Single molecule force spectroscopy of spectrin repeats: low unfolding forces in helix bundles

Conformational equilibria in monomeric alpha-synuclein at the single-molecule level

Human α-Synuclein (αSyn) is a natively unfolded protein whose aggregation into amyloid fibrils is involved in the pathology of Parkinson disease. A full comprehension of the structure and dynamics of early intermediates leading to the aggregated states is an unsolved problem of essential importance to researchers attempting to decipher the molecular mechanisms of αSyn aggregation and formation of fibrils. Traditional bulk techniques used so far to solve this problem point to a direct correlation between αSyn's unique conformational properties and its propensity to aggregate, but these techniques can only provide ensemble-averaged information for monomers and oligomers alike. They therefore cannot characterize the full complexity of the conformational equilibria that trigger the aggregation process. We applied atomic force microscopy–based single-molecule mechanical unfolding methodology to study the conformational equilibrium of human wild-type and mutant αSyn. The conformational heterogeneity of monomeric αSyn was characterized at the single-molecule level. Three main classes of conformations, including disordered and “β-like” structures, were directly observed and quantified without any interference from oligomeric soluble forms. The relative abundance of the “β-like” structures significantly increased in different conditions promoting the aggregation of αSyn: the presence of Cu²⁺, the pathogenic A30P mutation, and high ionic strength. This methodology can explore the full conformational space of a protein at the single-molecule level, detecting even poorly populated conformers and measuring their distribution in a variety of biologically important conditions. To the best of our knowledge, we present for the first time evidence of a conformational equilibrium that controls the population of a specific class of monomeric αSyn conformers, positively correlated with conditions known to promote the formation of aggregates. A new tool is thus made available to test directly the influence of mutations and pharmacological strategies on the conformational equilibrium of monomeric αSyn.

Natively unstructured proteins defy the classical “one sequence–one structure” paradigm of protein science. In pathological conditions, monomers of these proteins can aggregate in the cell, a process that underlies neurodegenerative diseases such as Alzheimer and Parkinson. A key step in the aggregation process—the formation of misfolded intermediates—remains obscure. To shed light on this process, we characterized the folding and conformational diversity of αSyn, a natively unstructured protein involved in Parkinson disease, by mechanically stretching single molecules of this protein and recording their mechanical properties. These experiments permitted us to observe directly and quantify three main classes of conformations that, under in vitro physiological conditions, exist simultaneously in the αSyn sample. We found that one class of conformations, “β-like” structures, is directly related to αSyn aggregation. In fact, their relative abundance increases drastically in three different conditions known to promote the formation of αSyn fibrils. We expect that a critical concentration of αSyn with a “β-like” structure must be reached to trigger fibril formation. This critical concentration is therefore controlled by a chemical equilibrium. Novel pharmacological strategies can now be tailored to act upstream, before the aggregation process ensues, by targeting this equilibrium. To this end, single-molecule force spectroscopy can be an effective tool to tailor and test new pharmacological agents.

A single-molecule study detects structured and unstructured conformers in equilibrium in monomeric α-synuclein. The β-like conformers increase with pathological mutations and under other conditions known to promote aggregation.

Elastic bond network model for protein unfolding mechanics

Recent advances in single molecule mechanics have made it possible to investigate the mechanical anisotropy of protein stability in great detail. A quantitative prediction of protein unfolding forces at experimental time scales has so far been difficult. Here, we present an elastically bonded network model to describe the mechanical unfolding forces of green fluorescent protein in eight different pulling directions. The combination of an elastic network and irreversible bond fracture kinetics offers a new concept to understand the determinants of mechanical protein stability.

Geometric confinement governs the rupture strength of H-bond assemblies at a critical length scale

The ultrastructure of protein materials such as spider silk, muscle tissue, or amyloid fibers consists primarily of beta-sheets structures, composed of hierarchical assemblies of H-bonds. Despite the weakness of H-bond interactions, which have intermolecular bonds 100 to 1000 times weaker than those in ceramics or metals, these materials combine exceptional strength, robustness, and resilience. We discover that the rupture strength of H-bond assemblies is governed by geometric confinement effects, suggesting that clusters of at most 3-4 H-bonds break concurrently, even under uniform shear loading of a much larger number of H-bonds. This universally valid result leads to an intrinsic strength limitation that suggests that shorter strands with less H-bonds achieve the highest shear strength at a critical length scale. The hypothesis is confirmed by direct large-scale full-atomistic MD simulation studies of beta-sheet structures in explicit solvent. Our finding explains how the intrinsic strength limitation of H-bonds can be overcome by the formation of a nanocomposite structure of H-bond clusters, thereby enabling the formation of larger and much stronger beta-sheet structures. Our results explain recent experimental proteomics data, suggesting a correlation between the shear strength and the prevalence of beta-strand lengths in biology.

Toward a molecular understanding of the anisotropic response of proteins to external forces: insights from elastic network models

With recent advances in single-molecule manipulation techniques, it is now possible to measure the mechanical resistance of proteins to external pulling forces applied at specific positions. Remarkably, such recent studies demonstrated that the pulling/stretching forces required to initiate unfolding vary considerably depending on the location of the application of the forces, unraveling residue/position-specific response of proteins to uniaxial tension. Here we show that coarse-grained elastic network models based on the topology of interresidue contacts in the native state can satisfactory explain the relative sizes of such stretching forces exerted on different residue pairs. Despite their simplicity, such models presumably capture a fundamental property that dominates the observed behavior: deformations that can be accommodated by the relatively lower frequency modes of motions intrinsically favored by the structure require weaker forces and vice versa. The mechanical response of proteins to external stress is therefore shown to correlate with the anisotropic fluctuation dynamics intrinsically accessible in the folded state. The dependence on the overall fold implies that evolutionarily related proteins sharing common structural features tend to possess similar mechanical properties. However, the theory cannot explain the differences observed in a number of structurally similar but sequentially distant domains, such as the fibronectin domains.

Unique elastic properties of the spectrin tetramer as revealed by multiscale coarse-grained modeling

The force-extension profile of tetrameric spectrin is determined by using multiscale computer simulation. Fluctuation results of atomistic simulations of double spectrin repeat units (DSRU) are used to systematically build a coarse-grained (CG) model for the tetrameric form of spectrin. It is found that the spectrin tetramer can be modeled as a soft polymer with a unique flat force-extension profile over the range of biologically important lengths. It is also concluded that in the cytoskeletal network of the red blood cell the tetramer is in an "overcompressed" state. These findings are in contrast to the commonly used models of spectrin tetramer elasticity, namely the "entropic spring" polymer models. From these results, it is concluded that stable intact helical linker regions are needed to maintain the soft elasticity of the spectrin tetramer.

Mechanical biochemistry of proteins one molecule at a time

The activity of proteins and their complexes often involves the conversion of chemical energy (stored or supplied) into mechanical work through conformational changes. Mechanical forces are also crucial for the regulation of the structure and function of cells and tissues. Thus, the shape of eukaryotic cells (and by extension, that of the multicellular organisms they form) is the result of cycles of mechanosensing, mechanotransduction, and mechanoresponse. Recently developed single-molecule atomic force microscopy techniques can be used to manipulate single molecules, both in real time and under physiological conditions, and are ideally suited to directly quantify the forces involved in both intra- and intermolecular protein interactions. In combination with molecular biology and computer simulations, these techniques have been applied to characterize the unfolding and refolding reactions in a variety of proteins. Single-molecule mechanical techniques are providing fundamental information on the structure and function of proteins and are becoming an indispensable tool to understand how these molecules fold and work.

Chapter 15: Live-cell single-molecule force spectroscopy

We describe a method to measure the kinetics and micromechanical properties of individual receptor-ligand bonds formed between two living cells. Using living cells rather than recombinant proteins ensures that the orientation, surface density, and posttranslational modifications of the probed receptors are physiological and that their regulated attachment to the cytoskeleton can occur. A cell is tethered to a flexible cantilever and brought into contact with cells adherent to a substratum before being pulled at a controlled retraction velocity. Measurements of bond rupture forces and associated bond loading rates over an extended range of retraction velocities allow us to compute precisely the tensile strength, reactive compliance, lifetime, and dissociation rate of individual intercellular receptor-ligand bonds. We also describe tests of specificity and Monte Carlo simulations, which ensure that measurements obtained by this method correspond to a single type of intercellular adhesion bond. We illustrate this live-cell single molecule force spectroscopy assay by characterizing homotypic bonds composed of vascular endothelial -cadherin pairs formed between living endothelial cells. This versatile assay could be used to establish the molecular principles that drive a wide range of important physiological processes involving receptor-mediated intercellular adhesion, such as the immunological synapse between a lymphocyte and an antigen-presenting cell and synaptic interactions between neuron cells, and pathological processes resulting in altered intercellular adhesion.

Direct observation of chaperone-induced changes in a protein folding pathway

How chaperone interactions affect protein folding pathways is a central problem in biology. With the use of optical tweezers and all-atom molecular dynamics simulations, we studied the effect of chaperone SecB on the folding and unfolding pathways of maltose binding protein (MBP) at the single-molecule level. In the absence of SecB, we find that the MBP polypeptide first collapses into a molten globulelike compacted state and then folds into a stable core structure onto which several alpha helices are finally wrapped. Interactions with SecB completely prevent stable tertiary contacts in the core structure but have no detectable effect on the folding of the external alpha helices. It appears that SecB only binds to the extended or molten globulelike structure and retains MBP in this latter state. Thus during MBP translocation, no energy is required to disrupt stable tertiary interactions.

Spectrin folding versus unfolding reactions and RBC membrane stiffness

Spectrin (Sp), a key component of the erythrocyte membrane, is routinely stretched to near its fully folded contour length during cell deformations. Such dynamic loading may induce domain unfolding as suggested by recent experiments. Herein we develop a model to describe the folding/unfolding of spectrin during equilibrium or nonequilibrium extensions. In both cases, our model indicates that there exists a critical extension beyond which unfolding occurs. We further deploy this model, together with a three-dimensional model of the junctional complex in the erythrocyte membrane, to explore the effect of Sp unfolding on the membrane's mechanical properties, and on the thermal fluctuation of membrane-attached beads. At large deformations our results show a distinctive strain-induced unstiffening behavior, manifested in the slow decrease of the shear modulus, and accompanied by an increase in bead fluctuation. Bead fluctuation is also found to be influenced by mode switching, a phenomenon predicted by our three-dimensional model. The amount of stiffness reduction, however, is modest compared with that reported in experiments. A possible explanation for the discrepancy is the occurrence of spectrin head-to-head disassociation which is also included within our modeling framework and used to analyze bead motion as observed via experiment.

Molecular basis of the C-terminal tail-to-tail assembly of the sarcomeric filament protein myomesin

Sarcomeric filament proteins display extraordinary properties in terms of protein length and mechanical elasticity, requiring specific anchoring and assembly mechanisms. To establish the molecular basis of terminal filament assembly, we have selected the sarcomeric M-band protein myomesin as a prototypic filament model. The crystal structure of the myomesin C-terminus, comprising a tandem array of two immunoglobulin (Ig) domains My12 and My13, reveals a dimeric end-to-end filament of 14.3 nm length. Although the two domains share the same fold, an unexpected rearrangement of one beta-strand reveals how they are evolved into unrelated functions, terminal filament assembly (My13) and filament propagation (My12). The two domains are connected by a six-turn alpha-helix, of which two turns are void of any interactions with other protein parts. Thus, the overall structure of the assembled myomesin C-terminus resembles a three-body beads-on-the-string model with potentially elastic properties. We predict that the found My12-helix-My13 domain topology may provide a structural template for the filament architecture of the entire C-terminal Ig domain array My9-My13 of myomesin.

Fragility and mechanosensing in a thermalized cytoskeleton model with forced protein unfolding

We describe a model of cytoskeletal mechanics based on the force-induced conformational change of protein cross-links in a stressed polymer network. Slow deformation of simulated networks containing cross-links that undergo repeated, serial domain unfolding leads to an unusual state-with many cross-links accumulating near the critical force for further unfolding. This state is robust to thermalization and does not occur in similar protein unbinding based simulations. Moreover, we note that the unusual configuration of near-critical protein cross-links in the fragile state provides a physical mechanism for the chemical transduction of cell-level mechanical strain and extra-cellular matrix stiffness.

Single-molecule force spectroscopy of mycobacterial adhesin-adhesin interactions

The heparin-binding hemagglutinin (HBHA) is one of the few virulence factors identified for Mycobacterium tuberculosis. It is a surface-associated adhesin that expresses a number of different activities, including mycobacterial adhesion to nonphagocytic cells and microbial aggregation. Previous evidence indicated that HBHA is likely to form homodimers or homopolymers via a predicted coiled-coil region located within the N-terminal portion of the molecule. Here, we used single-molecule atomic-force microscopy to measure individual homophilic HBHA-HBHA interaction forces. Force curves recorded between tips and supports derivatized with HBHA proteins exposing their N-terminal domains showed a bimodal distribution of binding forces reflecting the formation of dimers or multimers. Moreover, the binding peaks showed elongation forces that were consistent with the unfolding of alpha-helical coiled-coil structures. By contrast, force curves obtained for proteins exposing their lysine-rich C-terminal domains showed a broader distribution of binding events, suggesting that they originate primarily from intermolecular electrostatic bridges between cationic and anionic residues rather than from specific coiled-coil interactions. Notably, similar homophilic HBHA-HBHA interactions were demonstrated on live mycobacteria producing HBHA, while they were not observed on an HBHA-deficient mutant. Together with the fact that HBHA mediates bacterial aggregation, these observations suggest that the single homophilic HBHA interactions measured here reflect the formation of multimers that may promote mycobacterial aggregation.

Transient violations of the second law of thermodynamics in protein unfolding examined using synthetic atomic force microscopy and the fluctuation theorem

The synthetic atomic force microscopy (AFM) method is developed to simulate a periodically replicated atomistic system subject to force and length fluctuations characteristic of an AFM experiment. This new method is used to examine the forced-extension and subsequent rupture of the alpha-helical linker connecting periodic images of a spectrin protein repeat unit. A two-dimensional potential of mean force (PMF) along the length and a reaction coordinate describing the state of the linker was calculated. This PMF reveals that the basic material properties of the spectrin repeat unit are sensitive to the state of linker, an important feature that cannot be accounted for in a one-dimensional PMF. Furthermore, nonequilibrium simulations were generated to examine the rupture event in the context of the fluctuation theorem. These atomistic simulations demonstrate that trajectories which are in apparent violation of the second law can overcome unfolding barriers at significantly reduced rupture forces.

Forced unfolding of proteins within cells

To identify cytoskeletal proteins that change conformation or assembly within stressed cells, in situ labeling of sterically shielded cysteines with fluorophores was analyzed by fluorescence imaging, quantitative mass spectrometry, and sequential two-dye labeling. Within red blood cells, shotgun labeling showed that shielded cysteines in the two isoforms of the cytoskeletal protein spectrin were increasingly labeled as a function of shear stress and time, indicative of forced unfolding of specific domains. Within mesenchymal stem cells-as a prototypical adherent cell-nonmuscle myosin IIA and vimentin are just two of the cytoskeletal proteins identified that show differential labeling in tensed versus drug-relaxed cells. Cysteine labeling of proteins within live cells can thus be used to fluorescently map out sites of molecular-scale deformation, and the results also suggest means to colocalize signaling events such as phosphorylation with forced unfolding.

Stretching to understand proteins - a survey of the protein data bank

We make a survey of resistance of 7510 proteins to mechanical stretching at constant speed as studied within a coarse-grained molecular dynamics model. We correlate the maximum force of resistance with the native structure, predict proteins which should be especially strong, and identify the nature of their force clamps.

High-resolution, single-molecule measurements of biomolecular motion

Many biologically important macromolecules undergo motions that are essential to their function. Biophysical techniques can now resolve the motions of single molecules down to the nanometer scale or even below, providing new insights into the mechanisms that drive molecular movements. This review outlines the principal approaches that have been used for high-resolution measurements of single-molecule motion, including centroid tracking, fluorescence resonance energy transfer, magnetic tweezers, atomic force microscopy, and optical traps. For each technique, the principles of operation are outlined, the capabilities and typical applications are examined, and various practical issues for implementation are considered. Extensions to these methods are also discussed, with an eye toward future application to outstanding biological problems.

Nanoscale ion mediated networks in bone: osteopontin can repeatedly dissipate large amounts of energy

In the nanocomposite bone, inorganic material is combined with several types of organic molecules, and these complexes have been proposed to increase the bone strength. Here we report on a mechanism of how one of these components, human osteopontin, forms large mechanical networks that can repeatedly dissipate energy through work against entropy by breaking sacrificial bonds and stretching hidden length. The behavior of these in vitro networks is similar to that of organic components in bone, acting as an adhesive layer in between mineralized fibrils.

Secondary structure, mechanical stability, and location of transition state of proteins

It is well known that the unfolding times of proteins, tauu, scales with the external mechanical force f as tauu=tauu0exp(-fxu/kBT), where xu is the location of the average transition state along the reaction coordinate given by the end-to-end distance. Using the off-lattice Go-like models, we have shown that in terms of xu, proteins may be divided into two classes. The first class, which includes beta- and beta/alpha-proteins, has xu approximately 2-5 A whereas the second class of alpha-proteins has xu about three times larger than that of the first class, xu approximately 7-15 A. These results are in good agreement with the experimental data. The secondary structure is found to play the key role in determining the shape of the free energy landscape. Namely, the distance between the native state and the transition state depends on the helix content linearly. It is shown that xu has a strong correlation with mechanical stability of proteins. Defining the unfolding force, fu, from the constant velocity pulling measurements as a measure of the mechanical stability, we predict that xu decays with fu by a power law, xu approximately fu(-mu), where the exponent mu is approximately 0.4. We have demonstrated that the unfolding force correlates with the helix content of a protein. The contact order, which is a measure of fraction of local contacts, was found to strongly correlate with the mechanical stability and the distance between the transition state and native state. Our study reveals that xu and fu might be estimated using either the helicity or the contact order.

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

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

Axons break in animals lacking beta-spectrin

Axons and dendrites can withstand acute mechanical strain despite their small diameter. In this study, we demonstrate that β-spectrin is required for the physical integrity of neuronal processes in the nematode Caenorhabditis elegans. Axons in β-spectrin mutants spontaneously break. Breakage is caused by acute strain generated by movement because breakage can be prevented by paralyzing the mutant animals. After breaking, the neuron attempts to regenerate by initiating a new growth cone; this second round of axon extension is error prone compared with initial outgrowth. Because spectrin is a major target of calpain proteolysis, it is possible that some neurodegenerative disorders may involve the cleavage of spectrin followed by the breakage of neural processes.

Single-Molecule Experiments in Vitro and in Silico

Single-molecule force experiments in vitro enable the characterization of the mechanical response of biological matter at the nanometer scale. However, they do not reveal the molecular mechanisms underlying mechanical function. These can only be readily studied through molecular dynamics simulations of atomic structural models: "in silico" (by computer analysis) single-molecule experiments. Steered molecular dynamics simulations, in which external forces are used to explore the response and function of macromolecules, have become a powerful tool complementing and guiding in vitro single-molecule experiments. The insights provided by in silico experiments are illustrated here through a review of recent research in three areas of protein mechanics: elasticity of the muscle protein titin and the extracellular matrix protein fibronectin; linker-mediated elasticity of the cytoskeleton protein spectrin; and elasticity of ankyrin repeats, a protein module found ubiquitously in cells but with an as-yet unclear function.

Exploring the molecular forces within and between CbsA S-layer proteins using single molecule force spectroscopy

We used single molecule atomic force microscopy (AFM) to gain insight into the molecular forces driving the folding and assembly of the S-layer protein CbsA. Force curves recorded between tips and supports modified with CbsA proteins showed sawtooth patterns with multiple force peaks of 58+/-26pN that we attribute to the unfolding of alpha-helices, in agreement with earlier secondary structure predictions. The average unfolding force increased with the pulling speed but was independent on the interaction time. Force curves obtained for CbsA peptides truncated in their C-terminal region showed similar periodic features, except that fewer force peaks were seen. Furthermore, the average unfolding force was 83+/-45pN, suggesting the domains were more stable. By contrast, cationic peptides truncated in their N-terminal region showed single force peaks of 366+/-149pN, presumably reflecting intermolecular electrostatic bridges rather than unfolding events. Interestingly, these large intermolecular forces increased not only with pulling speed but also with interaction time. We expect that the intra- and intermolecular forces measured here may play a significant role in controlling the stability and assembly of the CbsA protein.

A hybrid model for erythrocyte membrane: a single unit of protein network coupled with lipid bilayer

To investigate the nanomechanics of the erythrocyte membrane we developed a hybrid model that couples the actin-spectrin network to the lipid bilayer. This model features a Fourier space Brownian dynamics model of the bilayer, a Brownian dynamics model of the actin protofilament, and a modified wormlike-chain model of the spectrin (including a cable-dynamics model to predict the oscillation in tension). This model enables us to predict the nanomechanics of single or multiple units of the protein network, the lipid bilayer, and the effect of their interactions. The present work is focused on the attitude of the actin protofilament at the equilibrium states coupled with the elevations of the lipid bilayer through their primary linkage at the suspension complex in deformations. Two different actin-spectrin junctions are considered at the junctional complex. With a point-attachment junction, large pitch angles and bifurcation of yaw angles are predicted. Thermal fluctuations at bifurcation may lead to mode-switching, which may affect the network and the physiological performance of the membrane. In contrast, with a wrap-around junction, pitch angles remain small, and the occurrence of bifurcation is greatly reduced. These simulations suggest the importance of three-dimensional molecular junctions and the lipid bilayer/protein network coupling on cell membrane mechanics.

Mechanical unfolding of proteins: insights into biology, structure and folding

Since user-friendly atomic force microscopes came onto the market a few years ago, scientists have explored the response of many proteins to applied force. This field has now matured beyond the phenomenological with exciting recent developments, particularly with regards to research into biological questions. For example, detailed mechanistic studies have suggested how mechanically active proteins perform their functions. Also, in vitro forced unfolding has been compared with in vivo protein import and degradation. Additionally, investigations have been carried out that probe the relationship between protein structure and response to applied force, an area that has benefited significantly from synergy between experiments and simulations. Finally, recent technological developments offer exciting new avenues for experimental studies.

Spectrin domains lose cooperativity in forced unfolding

Spectrin is a multidomain cytoskeletal protein, the component three-helix bundle domains are expected to experience mechanical force in vivo. In thermodynamic and kinetic studies, neighboring domains of chicken brain alpha-spectrin R16 and R17 have been shown to behave cooperatively. Is this cooperativity maintained under force? The effect of force on these spectrin domains was investigated using atomic force microscopy. The response of the individual domains to force was compared to that of the tandem repeat R1617. Importantly, nonhelical linkers (all-beta immunoglobulin domains) were used to avoid formation of nonnative helical linkers. We show that, in contrast to previous studies on spectrin repeats, only 3% of R1617 unfolding events gave an increase in contour length consistent with cooperative two-domain unfolding events. Furthermore, the unfolding forces for R1617 were the same as those for the unfolding of R16 or R17 alone. This is a strong indication that the cooperative unfolding behavior observed in the stopped-flow studies is absent between these spectrin domains when force is acting as a denaturant. Our evidence suggests that the rare double unfolding events result from misfolding between adjacent repeats. We suggest that this switch from cooperative to independent behavior allows multidomain proteins to maintain integrity under applied force.

Internal protein dynamics shifts the distance to the mechanical transition state

Mechanical unfolding of polyproteins by force spectroscopy provides valuable insight into their free energy landscapes. Most experiments of the unfolding process have been fit to two-state and/or one dimensional models, with the details of the protein and its dynamics often subsumed into a zero-force unfolding rate and a distance x{u}{1D} to the transition state. We consider the entire phase space of a model protein under a constant force, and show that x{u}{1D} contains a sizeable contribution from exploring the full multidimensional energy landscape. This effect is greater for proteins with many degrees of freedom that are affected by force; and surprisingly, we predict that externally attached flexible linkers also contribute to the measured unfolding characteristics.

Mechanical response and conformational changes of alpha-actinin domains during unfolding: a molecular dynamics study

Alpha-actinin is a cytoskeleton-binding protein involved in the assembly and regulation of the actin filaments. In this work molecular dynamics method was applied to investigate the mechanical behaviour of the human skeletal muscle alpha-actinin. Five configurations were unfolded at an elongation speed of 0.1 nm/ps in order to investigate the conformational changes occurring during the extension process. Moreover, a sensitivity analysis at different velocities was performed for one of the R2-R3 spectrin-like repeat configuration extracted in order to evaluate the effect of the pulling speed on the mechanical behaviour of the molecule. Two different behaviours were recognized with respect to the pulling speed. In particular, at speed higher than 0.025 nm/ps a continuous rearrangement without evident force peaks was obtained, on the contrary at lower speed evident peaks in the range 500-750 pN were detected. R3 repeat resulted more stable than R2 during mechanical unfolding, due to the lower hydrophobic surface available to the solvent. The characterization of the R2-R3 units can be useful for the development of cytoskeleton network models based on stiffness values obtained by analyses performed at the molecular level.

Age determination of blood spots in forensic medicine by force spectroscopy

We present a new tool for the estimation of the age of bloodstains, which could probably be used during forensic casework. For this, we used atomic force microscopy (AFM) for high-resolution imaging of erythrocytes in a blood sample and the detection of elasticity changes on a nanometer scale. For the analytic procedure we applied a fresh blood spot on a glass slide and started the AFM detection after drying of the blood drop. In a first step, an overview image was generated showing the presence of several red blood cells, which could easily be detected due to their typical "doughnut-like" appearance. The consecutively morphological investigations in a timeframe of 4 weeks could not show any alterations. Secondly, AFM was used to test the elasticity by recording force-distance curves. The measurements were performed immediately after drying, 1.5 h, 30 h and 31 days. The conditions were kept constant at room temperature (20 degrees C) and a humidity of 30%. The obtained elasticity parameters were plotted against a timeline and repeated several times. The elasticity pattern showed a decrease over time, which are most probably influenced by the alteration of the blood spot during the drying and coagulation process. The preliminary data demonstrates the capacity of this method to use it for development of calibration curves, which can be used for estimation of bloodstain ages during forensic investigations.

Tropomyosin modulates erythrocyte membrane stability

The ternary complex of spectrin, actin, and 4.1R (human erythrocyte protein 4.1) defines the nodes of the erythrocyte membrane skeletal network and is inseparable from membrane stability under mechanical stress. These junctions also contain tropomyosin (TM) and the other actin-binding proteins, adducin, protein 4.9, tropomodulin, and a small proportion of capZ, the functions of which are poorly defined. Here, we have examined the consequences of selective elimination of TM from the membrane. We have shown that the mechanical stability of the membranes of resealed ghosts devoid of TM is grossly, but reversibly, impaired. That the decreased membrane stability of TM-depleted membranes is the result of destabilization of the ternary complex of the network junctions is demonstrated by the strongly facilitated entry into the junctions in situ of a beta-spectrin peptide, containing the actin- and 4.1R-binding sites, after extraction of the TM. The stabilizing effect of TM is highly specific, in that it is only the endogenous isotype, and not the slightly longer muscle TM that can bind to the depleted membranes and restore their mechanical stability. These findings have enabled us identify a function for TM in elevating the mechanical stability of erythrocyte membranes by stabilizing the spectrin-actin-4.1R junctional complex.

A toy model of polymer stretching

We present an extremely simplified model of multiple-domain polymer stretching in an atomic force microscopy experiment. We portray each module as a binary set of contacts and decompose the system energy into a harmonic term (the cantilever) and long-range interaction terms inside each domain. Exact equilibrium computations and Monte Carlo simulations qualitatively reproduce the experimental sawtooth pattern of force-extension profiles, corresponding (in our model) to first-order phase transitions. We study the influence of the coupling induced by the cantilever and the pulling speed on the relative heights of the force peaks. The results suggest that the increasing height of the critical force for subsequent unfolding events is an out-of-equilibrium effect due to a finite pulling speed. The dependence of the average unfolding force on the pulling speed is shown to reproduce the experimental logarithmic law.

Single-molecule experiments in biological physics: methods and applications

I review single-molecule experiments (SMEs) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize individual molecules and measure microscopic forces. Using SMEs it is possible to manipulate molecules one at a time and measure distributions describing molecular properties, characterize the kinetics of biomolecular reactions and detect molecular intermediates. SMEs provide additional information about thermodynamics and kinetics of biomolecular processes. This complements information obtained in traditional bulk assays. In SMEs it is also possible to measure small energies and detect large Brownian deviations in biomolecular reactions, thereby offering new methods and systems to scrutinize the basic foundations of statistical mechanics. This review is written at a very introductory level, emphasizing the importance of SMEs to scientists interested in knowing the common playground of ideas and the interdisciplinary topics accessible by these techniques. The review discusses SMEs from an experimental perspective, first exposing the most common experimental methodologies and later presenting various molecular systems where such techniques have been applied. I briefly discuss experimental techniques such as atomic-force microscopy (AFM), laser optical tweezers (LOTs), magnetic tweezers (MTs), biomembrane force probes (BFPs) and single-molecule fluorescence (SMF). I then present several applications of SME to the study of nucleic acids (DNA, RNA and DNA condensation) and proteins (protein-protein interactions, protein folding and molecular motors). Finally, I discuss applications of SMEs to the study of the nonequilibrium thermodynamics of small systems and the experimental verification of fluctuation theorems. I conclude with a discussion of open questions and future perspectives.

Examining the influence of linkers and tertiary structure in the forced unfolding of multiple-repeat spectrin molecules

The unfolding pathways of multiple-repeat spectrin molecules were examined using steered molecular dynamics (SMD) simulations to forcibly unfold double- and triple-repeat spectrin molecules. Although SMD has previously been used to study other repeating-domain proteins, spectrin offers a unique challenge in that the linker connecting repeat units has a definite secondary structure, that of an alpha-helix. Therefore, the boundary conditions imposed on a double- or triple-repeat spectrin must be carefully considered if any relationship to the real system is to be deduced. This was accomplished by imposing additional forces on the system which ensure that the terminal alpha-helices behave as if there were no free noncontiguous helical ends. The results of the SMD simulations highlight the importance of the rupture of the alpha-helical linker on the subsequent unfolding events. Rupture of the linker propagates unfolding in the adjacent repeat units by destabilizing the tertiary structure, ultimately resulting in complete unfolding of the affected repeat unit. Two dominant classes of unfolding pathways are observed after the initial rupture of a linker which involve either rupture of another linker (possibly adjacent) or rupture of the basic tertiary structure of a repeat unit. The relationship between the force response observed on simulation timescales and those of experiment or physiological conditions is also discussed.

Mechanotransduction involving multimodular proteins: converting force into biochemical signals

Cells can sense and transduce a broad range of mechanical forces into distinct sets of biochemical signals that ultimately regulate cellular processes, including adhesion, proliferation, differentiation, and apoptosis. Deciphering at the nanoscale the design principles by which sensory elements are integrated into structural protein motifs whose conformations can be switched mechanically is crucial to understand the process of transduction of force into biochemical signals that are then integrated to regulate mechanoresponsive pathways. While the major focus in the search for mechanosensory units has been on membrane proteins such as ion channels, integrins, and associated cytoplasmic complexes, a multimodular design of tandem repeats of various structural motifs is ubiquitously found among extracellular matrix proteins, as well as cell adhesion molecules, and among many intracellular players that physically link transmembrane proteins to the contractile cytoskeleton. Single-molecule studies have revealed an unexpected richness of mechanosensory motifs, including force-regulated conformational changes of loop-exposed molecular recognition sites, intermediate states in the unraveling pathway that might either expose cryptic binding or phosphorylation sites, or regions that display enzymatic activity only when unmasked by force. Insights into mechanochemical signal conversion principles will also affect various technological fields, from biotechnology to tissue engineering and drug development.

The consensus mechanics of cultured mammalian cells

Although understanding cells' responses to mechanical stimuli is seen as increasingly important for understanding cell biology, how to best measure, interpret, and model cells' mechanical properties remains unclear. We determine the frequency-dependent shear modulus of cultured mammalian cells by using four different methods, both unique and well established. This approach clarifies the effects of cytoskeletal heterogeneity, ATP-dependent processes, and cell regional variations on the interpretation of such measurements. Our results clearly indicate two qualitatively similar, but distinct, mechanical responses, corresponding to the cortical and intracellular networks, each having an unusual, weak power-law form at low frequency. The two frequency-dependent responses we observe are remarkably similar to those reported for a variety of cultured mammalian cells measured with different techniques, suggesting it is a useful consensus description. Finally, we discuss possible physical explanations for the observed mechanical response.

Dystrophin, its interactions with other proteins, and implications for muscular dystrophy

Duchenne muscular dystrophy is the most prevalent and severe form of human muscular dystrophy. Investigations into the molecular basis for Duchenne muscular dystrophy were greatly facilitated by seminal studies in the 1980s that identified the defective gene and its major protein product, dystrophin. Biochemical studies revealed its tight association with a multi-subunit complex, the so-named dystrophin-glycoprotein complex. Since its description, the dystrophin-glycoprotein complex has emerged as an important structural unit of muscle and also as a critical nexus for understanding a diverse array of muscular dystrophies arising from defects in several distinct genes. The dystrophin homologue utrophin can compensate at the cell/tissue level for dystrophin deficiency, but functions through distinct molecular mechanisms of protein-protein interaction.

Understanding the elasticity of fibronectin fibrils: Unfolding strengths of FN-III and GFP domains measured by single molecule force spectroscopy

While it is well established that fibronectin (FN) matrix fibrils are elastic, the mechanism of fibril elasticity during extension is still debated. To investigate the molecular origin of FN fibril elasticity, we used single molecule force spectroscopy (SMFS) to determine the unfolding behavior of a recombinant FN-III protein construct that contained eight FN-III domains ((1-8)FN-III) and two green fluorescent protein (GFP) domains. FN-III domains were distinguished from GFP domains by their shorter unfolding lengths. The unfolding strengths of both domains were determined for a wide range of pulling rates (50 to 1,745 nm/s). We found that the mechanical stabilities of FN-III and GFP domains were very similar to each other over the entire range of pulling speeds. FN fibrils containing GFP remain brightly fluorescent, even when stretched, meaning that GFP domains remain largely folded. Since GFP and FN-III have equal unfolding strengths, this suggests that FN-III domains are not extensively unraveled in stretched FN fibrils. Our results thus favor an alternative model, which invokes a conformational change from a compact to an extended conformation, as the basis for FN fibril elasticity.

Mapping the energy landscape of biomolecules using single molecule force correlation spectroscopy: theory and applications

We present, to our knowledge, a new theory that takes internal dynamics of proteins into account to describe forced-unfolding and force-quench refolding in single molecule experiments. In the current experimental setup (using either atomic force microscopy or laser optical tweezers) the distribution of unfolding times, P(t), is measured by applying a constant stretching force f(S) from which the apparent f(S)-dependent unfolding rate is obtained. To describe the complexity of the underlying energy landscape requires additional probes that can incorporate the dynamics of tension propagation and relaxation of the polypeptide chain upon force quench. We introduce a theory of force correlation spectroscopy to map the parameters of the energy landscape of proteins. In force correlation spectroscopy, the joint distribution P(T, t) of folding and unfolding times is constructed by repeated application of cycles of stretching at constant f(S) separated by release periods T during which the force is quenched to f(Q) < f(S). During the release period, the protein can collapse to a manifold of compact states or refold. We show that P(T, t) at various f(S) and f(Q) values can be used to resolve the kinetics of unfolding as well as formation of native contacts. We also present methods to extract the parameters of the energy landscape using chain extension as the reaction coordinate and P(T, t). The theory and a wormlike chain model for the unfolded states allows us to obtain the persistence length l(p) and the f(Q)-dependent relaxation time, giving us an estimate of collapse timescale at the single molecular level, in the coil states of the polypeptide chain. Thus, a more complete description of landscape of protein native interactions can be mapped out if unfolding time data are collected at several values of f(S) and f(Q). We illustrate the utility of the proposed formalism by analyzing simulations of unfolding-refolding trajectories of a coarse-grained protein (S1) with beta-sheet architecture for several values of f(S), T, and f(Q) = 0. The simulations of stretch-relax trajectories are used to map many of the parameters that characterize the energy landscape of S1.

Dystrophin and utrophin bind actin through distinct modes of contact

This study was designed to define the molecular epitopes of dystrophin-actin interaction and to directly compare the actin binding properties of dystrophin and utrophin. According to our data, dystrophin and utrophin both bound alongside actin filaments with submicromolar affinities. However, the molecular epitopes involved in actin binding differed between the two proteins. In utrophin, the amino-terminal domain and an adjacent string of the first 10 spectrin-like repeats more fully recapitulated the activities measured for full-length protein. The homologous region of dystrophin bound actin with low affinity and near 1:1 stoichiometry as previously measured for the isolated amino-terminal, tandem (CH) domain. In contrast, a dystrophin construct including a cluster of basic spectrin-like repeats and spanning from the amino terminus through repeat 17, bound actin with properties most similar to full-length dystrophin. Dystrophin and utrophin both stabilized preformed actin filaments from forced depolymerization with similar efficacies but did not appear to compete for binding sites on actin. We also found that dystrophin binding to F-actin was markedly sensitive to increasing ionic strength, although utrophin binding was unaffected. Although dystrophin and utrophin are functionally homologous actin-binding proteins, these results indicate that their respective modes of contact with actin filaments are markedly different. Finally, we reassessed the abundance of dystrophin in striated muscle using full-length protein as the standard and measured greater than 10-fold higher values than previously reported.

Connecting filament mechanics in the relaxed sarcomere

By examining the mechanical properties of single unactivated myofibrils it has been shown that shortening and stretching of sarcomeres occurs in stepwise fashion, and that steps are seen also in the relaxed state (Yang et al. (1998) Biophys J 74: 1473-1483; Blyakhman et al. (2001) Biophys J 81: 1093-1100; Nagornyak et al. (2004) J. Muscle. Res. Cell Motil. 25: 37-43). The latter are inevitably associated with connecting filaments. Here, we carried out measurements on single myofibrils from rabbit psoas muscle to investigate steps in unactivated specimens in more detail. Myofibrils were stretched and released in ramp-like fashion. For the single sarcomere the time course of length change was consistently stepwise. We found that in the unactivated myofibrils, step size depended on initial sarcomere length, diminishing progressively with increase of initial sarcomere length, whereas in the case of activated sarcomeres, step size was consistently 2.7 nm.

Coiled-coil nanomechanics and uncoiling and unfolding of the superhelix and alpha-helices of myosin

The nanomechanical properties of the coiled-coils of myosin are fundamentally important in understanding muscle assembly and contraction. Force spectra of single molecules of double-headed myosin, single-headed myosin, and coiled-coil tail fragments were acquired with an atomic force microscope and displayed characteristic triphasic force-distance responses to stretch: a rise phase (R) and a plateau phase (P) and an exponential phase (E). The R and P phases arise mainly from the stretching of the coiled-coils, with the hinge region being the main contributor to the rise phase at low force. Only the E phase was analyzable by the worm-like chain model of polymer elasticity. Restrained molecular mechanics simulations on an existing x-ray structure of scallop S2 yielded force spectra with either two or three phases, depending on the mode of stretch. It revealed that coiled-coil chains separate completely near the end of the P phase and the stretching of the unfolded chains gives rise to the E phase. Extensive conformational searching yielded a P phase force near 40 pN that agreed well with the experimental value. We suggest that the flexible and elastic S2 region, particularly the hinge region, may undergo force-induced unfolding and extend reversibly during actomyosin powerstroke.

Nanospring behaviour of ankyrin repeats

Ankyrin repeats are an amino-acid motif believed to function in protein recognition; they are present in tandem copies in diverse proteins in nearly all phyla. Ankyrin repeats contain antiparallel alpha-helices that can stack to form a superhelical spiral. Visual inspection of the extrapolated structure of 24 ankyrin-R repeats indicates the possibility of spring-like behaviour of the putative superhelix. Moreover, stacks of 17-29 ankyrin repeats in the cytoplasmic domains of transient receptor potential (TRP) channels have been identified as candidates for a spring that gates mechanoreceptors in hair cells as well as in Drosophila bristles. Here we report that tandem ankyrin repeats exhibit tertiary-structure-based elasticity and behave as a linear and fully reversible spring in single-molecule measurements by atomic force microscopy. We also observe an unexpected ability of unfolded repeats to generate force during refolding, and report the first direct measurement of the refolding force of a protein domain. Thus, we show that one of the most common amino-acid motifs has spring properties that could be important in mechanotransduction and in the design of nanodevices.

Force meets chemistry: Analysis of mechanochemical conversion in focal adhesions using fluorescence recovery after photobleaching

Mechanotransduction--the process by which mechanical forces are converted into changes of intracellular biochemistry--is critical for normal cell and tissue function. Integrins facilitate mechanochemical conversion by transferring physical forces from the extracellular matrix, across the cell surface, and to cytoskeletal-associated proteins within focal adhesions. It is likely that force alters biochemistry at these sites by altering molecular binding affinities of a subset of focal adhesion proteins, but this has been difficult to quantify within living cells. Here, we describe how the fluorescence recovery after photobleaching (FRAP) technique can be adapted and used in conjunction with mathematical models to directly measure force-dependent alterations in molecular binding and unbinding rate constants of individual focal adhesion proteins in situ. We review these recent findings, and discuss the strengths and limitations of this approach for analysis of mechanochemical signaling in focal adhesions and other cellular structures. The ability to quantify molecular binding rate constants in the physical context of the living cytoplasm should provide new insight into the molecular basis of cellular mechanotransduction. It also may facilitate future efforts to bridge biological experimentation and mathematical modeling in our quest for a systems biology level description of cell regulation.

Structure - Property and Structure - Function Relations of Leafhopper (Kahaono montana) Silk

Kahaono montana Evans (Insecta: Hemiptera: Cicadellidae), an endemic Australian leafhopper, is unique among the insect order Hemiptera in producing a silk. In this study, the secondary structure of the protein comprising leafhopper silk, and the surface stretching mechanical properties of this biopolymer, were investigated using Fourier-transform infrared microscopy and atomic force microscopy, respectively. The curve-fitted amide I and amide III bands revealed a composition of 13.1% α-helix, 23.8% β-sheet, 25.5% random coil, and 37.6% aggregated side chains. The molecular stretching behaviour of raw and cleaned silk fibres differed markedly. Analysis of the AFM force curves showed an adhesive property of the raw silk, while the pure fibre showed only the presence of protein. These findings suggest that the silk fibres act as a structural support for other leafhopper secretions and together form a hydrophobic barrier that may protect the insects from rain and natural enemies. This is the first time such a use of silk has been found in a biological system.