-links can be easily destroyed by adding cross-links at random. The present findings are relevant for the interpretation of single molecule force probe spectroscopy studies of the mechanical unfolding of "load-bearing" proteins, whose native topology often involves parallel strand arrangements similar to the optimal configurations identified in the study.

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.

Simulation of the mechanical unfolding of ubiquitin: Probing different unfolding reaction coordinates by changing the pulling geometry

Motivated by the recent experimental atomic force microscopy (AFM) measurements of the mechanical unfolding of proteins pulled in different directions [D. J. Brockwell et al., Nat. Struct. Biol. 10, 731 (2003); M. Carrion-Vazquez et al., ibid 10, 738 (2003)] we have computed the unfolding free energy profiles for the ubiquitin domain when it is stretched between its (A) N and C termini, (B) Lys48 and C terminus, (C) Lys11 and C terminus, and (D) N terminus and Lys63. Our results for cases (A) and (B) are in good agreement with the experimental unfolding forces measured for the N-C and Lys48-C linked polyubiquitin, in particular, indicating a considerably lower unfolding force in the latter case. Mechanical unfolding in case (A) involves longitudinal shearing of the terminal parallel strands while in case (C) the same strands are "unzipped" by the force. The computed unfolding forces in case (C) are found to be very low, less than 50 pN for pulling rates typical of AFM experiments. The unfolding free energy barrier found in case (C) is approximately 13 kcal/mol, which corresponds to a zero-force unfolding rate constant that is comparable to the rate of chemical unfolding extrapolated to zero denaturant concentration. The unfolding barrier calculated in case (A) in the limit of zero force is much higher, suggesting that mechanical unfolding in this case follows a pathway that is different from that of thermal/chemical denaturation.