Search

Friction force microscopy (FFM) explores the interaction in a sliding contact on the nanoscale, providing information on the frictional dynamics and lateral contact stiffness with lattice resolution. Recent FFM measurements on a NaCl crystal immersed in liquid (ethanol) surroundings displayed an increase of the effective contact stiffness, Keff, with the applied load, differently from similar measurements performed under ultra-high vacuum (UHV) conditions, where Keff showed negligible load dependency. Additionally, under UHV conditions multiple slip length friction with increasing load was reported, while in ethanol surroundings only single (lattice unit length) slips were observed. Our current understanding of this behavior relates the transition from single jumps to multiple jumps dynamics to the normal load (manifested through the amplitude of the interaction potential at the contact, U0) and to the damping of the system. Here we have incorporated the effect of the load dependency on both U0 and Keff within Prandtl—Tomlinson based simulations, accompanied by variations in the damping coefficient of the system. Introducing the experimentally observed load dependency to Keff resulted indeed in single slip jumps at critical damping, while multiple slip jumps were obtained at constant Keff. The average slip length increased with the normal load, particularly when the system became underdamped. Our work provides a glimpse on the relation between the characteristic observables in atomic-scale sliding friction (maximal slip forces, stiffness, and slip dynamics) with respect to their governing parameters (corrugation energy, effective stiffness, and damping). While common understanding in nanotribology relates the effect of surrounding media mainly to the interaction potential at the contact, here we show that the media can also greatly affect the elastic interaction, and consequently play an important role on the transition from single to multiple stick-slip.

The opportunistic pathogen, Pseudomonas aeruginosa, a flagellated bacterium, is one of the top model organisms for biofilm studies. To elucidate the location of bacterial flagella throughout the biofilm life cycle, we developed a new flagella biotracking tool. Bacterial flagella were site-specifically labeled via genetic code expansion. This enabled us to track bacterial flagella during biofilm maturation. Live flagella imaging revealed the presence and synthesis of flagella throughout the biofilm life cycle. To study the possible role of flagella in a biofilm, we produced a flagella knockout strain and compared its biofilm to that of the wild-type strain. Results showed a one order of magnitude stronger biofilm structure in the wild type in comparison with the flagella knockout strain. This suggests a possible structural role for flagella in a biofilm, conceivably as a scaffold. Our findings suggest a new model for biofilm maturation dynamic which underscores the importance of direct evidence from within the biofilm.

P. aeruginosa flagella are recorded across the entire biofilm life cycle as likely biofilm structural scaffolds., The opportunistic pathogen, Pseudomonas aeruginosa, a flagellated bacterium, is one of the top model organisms for biofilm studies. To elucidate the location of bacterial flagella throughout the biofilm life cycle, we developed a new flagella biotracking tool. Bacterial flagella were site-specifically labeled via genetic code expansion. This enabled us to track bacterial flagella during biofilm maturation. Live flagella imaging revealed the presence and synthesis of flagella throughout the biofilm life cycle. To study the possible role of flagella in a biofilm, we produced a flagella knockout strain and compared its biofilm to that of the wild-type strain. Results showed a one order of magnitude stronger biofilm structure in the wild type in comparison with the flagella knockout strain. This suggests a possible structural role for flagella in a biofilm, conceivably as a scaffold. Our findings suggest a new model for biofilm maturation dynamic which underscores the importance of direct evidence from within the biofilm.

Friction Force Microscopy (FFM) measurements on NaCl immersed in ethanol display an increase of the effective contact stiffness with the applied load. This stiffness is estimated from the measured local contact interaction of the tip with the NaCl surface and the Prandtl–Tomlinson (PT) parameter, which reflects the relation between the corrugation stiffness and the effective contact stiffness. Different from FFM measurements in ultrahigh vacuum, for measurements in ethanol surroundings the PT parameters showed a maximum with the applied load. We incorporated this measured load-dependent effective stiffness together with the load-dependent amplitude of the corrugation energy into simulations based on the PT model, and studied its effect on the lateral friction for symmetric 1D and 2D potentials, as well as for an asymmetric 1D potentials. The simulations reproduced the experimentally observed non-monotonous behavior of the PT parameter, and enabled a glimpse on the relation of the characteristic observables (mean maximal slip forces and stiffness) with respect to their governing parameters (corrugation energy, effective stiffness). In all, apart from large deviations from symmetry in the interaction potential, the PT parameter provides a reliable estimate for nanoscale friction over periodic surfaces.

The opportunistic pathogen, Pseudomonas aeruginosa, a flagellated bacterium, is one of the top model organisms for studying biofilm formation. In order to elucidate the role of the bacteria flagella in biofilm formation, we developed a new tool for flagella bio-tracking. We have site-specifically labeled the bacterial flagella by incorporating an unnatural amino acid into the flagella monomer via genetic code expansion. This enabled us to label and track the bacterial flagella during biofilm maturation. Direct, live imaging revealed for the first-time presence and synthesis of flagella throughout the biofilm lifecycle. To ascertain the possible role of the flagella in the strength of a biofilm we produced a “flagella knockout” strain and compared its biofilm to that of the wild type strain. Results showed a one order of magnitude stronger biofilm structure in the wild type in comparison to the flagella knockout strain. This suggests a newly discovered structural role for bacterial flagella in biofilm structure, possibly acting as a scaffold. Based on our findings we suggest a new model for biofilm maturation dynamic and underscore the importance of direct evidence from within the biofilm.

Friction force microscopy (FFM) of materials with well-defined crystalline surfaces is interpreted within the framework of the Prandtl–Tomlinson (PT) model. This model portrays the interaction with...

The application of direct force to a protein enables to probe wide regions of its energy surface through conformational transitions as unfolding, extending, recoiling, collapsing, and refolding. While unfolding under force typically displayed a two-state behavior, refolding under force, from highly extended unfolded states, displayed a more complex behavior. The first recording of protein refolding at a force quench step displayed an initial rapid elastic recoil, followed by a plateau phase at some extension, concluding with a collapse to a final state, at which refolding occurred. These findings stirred a lively discussion, which led to further experimental and theoretical investigation of this behavior. It was demonstrated that the polymeric chain of the unfolded protein is required to fully collapse to a globular conformation for the maturation of native structure. This behavior was modeled using one-dimensional free energy landscape over the end-to-end length reaction coordinate, the collective measured variable. However, at low forces, conformational space is not well captured by such models, and using two-dimensional energy surfaces provides further insight into the dynamics of this process. This work reviews the main concepts of protein refolding under constant force, which is essential for understanding how mechanotransducing proteins operate in vivo.

Ultrafast folding proteins have limited cooperativity and thus are excellent models to resolve, via single-molecule experiments, the fleeting molecular events that proteins undergo during folding. Here we report single-molecule atomic force microscopy experiments on gpW, a protein that, in bulk, folds in a few microseconds over a marginal folding barrier (∼1 kBT). Applying pulling forces of only 5 pN, we maintain gpW in quasi-equilibrium near its mechanical unfolding midpoint and detect how it interconverts stochastically between the folded and an extended state. The interconversion pattern is distinctly binary, indicating that, under an external force, gpW (un)folds over a significant free-energy barrier. Using molecular simulations and a theoretical model we rationalize how force induces such barrier in an otherwise downhill free-energy surface. Force-induced folding barriers are likely a general occurrence for ultrafast folding biomolecules studied with single-molecule force spectroscopy. Single-molecule studies of fast-folding proteins can reveal key mechanisms of folding. Here atomic force microscopy studies of single gpW proteins reveals an energetic barrier to folding induced by the low external force of 3–10 pN applied by the microscope.

Single-molecule force spectroscopy utilizes polyproteins, which are composed of tandem modular domains, to study their mechanical and structural properties. Under the application of external load, the polyproteins respond by unfolding and refolding domains to acquire the most favored extensibility. However, unlike single-domain proteins, the sequential unfolding of the each domain modifies the free energy landscape (FEL) of the polyprotein nonlinearly. Here we use force-clamp (FC) spectroscopy to measure unfolding and collapse-refolding dynamics of polyubiquitin and poly(I91). Their reconstructed unfolding FEL involves hundreds of kB T in accumulating work performed against conformational entropy, which dwarfs the ∼30 kB T that is typically required to overcome the free energy difference of unfolding. We speculate that the additional entropic energy caused by segmentation of the polyprotein to individual proteins plays a crucial role in defining the "shock absorber" properties of elastic proteins such as the giant muscle protein titin.

Single molecule force spectroscopy is a useful technique for investigating mechanically induced protein unfolding and refolding under reduced forces by monitoring the end-to-end distance of the protein. The data is often interpreted via a "two-state" model based on the assumption that the end-to-end distance alone is a good reaction coordinate and the thermodynamic behavior is then ascribed to the free energy as a function of this one reaction coordinate. In this paper, we determined the free energy surface (PMF) of GB1 protein from atomistic simulations in explicit solvent under different applied forces as a function of two collective variables (the end-to-end-distance, and the fraction of native contacts ρ). The calculated 2-d free energy surfaces exhibited several distinct states, or basins, mostly visible along the ρ coordinate. Brownian dynamics (BD) simulations on the smoothed free energy surface show that the protein visits a metastable molten globule state and is thus a three state folder, not the two state folder inferred using the end-to-end distance as the sole reaction coordinate. This study lends support to recent experiments that suggest that GB1 is not a two-state folder.

Polyproteins are unique constructs, comprised of folded protein domains in tandem and polymeric linkers. These macromolecules perform under biological stresses by modulating their response through partial unfolding and extending. Although these unfolding events are considered independent, a history dependence of forced unfolding within polyproteins was reported. Here we measure the unfolding of single poly(I91) octamers, complemented with Brownian dynamics simulations, displaying increasing hierarchy in unfolding-foces, accompanied by a decrease in the effective stiffness. This counters the existing understanding that relates stiffness with variations in domain size and probe stiffness, which is expected to reduce the unfolding forces with every consecutive unfolding event. We utilize a simple mechanistic viscoelastic model to show that two effects are combined within a sequential forced unfolding process: the viscoelastic properties of the growing linker chain lead to a hierarchy of the unfolding events, and force-rate application governs the unfolding kinetics.

Polyproteins, comprised from proteins arrayed in tandem, respond to mechanical loads through partial unfolding and extension. This response to tension that enables their physiological function is related to the ability to dynamically regulate their elasticity. The unique arrangement of their individual mechanical components (proteins and polymeric linkers), and the interactions between them eventually determines their performance. The sequential unfolding-times within a polyprotein are inherently assumed to be independent and identically distributed (iid), thus expected to follow an exponential distribution. Nevertheless, a large body of literature using single molecule force spectroscopy (SMFS) provides evidence that forced unfolding-times of N proteins within a polyprotein do not follow the exponential distribution. Here we use SMFS with Atomic Force Microscopy to measure the unfolding kinetics of Poly-(I91)8 at 180 pN. The unfolding time-intervals were statistically analysed using three common approaches, all exhibiting an N-effect: hierarchical behavior with non-identical unfolding time distributions. Using continuous time random walk approach indicates that the unfolding times display subdiffusive features. Put together with free-energy reconstruction of the whole unfolding polyprotein, we provide physical explanation for this nontrivial behavior, according to which the elongating polypeptide chain with each unfolding event intervenes with the sequential unfolding probabilities and correlates them.

Friction force microscopy (FFM) in aqueous environments has recently proven to be a very effective method for lattice-resolution imaging of crystal surfaces. Here we demonstrate the use of ethanol for similar measurements on water-soluble materials. Lattice resolved frictional stick-slip traces of a cleaved NaCl(100) surface submerged in ethanol are compared with previous obtained FFM results in ultrahigh vacuum (UHV). We use the Prandtl-Tomlinson framework to estimate the amplitude of the corrugation potential and the contact stiffness. The surface potential amplitude scales with the applied normal loads are in good agreement with data obtained for NaCl measured under UHV conditions, but demonstrates deviations from the ideal periodic potential given by the Prandtl-Tomlinson model. An additional finding is that the use of ethanol allows us to explore higher load ranges without detectable evidence of surface wear. The contact stiffness does not vary significantly with the normal load up to 38 nN, while above it a sudden increase by almost one order of magnitude was observed. Comparing this to previous results suggests that considerable atom rearrangements may occur in the contact region, although the (100) surface structure is preserved by ethanol-assisted diffusion of Na and Cl ions., This work was supported by grants to R.B. from the I-CORE Program of the Planning and Budgeting Committee and The Israel Science Foundation (Grant No. 152/11). C.M.P. and C.P. thank the ICTS Centro Nacional de Microscopia Electrónica at the Complutense University for providing access to the AFM (Setup I). C.P. is grateful to the Spanish Government for a FPU Fellowship.

Biomolecular interactions frequently occur in orientation-specific manner. For example, prior nuclear magnetic resonance spectroscopy experiments in our lab have suggested the presence of a group of strongly binding residues on a particular face of the protein ubiquitin for interactions with Capto MMC multimodal ligands ("Capto" ligands) (Srinivasan, K.; et al. Langmuir 2014, 30 (44), 13205-13216). We present a clear confirmation of those studies by performing single-molecule force spectroscopy (SMFS) measurements of unbinding complemented with molecular dynamics (MD) calculations of the adsorption free energy of ubiquitin in two distinct orientations with self-assembled monolayers (SAMs) functionalized with "Capto" ligands. These orientations were maintained in the SMFS experiments by tethering ubiquitin mutants to SAM surfaces through strategically located cysteines, thus exposing the desired faces of the protein. Analogous orientations were maintained in MD simulations using suitable constraining methods. Remarkably, despite differences between the finer details of experimental and simulation methodologies, they confirm a clear preference for the previously hypothesized binding face of ubiquitin. Furthermore, MD simulations provided significant insights into the mechanism of protein binding onto this multimodal surface. Because SMFS and MD simulations both directly probe protein-surface interactions, this work establishes a key link between experiments and simulations at molecular scale through the determination of protein face-specific binding energetics. Our approach may have direct applications in biophysical systems where face- or orientation-specific interactions are important, such as biomaterials, sensors, and biomanufacturing.

The active site of the Haloalkane Dehydrogenase (HaloTag) enzyme can be covalently attached to a chloroalkane ligand providing a mechanically strong tether, resistant to large pulling forces. Here we demonstrate the covalent tethering of protein L and I27 polyproteins between an atomic force microscopy (AFM) cantilever and a glass surface using HaloTag anchoring at one end and thiol chemistry at the other end. Covalent tethering is unambiguously confirmed by the observation of full length polyprotein unfolding, combined with high detachment forces that range up to ∼2000 pN. We use these covalently anchored polyproteins to study the remarkable mechanical properties of HaloTag proteins. We show that the force that triggers unfolding of the HaloTag protein exhibits a 4-fold increase, from 131 to 491 pN, when the direction of the applied force is changed from the C-terminus to the N-terminus. Force-clamp experiments reveal that unfolding of the HaloTag protein is twice as sensitive to pulling force compared to protein L and refolds at a slower rate. We show how these properties allow for the long-term observation of protein folding-unfolding cycles at high forces, without interference from the HaloTag tether.

We use Langevin dynamics to investigate the role played by the recently discovered force-induced entropic energy barrier on the two-state hopping phenomena that has been observed in single RNA, DNA and protein molecules placed under a stretching force. Simple considerations about the free energy of a molecule readily show that the application of force introduces an entropic barrier separating the collapsed state of the molecule, from a force-driven extended conformation. A notable characteristic of the force induced barrier is its long distances to transition state, up to tens of nanometers, which renders the kinetics of crossing this barrier highly sensitive to an applied force. Langevin dynamics across such force induced barriers readily demonstrates the hopping behavior observed for a variety of single molecules placed under force. Such hopping is frequently interpreted as a manifestation of two-state folding/unfolding reactions observed in bulk experiments. However, given that such barriers do not exist at zero force these reactions do not take place at all in bulk.

Recent studies have provided a theoretical framework for including entropic elasticity in the free energy landscape of proteins under mechanical force. Accounting for entropic elasticity using polymer physics models has helped explain the hopping behavior seen in single molecule experiments in the low force regime. Here, we expand on the construction of the free energy of a single protein domain under force proposed by Berkovich et al. to provide a free energy landscape for N tandem domains along a continuous polypeptide. Calculation of the free energy of individual domains followed by their concatenation provides a continuous free energy landscape whose curvature is dominated by the worm-like chain at forces below 20 pN. We have validated our free energy model using Brownian dynamics and reproduce key features of protein folding. This free energy model can predict the effects of changes in the elastic properties of a multidomain protein as a consequence of biological modifications such as phosphorylation or the formation of disulfide bonds. This work lays the foundations for the modeling of tissue elasticity, which is largely determined by the properties of tandem polyproteins.

Cell-surface proteins are central for the interaction of cells with their surroundings and are also associated with numerous diseases. These molecules are exposed to mechanical forces, but the exact relation between force and the functions and pathologies associated with cell-surface proteins is unclear. An important cell-surface protein is CD4, the primary receptor of HIV-1. Here we show that mechanical force activates conformational and chemical changes on CD4 that may be important during viral attachment. We have used single-molecule force spectroscopy and analysis on HIV-1 infectivity to demonstrate that the mechanical extension of CD4 occurs in a time-dependent manner and correlates with HIV-1 infectivity. We show that Ibalizumab, a monoclonal antibody that blocks HIV-1, prevents the mechanical extension of CD4 domains 1 and 2. Furthermore, we demonstrate that thiol/disulfide exchange in CD4 requires force for exposure of cryptic disulfide bonds. This mechanical perspective provides unprecedented information that can change our understanding on how viruses interact with their hosts.

Single molecule force spectroscopy techniques have become important tools to study properties of proteins that operate under force; a common occurrence in Biology. Lack of specific attachment of single molecules to the force probe limits the measuring time and often leads to tethering at random places along a protein substrate. Here we present a technique based on polyprotein engineering and HaloTag attachment that is capable of avoiding these limitations. This method shows full-length polyprotein unfolding, high pick-up yield and detachment forces of ∼2 nN. Compared to other covalent attachments, this method shows a specific signature, given by the partial unfolding of HaloTag. We find that placing the HaloTag at the N-end of the construct shows an unfolding contour length of 66 nm and a mechanical strength of ∼131 pN. Placing the HaloTag at the C-end of the construct exposes to force a more stable part of the protein, which shows an increased mechanical strength of ∼491 pN and a contour length increment of 27 nm. We use HaloTag covalent attachment to study the folding of I27, a model protein from human titin. We expose I27 polyprotein constructs to successive cycles of high and low force, which unfolds and refolds the component protein domains. Covalent attachment greatly expands the tethering time of a polyprotein construct and allows for the measuring of the unfolding and folding rates from a single trace. Furthermore, repeated unfolding and refolding of the same polyprotein reveals subtle effects such as folding intermediates and slow oxidation of cysteines, which affects the mechanical stability of titin. This method opens a new approach to study protein folding at the human timescale, where proteins such as titin are slowly turned over after several days and to determine their energy landscape.

Single molecule force spectroscopy is a useful technique for investigating mechanically induced protein unfolding and refolding under reduced forces by monitoring the end-to-end distance of the protein. The data is often interpreted via a “two-state” model based on the assumption that the end-to-end distance alone is a good reaction coordinate and the thermodynamic behavior is then ascribed to the free energy as a function of this one reaction coordinate. In this paper, we determined the free energy surface (PMF) of GB1 protein from atomistic simulations in explicit solvent under different applied forces as a function of two collective variables (the end-to-end-distance, and the fraction of native contacts ρ). The calculated 2-d free energy surfaces exhibited several distinct states, or basins, mostly visible along the ρ coordinate. Brownian dynamics (BD) simulations on the smoothed free energy surface show that the protein visits a metastable molten globule state and is thus a three state folder, not the two state folder inferred using the end-to-end distance as the sole reaction coordinate. These BD simulations reproduce the unfolding and collapse-refolding patterns observed in the force-clamp experiments. This study lends support to recent experiments that suggest that GB1 is not a two-state folder.

Free energy is one of the most fundamental thermodynamic functions, determining relative phase stability and serving as a generating function for other thermodynamic quantities. The calculation of free energies is a challenging enterprise. In equilibrium statistical mechanics, the free energy is related to the canonical partition function. The partition function itself involves integrations over all degrees of freedom in the system and, in most cases, cannot be easily calculated directly. In 1997, Jarzynski proved a remarkable equality that allows computing the equilibrium free-energy difference between two states from the probability distribution of the nonequilibrium work done on the system to switch between the two states. The Jarzynski equality provides a powerful free-energy difference estimator from a set of irreversible experiments. This method is closely related to free-energy perturbation approach, which is also a computational technique for estimating free-energy differences. The ability to map potential profiles and topologies is of major significance to areas as diverse as biological recognition and nanoscale friction. This capability has been demonstrated for frictional studies where a force between the tip of the scanning force microscope and the surface is probed. The surface free-energy corrugation produces a detectable friction forces. Thus, friction force microscopy (FFM) should be able to discriminate between energetically different areas on the probed surface. Here, we apply the Jarzynski equality for the analysis of FFM measurements and thus obtain a variation of the free energy along a surface.

The elastic restoring force of tissues must be able to operate over the very wide range of loading rates experienced by living organisms. It is surprising that even the fastest events involving animal muscle tissues do not surpass a few hundred hertz. We propose that this limit is set in part by the elastic dynamics of tethered proteins extending and relaxing under a changing load. Here we study the elastic dynamics of tethered proteins using a fast force spectrometer with sub-millisecond time resolution, combined with Brownian and Molecular Dynamics simulations. We show that the act of tethering a polypeptide to an object, an inseparable part of protein elasticity in vivo and in experimental setups, greatly reduces the attempt frequency with which the protein samples its free energy. Indeed, our data shows that a tethered polypeptide can traverse its free-energy landscape with a surprisingly low effective diffusion coefficient D eff ∼ 1,200 nm 2 /s. By contrast, our Molecular Dynamics simulations show that diffusion of an isolated protein under force occurs at D eff ∼ 10 8 nm 2 /s. This discrepancy is attributed to the drag force caused by the tethering object. From the physiological time scales of tissue elasticity, we calculate that tethered elastic proteins equilibrate in vivo with D eff ∼ 10 4 –10 6 nm 2 /s which is two to four orders magnitude smaller than the values measured for untethered proteins in bulk.

Non-integral membrane proteins frequently act as transduction hubs in vital signaling pathways initiated at the plasma membrane (PM). Their biological activity depends on dynamic interactions with the PM, which are governed by their lateral and cytoplasmic diffusion and membrane binding/unbinding kinetics. Accurate quantification of the multiple kinetic parameters characterizing their membrane interaction dynamics has been challenging. Despite a fair number of approximate fitting functions for analyzing fluorescence recovery after photobleaching (FRAP) data, no approach was able to cope with the full diffusion-exchange problem. Here, we present an exact solution and matlab fitting programs for FRAP with a stationary Gaussian laser beam, allowing simultaneous determination of the membrane (un)binding rates and the diffusion coefficients. To reduce the number of fitting parameters, the cytoplasmic diffusion coefficient is determined separately. Notably, our equations include the dependence of the exchange kinetics on the distribution of the measured protein between the PM and the cytoplasm, enabling the derivation of both k(on) and k(off) without prior assumptions. After validating the fitting function by computer simulations, we confirm the applicability of our approach to live-cell data by monitoring the dynamics of GFP-N-Ras mutants under conditions with different contributions of lateral diffusion and exchange to the FRAP kinetics.

Single-molecule force spectroscopy has opened up new approaches to the study of protein dynamics. For example, an extended protein folding after an abrupt quench in the pulling force was shown to follow variable collapse trajectories marked by well-defined stages that departed from the expected two-state folding behavior that is commonly observed in bulk. Here, we explain these observations by developing a simple approach that models the free energy of a mechanically extended protein as a combination of an entropic elasticity term and a short-range potential representing enthalpic hydrophobic interactions. The resulting free energy of the molecule shows a force-dependent energy barrier of magnitude, DeltaE =epsilon(F - F(c))(3/2), separating the enthalpic and entropic minima that vanishes at a critical force F(c). By solving the Langevin equation under conditions of a force quench, we generate folding trajectories corresponding to the diffusional collapse of an extended polypeptide. The predicted trajectories reproduce the different stages of collapse, as well as the magnitude and time course of the collapse trajectories observed experimentally in ubiquitin and I27 protein monomers. Our observations validate the force-clamp technique as a powerful approach to determining the free-energy landscape of proteins collapsing and folding from extended states.

Single-molecule force spectroscopy has opened up new approaches to the study of protein dynamics. For example, an extended protein folding after an abrupt quench in the pulling force was shown to follow variable collapse trajectories marked by well-defined stages that departed from the expected two-state folding behavior that is commonly observed in bulk. Here, we explain these observations by developing a simple approach that models the free energy of a mechanically extended protein as a combination of an entropic elasticity term and a short-range potential representing enthalpic hydrophobic interactions. The resulting free energy of the molecule shows a force-dependent energy barrier of magnitude, ΔE = e(F - Fc)3/2, separating the collapsed state of the molecule from a force-driven extended conformation, that vanishes at a critical force Fc. By solving the Langevin equation under force quench conditions, we generate folding trajectories corresponding to the diffusional collapse of an extended polypeptide that mimics those observed experimentally. Further we apply this model to force extension conditions in order to investigate the role played by the force-induced energy barrier on the two-state hopping phenomena that has been observed in single protein molecules placed under a stretching force. Langevin dynamics across such force induced barrier readily demonstrates the hopping behavior observed for a variety of single molecules placed under force. Our model interprets AFM force-clamp data and accounts as well for force-extension and hopping observed in optical tweezers, thus unifying the field of protein force spectroscopy. Moreover, given that this barrier does not exist at zero force, extrapolating hopping trajectories to zero force could not be compared to bulk measurements.

We investigate the applicability of the Jarzynski equality for reconstructing the energy landscape from force measurements obtained in single molecular unbinding and friction experiments. We demonstrate that single-well molecular potentials, such as the Lennard-Jones potential, could be accurately recovered using a reasonable number of force traces (~100) obtained for velocities which are experimentally accessible, v≈5–100 nm s−1. The situation becomes more complex in the presence of potential barriers in the energy profile. These include the double-well and periodic potentials that we consider here. The slow convergence of the reconstruction procedure results from a large energy dissipation which occurs during jumps across the potential barriers. We suggest a modification of the reconstruction procedure which allows the recovering of the correct shape of the potential wells even in the presence of potential barriers. However, a reconstruction of the potential shape in the vicinity of potential maxima requires additional information.

The elasticity of muscle tissue relies on tandem modular proteins such as titin, which gives muscles passive elasticity. A free-energy model is the only way to understand and predict the behavior under force of such complex proteins, composed of hundreds of individual domains. Here we use magnetic tweezers to measure the dynamics of single tandem modular proteins under constant force conditions during hour-long recordings. At forces between 4 to 17 pN we measure unfolding/refolding of individual domains as upward/downward steps in the end-to-end protein length, while higher forces yield unfolding steps exclusively. We find a strong force dependency of the step size of proteins undergoing folding/unfolding reactions with the applied force. This finding contradicts current free energy models of proteins that typically do not consider the polymeric nature of a denatured polypeptide chain under force and simply scale the free energy of a protein with the mechanical work. To explain the measured step size dependency with force we propose a new free energy model that also considers the entropic work needed to extend the molecule. Brownian dynamics simulations over the proposed free energy landscape accurately reproduce our experimental benchmarks. The experimental and theoretical advances demonstrated in this work provide a novel view on the free energy of proteins under force, now permitting a more realistic modeling of tissue elasticity.

The trafficking, membrane localization and lipid raft association of oncogenic Ras proteins dictate their isoform-specific biological responses. Accordingly, their spatiotemporal dynamics are tightly regulated. While extensively studied for H- and K-Ras, such information on N-Ras, an etiological oncogenic factor, is limited. Here, we report a novel mechanism regulating the activation-dependent spatiotemporal organization of N-Ras, its modulation by biologically-relevant stimuli, and isoform-specific effects on signaling. We applied patch/FRAP, FRAP beam-size analysis and a novel quantitative FRAP analysis of the diffusion and membrane binding kinetics of non-integral membrane proteins to investigate N-Ras membrane interactions. Clustering of raft-associated proteins, either glycosylphosphatidylinositol-anchored influenza hemagglutinin (HA-GPI) or fibronectin receptors, selectively enhanced the plasma membrane-cytoplasm exchange of N-Ras-GTP (preferentially associated with raft domains) in a cholesterol-dependent manner. EM analysis showed N-Ras-GTP localization in cholesterol-sensitive clusters, from which it preferentially detached upon HA-GPI crosslinking. HA-GPI clustering enhanced the Golgi-accumulation and signaling of EGF-stimulated N-Ras-GTP. Notably, the crosslinking-mediated enhancement of N-Ras-GTP exchange and Golgi accumulation strictly depended on depalmitoylation. We propose that the N-Ras activation pattern (e.g., by EGF) is altered by raft protein clustering, which enhances N-Ras-GTP raft localization and depalmitoylation, entailing its exchange and Golgi accumulation following repalmitoylation. This mechanism demonstrates a functional signaling role for the activation-dependent differential association of Ras isoforms with raft nanodomains.

HIV-1 infection initiates when the viral envelope glycoprotein gp120 interacts with two receptors on the surface of the T lymphocytes, CD4 and a chemokine co-receptor (CCR5 or CXCR4). Upon binding, a cascade of conformational changes in CD4 triggers viral fusion to the cell membrane. However, the key factors that originate the structural alterations in CD4 are unclear. Here, we use single-molecule force spectroscopy to study the mechanochemical properties of the two more external domains of human CD4 (D1 and D2). The application of mechanical forces to the CD4 domains reveals that they can be unfolded in a time-dependent manner within a biological range of forces. Similarly to other tandem repeats proteins such as titin or tenascin, mechanical unfolding of CD4 modules might be an important process occurring in vivo acting as a shock absorber. This phenomenon would help to prevent viral detachment. Furthermore, we show that mechanical exposition of internal disulfide bonds in CD4 is required for redox regulation by thioredoxin enzymes, a process that has been suggested to occur during viral infection. In addition, we perform numerical calculations using suitable models for polymer elasticity to correlate viral infectivity (Freeman et al. Structure 18(12):163241) with mechanical extensibility of CD4 modules. The role of mechanical forces in HIV-1 infection is yet to be considered, but it might represent a new view to better understand viral infection.

Force Spectroscopy is a technique in which single proteins are probed under mechanical perturbation. The force-length course measured in force spectroscopy is commonly described in terms of a diffusive process over a one dimensional potential of mean force, which reflects the end to end motion of the protein. Accordingly, the diffusion coefficient of a protein or polypeptide over its potential of mean force, D, is a basic property that relates the detected kinetics to the applied load. So far, D had been calculated from measurements taken in bulk, where the molecule is free to diffuse without any applied mechanical loads. The reported values indicate rapid dynamics that cannot explain the substantially slower timescales observed by a collapse trajectory of a single molecule under force. To this end we built a fast AFM apparatus with an improved characteristic time response of ∼100 μs. Using this novel setup we pulled on poly-ubiquitin, which has a distinct fingerprint, and then applied a force quench protocol between 250 and 100 pN to probe its recoiling dynamics. We fitted this data with a high force approximation analytical expression, which was verified using Brownian Dynamics, to measure the value of D for the recoiling traces. We report here for the first time an averaged value of D = 1374 ± 222 nm2/s, which is interestingly about five orders of magnitude smaller than the ones measured in bulk. The value of D measured here accounts for the observed slow recoiling timescales (∼1 ms) of a single poly-ubiquitin under mechanical load. Moreover, this value is significant when describing elastic systems where proteins are bound on both sides and still go through conformational changes.