Reliability theory for receptor–ligand bond dissociation

Effects of Contact Surface Shape on Dynamic Lifetime and Strength of Molecular Bond Clusters under Displacement- and Force-Controlled Loading Conditions

Many experimental and theoretical studies have shown that the mechanical properties of cells and the extracellular matrix can significantly affect the lifetime and strength of the adhesion clusters of molecular bonds. However, there are few studies on how the shape of the contact surface affects the lifetime and strength of the adhesion clusters of molecular bonds, especially theoretical studies in this area. An idealized model of focal adhesion is adopted, in which two rigid media are bonded together by an array of receptor-ligand bonds modeled as Hookean springs on a complex surface topography, which is described by three parameters: the surface shape factor β, the length of a single identical surface shape L, and the amplitude of surface shapes w. In this study, systematic Monte Carlo simulations of this model are conducted to study the lifetime of the molecular bond cluster under linear incremental force loading and the strength of the molecular bond cluster under linear incremental displacement loading. We find that both small surface shape amplitudes and large surface shape factors will increase the lifetime and strength of the adhesion cluster, whereas the length of a single surface shape causes oscillations in the lifetime and strength of the cluster, and this oscillation amplitude is affected by the surface shape amplitude and the factor. At the same time, we also find that the pretension in the cluster will play a dominant role in the adhesion strength under large amplitudes and small factors of surface shapes. The physical mechanisms behind these phenomena are that the changes of the length of a single surface shape, the amplitude of surface shapes, and the surface shape factor cause the changes of stress concentration in the adhesion region, bond affinity, and the number of similar affinity bonds.

Two molecule force spectroscopy on ligand-receptor interactions

Many biological processes involve the rupture of multiple ligand-receptors or multivalent ligand-receptors. It is challenging to study the rupture of such parallelly arranged multiple ligand-receptors due to the difficulties in engineering such systems in a well-controlled fashion. Here we report the use of two-molecule force spectroscopy to investigate the rupture of two parallelly arranged monomeric streptavidin (mSA)-biotin complexes. By using SpyCatcher-SpyTag chemistry, we successfully engineered a molecular twin of biotin, in which two biotins are arranged in parallel. By reacting mSA with twin biotin, we constructed parallelly arranged two mSA-biotin complexes for force spectroscopy experiments. The incorporation of single molecule fingerprint domains into our mSA-biotin dimers allowed us to identify and assign the rupture events of the parallelly arranged mSA-biotin complexes without any ambiguity in the two-molecule force spectroscopy experiments. Our results revealed that the rupture force of the parallel dimer mSA-biotin is 172 pN at a pulling speed of 400 nm s-1, which is about 1.6 times of that of single mSA-biotin (105 pN). Furthermore, our findings indicate that the two mSA-biotin behave as non-interacting, independent ligand-receptors. The strategy we demonstrated here can be extended to other ligand-receptors and may open up an avenue toward rigorously testing the theoretic predictions proposed in various models regarding the rupture of multiple parallel ligand-receptors.

Single-Molecule Force Probing of RGD-Binding Integrins on Pancreatic Cancer Cells

Integrin-targeting arginine-glycine-aspartic acid (RGD)-based nanocarriers have been widely used for tumor imaging, monitoring of tumor development, and delivery of anticancer drugs. However, the thermodynamics of an RGD-integrin formation and dissociation associated with binding dynamics, affinity, and stability remains unclear. Here, we probed the binding strength of the binary complex to live pancreatic cancer cells using single-molecule binding force spectroscopy methods, in which RGD peptides were functionalized on a force probe tip through poly(ethylene glycol) (PEG)-based bifunctional linker molecules. While the density of integrin α_V receptors on the cell surface varies more than twofold from cell line to cell line, the individual RGD-integrin complexes exhibited a cell type-independent, monovalent bond strength. The load-dependent bond strength of multivalent RGD-integrin interactions scaled sublinearly with increasing bond number, consistent with the noncooperative, parallel bond model. Furthermore, the multivalent bonds ruptured sequentially either by one or in multiples, and the force strength was comparable to the synchronous rupture force. Comparison of energy landscapes of the bond number revealed a substantial decrease of kinetic off-rates for multivalent bonds, along with the increased width of the potential well and the increased potential barrier height between bound and unbound states, enhancing the stability of the multivalent bonds between them.

Nanoscale Functionalized Particles with Rotation-Controlled Capture in Shear Flow

Important processes in nature and technology involve the adhesive capture of flowing particles or cells on the walls of a conduit. This paper introduces engineered spherical microparticles whose capture rates are limited by their near surface motions in flow. Specifically, these microparticles are sparsely functionalized with nanoscopic regions ("patches") of adhesive functionality, without which they would be nonadhesive. Not only is particle capture on the wall of a shear-chamber limited by surface chemistry as opposed to transport, but also the capture rates depend specifically on particle rotations that result from the vorticity of the shear flow field. These particle rotations continually expose new particle surface to the opposing chamber wall, sampling the particle surface for an adhesive region and controlling the capture rate. Control studies with the same patchy functionality on the chamber wall rather than the particles reveal a related signature of particle capture but substantially faster (still surface limited) particle capture rates. Thus, when the same functionality is placed on the wall rather than the particles, the capture is faster because it depends on the particle translation past a functionalized wall rather than on the particle rotations. The dependence of particle capture on functionalization of the particles versus the wall is consistent with the faster near-wall particle translation in shearing flow compared with the velocity of the rotating particle surface near the wall. These findings, in addition to providing a new class of nanoscopically patchy engineered particles, provide insight into the capture and detection of cells presenting sparse distinguishing surface features and the design of delivery packages for highly targeted pharmaceutical delivery.

Intermolecular interactions between glycomodules of plant cell wall arabinogalactan-proteins and extensins

Hydroxyproline-rich glycoproteins (HRGPs) are a unique component of plant cell walls, undergoing extensive posttranslational modification such as proline hydroxylation and hydroxyproline-O-glycosylation. Arabinogalactan proteins (AGPs) and extensins are major members of the HRGP superfamily. AGPs have repetitive AlaHyp, SerHyp, and ThrHyp peptides, the Hyp residues being glycosylated with large type II arabinogalactan polysaccharides, while extensins contain characteristic SerHyp4 and SerHyp2 motifs with arabinosylated (1-4 residues) Hyp. Although they are less than ten percent in all wall materials, AGPs and extensins play important roles in all aspects of plant growth and development. The detailed mechanisms of their functions are still under investigation. However, many of the functions may be attributed to their adhesive properties. Here, we used a forced unbinding technique to measure relative adhesive potential of the well characterized (AlaHyp)51 and (SerHyp4)18 glycomodules representing AGPs and extensins, respectively. In the presence of different wall ions such as protons, Ca2+, and boron, the glycomodules exhibited different adhesive patterns, suggesting that the wall ion-regulated intermolecular interactions/adhesions between AGPs and/or extensins may be involved in maintaining wall-plasma membrane integrity during wall loosening processes such as wall elongation or expansion. This research applies a biophysical approach to understand the biological function of plant cell wall glycoproteins.

Single-Molecule Interactions of a Monoclonal Anti-DNA Antibody with DNA

Interactions of DNA with proteins are essential for key biological processes and have both a fundamental and practical significance. In particular, DNA binding to anti-DNA antibodies is a pathogenic mechanism in autoimmune pathology, such as systemic lupus erythematosus. Here we measured at the single-molecule level binding and forced unbinding of surface-attached DNA and a monoclonal anti-DNA antibody MRL4 from a lupus erythematosus mouse. In optical trap-based force spectroscopy, a microscopic antibodycoated latex bead is trapped by a focused laser beam and repeatedly brought into contact with a DNA-coated surface. After careful discrimination of non-specific interactions, we showed that the DNA-antibody rupture force spectra had two regimes, reflecting formation of weaker (20-40 pN) and stronger (>40 pN) immune complexes that implies the existence of at least two bound states with different mechanical stability. The two-dimensional force-free off-rate for the DNA-antibody complexes was ~2.2 × 10^-3 s^-1, the transition state distance was ~0.94 nm, the apparent on-rate was ~5.26 s^-1, and the stiffness of the DNA-antibody complex was characterized by a spring constant of 0.0021 pN/nm, suggesting that the DNA-antibody complex is a relatively stable, but soft and deformable macromolecular structure. The stretching elasticity of the DNA molecules was characteristic of single-stranded DNA, suggesting preferential binding of the MRL4 antibody to one strand of DNA. Collectively, the results provide fundamental characteristics of formation and forced dissociation of DNA-antibody complexes that help to understand principles of DNA-protein interactions and shed light on the molecular basis of autoimmune diseases accompanied by formation of anti-DNA antibodies.

Regulation of L-selectin-dependent hydrodynamic shear thresholding by leukocyte deformability and shear dependent bond number

BACKGROUND

During inflammation leukocyte attachment to the blood vessel wall is augmented by capture of near-wall flowing leukocytes by previously adherent leukocytes. Adhesive interactions between flowing and adherent leukocytes are mediated by L-selectin and P-selectin Glycoprotein Ligand-1 (PSGL-1) co-expressed on the leukocyte surface and ultimately regulated by hydrodynamic shear thresholding.

OBJECTIVE

We hypothesized that leukocyte deformability is a significant contributory factor in shear thresholding and secondary capture.

METHODS

Cytochalasin D (CD) was used to increase neutrophil deformability and fixation was used to reduce deformability. Neutrophil rolling on PSGL-1 coated planar surfaces and collisions with PSGL-1 coated microbeads were analyzed using high-speed videomicroscopy (250 fps).

RESULTS

Increased deformability led to an increase in neutrophil rolling flux on PSGL-1 surfaces while fixation led to a decrease in rolling flux. Abrupt drops in flow below the shear threshold resulted in extended release times from the substrate for CD-treated neutrophils, suggesting increased bond number. In a cell-microbead collision assay lower flow rates were correlated with briefer adhesion lifetimes and smaller adhesive contact patches.

CONCLUSIONS

Leukocyte deformation may control selectin bond number at the flow rates associated with hydrodynamic shear thresholding. Model analysis supported a requirement for both L-selectin catch-slip bond properties and multiple bond formation for shear thresholding.

Effect of amino groups of mesoporous silica nanoparticles on CpG oligodexynucleotide delivery

In this study, we proposed to modify mesoporous silica nanoparticles (MSNs) with 3-aminopropyltriethoxysilane (NH2-TES), aminoethylaminopropyltriethoxysilane (2NH2-TES) and 3-[2-(2-aminoethylamino)ethylamino] propyl-trimethoxysilane (3NH2-TES) for binding of cytosine-phosphate-guanosine oligodexynucleotides (CpG ODN), and investigated the effect of different amino groups of MSNs on the CpG ODN delivery. Serum stability, in vitro cytotoxicity, and cytokine interleukin-6 (IL-6) induction by MSN-NH2/CpG, MSN-2NH2/CpG and MSN-3NH2/CpG complexes were investigated in detail. The results showed that three kinds of aminated-MSN-based CpG ODN delivery systems had no cytotoxicity to RAW264.7 cells, and binding of CpG ODN to MSN-NH2, MSN-2NH2 and MSN-3NH2 nanoparticles enhanced the serum stability of CpG ODN due to protection by the nanoparticles. However, three aminated MSN-based CpG ODN delivery systems exhibited different CpG ODN delivery efficiency, and MSN-NH2/CpG complexes had the highest ability to induce IL-6 secretion.

Lifespan differences in hematopoietic stem cells are due to imperfect repair and unstable mean-reversion

The life-long supply of blood cells depends on the long-term function of hematopoietic stem cells (HSCs). HSCs are functionally defined by their multi-potency and self-renewal capacity. Because of their self-renewal capacity, HSCs were thought to have indefinite lifespans. However, there is increasing evidence that genetically identical HSCs differ in lifespan and that the lifespan of a HSC is predetermined and HSC-intrinsic. Lifespan is here defined as the time a HSC gives rise to all mature blood cells. This raises the intriguing question: what controls the lifespan of HSCs within the same animal, exposed to the same environment? We present here a new model based on reliability theory to account for the diversity of lifespans of HSCs. Using clonal repopulation experiments and computational-mathematical modeling, we tested how small-scale, molecular level, failures are dissipated at the HSC population level. We found that the best fit of the experimental data is provided by a model, where the repopulation failure kinetics of each HSC are largely anti-persistent, or mean-reverting, processes. Thus, failure rates repeatedly increase during population-wide division events and are counteracted and decreased by repair processes. In the long-run, a crossover from anti-persistent to persistent behavior occurs. The cross-over is due to a slow increase in the mean failure rate of self-renewal and leads to rapid clonal extinction. This suggests that the repair capacity of HSCs is self-limiting. Furthermore, we show that the lifespan of each HSC depends on the amplitudes and frequencies of fluctuations in the failure rate kinetics. Shorter and longer lived HSCs differ significantly in their pre-programmed ability to dissipate perturbations. A likely interpretation of these findings is that the lifespan of HSCs is determined by preprogrammed differences in repair capacity.

All hematopoietic stem cells (HSCs) are characterized by the capacities to produce all blood cell-types by differentiation and to maintain their own population through self-renewal divisions. Every individual HSC, therefore, can generate a complete blood system, or clone, conveying oxygenation and immune protection for a limited time. The time for which all mature blood cell-types can be found in a clone is called the lifespan. Interestingly, HSCs with different lifespans co-exist in the same host. We address the unresolved question: what controls the lifespan of HSCs of the same genotype exposed to the same environment? Here, we use a new approach to multi-scale modeling based on reliability theory and non-linear dynamics to address this question. Large-scale fluctuations in the experimental failure rate kinetics of HSC clones are identified to predict small-scale, genome level, events of deep penetrance, or magnitudes that approach population size. We broadly find that one condition explains our experimental data: repair mechanisms are a priori imperfect and do not improve, nor deteriorate, during the lifespan. As a result, progressively “worse-than-old” genome replicates are generated in self-renewal. A likely interpretation of our findings is that the lifespan of adult HSCs is determined by epigenetically pre-programmed differences in repair capacity.

Effect of viscous drag on multiple receptor-ligand bonds rupture force

Monte Carlo simulation of the rupture of multiple receptor-ligand bonds between two PMN cells suspended in a Newtonian fluid is performed. We demonstrate via micro-mechanical model of two cells adhered by multiple receptor-ligand bonds that viscous drag caused by relative motion of cell suspended in a Newtonian fluid modulates transmission of an applied external load to bonds. Specifically, it is demonstrated that at any time the intermolecular bond force is not equivalent to the instantaneous applied force. The difference in the instantaneous applied force and the intermolecular bond force depends on the viscosity of fluid, the size of cell, the applied loading rate, and the number of bonds at any instant of time. Viscous drag acting on cell reduces average bond rupture forces.

Cell-biomaterial mechanical interaction in the framework of tissue engineering: insights, computational modeling and perspectives

Tissue engineering is an emerging field of research which combines the use of cell-seeded biomaterials both in vitro and/or in vivo with the aim of promoting new tissue formation or regeneration. In this context, how cells colonize and interact with the biomaterial is critical in order to get a functional tissue engineering product. Cell-biomaterial interaction is referred to here as the phenomenon involved in adherent cells attachment to the biomaterial surface, and their related cell functions such as growth, differentiation, migration or apoptosis. This process is inherently complex in nature involving many physico-chemical events which take place at different scales ranging from molecular to cell body (organelle) levels. Moreover, it has been demonstrated that the mechanical environment at the cell-biomaterial location may play an important role in the subsequent cell function, which remains to be elucidated. In this paper, the state-of-the-art research in the physics and mechanics of cell-biomaterial interaction is reviewed with an emphasis on focal adhesions. The paper is focused on the different models developed at different scales available to simulate certain features of cell-biomaterial interaction. A proper understanding of cell-biomaterial interaction, as well as the development of predictive models in this sense, may add some light in tissue engineering and regenerative medicine fields.

Force-clamp measurements of receptor-ligand interactions

Protein-protein interactions are the basis of both biochemical and biophysical signaling of living cells. In many cases, the receptor is present on the cell surface while the ligand is in solution or linked to another support (extracellular matrix or another cell). In the case of cellular adhesion, forces are continuously applied to receptor-ligand complexes and, as a consequence, the dissociation kinetics of the bonds may change. It is, thus, relevant to study the kinetics of protein-protein interactions in response to applied forces, as this is the most physiologically relevant situation. The atomic force microscope (AFM) was one of the first nanotools to be applied to this end. However, new approaches need to be developed to better understand the complex energy landscape of molecular interactions under applied stress. In this chapter, we described the use of the AFM to carry out force-clamp measurements on receptor-ligand bonds. Force-clamp measurements on bonds consist of applying a constant and controlled force to a receptor-ligand bond and measure the resulting dissociation lifetime. The described methods include the required materials, functionalization of tips and substrates, force-clamping measurements, and processing and interpretation of the results. An illustrative example is given with the well-studied streptavidin-biotin complex.

Mg2+ modulates integrin-extracellular matrix interaction in vascular smooth muscle cells studied by atomic force microscopy

Atomic force microscopy (AFM) was used to investigate the interaction between alpha5beta1 integrin and fibronectin (FN) in the presence of divalent cations. AFM probes were labeled with FN and used to measure binding strength between alpha5beta1 integrin and FN by quantifying the force required to break single FN-integrin bonds on a physiological range of loading rates (100-10,000 pN/s). The force necessary to rupture single alpha5beta1-FN bond increased twofold over the regime of loading rates investigated. Changes in Mg(2+) and Ca(2+) concentration affected the thermodynamical parameters of the interaction and modulated the binding energy. These data indicate that the external ionic environment in which vascular smooth muscle cells reside, influences the mechanical parameters that define the interaction between the extracellular matrix and integrins. Thus, in a dynamic mechanical environment such as the vascular wall, thermodynamic binding properties between FN and alpha5beta1 integrin vary in relation to locally applied loads and divalent cations concentrations. These changes can be recorded as direct measurements on live smooth muscle cells by using AFM.

Molecular interaction studies of vascular endothelial growth factor with RNA aptamers

With widespread applications in biosensors, diagnostics and therapeutics, unraveling the mechanism of the interactions between aptamers and their targets has become extremely important. In this study, the interaction forces between an aptamer and its protein target were successfully measured via AFM-based force spectroscopy at the molecular level. The angiogenic protein, vascular endothelial growth factor (VEGF(165)) covalently tethered to a mixed self-assembled monolayer surface and an anti-VEGF(165) aptamer attached to an AFM cantilever was used to probe this interaction. By comparing the binding probability and the force distribution of this system in a series of experiments, the interaction between the aptamer and the protein was confirmed and the effect of loading rate on the rupture force was studied. The specificity of the aptamer was investigated by measuring interactions with VEGF(121), an isoform of VEGF missing a critical binding domain, and VEGF(165) isoform blocked with heparin. The lower frequency of binding events compared with that of VEGF(165) reflected that despite a high affinity to its preferential target, the selectivity of this aptamer is impaired to some extent due to the flexible structure of aptamers. By changing the concentration of Mg(2+) ion in the binding buffer, we could verify the effect of metal ions as stabilizers of aptamer conformation. The results provide evidence at the molecular level that the structural stability of aptamer is closely related to higher binding force and that rigid aptamer tertiary structures require higher forces to unbind the aptamer/protein complex.

Nano-motion dynamics are determined by surface-tethered selectin mechanokinetics and bond formation

The interaction of proteins at cellular interfaces is critical for many biological processes, from intercellular signaling to cell adhesion. For example, the selectin family of adhesion receptors plays a critical role in trafficking during inflammation and immunosurveillance. Quantitative measurements of binding rates between surface-constrained proteins elicit insight into how molecular structural details and post-translational modifications contribute to function. However, nano-scale transport effects can obfuscate measurements in experimental assays. We constructed a biophysical simulation of the motion of a rigid microsphere coated with biomolecular adhesion receptors in shearing flow undergoing thermal motion. The simulation enabled in silico investigation of the effects of kinetic force dependence, molecular deformation, grouping adhesion receptors into clusters, surface-constrained bond formation, and nano-scale vertical transport on outputs that directly map to observable motions. Simulations recreated the jerky, discrete stop-and-go motions observed in P-selectin/PSGL-1 microbead assays with physiologic ligand densities. Motion statistics tied detailed simulated motion data to experimentally reported quantities. New deductions about biomolecular function for P-selectin/PSGL-1 interactions were made. Distributing adhesive forces among P-selectin/PSGL-1 molecules closely grouped in clusters was necessary to achieve bond lifetimes observed in microbead assays. Initial, capturing bond formation effectively occurred across the entire molecular contour length. However, subsequent rebinding events were enhanced by the reduced separation distance following the initial capture. The result demonstrates that vertical transport can contribute to an enhancement in the apparent bond formation rate. A detailed analysis of in silico motions prompted the proposition of wobble autocorrelation as an indicator of two-dimensional function. Insight into two-dimensional bond formation gained from flow cell assays might therefore be important to understand processes involving extended cellular interactions, such as immunological synapse formation. A biologically informative in silico system was created with minimal, high-confidence inputs. Incorporating random effects in surface separation through thermal motion enabled new deductions of the effects of surface-constrained biomolecular function. Important molecular information is embedded in the patterns and statistics of motion.

Multipili attachment of bacteria with helixlike pili exposed to stress

A number of biomechanical properties of various types of pili expressed by Escherichia coli, predominantly their force-versus-elongation behavior, have previously been assessed in detail on a single pilus level. In vivo, however, bacteria bind in general to host cells by a multitude of pili, which presumably provides them with adhesion properties that differs from those of single pili. Based upon the previously assessed biomechanical properties of individual pili, this work presents a theoretical analysis of the adhesion properties of multipili-attaching bacteria expressing helixlike pili exposed to an external force. Expressions for the adhesion lifetime of dual- and multipili-attaching bacteria are derived and their validity is verified by Monte Carlo simulations. It is demonstrated that the adhesion lifetime of a multipili-binding bacterium depends to a large degree on the cooperativity of the attaching pili, which, in turn, depends strongly on their internal biomechanical properties, in particular their helixlike structure and its ability to elongate, which, in turn, depends on the intrinsic properties of the bonds, e.g., their lengths and activation energies. It is shown, for example, that a decrease in the length of a layer-to-layer bond in the rod of P pili, expressed by E. coli, by 50% leads to a decrease in the adhesion lifetime of a bacterium attaching by ten pili and exposed to a force of 500 pN by three orders of magnitude. The results indicate moreover that the intrinsic properties of the rod for this particular type of pili are optimized for multipili attachment under a broad range of external forces and presumably also to its in vivo environment. For example, P pili seems to be optimized to withstand a force exposure during approximately 3 s, which correspond to the time it takes for a bolus to pass a bacterium attached to the ureteral wall. Even though the results presented in this work apply quantitatively to one type of pilus, they are assumed to apply qualitatively to all helixlike pili systems expressing slip bonds.

Surface-bound selectin-ligand binding is regulated by carrier diffusion

Two-dimensional (2D) kinetics of receptor-ligand interactions governs cell adhesion in many biological processes. While the dissociation kinetics of receptor-ligand bond is extensively investigated, the association kinetics has much less been quantified. Recently receptor-ligand interactions between two surfaces were investigated using a thermal fluctuation assay upon biomembrane force probe technique (Chen et al. in Biophys J 94:694-701, 2008). The regulating factors on association kinetics, however, are not well characterized. Here we developed an alternative thermal fluctuation assay using optical trap technique, which enables to visualize consecutive binding-unbinding transition and to quantify the impact of microbead diffusion on receptor-ligand binding. Three selectin constructs (sLs, sPs, and PLE) and their ligand P-selectin glycoprotein ligand 1 were used to conduct the measurements. It was indicated that bond formation was reduced by enhancing the diffusivity of selectin-coupled carrier, suggesting that carrier diffusion is crucial to determine receptor-ligand binding. It was also found that 2D forward rate predicted upon first-order kinetics was in the order of sPs > sLs > PLE and bond formation was history-dependent. These results further the understandings in regulating association kinetics of surface-bound receptor-ligand interactions.

Low spring constant regulates P-selectin-PSGL-1 bond rupture

Forced dissociation of selectin-ligand bonds is crucial to such biological processes as leukocyte recruitment, thrombosis formation, and tumor metastasis. Although the bond rupture has been well known at high loading rate r(f) (>or=10(2) pN/s), defined as the product of spring constant k and retract velocity v, how the low r(f) (<10(2) pN/s) or the low k regulates the bond dissociation remains unclear. Here an optical trap assay was used to quantify the bond rupture at r(f) <or= 20 pN/s with low k ( approximately 10(-3)-10(-2) pN/nm) when P-selectin and P-selectin glycoprotein ligand 1 (PSGL-1) were respectively coupled onto two glass microbeads. Our data indicated that the bond rupture force f retained the similar values when r(f) increased up to 20 pN/s. It was also found that f varied with different combinations of k and v even at the same r(f). The most probable force, f*, was enhanced with the spring constant when k < 47.0 x 10(-3) pN/nm, indicating that the bond dissociation at low r(f) was spring constant dependent and that bond rupture force depended on both the loading rate and the mechanical compliance of force transducer. These results provide new insights into understanding the P-selectin glycoprotein ligand 1 bond dissociation at low r(f) or k.

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.

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.

Analyzing forced unfolding of protein tandems by ordered variates, 1: Independent unfolding times

Most of the mechanically active proteins are organized into tandems of identical repeats, (D)N, or heterogeneous tandems, D1-D2-...-DN. In current atomic force microscopy experiments, conformational transitions of protein tandems can be accessed by employing constant stretching force f (force-clamp) and by analyzing the recorded unfolding times of individual domains. Analysis of unfolding data for homogeneous tandems relies on the assumption that unfolding times are independent and identically distributed, and involves inference of the (parent) probability density of unfolding times from the histogram of the combined unfolding times. This procedure cannot be used to describe tandems characterized by interdomain interactions, or heteregoneous tandems. In this article, we introduce an alternative approach that is based on recognizing that the observed data are ordered, i.e., first, second, third, etc., unfolding times. The approach is exemplified through the analysis of unfolding times for a computer model of the homogeneous and heterogeneous tandems, subjected to constant force. We show that, in the experimentally accessible range of stretching forces, the independent and identically distributed assumption may not hold. Specifically, the uncorrelated unfolding transitions of individual domains at lower force may become correlated (dependent) at elevated force levels. The proposed formalism can be used in atomic force microscopy experiments to infer the unfolding time distributions of individual domains from experimental histograms of ordered unfolding times, and it can be extended to analyzing protein tandems that exhibit interdomain interactions.

Cell dynamic adhesion and elastic properties probed with cylindrical atomic force microscopy cantilever tips

Cell adhesion is required for essential biological functions such as migration, tissue formation and wound healing, and it is mediated by individual molecules that bind specifically to ligands on other cells or on the extracellular matrix. Atomic force microscopy (AFM) has been successfully used to measure cell adhesion at both single molecule and whole cell levels. However, the measurement of inherent cell adhesion properties requires a constant cell-probe contact area during indentation, a requirement which is not fulfilled in common pyramidal or spherical AFM tips. We developed a procedure using focused ion beam (FIB) technology by which we modified silicon pyramidal AFM cantilever tips to obtain flat-ended cylindrical tips with a constant and known area of contact. The tips were validated on elastic gels and living cells. Cylindrical tips showed a fairly linear force-indentation behaviour on both gels and cells for indentations >200 nm. Cylindrical tips coated with ligands were used to quantify inherent dynamic cell adhesion and elastic properties. Force, work of adhesion and elasticity showed a marked dynamic response. In contrast, the deformation applied to the cells before rupture was fairly constant within the probed dynamic range. Taken together, these results suggest that the dynamic adhesion strength is counterbalanced by the dynamic elastic response to keep a constant cell deformation regardless of the applied pulling rate.

Stochastic dynamics of adhesion clusters under shared constant force and with rebinding

Single receptor-ligand bonds have finite lifetimes, so that biological systems can dynamically react to changes in their environment. In cell adhesion, adhesion bonds usually act cooperatively in adhesion clusters. Outside the cellular context, adhesion clusters can be probed quantitatively by attaching receptors and ligands to opposing surfaces. Here we present a detailed theoretical analysis of the stochastic dynamics of a cluster of parallel bonds under shared constant loading and with rebinding. Analytical solutions for the appropriate one-step master equation are presented for special cases, while the general case is treated with exact stochastic simulations. If the completely dissociated state is modeled as an absorbing boundary, mean cluster lifetime is finite and can be calculated exactly. We also present a detailed analysis of fluctuation effects and discuss various approximations to the full stochastic description.

The role of flexible tethers in multiple ligand-receptor bond formation between curved surfaces

Ligands mounted to surfaces via extensible tethers are present in nature and represent a growing class of molecules used to engineer adhesion in drug targeting, biosensing, self-assembling nanostructures, and in other biophysical research. Using a continuum approach with geometric and thermodynamic arguments, we derive a number of analytical expressions that relate key properties of single-tethered ligand-receptor interactions to multiple bond formation between curved surfaces. The theoretical predictions are in good agreement with measurements made with the surface forces apparatus. We establish that, when ligated, many tethers commonly used in biophysical research exhibit a discrete binding range that can be accurately measured with force spectroscopy. The distribution of bound ligated tethers is independent of the surfaces' interaction radius, R. The bridging force scales linearly with R, the tether's effective spring constant and grafting density, and with the ligand-receptor bond energy when the surfaces are in direct contact. These results are contrasted to bridging forces that evolve between plane-parallel geometries. Last, we show how our simple analytical reductions can be used to predict adhesive forces for STEALTH liposomes and other targeted and self-assembled nanoparticles.

Catch-bond model derived from allostery explains force-activated bacterial adhesion

High shear enhances the adhesion of Escherichia coli bacteria binding to mannose coated surfaces via the adhesin FimH, raising the question as to whether FimH forms catch bonds that are stronger under tensile mechanical force. Here, we study the length of time that E. coli pause on mannosylated surfaces and report a double exponential decay in the duration of the pauses. This double exponential decay is unlike previous single molecule or whole cell data for other catch bonds, and indicates the existence of two distinct conformational states. We present a mathematical model, derived from the common notion of chemical allostery, which describes the lifetime of a catch bond in which mechanical force regulates the transitions between two conformational states that have different unbinding rates. The model explains these characteristics of the data: a double exponential decay, an increase in both the likelihood and lifetime of the high-binding state with shear stress, and a biphasic effect of force on detachment rates. The model parameters estimated from the data are consistent with the force-induced structural changes shown earlier in FimH. This strongly suggests that FimH forms allosteric catch bonds. The model advances our understanding of both catch bonds and the role of allostery in regulating protein activity.

Polymerization of fibrin: specificity, strength, and stability of knob-hole interactions studied at the single-molecule level

Using laser tweezers, we measured for the first time the forces of individual knob-into-hole interactions underlying fibrin polymerization. Exposure of A-knobs in desA-fibrin or its fragment from the central part of the molecule (N-terminal disulphide knot, NDSK) resulted in strong interactions with fibrinogen or fragment D (containing only a- and b-holes), producing a binding strength of approximately 125 to 130 pN. The interactions were not present in the absence of either knobs or holes and were abrogated by a specific inhibitor of fibrin polymerization, a peptide mimic of the A-knob (GPRPam). Exposure of both the A- and B-knobs in desAB-fibrin or desAB-NDSK did not change the rupture force spectra compared with the desA molecules, and their interactions with fibrinogen remained highly sensitive to GPRPam but not to GHRPam (B-knob), suggesting that neither A:b nor B:b nor B:a contacts contributed significantly to binding strength in addition to A:a contacts. The A:a interactions had a relatively small zero-force off-rate of approximately 10(-4) s(-1) and tight knob-to-hole contacts characterized by a transition state distance of approximately 0.3 nm. The results demonstrate that the knob-hole binding during thrombin-induced fibrin polymerization is driven by strong, stable, and highly specific A:a bonding, whereas A:b, B:b, or B:a interactions were not detected.

Enforced detachment of red blood cells adhering to surfaces: statics and dynamics

We investigated the mechanical strength of adhesion and the dynamics of unbinding of red blood cells to solid surfaces. Two different situations were tested: 1), native red blood cells nonspecifically adhered to glass surfaces coated with positively charged polymers and 2), biotinylated red blood cells specifically adhered to glass surfaces decorated with streptavidin, which has a high binding affinity for biotin. We used micropipette manipulation for forming and subsequently breaking the adhesive contact through a stepwise micromechanical procedure. Analysis of cell deformations provided the relation between force and contact radius, which was found to be in good agreement with theoretical predictions. We further demonstrated that the separation energy could be precisely derived from the measure of rupture forces and the cell shape. Finally, the dynamics of detachment was analyzed as a function of the applied force and the initial size of the adhesive patch. Our experiments were supported by original theoretical predictions, which allowed us to correlate the measured separation times with the molecular parameters (e.g., activation barrier, receptor-ligand characteristic length) derived from force measurements at the single bond level.

Brownian adhesive dynamics (BRAD) for simulating the receptor-mediated binding of viruses

Current viral docking models have relied upon the assumption that bond formation and breakage are independent of viral and docking surface geometry, as well as the forces exerted on the bonds. This assumption, known as the equivalent site hypothesis (ESH), is examined in detail using a newly developed simulation technique-Brownian adhesive dynamics (BRAD). The simulation couples the thermal motion of viral particles with adhesive dynamics models to characterize the effect of bonding on viral motion. We use the binding of HIV-like particles to CD4 expressing cells as a model system to illustrate the utility of BRAD. Comparison of the transition rates between bound states predicted by ESH and the rates resulting from BRAD simulations show dramatic differences; at values of the equilibrium crosslinking constant, K(x)R(T), where ESH suggests all virus adhesion proteins will be bound (K(x)R(T) = 10(6)), BRAD predicts not all virus adhesion proteins will be bound. At values of the equilibrium crosslinking constant used in typical ESH calculations of virus docking (K(x)R(T) = 1) we find BRAD simulations predict no binding. The mean bond density from BRAD models is often much lower than that predicted by ESH for equivalent parameter values. BRAD suggests that the viruses are much less well bound than ESH predicts. The differences suggest that binding models for viruses need to be reexamined closely. BRAD is a simulation technique that will be useful for quantifying the receptor-mediated binding of a wide variety of viruses to cells.

The effect of cellular receptor diffusion on receptor-mediated viral binding using Brownian adhesive dynamics (BRAD) simulations

Brownian adhesive dynamics (BRAD) is a new method for simulating the attachment of viruses to cell surfaces. In BRAD, the motion of the virus is subject to stochastic bond formation and breakage, and thermal motion owing to collisions from the solvent. In the model, the virus is approximated as a rigid sphere and the cell surface is approximated as a rigid plane coated with receptors. In this article, we extend BRAD to allow for the mobility of receptors in the plane of the membrane, both before and after they are ligated by viral attachment proteins. Allowing the proteins to move within the membrane produced several differences in behavior from when the receptors are immobilized. First, the mean steady-state bond number is unaffected by changes in cellular receptor density because proteins are now free to diffuse into the contact area, and the extent of binding is dictated by the availability of viral attachment proteins. Second, the time required to reach steady-state binding increases as both the cellular receptor number decreases and the receptor mobility decreases. This is because receptor diffusion is a slower process than the binding kinetics of the proteins. Decreasing the rate of protein binding was found to decrease the fraction of viruses bound to steady state, but not the extent of binding for those viruses that were bound. Increasing the binding rate increased the fraction of viruses bound, until no further viruses could bind. Alterations in receptor binding kinetics had no discernable effect on the mean steady-state bond number between virus and cell, because interactions were of sufficiently high affinity that all available receptor-viral attachment proteins were destined to bind at steady state.

L-selectin-mediated leukocyte tethering in shear flow is controlled by multiple contacts and cytoskeletal anchorage facilitating fast rebinding events

L-selectin-mediated tethers result in leukocyte rolling only above a threshold in shear. Here we present biophysical modeling based on recently published data from flow chamber experiments, which supports the interpretation that L-selectin-mediated tethers below the shear threshold correspond to single L-selectin carbohydrate bonds dissociating on the time scale of milliseconds, whereas L-selectin-mediated tethers above the shear threshold are stabilized by multiple bonds and fast rebinding of broken bonds, resulting in tether lifetimes on the time scale of 10(-1) seconds. Our calculations for cluster dissociation suggest that the single molecule rebinding rate is of the order of 10(4) Hz. A similar estimate results if increased tether dissociation for tail-truncated L-selectin mutants above the shear threshold is modeled as diffusive escape of single receptors from the rebinding region due to increased mobility. Using computer simulations, we show that our model yields first-order dissociation kinetics and exponential dependence of tether dissociation rates on shear stress. Our results suggest that multiple contacts, cytoskeletal anchorage of L-selectin, and local rebinding of ligand play important roles in L-selectin tether stabilization and progression of tethers into persistent rolling on endothelial surfaces.

Stability of adhesion clusters under constant force

We solve the stochastic equations for a cluster of parallel bonds with shared constant loading, rebinding, and the completely dissociated state as an absorbing boundary. In the small force regime, cluster lifetime grows only logarithmically with bond number for weak rebinding, but exponentially for strong rebinding. Therefore rebinding is essential to ensure physiological lifetimes. The number of bonds decays exponentially with time for most cases, but in the intermediate force regime a small increase in loading can lead to much faster decay. This effect might be used by cell-matrix adhesions to induce signaling events through cytoskeletal loading.

Force and Compliance Measurements on Living Cells Using Atomic Force Microscopy (AFM)

We describe the use of atomic force microscopy (AFM) in studies of cell adhesion and cell compliance. Our studies use the interaction between leukocyte function associated antigen-1 (LFA-1)/intercellular adhesion molecule-1 (ICAM-1) as a model system. The forces required to unbind a single LFA-1/ICAM-1 bond were measured at different loading rates. This data was used to determine the dynamic strength of the LFA-1/ICAM-1 complex and characterize the activation potential that this complex overcomes during its breakage. Force measurements acquired at the multiple- bond level provided insight about the mechanism of cell adhesion. In addition, the AFM was used as a microindenter to determine the mechanical properties of cells. The applications of these methods are described using data from a previous study.

Force spectroscopy of the leukocyte function-associated antigen-1/intercellular adhesion molecule-1 interaction

Interactions between leukocyte function-associated antigen-1 (LFA-1) with its cognate ligand, intercellular adhesion molecule-1 (ICAM-1) play a crucial role in leukocyte adhesion. Because the cell and its adhesive components are subject to external perturbation from the surrounding flow of blood, it is important to understand the binding properties of the LFA-1/ICAM-1 interaction in both steady state and in the presence of an external pulling force. Here we report on atomic force microscopy (AFM) measurements of the unbinding of LFA-1 from ICAM-1. The single molecule measurements revealed the energy landscape corresponding to the dissociation of the LFA-1/ICAM-1 complex and provided the basis for defining the energetic determinants of the complex at equilibrium and under the influence of an external force. The AFM force measurements were performed in an experimental system consisting of an LFA-1-expressing T cell hybridoma, 3A9, attached to the end of the AFM cantilever and an apposing surface expressing ICAM-1. In measurements covering three orders of magnitude change in force loading rate, the LFA-1/ICAM-1 force spectrum (i.e., unbinding force versus loading rate) revealed a fast and a slow loading regime that characterized a steep inner activation barrier and a wide outer activation barrier, respectively. The addition of Mg(2+), a cofactor that stabilizes the LFA-1/ICAM-1 interaction, elevated the unbinding force of the complex in the slow loading regime. In contrast, the presence of EDTA suppressed the inner barrier of the LFA-1/ICAM-1 complex. These results suggest that the equilibrium dissociation constant of the LFA-1/ICAM-1 interaction is regulated by the energetics of the outer activation barrier of the complex, while the ability of the complex to resist a pulling force is determined by the divalent cation-dependent inner activation barrier.

Characterization of biodegradable drug delivery vehicles with the adhesive properties of leukocytes

The site-specific expression of selectins (E- and P-selectin) on endothelial cells of blood vessels during inflammation provides an opportunity for the targeted delivery of anti-inflammatory drugs to inflammatory sites. Previous work in our laboratory has shown that artificial capsules with the adhesive properties of leukocytes can be made by attaching leukocyte adhesive ligands to polystyrene microspheres. In this work, we have adapted this technology to create a targeted delivery system using biodegradable, poly lactic-co-glycolic-acid (PLGA) microspheres. Biotinylated-Sialyl Lewis(x) (sLe(x)), a carbohydrate that serves as a ligand to selectins, was attached to the surface of avidin-linked PLGA microspheres. These carbohydrate-coated microspheres mimic the adhesive behavior of leukocytes on selectins in flow chambers, displaying slow rolling under flow. The rolling velocities displayed by sLe(x)-coated microspheres were similar to those displayed by leukocytes rolling on P- or E-selectin coated surfaces, and these rolling velocities, which relate to the residence time of the capsules, can be tuned by changing the density of carbohydrate residues on microsphere surfaces. We have also demonstrated that these microspheres will release model drugs on a time scale of several days. Therefore, we have made a targeted drug delivery vehicle that mimics the adhesive properties of leukocytes and is biodegradable.