On the detection of single bond ruptures in dynamic force spectroscopy by AFM.

Force spectroscopy is a novel tool in physical chemistry and biophysics. This methodology is aimed at providing kinetic parameters of dissociation at a single-molecule level by rupturing molecular bonds subjected to different loading rates. One persistent problem in the implementation of this methodology is a question about the single-bond nature of the rupture events detected in experiments based on atomic force microscopy. Here we address this question by considering the probability that the nearly simultaneous rupture of two molecular bonds might appear as a single bond rupture in the experimental data, complicating the data analysis and contributing to systematic errors in the extracted kinetic parameters. An approximate analytical model predicts that such events might be common in experiments employing soft cantilever force sensors and short tethers to immobilize the interacting molecules. These findings are confirmed by a more elaborate numerical model providing valuable guidelines on performing single-molecule force spectroscopy experiments.

Mechanical distortion of protein receptor decreases the lifetime of a receptor-ligand bond.

Substantial experimental evidence indicates that the mechanical force applied to pull apart non-covalent molecular bonds (such as receptor-ligand pairs) can significantly decrease the bond lifetime. This evidence is often generated in single-molecule experiments that are designed to specifically test effects of pulling forces. However, the effect of compressive forces on the lifetime of receptor-ligand bonds remains largely unexplored. Here we extend the common usage of the atomic force microscopy technique to study whether compressive forces applied to bound streptavidin-biotin species can significantly accelerate the rate of dissociation. Presented experimental data indicate that compressive forces can substantially decrease the lifetime of the molecular bond. Surprisingly, the efficiency of accelerating dissociation by compressive forces sometimes exceeds the enhancement of the dissociation rate measured in pulling experiments, indicating that compressive forces applied to the bound species might be efficiently used to control the lifetime of adhesion bonds.

Molecular stress relief through a force-induced irreversible extension in polymer contour length.

Single-molecule force spectroscopy is used to observe the irreversible extension of a gem-dibromocyclopropane (gDBC)-functionalized polybutadiene under tension, a process akin to polymer necking at a single-molecule level. The extension of close to 28% in the contour length of the polymer backbone occurs at roughly 1.2 nN (tip velocity of 3 µm/s) and is attributed to the force-induced isomerization of the gDBCs into 2,3-dibromoalkenes. The rearrangement represents a possible new mechanism for localized stress relief in polymers and polymer networks under load, and the quantification of the force dependency provides a benchmark value for further studies of mechanically triggered chemistry in bulk polymers.

Calcium dependence of fibrin nanomechanics: the γ1 calcium mediates the unfolding of fibrinogen induced by force applied to the "A-a" bond.

The interactions between the constituent monomers of fibrin, the polymerized protein network that provides the structural stability of blood clots, are frequently under stress because of the dynamic nature of blood flow. Herein, the calcium dependence of the structural unfolding linked to the forced dissociation of the "A-a" knob-hole bond between fibrin monomers is reported. The presence of calcium was shown to influence the incidence of the last event in the unfolding pattern characteristic of "A-a" rupture. This effect, attributed to the function of the γ1 calcium-binding site, was found to be reversible and specific. Our results indicate that binding of calcium at the γ1 site has no effect on the strength of the knob-hole bond prior to unfolding of the hole-containing γ module. Rather, calcium bound at the γ1 site makes the structure of the hole more resilient to such forced unfolding, leading to survival of the "A-a" knob-hole bond during larger extensions of the fibrinogen molecule but at the cost of rupture of the bond at lower forces.

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.

Association kinetics from single molecule force spectroscopy measurements.

Single molecule force spectroscopy is often used to study the dissociation of single molecules by applying mechanical force to the intermolecular bond. These measurements provide the kinetic parameters of dissociation. We present what to our knowledge is a new atomic force microscopy-based approach to obtain the activation energy of the association reaction and approximate grafting density of reactive receptors using the dependence of the probability to form molecular bonds on probe velocity when one of the interacting molecules is tethered by a flexible polymeric linker to the atomic force microscopy probe. Possible errors in the activation energy measured with this approach are considered and resulting corrections are included in the data analysis. This new approach uses the same experimental setup as traditional force spectroscopy measurements that quantify dissociation kinetics. We apply the developed methodology to measure the activation energy of biotin-streptavidin association (including a contribution from the steric factor) and obtain a value of 8 +/- 1 kT. This value is consistent with the association rate measured previously in solution. Comparison with the solution-derived activation energy indicates that kinetics of biotin-streptavidin binding is mainly controlled by the reaction step.

Kinetics of the multistep rupture of fibrin 'A-a' polymerization interactions measured using atomic force microscopy.

Fibrin, the structural scaffold of blood clots, spontaneously polymerizes through the formation of 'A-a' knob-hole bonds. When subjected to external force, the dissociation of this bond is accompanied by two to four abrupt changes in molecular dimension observable as rupture events in a force curve. Herein, the configuration, molecular extension, and kinetic parameters of each rupture event are examined. The increases in contour length indicate that the D region of fibrinogen can lengthen by approximately 50% of the length of a fibrin monomer before rupture of the 'A-a' interaction. The dependence of the dissociation rate on applied force was obtained using probability distributions of rupture forces collected at different pull-off velocities. These distributions were fit using a model in which the effects of the shape of the binding potential are used to quantify the kinetic parameters of forced dissociation. We found that the weak initial rupture (i.e., event 1) was not well approximated by these models. The ruptured bonds comprising the strongest ruptures, events 2 and 3, had kinetic parameters similar to those commonly found for the mechanical unfolding of globular proteins. The bonds ruptured in event 4 were well described by these analyses, but were more loosely bound than the bonds in events 2 and 3. We propose that the first event represents the rupture of an unknown interaction parallel to the 'A-a' bond, events 2 and 3 represent unfolding of structures in the D region of fibrinogen, and event 4 is the rupture of the 'A-a' knob-hole bond weakened by prior structural unfolding. Comparison of the activation energy obtained via force spectroscopy measurements with the thermodynamic free energy of 'A-a' bond dissociation indicates that the 'A-a' bond may be more resistant to rupture by applied force than to rupture by thermal dissociation.

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.

Pairwise interactions between linear alkanes in water measured by AFM force spectroscopy.

Pairwise interactions between n-alkanes from decane to octadecane in water have been studied by single-molecule force spectroscopy. The interacting molecules are covalently tethered to the glass substrate and to the probe of an atomic force microscope by water-soluble linkers to facilitate single-molecule detection. However, the measured distribution of rupture forces deviates significantly from the distribution predicted by theoretical models for rupture of individual bonds. To describe the statistics of rupture forces, an analytical model that considers near-simultaneous rupture of two bonds loaded by tethers with different lengths is introduced. The common most probable force analysis approach is used for comparison. In both data analyses, the possible systematic errors due to nonlinear elasticity of polymeric tethers and variations in the shape of the potential of mean force were considered. Experimental distributions of rupture forces are well-fit by the two-bond rupture model using a single set of kinetic parameters for different experiments, while the most probable force approach yields parameters that vary significantly for different samples. The measured activation energies for dissociation of alkanes are close to the free energies predicted by cavity models of hydrophobic interactions. The surface free-energy density is estimated to be approximately 21 kJ/(mol nm (2)) and is close to the upper limit of free energies used in the computer simulations of hydrophobic interactions in proteins. In contrast to the predictions of the cavity models, the measured activation energy does not increase monotonically with increase in alkane chain size. To explain this discrepancy and the measured distance to the transition-state barrier (approximately 0.6 nm), it is suggested that alkanes undergo conformational transition to the collapsed state upon dimerization. Change in the alkane conformation from extended to helical has been observed previously for binding of alkanes in water to hydrophobic synthetic receptors. Here, however, conformational change is suggested without geometrical constraints imposed by small cavitands. The proposed collapsed state of the alkane dimers has implications for the kinetics of self-assembly of surfactant micelles.

Surface elastic properties of human retinal pigment epithelium melanosomes.

Atomic force microscope (AFM) imaging and nanoindentation measurements in water were used to probe the mechanical properties of retinal pigment epithelium melanosomes isolated from 14-year-old and 76-year-old donors. Topographic imaging reveals surface roughness similar to previous measurements on dry melanosomes. Force-indentation measurements show different types of responses that were catalogued into four different categories. In these measurements no permanent surface damage of melanosomes was observed as revealed by imaging before and after indentation measurements. The indentation measurements that exhibited nearly elastic responses were used to determine the Young's modulus of melanosomes. The average Young's modulus values are similar for 14-year-old and 76-year-old melanosomes with a somewhat narrower distribution for the 14-year-old sample. These elastic modulus values are considerably higher than the modulus of organelles with cytoplasm (<1 MPa) and approaching values of the modulus of protein crystals (approximately 100 MPa) indicating rather high packing density of biologic material in melanosomes. The width of the Young's modulus distributions is considerable spanning from few megapascals to few tens of megapascals indicating large heterogeneity in the structure. A fraction of the force curves cannot be described by the homogeneous elastic sample model; these force curves are consistent with approximately 10 nm structural heterogeneity in melanosomes. The approach-withdraw hysteresis indicates a significant viscoelasticity, particularly in the samples from the 14-year-old sample. Adhesion of the AFM probe was detected on approximately 3% and approximately 20% of the surface of 14-year-old and 76-year-old samples, respectively. In light of previous studies on these same melanosomes using photoelectron emission microscopy, this adhesion is attributed to the presence of lipofuscin on the surface of the melanosomes. This suggestion indicates that part of the difference in photochemical properties between the old and young melanosomes originates from surface lipofuscin.

Correction of systematic errors in single-molecule force spectroscopy with polymeric tethers by atomic force microscopy.

Single-molecule force spectroscopy has become a valuable tool for the investigation of intermolecular energy landscapes for a wide range of molecular associations. Atomic force microscopy (AFM) is often used as an experimental technique in these measurements, and the Bell-Evans model is commonly used in the statistical analysis of rupture forces. Most applications of the Bell-Evans model consider a constant loading rate of force applied to the intermolecular bond. The data analysis is often inconsistent because either the probe velocity or the apparent loading rate is being used as an independent parameter. These approaches provide different results when used in AFM-based experiments. Significant variations in results arise from the relative stiffness of the AFM force sensor in comparison with the stiffness of polymeric tethers that link the molecules under study to the solid surfaces. An analytical model presented here accounts for the systematic errors in force-spectroscopy parameters arising from the nonlinear loading induced by polymer tethers. The presented analytical model is based on the Bell-Evans model of the kinetics of forced dissociation and on the asymptotic models of tether stretching. The two most common data reduction procedures are analyzed, and analytical expressions for the systematic errors are provided. The model shows that the barrier width is underestimated and that the dissociation rate is significantly overestimated when force-spectroscopy data are analyzed without taking into account the elasticity of the polymeric tether. Systematic error estimates for asymptotic freely jointed chain and wormlike chain polymer models are given for comparison. The analytical model based on the asymptotic freely jointed chain stretching is employed to analyze and correct the results of the double-tether force-spectroscopy experiments of disjoining "hydrophobic bonds" between individual hexadecane molecules that are covalently tethered via poly(ethylene glycol) linkers of different lengths to the substrates and to the AFM probes. Application of the correction algorithm decreases the spread of the data from the mean value, which is particularly important for measurements of the dissociation rate, and increases the barrier width to 0.43 nm, which might be indicative of the theoretically predicted hydrophobic dewetting.

Single-molecule force spectroscopy measurements of "hydrophobic bond" between tethered hexadecane molecules.

The hydrophobic effect is important for many biological and technological processes. Despite progress in theory, experimental data clarifying water structure and the interaction between hydrophobic solutes at the nanometer scale are scarce due to the very low solubility of hydrophobic species. This article describes an AFM single molecule force spectroscopy method to probe the interaction between molecules with low solubility and reports measurements of the strength and the length scale of the "hydrophobic bond" between hexadecane molecules. Hexadecane molecules are tethered by flexible poly(ethylene glycol) linkers to AFM probes and substrates, removing the aggregation state uncertainty of solution-based approaches as well as spurious surface effects. A shorter hydrophilic polymer layer is added to increase the accessibility of hydrophobic molecules for the force spectroscopy measurements. Statistical analysis of the rupture forces yields a barrier width of 0.24 nm, and a dissociation rate of 1.1 s(-1). The results of single molecule measurements are related to the theoretical predictions of the free energy of cavitation in water and to the empirical model of micellization of nonionic surfactants. It is estimated that approximately one-quarter of each molecule's surface is hydrated during forced dissociation, consistent with an extended (nonglobular) conformation of the hexadecane molecules in the dimer.

Force Modulation Elasticity Mapping of Plastic-embedded, Thin-sectioned Skeletal Muscle.

We have been researching the capability of atomic force microscopy to reveal nontopographic properties of tissue embedded in plastic and sectioned with standard electron microscopic techniques. We present topography and elasticity maps of plastic-embedded, thin sections of muscle tissue. The images show topography correlated with the normal repeating structure of the sarcomere. Elasticity mapping using force modulation revealed contrast between the actin- and myosin-rich areas. We attribute the observed contrast in elasticity to the difference in local concentrations of biological material in embedding plastic.

Assembly, tuning and use of an apertureless near field infrared microscope for protein imaging.

This paper aims to instruct the reader in the assembly and operation of an infrared near-field microscope for imaging beyond the diffraction limit. The apertureless near-field microscope is a light scattering-type instrument that provides infrared spectra at circa 20 nm resolution. A complete list of components and a step-by-step protocol for use is provided. Common errors in assembly and instrument tuning are discussed. A representative data set that shows the secondary structure of an amyloid fibril is presented.

Investigation of mechanical properties of insulin crystals by atomic force microscopy.

Mechanical properties of protein crystals and aggregates depend on the conformational and structural properties of individual protein molecules as well as on the packing density and structure within solid materials. An atomic force microscopy (AFM)-based approach is developed to measure the elastic modulus of small protein crystals by nanoindentation and is applied to measure the elasticity of insulin crystals. The top face of the crystals deposited on mica substrates is identified as the (001) face. Insulin crystals exhibit a nearly elastic response during the compression cycle. The elastic modulus measured on the top face has asymmetric distribution with a significant width. This width is related to the uncertainty in the deflection sensitivity. A model that takes into account the distribution of the sensitivity values is used to correct the elastic modulus. Measurements performed in aqueous buffer on several crystals at different locations with three different AFM probes give a mean elastic modulus of 164 +/- 10 MPa. This value is close to the static elastic moduli of other protein crystals measured by different techniques that are usually measured in the range from 100 MPa to 1 GPa. The measured modulus of insulin crystals falls between the elastic modulus values of insulin amyloid fibrils measured previously at two orthogonal directions (a modulus of 14 MPa was measured by compressing the fibril in the direction perpendicular to the fibril axis, and a modulus of 3.3 GPa was measured in the direction along the fibril axis). This comparison indicates the heterogeneous structure of fibrils in the direction perpendicular to the fibril axis, with a packing density of the amyloid fibril core that is higher than the average packing density in insulin crystals. The mechanical wear of insulin crystals is detected during AFM measurements. In nanoindentation experiments on insulin crystal, the compressive load by the AFM tip ( approximately 1 nN, corresponding to a pressure of around 5 MPa) occasionally removes protein molecules from the top or the second top layer of insulin crystal in a sequential manner. The molecular model of this surface damage is proposed. In addition, the removal of the multiple layers of molecules is observed during the AC-mode imaging in aqueous buffer. The number of removed layers depends on the scan size.

Complexity of "A-a" knob-hole fibrin interaction revealed by atomic force spectroscopy.

During blood vessel injury, fibrinogen is converted to fibrin, a polymer that serves as the structural scaffold of a blood clot. The primary function of fibrin is to withstand the large shear forces in blood and provide mechanical stability to the clot, protecting the wound. Understanding the biophysical forces involved in maintaining fibrin structure is of great interest to the biomedical community. Previous reports have identified the "A-a" knob-hole interaction as the dominant force responsible for fibrin's structural integrity. Herein, biochemical force spectroscopy is used to study knob-hole interactions between fibrin fragments and variant fibrinogen molecules to identify the forces occurring between individual fibrin molecules. The rupture of the "A-a" knob-hole interaction results in a characteristic profile previously unreported in fibrin force spectroscopy with two distinct populations of specific forces: 110 +/- 34 and 224 +/- 31 pN. In the absence of a functional "A" knob or hole "a", these forces cease to exist. We propose that the characteristic pattern represents the deformation of the D region of fibrinogen prior to the rupture of the "A-a" knob-hole bond.

Rupture force analysis and the associated systematic errors in force spectroscopy by AFM.

Force spectroscopy is a new and valuable tool in physical chemistry and biophysics. However, data analysis has yet to be standardized, hindering the advancement of the technique. In this article, treatment of the rupture forces is described in the framework of the Bell-Evans model, and the systematic errors associated with the tether effect for approaches that utilize the most probable, the median, and the mean rupture forces are compared. It is shown that significant systematic errors in the dissociation rate can result from nonlinear loading with polymeric tethers even if the apparent loading rate is used in the analysis. Analytical expressions for the systematic errors are provided for the most probable and median forces. The use of these expressions to correct the associated systematic errors is illustrated by the analysis of the measured rupture forces between single hexadecane molecules in water. It is noted that the measured distributions of rupture forces often contain high forces that are unaccounted for by theoretical models. Experimental data indicate that the most significant effect of the high forces "tail" is on the dissociation rate obtained from the median force analysis whereas the barrier width appears to be unaffected.

Packing density and structural heterogeneity of insulin amyloid fibrils measured by AFM nanoindentation.

A nanoindentation approach based on atomic force microscopy was applied to test the elastic properties of insulin amyloid fibrils. Fibrils exhibited a nearly elastic response to the compressive load. The results, corrected for the finite sample thickness effect, reveal that the fibril Young's modulus is considerably lower than the modulus of protein crystals, suggesting lower packing density in amyloid fibrils. Variation in elasticity among and within fibrils has been studied, showing that the Young's moduli of insulin fibrils have a relatively wide distribution of values, ranging from 5 to 50 MPa. Amyloid fibrils with higher modulus were found to be more wear-resistant during AFM scanning. The measured distribution of elasticity values of different fibrils together with wear-resistance tests indicates structural heterogeneity among fibrils, whereas the structure of individual fibrils appears to be homogeneous. The relative simplicity of the method used in this study can facilitate rapid collection of quantitative information related to the packing density and heterogeneity of fibrils formed by different proteins.

Conformational heterogeneity of surface-grafted amyloidogenic fragments of alpha-synuclein dimers detected by atomic force microscopy.

A force-spectroscopy-based approach is used to characterize separation between amyloidogenic peptide fragments of alpha-synuclein. Interactions between individual molecules are studied using a scanning-force-microscopy-based technique. Alpha-synuclein fragments are attached to the solid surfaces via flexible long poly-(ethylene glycol) linkers removing aggregation state uncertainty of solution-based approaches and spurious surface effects. Tethering one fragment to the scanning probe tip and another fragment to the second surface ensures that interactions between tethered molecules are studied. Control experiments with only one tethered peptide indicate peptide-peptide interactions as the source of observed interaction forces in the double-tether experiment. The temperature dependence of rupture forces from 17.5 degrees C to 40 degrees C reveals similar molecular parameters indicating that no significant conformational changes occur in the associated molecules over this temperature range. Rate-dependent measurements indicate conformational heterogeneity of joined peptide molecules.