The reaction-limited kinetics of membrane-to-surface adhesion and detachment

Biophysics of catch bonds

Receptor-ligand bonds strengthened by tensile mechanical force are referred to as catch bonds. This review examines experimental data and biophysical theory to analyze why mechanical force prolongs the lifetime of these bonds rather than shortens the lifetime by pulling the ligand out of the binding pocket. Although many mathematical models can explain catch bonds, experiments using structural variants have been more helpful in determining how catch bonds work. The underlying mechanism has been worked out so far only for the bacterial adhesive protein FimH. This protein forms catch bonds because it is allosterically activated when mechanical force pulls an inhibitory domain away from the ligand-binding domain. Other catch bond-forming proteins, including blood cell adhesion proteins called selectins and the motor protein myosin, show evidence of allosteric regulation between two domains, but it remains unclear if this is related to their catch bond behavior.

Adhesive dynamics simulation of neutrophil arrest with stochastic activation

The transition from rolling to firm adhesion is a key step in the adhesion cascade that permits a neutrophil to exit the bloodstream and make its way to a site of inflammation. In this work, we construct an integrated model of neutrophil activation and arrest that combines a biomechanical model of neutrophil adhesion and adhesive dynamics, with fully stochastic signal transduction modeling, in the form of kinetic Monte Carlo simulation within the microvilli. We employ molecular binding parameters gleaned from the literature and from simulation of cell-free rolling mediated by selectin molecules. We create a simplified model of lymphocyte function-associated antigen-1 activation that links P-selectin glycoprotein ligand-1 ligation to integrin activation. The model utilizes an energy profile of various integrin activation states drawn from literature data and permits manipulation of signal diffusivity within the microvillus. Our integrated model recreates neutrophil arrest within physiological timescales, and we demonstrate that increasing signal diffusivity within a microvillus accelerates arrest. If the energy barrier between free unactivated and free activated lymphocyte function-associated antigen-1 increases, the period of rolling before arrest increases. We further demonstrate that, within our model, modification of endothelial ligand surface densities can control arrest. In addition, the relative concentrations of signaling molecules control the fractional activation of the overall signaling pathway and the rolling time to arrest. This work presents the first, to our knowledge, fully stochastic model of neutrophil activation, which, though simplified, can recapitulate significant physiological details of neutrophil arrest yet retains the capacity to incorporate additional information regarding mechanisms of neutrophil signal transduction as they are elucidated.

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

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

Monte Carlo study of single molecule diffusion can elucidate the mechanism of B cell synapse formation

B cell receptors have been shown to cluster at the intercellular junction between a B cell and an antigen-presenting cell in the form of a segregated pattern of B cell receptor/antigen complexes known as an immunological synapse. We use random walk-based theoretical arguments and Monte Carlo simulations to study the effect of diffusion of surface-bound molecules on B cell synapse formation. Our results show that B cell synapse formation is optimal for a limited range of receptor-ligand complex diffusion coefficient values, typically one-to-two orders of magnitude lower than the diffusion coefficient of free receptors. Such lower mobility of receptor-ligand complexes can significantly affect the diffusion of a tagged receptor or ligand in an affinity dependent manner, as the binding/unbinding of such receptor or ligand molecules crucially depends on affinity. Our work shows how single molecule tracking experiments can be used to estimate the order of magnitude of the diffusion coefficient of receptor-ligand complexes, which is difficult to measure directly in experiments due to the finite lifetime of receptor-ligand bonds. We also show how such antigen movement data at the single molecule level can provide insight into the B cell synapse formation mechanism. Thus, our results can guide further single molecule tracking experiments to elucidate the synapse formation mechanism in B cells, and potentially in other immune cells.

Equilibrium and non-equilibrium charge-dependent quantification of endothelial cell hydrogel scaffolds

Using equilibrium swelling and non-equilibrium membrane potential measurements, this study assesses the charge density in two representative series of polyelectrolyte hydrogels and examines the morphological and proliferative responses of endothelial cells as a function of the prepared charge offset. The neutral monomers 2-hydroxyethylmethacrylate (HEMA) and poly(ethylene glycol) dimethacrylate (n = 1,000) (PEGDMA) were copolymerized with either the acidic monomer 2-sulfoethyl methacrylate (SEMA) or the basic monomer methacryloxy ethyltrimethylammonium chloride (MAETAC) to make membranes with pregelation charge offset concentrations varying from 0 to +/-200 mM. A thermodynamic analysis of swelling and membrane potential measurements quantified the hydrogel charge density state following equilibration at different ion strengths. Porcine pulmonary artery endothelial cells were seeded on samples of each HEMA and PEGDMA copolymer and the amount of cell coverage was measured over a 4-day period. Cellular attachment and proliferation increased with increasing proportions of charged monomers and showed a threshold pattern of attachment and growth on the positively charged HEMA-MAETAC copolymer hydrogels with increasing proportions of initially prepared charge. The series of PEGDMA copolymer hydrogels remained relatively resistant to cellular attachment and proliferation over the range of prepared charges considered in this study.

FimH forms catch bonds that are enhanced by mechanical force due to allosteric regulation

The bacterial adhesive protein, FimH, is the most common adhesin of Escherichia coli and mediates weak adhesion at low flow but strong adhesion at high flow. There is evidence that this occurs because FimH forms catch bonds, defined as bonds that are strengthened by tensile mechanical force. Here, we applied force to single isolated FimH bonds with an atomic force microscope in order to test this directly. If force was loaded slowly, most of the bonds broke up at low force (<60 piconewtons of rupture force). However, when force was loaded rapidly, all bonds survived until much higher force (140-180 piconewtons of rupture force), behavior that indicates a catch bond. Structural mutations or pretreatment with a monoclonal antibody, both of which allosterically stabilize a high affinity conformation of FimH, cause all bonds to survive until high forces regardless of the rate at which force is applied. Pretreatment of FimH bonds with intermediate force has the same strengthening effect on the bonds. This demonstrates that FimH forms catch bonds and that tensile force induces an allosteric switch to the high affinity, strong binding conformation of the adhesin. The catch bond behavior of FimH, the amount of force needed to regulate FimH, and the allosteric mechanism all provide insight into how bacteria bind and form biofilms in fluid flow. Additionally, these observations may provide a means for designing antiadhesive mechanisms.

Role of gp120 trimerization on HIV binding elucidated with Brownian adhesive dynamics

We simulated the docking of human immunodeficiency virus (HIV) with a cell membrane using Brownian adhesive dynamics. The main advance in the current version of Brownian adhesive dynamics is that we use a simple bead-spring model to coarsely approximate the role of gp120 trimerization on HIV docking. We used our simulations to elucidate the effect of env spike density on the rate and probability of HIV binding, as well as the probability that each individual gp120 trimer is fully engaged. We found that for typical CD4 surface densities, viruses expressing as few as 8 env spikes will dock with binding rate constants comparable to viruses expressing 72 spikes. We investigated the role of cellular receptor diffusion on the degree of binding achieved by the virus on both short timescales (where binding has reached steady state but before substantial receptor accumulation in the viral-cell contact zone has occurred) and long timescales (where the system has reached steady state). On short timescales, viruses with 10-23 env trimers most efficiently form fully engaged trimers. On long timescales, all gp120 in the contact area will become bound to CD4. We found that it takes seconds for engaged trimers to cluster CD4 molecules in the contact zone, which partially explains the deleay in viral entry.

Entropic-elasticity-controlled dissociation and energetic-elasticity-controlled rupture induce catch-to-slip bonds in cell-adhesion molecules

We develop a physical model to describe the kinetic behavior in cell-adhesion molecules. Unbinding of noncovalent biological bonds is assumed to occur by both bond dissociation and bond rupture. Such a decomposition of debonding processes is a space decomposition of the debonding events. Dissociation under thermal fluctuation is nondirectional in a three-dimensional space, and its energy barrier to escape is not influenced by a tensile force, but the microstates that could lead to dissociation are changed by the tensile force; rupture happens along the tensile force direction. An applied force effectively lowers the energy barrier to escape along the loading direction. The lifetime of the biological bond, due to the two concurrent off rates, may grow with increasing tensile force to a moderate amount and then decrease with further increasing load. We hypothesize that a catch-to-slip bond transition is a generic feature in biological bonds. The model also predicts that catch bonds in a more flexible molecular structure have longer lifetimes and need less force to be fully activated.

Modeling cell interactions under flow

In this review, we summarize the current state of understanding of the processes by which leukocytes, and other cells, such as tumor cells interact with the endothelium under various blood flow conditions. It is shown that the interactions are influenced by cell-cell adhesion properties, shear stresses due to the flow field and can also be modified by the cells microrheological properties. Different adhesion proteins are known to be involved leading to particular mechanisms by which interactions take place during inflammation or metastasis. Cell rolling, spreading, migration are discussed, as well as the effect of flow conditions on these mechanisms, including microfluidic effects. Several mathematical models proposed in recent years capturing the essential features of such interaction mechanisms are reviewed. Finally, we present a recent model in which the adhesion is given by a kinetics theory based model and the cell itself is modeled as a viscoelastic drop. Qualitative agreement is found between the predictions of this model and in vitro experiments.

Computational analysis of adhesion force in the indentation of cells using atomic force microscopy

A mechanical model was developed to study the indentation of an atomic force microscopic (AFM) tip on a cell with adhesion mediated by receptor-ligand binding. The effects of indentation rate, indentation depth, indenter size, and the mechanical properties of cells on the adhesion force were investigated. It was found that the presence of adhesion between the cell and AFM tip may affect both the loading curve and unloading curve, which may in turn change the extracted elastic modulus values using the conventional indentation models. It was found that an increase in the receptor-ligand reaction rate may lead to a transition from a decrease of the maximum adhesion force with the indentation rate to an increase of the maximum adhesion force with the indentation rate. It was also found that factors such as indenter size, indentation depth, and cell mechanical properties influence the maximum adhesion force, and their corresponding underlying mechanisms were discussed.

Integrin-like allosteric properties of the catch bond-forming FimH adhesin of Escherichia coli

FimH is the adhesive subunit of type 1 fimbriae of the Escherichia coli that is composed of a mannose-binding lectin domain and a fimbria-incorporating pilin domain. FimH is able to interact with mannosylated surface via a shear-enhanced catch bond mechanism. We show that the FimH lectin domain possesses a ligand-induced binding site (LIBS), a type of allosterically regulated epitopes characterized in integrins. Analogous to integrins, in FimH the LIBS epitope becomes exposed in the presence of the ligand (or "activating" mutations) and is located far from the ligand-binding site, close to the interdomain interface. Also, the antibody binding to the LIBS shifts adhesin from the low to high affinity state. Binding of streptavidin to the biotinylated residue within the LIBS also locks FimH in the high affinity state, suggesting that the allosteric perturbations in FimH are sustained by the interdomain wedging. In the presence of antibodies, the strength of bacterial adhesion to mannose is increased similar to the increase observed under shear force, suggesting the same allosteric mechanism, a shift in the interdomain configuration. Thus, an integrin-like allosteric link between the binding pocket and the interdomain conformation can serve as the basis for the catch bond property of FimH and, possibly, other adhesive proteins.

Bond tilting and sliding friction in a model of cell adhesion

As a simple theoretical model of a cell adhering to a biological interface, we consider a rigid cylinder moving in a viscous shear flow near a wall. Adhesion forces arise through intermolecular bonds between receptors on the cell and their ligands on the wall, which form flexible tethers that can stretch and tilt as the base of the cell moves past the wall; binding kinetics is assumed to follow a standard model for slip bonds. By introducing a finite resistance to bond tilting, we use our model to explore the territory between previous theoretical models that allow for either zero or infinite resistance to bond rotation. A microscale calculation (for two parallel sliding plates) reveals a nonlinear force–speed relation arising from bond formation, tilting and breakage. Two distinct types of macroscale cell motion are then predicted: either bonds adhere strongly and the cell rolls (or tank treads) over the wall without slipping, or the cell moves near its free-stream speed with bonds providing weak frictional resistance to sliding. The model predicts bistability between these two states, implying that at critical shear rates the system can switch abruptly between rolling and free sliding, and suggesting that sliding friction arising through bond tilting may play a significant dynamical role in some cell-adhesion applications.

Nonlinear mechanical modeling of cell adhesion

Cell adhesion, which is mediated by the receptor-ligand bonds, plays an essential role in various biological processes. Previous studies often described the force-extension relationship of receptor-ligand bond with linear assumption. However, the force-extension relationship of the bond is intrinsically nonlinear, which should have significant influence on the mechanical behavior of cell adhesion. In this work, a nonlinear mechanical model for cell adhesion is developed, and the adhesive strength was studied at various bond distributions. We find that the nonlinear mechanical behavior of the receptor-ligand bonds is crucial to the adhesive strength and stability. This nonlinear behavior allows more bonds to achieve large bond force simultaneously, and therefore the adhesive strength becomes less sensitive to the change of bond density at the outmost periphery of the adhesive area. In this way, the strength and stability of cell adhesion are soundly enhanced. The nonlinear model describes the cell detachment behavior better than the linear model.

Enhancement of L-selectin, but not P-selectin, bond formation frequency by convective flow

L-selectin-mediated leukocyte rolling has been proposed to require a high rate of bond formation compared to that of P-selectin to compensate for its much higher off-rate. To test this hypothesis, a microbead system was utilized to measure relative L-selectin and P-selectin bond formation rates on their common ligand P-selectin glycoprotein ligand-1 (PSGL-1) under shear flow. Using video microscopy, we tracked selectin-coated microbeads to detect the formation frequency of adhesive tether bonds. From velocity distributions of noninteracting and interacting microbeads, we observed that tether bond formation rates for P-selectin on PSGL-1 decreased with increasing wall shear stress, from 0.14 +/- 0.04 bonds/microm at 0.2 dyn/cm(2) to 0.014 +/- 0.003 bonds/microm at 1.0 dyn/cm(2). In contrast, L-selectin tether bond formation increased from 0.017 +/- 0.005 bonds/microm at 0.2 dyn/cm(2) to 0.031 +/- 0.005 bonds/microm at 1.0 dyn/cm(2). L-selectin tether bond formation rates appeared to be enhanced by convective transport, whereas P-selectin rates were inhibited. The transition force for the L-selectin catch-slip transition of 44 pN/bond agreed well with theoretical models (Pereverzev et al. 2005. Biophys. J. 89:1446-1454). Despite catch bond behavior, hydrodymanic shear thresholding was not detected with L-selectin beads rolling on PSGL-1. We speculate that shear flow generated compressive forces may enhance L-selectin bond formation relative to that of P-selectin and that L-selectin bonds with PSGL-1 may be tuned for the compressive forces characteristic of leukocyte-leukocyte collisions during secondary capture on the blood vessel wall. This is the first report, to our knowledge, comparing L-selectin and P-selectin bond formation frequencies in shear flow.

Interdomain Interaction in the FimH Adhesin of Escherichia coli Regulates the Affinity to Mannose

FimH is a mannose-specific adhesin located on the tip of type 1 fimbriae of Escherichia coli that is capable of mediating shear-enhanced bacterial adhesion. FimH consists of a fimbria-associated pilin domain and a mannose-binding lectin domain, with the binding pocket positioned opposite the interdomain interface. By using the yeast two-hybrid system, purified lectin and pilin domains, and docking simulations, we show here that the FimH domains interact with one another. The affinity for mannose is greatly enhanced (up to 300-fold) in FimH variants in which the interdomain interaction is disrupted by structural mutations in either the pilin or lectin domains. Also, affinity to mannose is dramatically enhanced in isolated lectin domains or in FimH complexed with the chaperone molecule that is wedged between the domains. Furthermore, FimH with native structure mediates weak binding at low shear stress but shifts to strong binding at high shear, whereas FimH with disrupted interdomain contacts (or the isolated lectin domain) mediates strong binding to mannose-coated surfaces even under low shear. We propose that interactions between lectin and pilin domains decrease the affinity of the mannose-binding pocket via an allosteric mechanism. We further suggest that mechanical force at high shear stress separates the two domains, allowing the lectin domain to switch from a low affinity to a high affinity state. This shift provides a mechanism for FimH-mediated shear-enhanced adhesion by enabling the adhesin to form catch bond-like interactions that are longer lived at high tensile force.

Fluorescent resonance energy transfer: A tool for probing molecular cell-biomaterial interactions in three dimensions

The current paradigm in designing biomaterials is to optimize material chemical and physical parameters based on correlations between these parameters and downstream biological responses, whether in vitro or in vivo. Extensive developments in molecular design of biomaterials have facilitated identification of several biophysical and biochemical variables (e.g. adhesion peptide density, substrate elastic modulus) as being critical to cell response. However, these empirical observations do not indicate whether different parameters elicit cell responses by modulating redundant variables of the cell-material interface (e.g. number of cell-material bonds, cell-matrix mechanics). Recently, fluorescence resonance energy transfer (FRET) has been applied to quantitatively analyze parameters of the cell-material interface for both two- and three-dimensional adhesion substrates. Tools based on FRET have been utilized to quantify several parameters of the cell-material interface relevant to cell response, including molecular changes in matrix proteins induced by interactions both with surfaces and cells, the number of bonds between integrins and their adhesion ligands, and changes in the crosslink density of hydrogel synthetic extracellular matrix analogs. As such techniques allow both dynamic and 3-D analyses they will be useful to quantitatively relate downstream cellular responses (e.g. gene expression) to the composition of this interface. Such understanding will allow bioengineers to fully exploit the potential of biomaterials engineered on the molecular scale, by optimizing material chemical and physical properties to a measurable set of interfacial parameters known to elicit a predictable response in a specific cell population. This will facilitate the rational design of complex, multi-functional biomaterials used as model systems for studying diseases or for clinical applications.

Interaction of micrometer-scale particles with nanotextured surfaces in shear flow

Dynamic particle adhesion from flow over collecting surfaces with nanoscale heterogeneity occurs in important natural systems and current technologies. Accurate modeling and prediction of the dynamics of particles interacting with such surfaces will facilitate their use in applications for sensing, separating, and sorting colloidal-scale objects. In this paper, the interaction of micrometer-scale particles with electrostatically heterogeneous surfaces is analyzed. The deposited polymeric patches that provide the charge heterogeneity in experiments are modeled as 11-nm disks randomly distributed on a planar surface. A novel technique based on surface discretization is introduced to facilitate computation of the colloidal interactions between a particle and the heterogeneous surface based on expressions for parallel plates. Combining these interactions with hydrodynamic forces and torques on a particle in a low Reynolds number shear flow allows particle dynamics to be computed for varying net surface coverage. Spatial fluctuations in the local surface density of the deposited patches are shown responsible for the dynamic adhesion phenomena observed experimentally, including particle capture on a net-repulsive surface.

The mechanism of pattern formation in the developing Drosophila retina

The biological patterning of the Drosophila retina in vivo has striking resemblance to liquid bubbles, in which the surface mechanics due to N-cadherin within a sub-group of retina cells can be mimicked by surface tension. In this work, the aggregating patterns were reasonably simplified into 2D clusters consisting of 2-6 identical bubbles confined within a shrinking boundary. By using a hybrid fluid dynamics model proposed for liquid foams, the aggregating process of 2-6 retina cells was studied. Assuming the minimal perimeter for patterning cells to be the condition of stability patterns, the stable converged patterns we simulated in this work are the same as the experimental observations. More importantly, a new pattern of 6 cells was obtained which was found physically more stable than the other two reported by Hayashi and Carthew. Aggregating perimeters of cells, i.e. the surface energy, showed a good linear fit with the cell numbers.

Mechanisms of B-cell synapse formation predicted by Monte Carlo simulation

The clustering of B-cell receptor (BCR) molecules and the formation of the protein segregation structure known as the "immunological synapse" at the contact region between B cells and antigen presenting cells appears to precede antigen (Ag) uptake by B cells. The mature B-cell synapse is characterized by a central cluster of BCR/Ag molecular complexes surrounded by a ring of LFA-1/ICAM-1 complexes. In this study, we investigate the biophysical mechanisms that drive immunological synapse formation in B cells by means of Monte Carlo simulation. Our approach simulates individual reaction and diffusion events on cell surfaces in a probabilistic manner with a clearly defined mapping between our model's probabilistic parameters and their physical equivalents. Our model incorporates the bivalent nature of the BCR as well as changes in membrane shape due to receptor-ligand binding. We find that differences in affinity and bond stiffness between BCR/Ag and LFA-1/ICAM-1 are sufficient to drive synapse formation in the absence of membrane deformation. When significant membrane deformation occurs as a result of receptor-ligand binding, our model predicts the affinity-dependent mechanism needs to be complemented by a BCR signaling-driven shift in LFA-1 affinity from low to high in order for synapses to form.

Extracting kinetics from single-molecule force spectroscopy: nanopore unzipping of DNA hairpins

Single-molecule force experiments provide powerful new tools to explore biomolecular interactions. Here, we describe a systematic procedure for extracting kinetic information from force-spectroscopy experiments, and apply it to nanopore unzipping of individual DNA hairpins. Two types of measurements are considered: unzipping at constant voltage, and unzipping at constant voltage-ramp speeds. We perform a global maximum-likelihood analysis of the experimental data at low-to-intermediate ramp speeds. To validate the theoretical models, we compare their predictions with two independent sets of data, collected at high ramp speeds and at constant voltage, by using a quantitative relation between the two types of measurements. Microscopic approaches based on Kramers theory of diffusive barrier crossing allow us to estimate not only intrinsic rates and transition state locations, as in the widely used phenomenological approach based on Bell's formula, but also free energies of activation. The problem of extracting unique and accurate kinetic parameters of a molecular transition is discussed in light of the apparent success of the microscopic theories in reproducing the experimental data.

Importance of force linkage in mechanochemistry of adhesion receptors

The alpha subunit-inserted (I) domain of integrin alphaLbeta2 [lymphocyte function-associated antigen-1 (LFA-1)] binds to intercellular adhesion molecule-1 (ICAM-1). The C- and N-termini of the alpha I domain are near one another on the "lower" face, opposite the metal ion-dependent adhesion site (MIDAS) on the "upper face". In conversion to the open alpha I domain conformation, a 7 A downward, axial displacement of C-terminal helix alpha7 is allosterically linked to rearrangement of the MIDAS into its high-affinity conformation. Here, we test the hypothesis that when an applied force is appropriately linked to conformational change, the conformational change can stabilize adhesive interactions that resist the applied force. Integrin alpha I domains were anchored to the cell surface through their C- or N-termini using type I or II transmembrane domains, respectively. C-terminal but not N-terminal anchorage robustly supported cell rolling on ICAM-1 substrates in shear flow. In contrast, when the alphaL I domain was mutationally stabilized in the open conformation with a disulfide bond, it mediated comparable levels of firm adhesion with type I and type II membrane anchors. To exclude other effects as the source of differential adhesion, these results were replicated using alpha I domains conjugated through the N- or C-terminus to polystyrene microspheres. Our results demonstrate a mechanical feedback system for regulating the strength of an adhesive bond. A review of crystal structures of integrin alpha and beta subunit I domains and selectins in high- and low-affinity conformations demonstrates a common mechanochemical design in which biologically applied tensile force stabilizes the more extended, high-affinity conformation.

IL-8 Response of Cyclically Stretching Alveolar Epithelial Cells Exposed to Non-fibrous Particles

Using a cell stretcher device, we have previously shown that A549 cells exposed to asbestos fibers gave significantly increased cytokine responses (IL-8) when they were cyclically stretched [Tsuda, A., B. K. Stringer, S. M. Mijailovich, R. A. Rogers, K. Hamada, and M. L. Gray. Am. J. Respir. Cell Mol. Biol. 21(4):455-462, 1999]. In the present study, cell stretching experiments were performed using non-fibrous riebeckite particles, instead of fibrous particles. Riebeckite particles are ground asbestos fibers with the size of a few microns and non-fibrous shape, and are often used as "non-toxic" control particles in the studies of fibrous particle-induced pathogenesis. Although it is generally assumed that riebeckite particles do not elicit strong biological responses, in our studies in cyclically stretched cell cultures, the riebeckite particles coated with adhesion proteins induced significant IL-8 responses, but in static cell cultures the treatment with adhesion protein-coated riebeckite did not induce comparable cytokine responses. To interpret these data, we have developed a simple mathematical model of adhesive interactions between a cell layer and rigid fibrous/non-fibrous particles that were subjected to external tensile forces. The analysis showed that because of considerable dissimilarity in deformations (i.e., strain mismatch) between the cells and particles during breathing, the attachment of particles as small as 1 micro in size could induce significant mechanical forces on the cell surface receptors, which may trigger subsequent adverse cell response under dynamic stretching conditions.

Force as a Facilitator of Integrin Conformational Changes during Leukocyte Arrest on Blood Vessels and Antigen-Presenting Cells

Integrins comprise a large family of cell-cell and cell-matrix adhesion receptors that rapidly modulate their adhesiveness. The arrest of leukocyte integrins on target vascular beds involves instantaneous conformational switches generating shear-resistant adhesions. Structural data suggest that these integrins are maintained in low-affinity conformations and must rapidly undergo conformational switches transduced via cytoplasmic changes ("inside-out" signaling) and simultaneous ligand-induced rearrangements ("outside-in"). This bidirectional activation is accelerated by signals from endothelial chemoattractants (chemokines). Recent studies predict that shear forces in the piconewton (pN) range per integrin can facilitate these biochemical switches. After extravasation, antigen recognition involves smaller internal forces from cytoskeletal motors and actin polymers forming the immune synapse. In this review, we address how forces facilitate allosteric integrin activation by biochemical signals. Evidence suggests that preformed cytoskeletal anchorage rather than free integrin mobility is key for force-enhanced integrin activation by chemokines and TCR signals.

Universal laws in the force-induced unraveling of biological bonds

Universal laws in the force-induced unbinding of receptor-ligand complexes are established for a general functional dependence of the dissociation rate constant on the applied force and are detailed with the two-pathway model that describes the recently discovered biological catch bond. The relationships link the data obtained with constant and time-dependent forces in different regimes, provide common representation for the previously unrelated data sets, and, thereby, greatly facilitate analysis and interpretation of experiments. The universal laws are demonstrated with the monomeric and dimeric catch-slip bonds between P-selectins and P-selectin glycoprotein ligands-1, and the slip bond between E-selectin and sialyl Lewis;{x} antigen.

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.

A structure-based sliding-rebinding mechanism for catch bonds

Catch bonds, whose lifetimes are prolonged by force, have been observed in selectin-ligand interactions and other systems. Several biophysical models have been proposed to explain this counterintuitive phenomenon, but none was based on the structure of the interacting molecules and the noncovalent interactions at the binding interface. Here we used molecular dynamics simulations to study changes in structure and atomic-level interactions during forced unbinding of P-selectin from P-selectin glycoprotein ligand-1. A mechanistic model for catch bonds was developed based on these observations. In the model, "catch" results from forced opening of an interdomain hinge that tilts the binding interface to allow two sides of the contact to slide against each other. Sliding promotes formation of new interactions and even rebinding to the original state, thereby slowing dissociation and prolonging bond lifetimes. Properties of this sliding-rebinding mechanism were explored using a pseudoatom representation and Monte Carlo simulations. The model has been supported by its ability to fit experimental data and can be related to previously proposed two-pathway models.

Dynamic strength of molecularly bonded surfaces

This study reports a theoretical analysis of the forced separation of two adhesive surfaces linked via a large number of parallel noncovalent bonds. To describe the bond kinetics, we implement a three-state reaction model with kinetic rates obtained from a simple integral expression of the mean first passage time for diffusive barrier crossing in a pulled-distance-dependent potential. We then compute the rupture force for the separation of adhesive surfaces at a constant rate. The results correspond well with a Brownian dynamics simulation of the same system. The separation rate relative to the intrinsic relaxation time of the bonds defines three loading regimes and the general dependence of the adhesion on kinetic or thermodynamic parameters of the bonds. In the equilibrium regime, the rupture force asymptotically approaches the equilibrium rupture force, which increases linearly with the equilibrium bond energy. In the near-equilibrium regime, the rupture force increases with the separation rate and increasingly correlates with the bond rupture barrier. In the far-from-equilibrium regime where rebinding is irrelevant, the rupture force varies linearly with the rupture barrier.

Adhesive dynamics simulations of the shear threshold effect for leukocytes

Many experiments have measured the effect of force on the dissociation of single selectin bonds, but it is not yet clear how the force dependence of molecular dissociation can influence the rolling of cells expressing selectin molecules. Recent experiments using constant-force atomic force microscopy or high-resolution microscopic observations of pause-time distributions of cells in a flow chamber show that for some bonds, the dissociation rate is high at low force and initially decreases with force, indicating a catch bond. As the force continues to increase, the dissociation rate increases again, like a slip bond. It has been proposed that this catch-slip bond leads to the shear threshold effect, in which a certain level of shear rate is required to achieve rolling. We have incorporated a catch-slip dissociation rate into adhesive dynamics simulations of cell rolling. Using a relatively simple model for the shear-controlled association rate for selectin bonds, we were able to recreate characteristics of the shear threshold effect seen most prominently for rolling through L-selectin. The rolling velocity as a function of shear rate showed a minimum near 100 s-1. Furthermore, cells were observed to roll at a shear rate near the threshold, but detach and move more quickly when the shear rate was dropped below the threshold. Finally, using adhesive dynamics, we were able to determine ranges of parameters necessary to see the shear threshold effect in the rolling velocity. In summary, we found through simulation that the catch-slip behavior of selectin bonds can be responsible for the shear threshold effect.

Force modulating dynamic disorder: a physical model of catch-slip bond transitions in receptor-ligand forced dissociation experiments

Recent experiments found that some adhesive receptor-ligand complexes have counterintuitive catch-slip transition behaviors: the mean lifetimes of these complexes first increase (catch) with initial application of a small external force, and then decrease (slip) when the force is beyond some threshold. In this work we suggest that the forced dissociation of these complexes might be a typical rate process with dynamic disorder. The one-dimensional force modulating Agmon-Hopfield model is used to describe the transitions in the single-bond P-selectin glycoprotein ligand 1-P-selectin forced dissociation experiments, which were respectively performed in the constant force [Marshall, Nature (Landon) 423, 190 (2003)] and the ramping force [Evans, Proc. Natl. Acad. Sci. U.S.A 98, 11281 (2004)] modes. We find that, an external force can not only accelerate the bond dissociation, but also modulate the complex from the lower-energy barrier to the higher one; the catch-slip bond transition can arise from a particular energy barrier shape. The agreement between our calculation and the experimental data is satisfactory.

Transport governs flow-enhanced cell tethering through L-selectin at threshold shear

Flow-enhanced cell adhesion is a counterintuitive phenomenon that has been observed in several biological systems. Flow augments L-selectin-dependent adhesion by increasing the initial tethering of leukocytes to vascular surfaces and by strengthening their subsequent rolling interactions. Tethering or rolling might be influenced by physical factors that affect the formation or dissociation of selectin-ligand bonds. We recently demonstrated that flow enhanced rolling of L-selectin-bearing microspheres or neutrophils on P-selectin glycoprotein ligand-1 by force decreased bond dissociation. Here, we show that flow augmented tethering of these microspheres or cells to P-selectin glycoprotein ligand-1 by three transport mechanisms that increased bond formation: sliding of the sphere bottom on the surface, Brownian motion, and molecular diffusion. These results elucidate the mechanisms for flow-enhanced tethering through L-selectin.

Analysis of inflammation

In the past, inflammation has been associated with infections and with the immune system. But more recent evidence suggests that a much broader range of diseases have telltale markers for inflammation. Inflammation is the basic mechanism available for repair of tissue after an injury and consists of a cascade of cellular and microvascular reactions that serve to remove damaged and generate new tissue. The cascade includes elevated permeability in microvessels, attachment of circulating cells to the vessels in the vicinity of the injury site, migration of several cell types, cell apoptosis, and growth of new tissue and blood vessels. This review provides a summary of the major microvascular, cellular, and molecular mechanisms that regulate elements of the inflammatory cascade. The analysis is largely focused on the identification of the major participants, notably signaling and adhesion molecules, and their mode of action in the inflammatory cascade. We present a new hypothesis for the generation of inflammatory mediators in plasma that are derived from the digestive pancreatic enzymes responsible for digestion. The inflammatory cascade offers a large number of opportunities for development of quantitative models that describe various aspects of human diseases.

Model of integrin-mediated cell adhesion strengthening

Cell adhesion to extracellular matrix components involves integrin binding, receptor clustering, and recruitment of cytoskeletal elements, leading to the formation of discrete adhesive structures (focal adhesions). A force balance, macroscopic-to-microscopic model of these adhesive events is presented in the context of experimentally measured parameters. Integrin bond force, bond numbers, and distribution along the contact area strongly modulated the resulting adhesive force. Furthermore, focal adhesion assembly enhanced adhesion strength by 30% over integrin clustering alone. Predicted values are in excellent agreement with experimental results. This model provides a simple framework to systematically analyze the contributions of different adhesive parameters to overall adhesion strength.

Mechanics of actomyosin bonds in different nucleotide states are tuned to muscle contraction

Muscle contraction and many other cell movements are driven by cyclic interactions between actin filaments and the motor enzyme myosin. Conformational changes in the actin-myosin binding interface occur in concert with the binding of ATP, binding to actin, and loss of hydrolytic by-products, but the effects of these conformational changes on the strength of the actomyosin bond are unknown. The force-dependent kinetics of the actomyosin bond may be particularly important at high loads, where myosin may detach from actin before achieving its full power stroke. Here we show that over a physiological range of rapidly applied loads, actomyosin behaves as a "catch" bond, characterized by increasing lifetimes with increasing loads up to a maximum at approximately 6 pN. Surprisingly, we found that the myosin-ADP bond is possessed of longer lifetimes under load than rigor bonds, although the load at which bond lifetime is maximal remains unchanged. We also found that actomyosin bond lifetime is ultimately dependent not only on load, but loading history as well. These data suggest a complex relationship between the rate of actomyosin dissociation and muscle force and shortening velocity. The 6-pN load for maximum bond lifetime is near the force generated by a single myosin molecule during isometric contraction. This raises the possibility that all catch bonds between load-bearing molecules are "mechanokinetically" tuned to their physiological environment.

Ligand detection and discrimination by spatial relocalization: A kinase-phosphatase segregation model of TCR activation

We develop a model of tyrosine phosphorylation and activation of the T-cell receptor (TCR) by localization to regions of close membrane-membrane proximity (close contact) that physically exclude tyrosine phosphatases such as CD45. Phosphatase exclusion generates regions of low phosphatase and high kinase activity and thus our model provides a framework to examine the kinetic segregation model of TCR activation. We incorporate a sequence of activation steps modeling the construction of the signalosome with a final sequestered, or high-stability, signaling state. The residence time of unbound TCRs in tyrosine kinase-rich domains is shown to be too short for accumulation of activation steps, whereas binding to an agonist lengthens the localization time and leads to generation of fully active TCRs. Agonist detection depends only on this localization, and therefore kinetic segregation represents a viable ligand detection mechanism, or signal transduction mechanism across membranes, distinct from receptor oligomerization and conformational change. We examine the degree of discrimination of agonists from a background of null (self) peptides, and from weak agonists achievable by this mechanism.

Dissociation of biological catch-bond by periodic perturbation

The analysis of the P-selectin/PSGL-1 catch-slip bond that is periodically driven by a detaching force predicts that in the frequency range on the order of 1 s(-1) the bond lifetime undergoes significant changes with respect to both frequency and amplitude of the force. The result indicates how variations in the heart rate could have a substantial effect on leukocyte and lymphoid cell transport and adhesion to endothelial cells and platelets during inflammatory processes.

Local force and geometry sensing regulate cell functions

The shapes of eukaryotic cells and ultimately the organisms that they form are defined by cycles of mechanosensing, mechanotransduction and mechanoresponse. Local sensing of force or geometry is transduced into biochemical signals that result in cell responses even for complex mechanical parameters such as substrate rigidity and cell-level form. These responses regulate cell growth, differentiation, shape changes and cell death. Recent tissue scaffolds that have been engineered at the micro- and nanoscale level now enable better dissection of the mechanosensing, transduction and response mechanisms.

Force-induced deformations and stability of biological bonds

A deformation model of the forced-induced dissociation of biological bonds is developed. A simple illustration shows that protein deformations can change the receptor-ligand interaction linearly with applied force at small forces, either increasing or decreasing the bond stability, and that a minor external work can lead to notable changes in the interaction energy. The deformation-induced increase of bond stability is illustrated with the remarkable catch-bond phenomenon in P and L selections. Additionally, the model rationalizes the frequently seen disparity between the bond dissociation rates of many free complexes and the zero-force asymptotic rates measured by force spectroscopy.

Immersed finite element method and its applications to biological systems

This paper summarizes the newly developed immersed finite element method (IFEM) and its applications to the modeling of biological systems. This work was inspired by the pioneering work of Professor T.J.R. Hughes in solving fluid-structure interaction problems. In IFEM, a Lagrangian solid mesh moves on top of a background Eulerian fluid mesh which spans the entire computational domain. Hence, mesh generation is greatly simplified. Moreover, both fluid and solid domains are modeled with the finite element method and the continuity between the fluid and solid subdomains is enforced via the interpolation of the velocities and the distribution of the forces with the reproducing Kernel particle method (RKPM) delta function. The proposed method is used to study the fluid-structure interaction problems encountered in human cardiovascular systems. Currently, the heart modeling is being constructed and the deployment process of an angioplasty stent has been simulated. Some preliminary results on monocyte and platelet deposition are presented. Blood rheology, in particular, the shear-rate dependent de-aggregation of red blood cell (RBC) clusters and the transport of deformable cells, are modeled. Furthermore, IFEM is combined with electrokinetics to study the mechanisms of nano/bio filament assembly for the understanding of cell motility.

Force-controlled equilibria of specific vesicle-substrate adhesion

We have developed "vertical" magnetic tweezers capable of exerting controlled pico and subpico Newton forces. Using this apparatus, we apply a point-like force to a vesicle that is adhered by means of specific bonds between the vesicle-carrying oligosaccharide sialyl LewisX and the surface-grafted E-selectin. An exponential decrease of the bound vesicle area with the decay rate that is insensitive to the force and the composition of the system is observed. We measure an equilibrium under force that is associated with an increased binding in the center of the contact zone. We also show that the determination of the shape is potentially sufficient to determine the number of formed specific bonds.

Effects of mixing intensity on cell seeding and proliferation in three-dimensional fibrous matrices

Nonwoven fibrous matrices have been widely used in cell and tissue cultures because their three-dimensional (3-D) structures with large surface areas and pore spaces can support high-density cell growth. Although cell adherence and growth on 2-D surfaces have been thoroughly investigated, very little is known for cells cultured in 3-D matrices. The effects of mixing intensity on cell seeding, adherence, and growth in fibrous matrices were thus investigated. Chinese Hamster Ovary and osteosarcoma cells were inoculated into nonwoven polyethylene terephthalate matrices by dynamic and static seeding methods, of which the former was found to be superior in seeding efficiency and cell distribution in the matrices. Dynamic seeding increased seeding efficiency from approximately 40% to more than 90%. When higher mixing intensities were applied, both cell attachment and detachment rates increased. Cell attachment was transport limited, as indicated by the increased attachment rate with increasing the mass transfer coefficient of the cells. Meanwhile, cell detachment from the 3-D matrix can be described by the Bell model. The effects of matrix pore size on cell adherence and proliferation were also investigated. In general, the smaller pore size is favorable to cell attachment and proliferation. Further analysis revealed that the interaction between mixing intensity and pore size played a vital role in hydrodynamic damage to cells, which was found to be significant when the Kolomogorov eddy size was smaller than the matrix pores. Increasing mixing intensity also increased oxygen transfer, decreased the lactate yield from glucose, and improved cell growth.

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

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

Dynamic disorder in receptor-ligand forced dissociation experiments

Recently experiments showed that some biological noncovalent bonds increase their lifetimes when they are stretched by an external force, and their lifetimes will decrease when the force increases further. Several specific quantitative models have been proposed to explain the intriguing transitions from the "catch bond" to the "slip bond." In this work we propose that the dynamic disorder of the force-dependent dissociation rate can account for the counterintuitive behaviors of the bonds. A Gaussian stochastic rate model is used to quantitatively describe the transitions observed recently in the single bond P-selctin glycoprotein ligand 1-P-selectin force rupture experiment [Marshall, Nature 423, 190 (2003)]. Our model agrees well with the experimental data. We conclude that the catch bonds could arise from the stronger positive correlation between the height of the intrinsic energy barrier and the distance from the bound state to the barrier; classical pathway scenario or a priori catch bond assumption is not essential.

Lifetime measurements reveal kinetic differences between homophilic cadherin bonds

Cadherins are multidomain adhesion proteins whose interactions direct cell sorting during histogenesis. They determine cell adhesion specificity, but prior studies failed to identify physical differences that could underlie cell sorting. These single molecule studies identify kinetic and strength differences between different cadherins. They further demonstrate that the modular extracellular architecture of cleavage stage C-cadherin supports a multistate binding mechanism. These multiple bonds exhibit a kinetic hierarchy of strengths that map to the different cadherin domains. The outer two N-terminal domains of C-cadherin form two bound states with dissociation rates of 3.9 and 0.02 s(-1). The latter is 25-fold slower than between the corresponding epithelial cadherin segments. In addition to the two fast bonds, the five-domain fragment (CEC1-5) forms two additional stronger, longer-lived bonds with dissociation rates of 0.00039 and 0.00001 s(-1). We further quantified the lifetimes of bonds subject to a constant force, and thus identified multiple dissociation events with rates that agree quantitatively with the force spectroscopy data. The qualitative features are similar to those reported for epithelial cadherin. However, the significant differences in the dissociation rates of the outer domains, which include the specificity-determining region, suggest that kinetic differences may determine cadherin discrimination, rather than adhesion energies.

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.

Cell adhesion strengthening: contributions of adhesive area, integrin binding, and focal adhesion assembly

Mechanical interactions between a cell and its environment regulate migration, contractility, gene expression, and cell fate. We integrated micropatterned substrates to engineer adhesive area and a hydrodynamic assay to analyze fibroblast adhesion strengthening on fibronectin. Independently of cell spreading, integrin binding and focal adhesion assembly resulted in rapid sevenfold increases in adhesion strength to steady-state levels. Adhesive area strongly modulated adhesion strength, integrin binding, and vinculin and talin recruitment, exhibiting linear increases for small areas. However, above a threshold area, adhesion strength and focal adhesion assembly reached a saturation limit, whereas integrin binding transitioned from a uniform distribution to discrete complexes. Adhesion strength exhibited exponential increases with bound integrin numbers as well as vinculin and talin recruitment, and the relationship between adhesion strength and these biochemical events was accurately described by a simple mechanical model. Furthermore, adhesion strength was regulated by the position of an adhesive patch, comprised of bound integrins and cytoskeletal elements, which generated a constant 200-nN adhesive force. Unexpectedly, focal adhesion assembly, in particular vinculin recruitment, contributed only 30% of the adhesion strength. This work elucidates the roles of adhesive complex size and position in the generation of cell-extracellular matrix forces.

Distinctive features of the biological catch bond in the jump-ramp force regime predicted by the two-pathway model

The receptor-ligand unbinding in the biological catch bond is analyzed within a simple model that comprises a single bound state and two unbinding pathways. This model is investigated in detail for the jump-ramp force regime, where the pulling force quickly jumps to a finite value and then is ramped linearly with time. Two qualitative criteria are identified that distinguish the catch bond from the slip bond. First, the rupture force probability density of the catch-bond exhibits a maximum-minimum pair, which develops at finite forces. In contrast, the slip bond produces a maximum that first appears at zero force. Second, the catch bond can be identified over a wide range of ramp rates by high rupture probabilities at low forces relative to the probability at the maximum, in contrast to the slip bond, where the probability at the maximum always corresponds to the most likely rupture force. Both distinctive features of the catch bond are masked by large jump forces, indicating that the catch bond is best identified in experiments with moderate loading rates and small jump forces. The catch-bond lifetime in the constant force regime is related to the probability density in the jump-ramp regime, allowing one to determine the bond lifetime for a constant force by measuring the initial probability density in the jump-ramp experiments with different jump forces and a fixed ramp rate. The key analytic results are illustrated with the P -selectin/P-selectin glucoprotein ligand-1 bond.