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.     

Strength of multiple parallel biological bonds

Multivalent interactions play a critical role in a variety of biological processes on both molecular and cellular levels. We have used molecular force spectroscopy to investigate the strength of multiple parallel peptide-antibody bonds using a system that allowed us to determine the rupture forces and the number of ruptured bonds independently. In our experiments the interacting molecules were attached to the surfaces of the probe and sample of the atomic force microscope with flexible polymer tethers, and the unique mechanical signatures of the tethers determined the number of ruptured bonds. We show that the rupture forces increase with the number of interacting molecules and that the measured forces obey the predictions of a Markovian model for the strength of multiple parallel bonds. We also discuss the implications of our results to the interpretation of force spectroscopy measurements in multiple bond systems.     

Forces Required to Initiate Membrane Tether Extrusion from Cell Surface Depend on Cell Type But Not on the Surface Molecule

When a cell adhered to another cell or substratum via surface proteins is forced to detach, lipid membrane tethers are often extruded from the cell surface before the protein bond dissociates. For example, during the inflammatory reaction leukocytes roll on the surface of activated endothelial cells. The rolling adhesion is mediated by interactions of selectins with their ligands, e.g., P-selectin glycoprotein ligand (PSGL)-1, which extrudes membrane tethers from the surfaces of both leukocytes and endothelial cells. Membrane tether extrusion has been suggested to regulate leukocyte rolling. Here we examine several factors that may affect forces required to initiate membrane tethers, or initial tether force. It was found that initial tether forces were similar regardless of the presence or absence of the cytoplasmic tail of P-selectin and regardless of whether the tethers were extruded via binding to PSGL-1 or Fcγ receptors. Initial tether forces were found to depend on the cell types tested and were greatly reduced by treatment of latrunculin A, which inhibits actin polymerization. These data provide additional insights to the control of membrane tether extrusion, which should be taken into account when cellular functions such as rolling where tether extrusion plays a regulatory role are compared using different cell types expressing the same molecule.     

Stability of molecular adhesion mediated by confined polymer repellers and ligand-receptor bonds

Experiments have shown that stable adhesion of a variety of animal cells on substrates prepared with precisely controlled ligand distribution can be formed only if the ligand spacing is below 58 nm. To explain this phenomenon, here we propose a confined polymer model to study the stability of molecular adhesion mediated by polymer repellers and ligand-receptor bonds. In this model, both repellers and binders are treated as wormlike chains confined in a nanoslit, and the stability of adhesion is considered as a competition between attractive interactions of ligand-receptor binding and repulsive forces due to the size mismatch between repellers and binders. The force on each ligand-receptor bond is calculated from the confined polymer model, and the classic model of Bell is used to describe the association/dissociation reactions of ligand-receptor bonds. The calculated equilibrium bond distribution shows that there exists a critical ligand density for stable adhesion, corresponding to a critical ligand spacing which agrees not only qualitatively but also quantitatively with the experimental observation. In the case of stable adhesion, the model predicts an equilibrium separation between adhesion surfaces below 60% of the contour length of the ligand-receptor bonds.     

Membrane tether extraction from human umbilical vein endothelial cells and its implication in leukocyte rolling

During the rolling of human neutrophils on the endothelium, tethers (cylindrical membrane tubes) are likely extracted from the neutrophil. Tether extraction reduces the force imposed on the adhesive bond between the neutrophil and endothelium, thereby facilitating the rolling. However, whether tethers can be extracted from the endothelium is still unknown. Here, with the micropipette-aspiration technique, we show that tethers can be extracted from either suspended or attached human umbilical vein endothelial cells. We also show that a linear relationship between the pulling force and tether growth velocity exists and this relationship does not depend on the receptor type (used to impose point forces), tumor necrosis factor-alpha stimulation, or cell attachment state. With linear regression, we determined that the threshold force was 50 pN and the effective viscosity was 0.50 pN.s/microm. Therefore, tethers might be simultaneously extracted from the neutrophil and endothelial cell during the rolling and, more importantly, the endothelial cell might contribute much more to the total composite tether length than the neutrophil. Compared with tether extraction from the neutrophil alone, simultaneous tether extraction results in a larger increase in the lifetime of the adhesive bond, and thus further stabilizes the rolling of neutrophils under high physiological shear stresses.     

Biomechanics of leukocyte rolling

Leukocyte rolling on endothelial cells and other P-selectin substrates is mediated by P-selectin binding to P-selectin glycoprotein ligand-1 expressed on the tips of leukocyte microvilli. Leukocyte rolling is a result of rapid, yet balanced formation and dissociation of selectin-ligand bonds in the presence of hydrodynamic shear forces. The hydrodynamic forces acting on the bonds may either increase (catch bonds) or decrease (slip bonds) their lifetimes. The force-dependent 'catch-slip' bond kinetics are explained using the 'two pathway model' for bond dissociation. Both the 'sliding-rebinding' and the 'allosteric' mechanisms attribute 'catch-slip' bond behavior to the force-induced conformational changes in the lectin-EGF domain hinge of selectins. Below a threshold shear stress, selectins cannot mediate rolling. This 'shear-threshold' phenomenon is a consequence of shear-enhanced tethering and catch bond-enhanced rolling. Quantitative dynamic footprinting microscopy has revealed that leukocytes rolling at venular shear stresses (>0.6 Pa) undergo cellular deformation (large footprint) and form long tethers. The hydrodynamic shear force and torque acting on the rolling cell are thought to be synergistically balanced by the forces acting on tethers and stressed microvilli, however, their relative contribution remains to be determined. Thus, improvement beyond the current understanding requires in silico models that can predict both cellular and microvillus deformation and experiments that allow measurement of forces acting on individual microvilli and tethers.     

Yielding Elastic Tethers Stabilize Robust Cell Adhesion

Many bacteria and eukaryotic cells express adhesive proteins at the end of tethers that elongate reversibly at constant or near constant force, which we refer to as yielding elasticity. Here we address the function of yielding elastic adhesive tethers with Escherichia coli bacteria as a model for cell adhesion, using a combination of experiments and simulations. The adhesive bond kinetics and tether elasticity was modeled in the simulations with realistic biophysical models that were fit to new and previously published single molecule force spectroscopy data. The simulations were validated by comparison to experiments measuring the adhesive behavior of E. coli in flowing fluid. Analysis of the simulations demonstrated that yielding elasticity is required for the bacteria to remain bound in high and variable flow conditions, because it allows the force to be distributed evenly between multiple bonds. In contrast, strain-hardening and linear elastic tethers concentrate force on the most vulnerable bonds, which leads to failure of the entire adhesive contact. Load distribution is especially important to noncovalent receptor-ligand bonds, because they become exponentially shorter lived at higher force above a critical force, even if they form catch bonds. The advantage of yielding is likely to extend to any blood cells or pathogens adhering in flow, or to any situation where bonds are stretched unequally due to surface roughness, unequal native bond lengths, or conditions that act to unzip the bonds.     

Uncoiling Mechanics of Escherichia coli Type I Fimbriae Are Optimized for Catch Bonds

We determined whether the molecular structures through which force is applied to receptor–ligand pairs are tuned to optimize cell adhesion under flow. The adhesive tethers of our model system, Escherichia coli, are type I fimbriae, which are anchored to the outer membrane of most E. coli strains. They consist of a fimbrial rod (0.3–1.5 μm in length) built from a helically coiled structural subunit, FimA, and an adhesive subunit, FimH, incorporated at the fimbrial tip. Previously reported data suggest that FimH binds to mannosylated ligands on the surfaces of host cells via catch bonds that are enhanced by the shear-originated tensile force. To understand whether the mechanical properties of the fimbrial rod regulate the stability of the FimH–mannose bond, we pulled the fimbriae via a mannosylated tip of an atomic force microscope. Individual fimbriae rapidly elongate for up to 10 μm at forces above 60 pN and rapidly contract again at forces below 25 pN. At intermediate forces, fimbriae change length more slowly, and discrete 5.0 ± 0.3–nm changes in length can be observed, consistent with uncoiling and coiling of the helical quaternary structure of one FimA subunit at a time. The force range at which fimbriae are relatively stable in length is the same as the optimal force range at which FimH–mannose bonds are longest lived. Higher or lower forces, which cause shorter bond lifetimes, cause rapid length changes in the fimbria that help maintain force at the optimal range for sustaining the FimH–mannose interaction. The modulation of force and the rate at which it is transmitted from the bacterial cell to the adhesive catch bond present a novel physiological role for the fimbrial rod in bacterial host cell adhesion. This suggests that the mechanical properties of the fimbrial shaft have codeveloped to optimize the stability of the terminal adhesive under flow.     

Uncoiling mechanics of Escherichia coli type I fimbriae are optimized for catch bonds

We determined whether the molecular structures through which force is applied to receptor–ligand pairs are tuned to optimize cell adhesion under flow. The adhesive tethers of our model system, Escherichia coli, are type I fimbriae, which are anchored to the outer membrane of most E. coli strains. They consist of a fimbrial rod (0.3–1.5 μm in length) built from a helically coiled structural subunit, FimA, and an adhesive subunit, FimH, incorporated at the fimbrial tip. Previously reported data suggest that FimH binds to mannosylated ligands on the surfaces of host cells via catch bonds that are enhanced by the shear-originated tensile force. To understand whether the mechanical properties of the fimbrial rod regulate the stability of the FimH–mannose bond, we pulled the fimbriae via a mannosylated tip of an atomic force microscope. Individual fimbriae rapidly elongate for up to 10 μm at forces above 60 pN and rapidly contract again at forces below 25 pN. At intermediate forces, fimbriae change length more slowly, and discrete 5.0 ± 0.3–nm changes in length can be observed, consistent with uncoiling and coiling of the helical quaternary structure of one FimA subunit at a time. The force range at which fimbriae are relatively stable in length is the same as the optimal force range at which FimH–mannose bonds are longest lived. Higher or lower forces, which cause shorter bond lifetimes, cause rapid length changes in the fimbria that help maintain force at the optimal range for sustaining the FimH–mannose interaction. The modulation of force and the rate at which it is transmitted from the bacterial cell to the adhesive catch bond present a novel physiological role for the fimbrial rod in bacterial host cell adhesion. This suggests that the mechanical properties of the fimbrial shaft have codeveloped to optimize the stability of the terminal adhesive under flow.     

Single membrane tether extraction from adult and neonatal dermal microvascular endothelial cells

Membrane tethers were found to be extracted from leukocytes and macrovascular endothelial cells (e.g., human umbilical vein endothelial cells or HUVECs) when a point pulling force was exerted. These tethers stabilize leukocyte rolling on the endothelium during the inflammatory response. However, little is known about tether extraction from other vascular cells like microvascular endothelial cells (MECs). In this study, we extracted tethers from both adult and neonatal dermal MECs with the micropipette aspiration technique. We found a linear relationship between the pulling force and tether growth velocity for both cell lines. This constitutive relationship is mainly determined by the membrane mechanical property and the underlying actin-based cytoskeleton for both attached and suspended endothelial cells. It is independent of cell surface receptor type, attachment state, cytokine stimulation, or cell lineage. For both types of MECs, the threshold forces are 50 pN and the effective viscosities are around 0.5 pN·s/µm. These results, which are close to what was obtained from HUVECs, indicate that homogeneity is preserved in terms of tether extraction among different types of endothelial cells, and simultaneous tethers are likely extracted when leukocytes roll on either microvascular or macrovascular surfaces. leukocyte rolling; cell mechanics; micropipette; cytoskeleton     

The influence of inhomogeneous adhesion on the detachment dynamics of adhering cells

The adhesion of cells to surfaces plays a crucial role in processes related to motility and tissue growth. Nonspecific interactions with a surface, e.g., by electrostatic or van der Waals forces, can complement specific molecular interactions and can themselves support strong adhesion. In order to understand the mechanism by which cells establish an adhesive interface in the absence of specific proteins, we have studied the detachment kinetics of monocytic cells from glass surfaces coated with poly-l-lysine. We exposed adhering cells to a shear flow and studied their deformation and detachment trajectories. Our experiments reveal that between 20 and 60 parallel membrane tethers form prior to detachment from the surface. We propose that the extraction of tethers is the consequence of an inhomogeneous adhesion interface and model the detachment mechanism as the dynamic extrusion of cooperatively loaded tethers. In our model, individual tethers detach by a peeling process in which a zone of a few nanometers is loaded by the externally applied force. Our findings suggest that the formation of an inhomogeneous non-specific adhesion interface between a cell and its substrate gives rise to more complex dynamics of detachment than previously discussed.     

Direct force measurements of the streptavidin-biotin interaction

The interaction between streptavidin and its ligand, biotin, were studied by direct force measurements. The complimentary approaches of surface force apparatus (SFA) and atomic force microscopy (AFM) were used to elucidate both long-range and short-range adhesive interactions of the streptavidin biotin interaction. The high spatial resolution of the SFA provided a detailed profile of the intersurface forces of apposing surfaces functionalized with streptavidin and biotin. Measurements obtained by the SFA corresponded to long and intermediate-range forces that are important in determining ligand receptor association. AFM was used to measure the unbinding force of individual streptavidin biotin complexes. These measurements revealed the short-range interactions (i.e. hydrophobic and hydrogen bonding forces) that stabilize the intermolecular bond.     

An analytical model for determining two-dimensional receptor-ligand kinetics

Cell-cell adhesive interactions play a pivotal role in major pathophysiological vascular processes, such as inflammation, infection, thrombosis, and cancer metastasis, and are regulated by hemodynamic forces generated by blood flow. Cell adhesion is mediated by the binding of receptors to ligands, which are both anchored on two-dimensional (2-D) membranes of apposing cells. Biophysical assays have been developed to determine the unstressed (no-force) 2-D affinity but fail to disclose its dependence on force. Here we develop an analytical model to estimate the 2-D kinetics of diverse receptor-ligand pairs as a function of force, including antibody-antigen, vascular selectin-ligand, and bacterial adhesin-ligand interactions. The model can account for multiple bond interactions necessary to mediate adhesion and resist detachment amid high hemodynamic forces. Using this model, we provide a generalized biophysical interpretation of the counterintuitive force-induced stabilization of cell rolling observed by a select subset of receptor-ligand pairs with specific intrinsic kinetic properties. This study enables us to understand how single-molecule and multibond biophysics modulate the macroscopic cell behavior in diverse pathophysiological processes.     

Eukaryotic membrane tethers revisited using magnetic tweezers

Membrane nanotubes, under physiological conditions, typically form en masse. We employed magnetic tweezers (MTW) to extract tethers from human brain tumor cells and compared their biophysical properties with tethers extracted after disruption of the cytoskeleton and from a strongly differing cell type, Chinese hamster ovary cells. In this method, the constant force produced with the MTW is transduced to cells through super-paramagnetic beads attached to the cell membrane. Multiple sudden jumps in bead velocity were manifest in the recorded bead displacement-time profiles. These discrete events were interpreted as successive ruptures of individual tethers. Observation with scanning electron microscopy supported the simultaneous existence of multiple tethers. The physical characteristics, in particular, the number and viscoelastic properties of the extracted tethers were determined from the analytic fit to bead trajectories, provided by a standard model of viscoelasticity. Comparison of tethers formed with MTW and atomic force microscopy (AFM), a technique where the cantilever-force transducer is moved at constant velocity, revealed significant differences in the two methods of tether formation. Our findings imply that extreme care must be used to interpret the outcome of tether pulling experiments performed with single molecular techniques (MTW, AFM, optical tweezers, etc). First, the different methods may be testing distinct membrane structures with distinct properties. Second, as soon as a true cell membrane (as opposed to that of a vesicle) can attach to a substrate, upon pulling on it, multiple nonspecific membrane tethers may be generated. Therefore, under physiological conditions, distinguishing between tethers formed through specific and nonspecific interactions is highly nontrivial if at all possible.     

Simultaneous tether extraction from endothelial cells and leukocytes: observation, mechanics, and significance

It has been hypothesized, from earlier studies on single-tether extraction from individual leukocytes and human umbilical vein endothelial cells, that during rolling of leukocytes on the endothelium, simultaneous extraction of membrane nanotubes (tethers) occurs, resulting in enhancement of the force decrease on the adhesive bond. In this study, using the micropipette aspiration technique and fluorescence microscopy, we show that tethers are indeed extracted simultaneously when an endothelial cell and a leukocyte are separated after brief contact and adhesion, and the endothelial cell contributes much more to the composite tether length. In addition, the constitutive relationship for simultaneous tether extraction is determined with neutrophils and T-lymphocytes as force transducers, and cytokine-stimulated human umbilical vein and dermal microvascular endothelial cells as substrates, respectively. This relationship is consistent with that derived theoretically from the constitutive equations for single-tether extraction from either cell alone. Moreover, we show that simultaneous tether extraction was likely terminated by receptor-ligand bond dissociation. With a biomechanical model of leukocyte rolling, we predict the force history of the adhesive receptor-ligand bond and show that it is remarkably similar for different leukocyte-endothelial cell pairs. Simultaneous tether extraction therefore represents a generic mechanism for stabilizing leukocyte rolling on the endothelium.     

Force spectroscopy of the double-tethered concanavalin-A mannose bond

We present the measurement of the force required to rupture a single protein-sugar bond using a methodology that provides selective discrimination between specific and nonspecific binding events and helps verify the presence of a single functional molecule on the atomic force microscopy tip. In particular, the interaction force between a polymer-tethered concanavalin-A protein (ConA) and a similarly tethered mannose carbohydrate was measured as 47 +/- 9 pN at a bond loading rate of approximately 10 nN/s. Computer simulations of the polymer molecular configurations were used to determine the angles that the polymers could sweep out during binding and, in conjunction with mass spectrometry, used to separate the angular effects from the effects due to a distribution of tether lengths. We find that when using commercially available polymer tethers that vary in length from 19 to 29 nm, the angular effects are relatively small and the rupture distributions are dominated by the 10-nm width of the tether length distribution. In all, we show that tethering both a protein and its ligand allows for the determination of the single-molecule bond rupture force with high sensitivity and includes some validation for the presence of a single-tethered functional molecule on the atomic force microscopy tip.     

Molecular structure of membrane tethers

Membrane tethers are nanotubes formed by a lipid bilayer. They play important functional roles in cell biology and provide an experimental window on lipid properties. Tethers have been studied extensively in experiments and described by theoretical models, but their molecular structure remains unknown due to their small diameters and dynamic nature. We used molecular dynamics simulations to obtain molecular-level insight into tether formation. Tethers were pulled from single-component lipid bilayers by application of an external force to a lipid patch along the bilayer normal or by lateral compression of a confined bilayer. Tether development under external force proceeded by viscoelastic protrusion followed by viscous lipid flow. Weak forces below a threshold value produced only a protrusion. Larger forces led to a crossover to tether elongation, which was linear at a constant force. Under lateral compression, tethers formed from undulations of unrestrained bilayer area. We characterized in detail the tether structure and its formation process, and obtained the material properties of the membrane. To our knowledge, these results provide the first molecular view of membrane tethers.     

Nanoscale characterization and determination of adhesion forces of Pseudomonas aeruginosa pili by using atomic force microscopy

Type IV pili play an important role in bacterial adhesion, motility, and biofilm formation. Here we present high-resolution atomic force microscopy (AFM) images of type IV pili from Pseudomonas aeruginosa bacteria. An individual pilus ranges in length from 0.5 to 7 microm and has a diameter from 4 to 6 nm, although often, pili bundles in which the individual filaments differed in both length and diameter were seen. By attaching bacteria to AFM tips, it was possible to fasten the bacteria to mica surfaces by pili tethers. Force spectra of tethered pili gave rupture forces of 95 pN. The slopes of force curves close to the rupture force were nearly linear but showed little variation with pilus length. Furthermore, force curves could not be fitted with wormlike-chain polymer stretch models when using realistic persistence lengths for pili. The observation that the slopes near rupture did not depend on the pili length suggests that they do not represent elastic properties of the pili. It is possible that this region of the force curves is determined by an elastic element that is part of the bacterial wall, although further experiments are needed to confirm this.