Strength of a weak bond connecting flexible polymer chains

Nanoengineering a single-molecule mechanical switch using DNA self-assembly

The ability to manipulate and observe single biological molecules has led to both fundamental scientific discoveries and new methods in nanoscale engineering. A common challenge in many single-molecule experiments is reliably linking molecules to surfaces, and identifying their interactions. We have met this challenge by nanoengineering a novel DNA-based linker that behaves as a force-activated switch, providing a molecular signature that can eliminate errant data arising from non-specific and multiple interactions. By integrating a receptor and ligand into a single piece of DNA using DNA self-assembly, a single tether can be positively identified by force-extension behavior, and receptor-ligand unbinding easily identified by a sudden increase in tether length. Additionally, under proper conditions the exact same pair of molecules can be repeatedly bound and unbound. Our approach is simple, versatile and modular, and can be easily implemented using standard commercial reagents and laboratory equipment. In addition to improving the reliability and accuracy of force measurements, this single-molecule mechanical switch paves the way for high-throughput serial measurements, single-molecule on-rate studies, and investigations of population heterogeneity.

Cytosine methylation alters DNA mechanical properties

DNA methylation plays an essential role in transcriptional control of organismal development in epigenetics, from turning off a specific gene to inactivation of entire chromosomes. While the biological function of DNA methylation is becoming increasingly clear, the mechanism of methylation-induced gene regulation is still poorly understood. Through single-molecule force experiments and simulation we investigated the effects of methylation on strand separation of DNA, a crucial step in gene expression. Molecular force assay and single-molecule force spectroscopy revealed a strong methylation dependence of strand separation. Methylation is observed to either inhibit or facilitate strand separation, depending on methylation level and sequence context. Molecular dynamics simulations provided a detailed view of methylation effects on strand separation, suggesting the underlying physical mechanism. According to our study, methylation in epigenetics may regulate gene expression not only through mechanisms already known but also through changing mechanical properties of DNA.

Probing binding pocket of serotonin transporter by single molecular force spectroscopy on living cells

The serotonin transporter (SERT) terminates neurotransmission by removing serotonin from the synaptic cleft. In addition, it is the site of action of antidepressants (which block the transporter) and of amphetamines (which induce substrate efflux). The interaction energies involved in binding of such compounds to the transporter are unknown. Here, we used atomic force microscopy (AFM) to probe single molecular interactions between the serotonin transporter and MFZ2-12 (a potent cocaine analog) in living CHOK1 cells. For the AFM measurements, MFZ2-12 was immobilized on AFM tips by using a heterobifunctional cross-linker. By varying the pulling velocity in force distance cycles drug-transporter complexes were ruptured at different force loadings allowing for mapping of the interaction energy landscape. We derived chemical rate constants from these recordings and compared them with those inferred from inhibition of transport and ligand binding: k_off values were in good agreement with those derived from uptake experiments; in contrast, the k_on values were scaled down when determined by AFM. Our observations generated new insights into the energy landscape of the interaction between SERT and inhibitors. They thus provide a useful framework for molecular dynamics simulations by exploring the range of forces and energies that operate during the binding reaction.

Atomic force microscopy studies of the influence of convex and concave nanostructures on the adsorption of fibronectin

Atomic force microscopy (AFM)-based force spectroscopy was used to analyze the adsorption of bovine plasma fibronectin on periodically grooved nanostructures (groove/summit width: 90 nm; depth: 120 nm). We present a simple procedure that allowed us to directly compare the local protein density and conformation for the convex summits, the concave grooves and planar reference regions of the substrate. At a bulk fibronectin concentration of 5 μg/ml, the amount of adsorbed protein per surface area was significantly higher in all regions of the nanostructure than on the planar reference, and fibronectin tended to adsorb preferentially in the concave grooves. The increased surface concentration resulted in an additional stabilization of the molecules by protein-protein interactions and a lower degree of denaturized fibronectin in the nanostructured regions. The stabilization was less pronounced in concave regions, indicating that the increased contact area in the grooves counteracted the stabilization by increased protein-substrate interactions and must be compensated for by additional protein-protein interactions. Less favorable sites were occupied at higher bulk fibronectin concentrations (25 μg/ml, 100 μg/ml), and a high degree of native folded fibronectin was observed in both the nanostructured and planar regions. Our results demonstrate that the amount of adsorbed fibronectin per surface area can be increased if a substrate is provided with a topographic nanostructure. Our results also show that the local conformational state of fibronectin is determined by the locally different interplay of protein-protein and protein-substrate interactions.

Direction-dependent mechanical unfolding and green fluorescent protein as a force sensor

An Ising-like model of proteins is used to investigate the mechanical unfolding of the green fluorescent protein along different directions. When the protein is pulled from its ends, we recover the major and minor unfolding pathways observed in experiments. Upon varying the pulling direction, we find the correct order of magnitude and ranking of the unfolding forces. Exploiting the direction dependence of the unfolding force at equilibrium, we propose a force sensor whose luminescence depends on the applied force.

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

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

Molecular recognition force spectroscopy: a new tool to tailor targeted nanoparticles

The density of targeting moieties in a nanoparticle-based gene-delivery system has been shown to play a fundamental role in its vectoring performance. Here, molecular recognition force spectroscopy is proposed as a novel screening tool to optimize the density of targeting moieties of functionalized nanoparticles towards attaining cell-specific interaction. By tailoring the nanoparticle formulation, the unbinding event probability between nanoparticles tethered to an atomic force microscopy tip and neuronal cells is directly correlated to the nanoparticle gene-vectoring capacity. Additionally, new insights into protein-receptor interaction are revealed. This novel approach opens new avenues in the field of nanomedicine.

Nanomechanics of the cadherin ectodomain: "canalization" by Ca2+ binding results in a new mechanical element

Cadherins form a large family of calcium-dependent cell-cell adhesion receptors involved in development, morphogenesis, synaptogenesis, differentiation, and carcinogenesis through signal mechanotransduction using an adaptor complex that connects them to the cytoskeleton. However, the molecular mechanisms underlying mechanotransduction through cadherins remain unknown, although their extracellular region (ectodomain) is thought to be critical in this process. By single molecule force spectroscopy, molecular dynamics simulations, and protein engineering, here we have directly examined the nanomechanics of the C-cadherin ectodomain and found it to be strongly dependent on the calcium concentration. In the presence of calcium, the ectodomain extends through a defined ("canalized") pathway that involves two mechanical resistance elements: a mechanical clamp from the cadherin domains and a novel mechanostable component from the interdomain calcium-binding regions ("calcium rivet") that is abolished by magnesium replacement and in a mutant intended to impede calcium coordination. By contrast, in the absence of calcium, the mechanical response of the ectodomain becomes largely "decanalized" and destabilized. The cadherin ectodomain may therefore behave as a calcium-switched "mechanical antenna" with very different mechanical responses depending on calcium concentration (which would affect its mechanical integrity and force transmission capability). The versatile mechanical design of the cadherin ectodomain and its dependence on extracellular calcium facilitate a variety of mechanical responses that, we hypothesize, could influence the various adhesive properties mediated by cadherins in tissue morphogenesis, synaptic plasticity, and disease. Our work represents the first step toward the mechanical characterization of the cadherin system, opening the door to understanding the mechanical bases of its mechanotransduction.

Binding strength and dynamics of invariant natural killer cell T cell receptor/CD1d-glycosphingolipid interaction on living cells by single molecule force spectroscopy

Invariant natural killer T (iNKT) cells are a population of T lymphocytes that play an important role in regulating immunity to infection and tumors by recognizing endogenous and exogenous CD1d-bound lipid molecules. Using soluble iNKT T cell receptor (TCR) molecules, we applied single molecule force spectroscopy for the investigation of the iNKT TCR affinity for human CD1d molecules loaded with glycolipids differing in the length of the phytosphingosine chain using either recombinant CD1d molecules or lipid-pulsed THP1 cells. In both settings, the dissociation of the iNKT TCR from human CD1d molecules loaded with the lipid containing the longer phytosphingosine chain required higher unbinding forces compared with the shorter phytosphingosine lipid. Our findings are discussed in the context of previous results obtained by surface plasmon resonance measurements. We present new insights into the energy landscape and the kinetic rate constants of the iNKT TCR/human CD1d-glycosphingolipid interaction and emphasize the unique potential of single molecule force spectroscopy on living cells.

Influence of pulling handles and device stiffness in single-molecule force spectroscopy

In single-molecule force spectroscopy, individual molecules and complexes are often stretched by pulling devices via intervening molecular handles. Accurate interpretation of measurements from such experiments in terms of the underlying energy landscape, defined by activation barriers and intrinsic rates of transition, relies on our understanding, and proper theoretical treatment, of the effects of the pulling device and handle. Here, we present a framework based on Kramers' theory that elucidates the dependence of measured rupture forces and rates on the pulling device stiffness and attributes of the handle, contour length and persistence length. We also introduce a simple analytic model that improves prediction of activation barriers and intrinsic rates for all device stiffnesses and handle properties, thus allowing for a more reliable interpretation of experiments. Our analyses also suggests intuitive ways of displaying the measured force spectra for proper prognosis of device and handle effects and provides the range of device and handle attributes over which these effects can be neglected.

DNA condensation by TmHU studied by optical tweezers, AFM and molecular dynamics simulations

The compaction of DNA by the HU protein from Thermotoga maritima (TmHU) is analysed on a single-molecule level by the usage of an optical tweezers-assisted force clamp. The condensation reaction is investigated at forces between 2 and 40 pN applied to the ends of the DNA as well as in dependence on the TmHU concentration. At 2 and 5 pN, the DNA compaction down to 30% of the initial end-to-end distance takes place in two regimes. Increasing the force changes the progression of the reaction until almost nothing is observed at 40 pN. Based on the results of steered molecular dynamics simulations, the first regime of the length reduction is assigned to a primary level of DNA compaction by TmHU. The second one is supposed to correspond to the formation of higher levels of structural organisation. These findings are supported by results obtained by atomic force microscopy.

A mechanically stabilized receptor-ligand flex-bond important in the vasculature

Haemostasis in the arteriolar circulation mediated by von Willebrand factor (VWF) binding to platelets is an example of an adhesive interaction that must withstand strong hydrodynamic forces acting on cells. VWF is a concatenated, multifunctional protein that has binding sites for platelets as well as subendothelial collagen. Binding of the A1 domain in VWF to the glycoprotein Ib alpha subunit (GPIbalpha) on the surface of platelets mediates crosslinking of platelets to one another and the formation of a platelet plug for arterioles. The importance of VWF is illustrated by its mutation in von Willebrand disease, a bleeding diathesis. Here, we describe a novel mechanochemical specialization of the A1-GPIbalpha bond for force-resistance. We have developed a method that enables, for the first time, repeated measurements of the binding and unbinding of a receptor and ligand in a single molecule (ReaLiSM). We demonstrate two states of the receptor-ligand bond, that is, a flex-bond. One state is seen at low force; a second state begins to engage at 10 pN with a approximately 20-fold longer lifetime and greater force resistance. The lifetimes of the two states, how force exponentiates lifetime, and the kinetics of switching between the two states are all measured. For the first time, single-molecule measurements on this system are in agreement with bulk phase measurements. The results have important implications not only for how platelets bound to VWF are able to resist force to plug arterioles, but also how increased flow activates platelet plug formation.

Effect of hydrodynamic interaction on polymeric tethers

Weak bonds are ubiquitous in biological structures. They often act as adhesive contacts within an extended structure, for example, the internal bonds in a folded protein or a DNA/RNA loop. They also act as linkers between two structures, for example, a protein grafted in a cell membrane or a protein linking the cell membranes of two neighboring cells. Typically, the breakage of a bond depends on the strength of the binding potential and viscosity of the medium. But when extended structures couple to the bond, as in the above examples, the dynamics of the structure also has to be considered in order to understand the bond breakage phenomenon. Here we consider a generic model, a stretched polymer (an extended structure) tethered to a soft bond and study how the dynamics of the polymer, in addition to thermal noise, influences bond breakage. We also explore how the hydrodynamic interaction due to the fluid medium, which couples the distant parts of the polymer, change the bond breakage rate. We find that hydrodynamic interaction enhances the breakage rate and also makes the motion of the unstable collective mode of the polymer more coherent.

A microscopic formulation for the actin-driven motion of listeria in curved paths

Using a generalized Brownian ratchet model that accounts for the interactions of actin filaments with the surface of Listeria mediated by proteins like ActA and Arp2/3, we have developed a microscopic model for the movement of Listeria. Specifically, we show that a net torque can be generated within the comet tail, causing the bacteria to spin about its long axis, which in conjunction with spatially varying polymerization at the surface leads to motions of bacteria in curved paths that include circles, sinusoidal-like curves, translating figure eights, and serpentine shapes, as observed in recent experiments. A key ingredient in our formulation is the coupling between the motion of Listeria and the force-dependent rate of filament growth. For this reason, a numerical scheme was developed to determine the kinematic parameters of motion and stress distribution among filaments in a self-consistent manner. We find that a 5-15% variation in polymerization rates can lead to radii of curvatures of the order of 4-20 microm, measured in experiments. In a similar way, our results also show that most of the observed trajectories can be produced by a very low degree of correlation, <10%, among filament orientations. Since small fluctuations in polymerization rate, as well as filament orientation, can easily be induced by various factors, our findings here provide a reasonable explanation for why Listeria can travel along totally different paths under seemingly identical experimental conditions. Besides trajectories, stress distributions corresponding to different polymerization profiles are also presented. We have found that although some actin filaments generate propelling forces that push the bacteria forward, others can exert forces opposing the movement of Listeria, consistent with recent experimental observations.

Kinetic parameters from detection probability in single molecule force spectroscopy

The detection probability of rupture events in AFM force spectroscopy measurements presents a viable alternative to standard methods for extracting kinetic parameters of dissociation. The detection probability has a maximum as a function of the probe velocity where (1) the probability to form a molecular bond is independent of the probe velocity and (2) the detection of rupture events is limited by noise and performed with a constant density of data points per distance of the probe displacement. This newly developed model indicates that the optimal detection velocity is independent of dissociation rate and depends on the distance to the barrier kinetic parameter. Therefore, the kinetic parameters of bond dissociation can be extracted from the dependence of detection probability on probe velocity and the detection threshold. This approach is sensitive to low rupture forces and therefore is complementary to the common most probable force data analysis approach. The developed approach is tested using rupture forces measured with specific bonds between biotin and streptavidin and with nonspecific bonds between linear alkanes in water. Results for the analysis of specific bonds rupture are consistent with the previous measurements, suggesting that rupture forces spanning a wide range of values originate from the same binding potential. Kinetic parameters obtained for linear alkanes are significantly different from previous measurements suggesting possible heterogeneity of the bound state.

Modeling of protrusion phenotypes driven by the actin-membrane interaction

We propose a mathematical model for simulating the leading-edge dynamics of a migrating cell from the interplay among elastic properties, architecture of the actin cytoskeleton, and the mechanics of the membrane. Our approach is based on the description of the length and attachment dynamics of actin filaments in the lamellipodium network. It is used to determine the total force exerted on the membrane at each position along the leading edge and at each time step. The model reproduces the marked state switches in protrusion morphodynamics found experimentally between epithelial cells in control conditions and cells expressing constitutively active Rac, a signaling molecule involved in the regulation of lamellipodium network assembly. The model also suggests a mechanistic explanation of experimental distortions in protrusion morphodynamics induced by deregulation of Arp2/3 and cofilin activity.

Force-induced lysozyme--HyHEL5 antibody dissociation and its analysis by means of a cooperative binding model

Dynamic force spectroscopy probes the kinetic properties of molecules interacting with each other such as antibody-antigen, receptor-ligand, etc. In this article, a statistical model for the dissociation of such cooperative systems is presented. The partner molecules are assumed to be linked by a number of relatively weak bonds that can be grouped together into cooperative units. Single bonds are assumed to open and close statistically. Our model was used to analyze molecular recognition experiments of single receptor-ligand pairs in which the two molecules are brought into contact using an atomic force microscope, which leads to the formation of a strong and specific bond. Then a prescribed time-dependent force is applied to the complex and the statistical distribution of forces needed to pull the molecules completely apart is measured. This quantity is also calculated from our model. Furthermore, its dependence on the model parameters, such as binding free energy, number of bonds and groups, number of cooperative elementary bonds and degree of cooperativity within a group, influence of the force on the binding free energy, and the rate of change of the pulling force, is determined.

Unravelling the design principles for single protein mechanical strength

In recent years single molecule manipulation techniques have improved to the extent that measurements of the mechanical strength of single proteins can now be undertaken routinely. This powerful new tool, coupled with theoretical frameworks to characterise the unfolding process, has enabled significant progress to be made in understanding the physical mechanisms that underlie protein mechanical strength. These design concepts have allowed the search for proteins with novel, mechanically strong folds to be automated and for previously mechanically characterised proteins to be engineered rationally. Methods to achieve the latter are diverse and include re-engineering of specific hydrophobic core residues, changing solvent conditions and the 'cross-linking' of side-chains that are separated in the rate-limiting unfolding transition. Predicting the mechanical behaviour of larger proteins and those with more complex structures remains a significant challenge while on-going instrument development is beginning to allow the examination of mechanical strength of protein across a wide range of force loading rates. The integral role of force in biology and the potential for exploitation of catalytic and structural proteins as functional bio-materials makes this a particularly important area of research.

Reconsideration of dynamic force spectroscopy analysis of streptavidin-biotin interactions

To understand and design molecular functions on the basis of molecular recognition processes, the microscopic probing of the energy landscapes of individual interactions in a molecular complex and their dependence on the surrounding conditions is of great importance. Dynamic force spectroscopy (DFS) is a technique that enables us to study the interaction between molecules at the single-molecule level. However, the obtained results differ among previous studies, which is considered to be caused by the differences in the measurement conditions. We have developed an atomic force microscopy technique that enables the precise analysis of molecular interactions on the basis of DFS. After verifying the performance of this technique, we carried out measurements to determine the landscapes of streptavidin-biotin interactions. The obtained results showed good agreement with theoretical predictions. Lifetimes were also well analyzed. Using a combination of cross-linkers and the atomic force microscope that we developed, site-selective measurement was carried out, and the steps involved in bonding due to microscopic interactions are discussed using the results obtained by site-selective analysis.

Monte Carlo simulation of mechanical unfolding of proteins based on a simple two-state model

Single molecule methods are becoming routine biophysical techniques for studying biological macromolecules. In mechanical unfolding of proteins, an externally applied force is used to induce the unfolding of individual protein molecules. Such experiments have revealed novel information that has significantly enhanced our understanding of the function and folding mechanisms of several types of proteins. To obtain information on the unfolding kinetics and the free energy landscape of the protein molecule from mechanical unfolding data, a Monte Carlo simulation based on a simple two-state kinetic model is often used. In this paper, we provide a detailed description of the procedure to perform such simulations and discuss the approximations and assumptions involved. We show that the appearance of the force versus extension curves from mechanical unfolding of proteins is affected by a variety of experimental parameters, such as the length of the protein polymer and the force constant of the cantilever. We also analyze the errors associated with different methods of data pooling and present a quantitative measure of how well the simulation results fit experimental data. These findings will be helpful in experimental design, artifact identification, and data analysis for single molecule studies of various proteins using the mechanical unfolding method.

Direct and model free calculation of force-dependent dissociation rates from force spectroscopic data

Force spectroscopy allows testing the free energy landscapes of molecular interactions. Usually, the dependency of the most probable rupture force on the force rate or the shape of the rupture force histogram is fitted with different models that contain approximations and basic assumptions. We present a simple and model free approach to extract the force-dependent dissociation rates directly from the force curve data. Simulations show that the dissociation rates at any force are given directly by the ratio of the number of detected rupture events to the time this force was acting on the bond. To calculate these total times of acting forces, all force curve data points of all curves measured are taken into account, which significantly increases the amount of information which is considered for data analysis compared to other methods. Moreover, by providing force-dependent dissociation rates this method allows direct testing and validating of any energy landscape model.

Mechanical strength of 17,134 model proteins and cysteine slipknots

A new theoretical survey of proteins' resistance to constant speed stretching is performed for a set of 17 134 proteins as described by a structure-based model. The proteins selected have no gaps in their structure determination and consist of no more than 250 amino acids. Our previous studies have dealt with 7510 proteins of no more than 150 amino acids. The proteins are ranked according to the strength of the resistance. Most of the predicted top-strength proteins have not yet been studied experimentally. Architectures and folds which are likely to yield large forces are identified. New types of potent force clamps are discovered. They involve disulphide bridges and, in particular, cysteine slipknots. An effective energy parameter of the model is estimated by comparing the theoretical data on characteristic forces to the corresponding experimental values combined with an extrapolation of the theoretical data to the experimental pulling speeds. These studies provide guidance for future experiments on single molecule manipulation and should lead to selection of proteins for applications. A new class of proteins, involving cystein slipknots, is identified as one that is expected to lead to the strongest force clamps known. This class is characterized through molecular dynamics simulations.

The advances in nanotechnology have allowed for manipulation of single biomolecules and determination of their elastic properties. Titin was among the first proteins studied in this way. Its unravelling by stretching requires a 204 pN force. The resistance to stretching comes mostly from a localized region known as a force clamp. In titin, the force clamp is simple as it is formed by two parallel β-strands that are sheared on pulling. Studies of a set of under a hundred proteins accomplished in the last decade have revealed a variety of the force clamps that lead to forces ranging from under 20 pN to about 500 pN. This set comprises only a tiny fraction of proteins known. Thus one needs guidance as to what proteins should be considered for specific mechanical properties. Such a guidance is provided here through simulations within simplified coarse-grained models on 17 134 proteins that are stretched at constant speed. We correlate their unravelling forces with two structure classification schemes. We identify proteins with large resistance to unravelling and characterize their force clamps. Quite a few top strength proteins owe their sturdiness to a new type of the force clamp: the cystein slipknot in which the force peak is due to dragging of a piece of the backbone through a closed ring formed by two other pieces of the backbone and two connecting disulphide bonds.

Stochastic emergence of multiple intermediates detected by single-molecule quasi-static mechanical unfolding of protein

Experimental probing of a protein-folding energy landscape can be challenging, and energy landscapes comprising multiple intermediates have not yet been defined. Here, we quasi-statically unfolded single molecules of staphylococcal nuclease by constant-rate mechanical stretching with a feedback positioning system. Multiple discrete transition states were detected as force peaks, and only some of the multiple transition states emerged stochastically in each trial. This finding was confirmed by molecular dynamics simulations, and agreed with another result of the simulations which showed that individual trajectories took highly heterogeneous pathways. The presence of Ca²⁺ did not change the location of the transition states, but changed the frequency of the emergence. Transition states emerged more frequently in stabilized domains. The simulations also confirmed this feature, and showed that the stabilized domains had rugged energy surfaces. The mean energy required per residue to disrupt secondary structures was a few times the thermal energy (1-3 k_BT), which agreed with the stochastic feature. Thus, single-molecule quasi-static measurement has achieved notable success in detecting stochastic features of a huge number of possible conformations of a protein.

Single molecular pair interactions between hydrophobically modified hydroxyethyl cellulose and amylose determined by dynamic force spectroscopy

Interactions among HMHEC (hydrophobically modified hydroxyethyl cellulose) and between HMHEC and amylose were investigated by means of dynamic force spectroscopy of single molecular pairs. The technique was realized using a scanning probe based platform, and the molecular pair interactions were investigated in aqueous solutions over a range of force loading rates. Both hydrophobic interactions among hydrophobe C(16) alkyl side chains in HMHEC and association between these hydrophobes in HMHEC and amylose showed a stretching type peak. The distribution analysis of rupture force based on Bell-Evans's model revealed that the peaks had a most probable rupture force ranging from 27 pN at a force loading rate r(f) = 0.43 nN/s to 125 pN at r(f) = 170 nN/s for HMHEC-HMHEC, and from 13 pN at r(f) = 0.20 nN/s to 34 pN at r(f) = 33.7 nN/s for HMHEC-amylose interactions. The distance of the energy barrier relative to the minimum, x(beta), and the apparent lifetime in the absence of external force, tau, were found to depend on the force loading rate, and the average values are estimated to be 0.99 nm and 0.89s for HMHEC-HMHEC and 0.31 nm and 0.075s for HMHEC-amylose interactions. The obtained data for these pairwise molecular interactions are underpinning the associative behavior of the macroscopic properties of aqueous solutions of these polysaccharides.

A theoretical model for the mechanical unfolding of repeat proteins

We consider the mechanical stretching of a polypeptide chain formed by multiple interacting repeats. The folding thermodynamics and the interactions among the repeats are described by the Ising model. Unfolded repeats act as soft entropic springs, whereas folded repeats respond to a force as stiffer springs. We show that the resulting force-extension curve may exhibit a pronounced force maximum corresponding to the unfolding of the first repeat. This event is followed by the unfolding of the remaining repeats, which takes place at a lower force. As the protein extension is increased, the force-extension curve of a sufficiently long repeat protein displays a plateau, where the force remains nearly constant and the protein unfolds sequentially so that the number of unfolded repeats is proportional to the extension. Such a sequential mechanical unfolding mechanism is displayed even by the repeat proteins whose thermal denaturation is highly cooperative, provided that they are long enough. By contrast, the unfolding of short repeat progressions can be cooperative.

Periodic forces trigger a complex mechanical response in ubiquitin

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

Mechanics model for actin-based motility

We present here a mechanics model for the force generation by actin polymerization. The possible adhesions between the actin filaments and the load surface, as well as the nucleation and capping of filament tips, are included in this model on top of the well-known elastic Brownian ratchet formulation. A closed form solution is provided from which the force-velocity relationship, summarizing the mechanics of polymerization, can be drawn. Model predictions on the velocity of moving beads driven by actin polymerization are consistent with experiment observations. This model also seems capable of explaining the enhanced actin-based motility of Listeria monocytogenes and beads by the presence of Vasodilator-stimulated phosphoprotein, as observed in recent experiments.

Dynamic force spectroscopy: Analysis of reversible bond-breaking dynamics

The problem of diffusive bond dissociation in a double well potential under application of an external force is scrutinized. We compute the probability distribution of rupture forces and present a detailed discussion of the influence of finite rebinding probabilities on the dynamic force spectrum. In particular, we focus on barrier crossing upon extension, i.e., under linearly increased load, and upon relaxation starting from completely separated bonds. For large loading rates the rupture force and the rejoining force depend on the loading rate in the expected manner determined by the shape of the potential. For small loading rates the mean forces obtained from pull and relax modes approach each other as the system reaches equilibrium. We investigate the dependence of the rupture force distributions and mean rupture forces on external parameters such as cantilever stiffness and influence of a soft linker. We find that depending on the implementation of a soft linker the equilibrium rupture force is either unaffected by the presence of the linker or changes in a predictable way with the linker compliance. Additionally, we show that it is possible to extract the equilibrium constant of the on and off rates from the determination of the equilibrium rupture forces.

Beyond molecular recognition: using a repulsive field to tune interfacial valency and binding specificity between adhesive surfaces

Surface-bound biomolecular fragments enable "smart" materials to recognize cells and other particles in applications ranging from tissue engineering and medical diagnostics to colloidal and nanoparticle assembly. Such smart surfaces are, however, limited in their design to biomolecular selectivity. This feature article demonstrates, using a completely nonbiological model system, how specificity can be achieved for particle (and cell) binding, employing surface designs where immobilized nanoscale adhesion elements are entirely nonselective. Fundamental principles are illustrated by a model experimental system where 11 nm cationic nanoparticles on a planar negative silica surface interact with flowing negative silica microspheres having 1.0 and 0.5 microm diameters. In these systems, the interfacial valency, defined as the number of cross-bonds needed to capture flowing particles, is tunable through ionic strength, which alters the range of the background repulsion and therefore the effective binding strength of the adhesive elements themselves. At high ionic strengths where long-range electrostatic repulsions are screened, single surface-bound nanoparticles capture microspheres, defining the univalent regime. At low ionic strengths, competing repulsions weaken the effective nanoparticle adhesion so that multiple nanoparticles are needed for microparticle capture. This article discusses important features of the univalent regime and then illustrates how multivalency produces interfacial-scale selectivity. The arguments are then generalized, providing a possible explanation for highly specific cell binding in nature, despite the degeneracy of adhesion molecules and cell types. The mechanism for the valency-related selectivity is further developed in the context of selective flocculation in the colloidal literature. Finally, results for multivalent binding are contrasted with the current thinking for interfacial design and the presentation of adhesion moieties on engineered surfaces.

Multiple receptors involved in human rhinovirus attachment to live cells

Minor group human rhinoviruses (HRVs) attach to members of the low-density lipoprotein receptor family and are internalized via receptor-mediated endocytosis. The attachment of HRV2 to the cell surface, the first step in infection, was characterized at the single-molecule level by atomic force spectroscopy. Sequential binding of multiple receptors was evident from recordings of characteristic quantized force spectra, which suggests that multiple receptors bound to the virus in a timely manner. Unbinding forces required to detach the virus from the cell membrane increased within a time frame of several hundred milliseconds. The number of receptors involved in virus binding was determined, and estimates for on-rate, off-rate, and equilibrium binding constant of the interaction between HRV2 and plasma membrane-anchored receptors were obtained.

Theory, analysis, and interpretation of single-molecule force spectroscopy experiments

Dynamic force spectroscopy probes the kinetic and thermodynamic properties of single molecules and molecular assemblies. Here, we propose a simple procedure to extract kinetic information from such experiments. The cornerstone of our method is a transformation of the rupture-force histograms obtained at different force-loading rates into the force-dependent lifetimes measurable in constant-force experiments. To interpret the force-dependent lifetimes, we derive a generalization of Bell's formula that is formally exact within the framework of Kramers theory. This result complements the analytical expression for the lifetime that we derived previously for a class of model potentials. We illustrate our procedure by analyzing the nanopore unzipping of DNA hairpins and the unfolding of a protein attached by flexible linkers to an atomic force microscope. Our procedure to transform rupture-force histograms into the force-dependent lifetimes remains valid even when the molecular extension is a poor reaction coordinate and higher-dimensional free-energy surfaces must be considered. In this case the microscopic interpretation of the lifetimes becomes more challenging because the lifetimes can reveal richer, and even nonmonotonic, dependence on the force.

The effects of macromolecular crowding on the mechanical stability of protein molecules

Macromolecular crowding, a common phenomenon in the cellular environments, can significantly affect the thermodynamic and kinetic properties of proteins. A single-molecule method based on atomic force microscopy (AFM) was used to investigate the effects of macromolecular crowding on the forces required to unfold individual protein molecules. It was found that the mechanical stability of ubiquitin molecules was enhanced by macromolecular crowding from added dextran molecules. The average unfolding force increased from 210 pN in the absence of dextran to 234 pN in the presence of 300 g/L dextran at a pulling speed of 0.25 microm/sec. A theoretical model, accounting for the effects of macromolecular crowding on the native and transition states of the protein molecule by applying the scaled-particle theory, was used to quantitatively explain the crowding-induced increase in the unfolding force. The experimental results and interpretation presented could have wide implications for the many proteins that experience mechanical stresses and perform mechanical functions in the crowded environment of the cell.

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

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

Optimum size of a molecular bond cluster in adhesion

The strength of a bonded interface is considered for the case in which bonding is the result of clusters of discrete bonds distributed along the interface. Assumptions appropriate for the case of adhesion of biological cells to an extracellular matrix are introduced as a basis for the discussion. It is observed that those individual bonds nearest to the edges of a cluster are necessarily subjected to disproportionately large forces in transmitting loads across the interface, in analogy with well-known behavior in elastic crack mechanics. Adopting Bell's model for the kinetics of bond response under force, a stochastic model leading to a dependence of interface strength on cluster size is developed and analyzed. On the basis of this model, it is demonstrated that there is an optimum cluster size for maximum strength. This size arises from the competition between the nonuniform force distribution among bonds, which tends to promote smaller clusters, and stochastic response allowing bond reformation, which tends to promote larger clusters. The model results have been confirmed by means of direct Monte Carlo simulations. This analysis may be relevant to the observation that mature focal adhesion zones in cell bonding are found to have a relatively uniform size.

Effects of multiple-bond ruptures on kinetic parameters extracted from force spectroscopy measurements: revisiting biotin-streptavidin interactions

Force spectroscopy measurements of the rupture of the molecular bond between biotin and streptavidin often results in a wide distribution of rupture forces. We attribute the long tail of high rupture forces to the nearly simultaneous rupture of more than one molecular bond. To decrease the number of possible bonds, we employed hydrophilic polymeric tethers to attach biotin molecules to the atomic force microscope probe. It is shown that the measured distributions of rupture forces still contain high forces that cannot be described by the forced dissociation from a deep potential well. We employed a recently developed analytical model of simultaneous rupture of two bonds connected by polymer tethers with uneven length to fit the measured distributions. The resulting kinetic parameters agree with the energy landscape predicted by molecular dynamics simulations. It is demonstrated that when more than one molecular bond might rupture during the pulling measurements there is a noise-limited range of probe velocities where the kinetic parameters measured by force spectroscopy correspond to the true energy landscape. Outside this range of velocities, the kinetic parameters extracted by using the standard most probable force approach might be interpreted as artificial energy barriers that are not present in the actual energy landscape. Factors that affect the range of useful velocities are discussed.

Measuring molecular rupture forces between single actin filaments and actin-binding proteins

Actin-binding proteins (ABPs) regulate the assembly of actin filaments (F-actin) into networks and bundles that provide the structural integrity of the cell. Two of these ABPs, filamin and alpha-actinin, have been extensively used to model the mechanical properties of actin networks grown in vitro; however, there is a lack in the understanding of how the molecular interactions between ABPs and F-actin regulate the dynamic properties of the cytoskeleton. Here, we present a native-like assay geometry to test the rupture force of a complex formed by an ABP linking two quasiparallel actin filaments. We readily demonstrate the adaptability of this assay by testing it with two different ABPs: filamin and alpha-actinin. For filamin/actin and alpha-actinin/actin, we measured similar rupture forces of 40-80 pN for loading rates between 4 and 50 pN/s. Both ABP unfolding and conformational transition events were observed, demonstrating that both are important and may be a significant mechanism for the temporal regulation of the mechanical properties of the actin cytoskeleton. With this modular, single-molecule assay, a wide range of ABP/actin interactions can be studied to better understand cytoskeletal and cell dynamics.

Mechanical regulation of cell adhesion

Cellular adhesion against external forces is governed by both the equilibrium affinity of the involved receptor-ligand bonds and the mechanics of the cell. Certain receptors like integrins change their affinity as well as the mechanics of their anchorage to tune the adhesiveness. Whereas in the last few years the focus of integrin research has lain on the affinity regulation of the adhesion receptors, more recently the importance of cellular mechanics became apparent. Here, we focus on different aspects of the mechanical regulation of the cellular adhesiveness.

What is the biological relevance of the specific bond properties revealed by single-molecule studies?

During the last decade, many authors took advantage of new methodologies based on atomic force microscopy (AFM), biomembrane force probes (BFPs), laminar flow chambers or optical traps to study at the single-molecule level the formation and dissociation of bonds between receptors and ligands attached to surfaces. Experiments provided a wealth of data revealing the complexity of bond response to mechanical forces and the dependence of bond rupture on bond history. These results supported the existence of multiple binding states and/or reaction pathways. Also, single bond studies allowed us to monitor attachments mediated by a few bonds. The aim of this review is to discuss the impact of this new information on our understanding of biological molecules and phenomena. The following points are discussed: (i) which parameters do we need to know in order to predict the behaviour of an encounter between receptors and ligands, (ii) which information is actually yielded by single-molecule studies and (iii) is it possible to relate this information to molecular structure?

The viscoelasticity of membrane tethers and its importance for cell adhesion

Cell adhesion mechanically couples cells to surfaces. The durability of individual bonds between the adhesive receptors and their ligands in the presence of forces determines the cellular adhesion strength. For adhesive receptors such as integrins, it is a common paradigm that the cell regulates its adhesion strength by altering the affinity state of the receptors. However, the probability distribution of rupture forces is dependent not only on the affinity of individual receptor-ligand bonds but also on the mechanical compliance of the cellular anchorage of the receptor. Hence, by altering the anchorage, the cell can regulate its adhesion strength without changing the affinity of the receptor. Here, we analyze the anchorage of the integrin VLA-4 with its ligand VCAM-1. For this purpose, we develop a model based on the Kelvin body, which allows one to quantify the mechanical properties of the adhesive receptor's anchorage using atomic force microscopy on living cells. As we demonstrate, the measured force curves give valuable insight into the mechanics of the cellular anchorage of the receptor, which is described by the tether stiffness, the membrane rigidity, and the membrane viscosity. The measurements relate to a tether stiffness of k(t) = 1.6 microN/m, an initial membrane rigidity of k(i) = 260 microN/m, and a viscosity of mu = 5.9 microN x s/m. Integrins exist in different activation states. When activating the integrin with Mg(2+), we observe altered viscoelastic parameters of k(t) = 0.9 microN/m, k(i) = 190 microN/m, and mu = 6.0 microN x s/m. Based on our model, we postulate that anchorage-related effects are common regulating mechanisms for cellular adhesion beyond affinity regulation.

Dynamic strength of the silicon-carbon bond observed over three decades of force-loading rates

The mechanical strength of individual Si-C bonds was determined as a function of the applied force-loading rate by dynamic single-molecule force spectroscopy, using an atomic force microscope. The applied force-loading rates ranged from 0.5 to 267 nN/s, spanning 3 orders of magnitude. As predicted by Arrhenius kinetics models, a logarithmic increase of the bond rupture force with increasing force-loading rate was observed, with average rupture forces ranging from 1.1 nN for 0.5 nN/s to 1.8 nN for 267 nN/s. Three different theoretical models, all based on Arrhenius kinetics and analytic forms of the binding potential, were used to analyze the experimental data and to extract the parameters fmax and D(e) of the binding potential, together with the Arrhenius A-factor. All three models well reproduced the experimental data, including statistical scattering; nevertheless, the three free parameters allow so much flexibility that they cannot be extracted unambiguously from the experimental data. Successful fits with a Morse potential were achieved with fmax = 2.0-4.8 nN and D(e) = 76-87 kJ/mol, with the Arrhenius A-factor covering 2.45 x 10(-10)-3 x 10(-5) s(-1), respectively. The Morse potential parameters and A-factor taken from gas-phase density functional calculations, on the other hand, did not reproduce the experimental forces and force-loading rate dependence.