Probabilistic modeling of shear-induced formation and breakage of doublets cross-linked by receptor-ligand bonds

Memory in repetitive protein–protein interaction series

Interactions between proteins coordinate biological processes in an organism and may impact its responses to changing environments and diseases through feedback systems. Feedback systems function by using changes in the past to influence behaviors in the future, which we refer to here as memory. Here, we summarized several observations made, ideas conceptualized, and mathematical models developed for quantitatively analyzing memory effects in repetitive protein–protein interactions (PPIs). Specifically, we consider how proteins on the cell or in isolation retain information about prior interactions to impact current interactions. The micropipette, biomembrane force probe, and atomic force microscopic techniques were used to repeatedly assay PPIs. The resulting time series were analyzed by a previous and two new models to extract three memory indices of short (seconds), intermediate (minutes), and long (hours) timescales. We found that interactions of cell membrane, but not soluble, T cell receptor (TCR) with peptide-major histocompatibility complex (pMHC) exhibits short-term memory that impacts on-rate, but not off-rate of the binding kinetics. Peptide dissociation from MHC resulted in intermediate- and long-term memories in TCR–pMHC interactions. However, we observed no changes in kinetic parameters by repetitive measurements on living cells over intermediate timescales using stable pMHCs. Parameters quantifying memory effects in PPIs could provide additional information regarding biological mechanisms. The methods developed herein also provide tools for future research.

Mechanical Model for Catch-Bond-Mediated Cell Adhesion in Shear Flow

Catch bond, whose lifetime increases with applied tensile force, can often mediate rolling adhesion of cells in a hydrodynamic environment. However, the mechanical mechanism governing the kinetics of rolling adhesion of cells through catch-bond under shear flow is not yet clear. In this study, a mechanical model is proposed for catch-bond-mediated cell adhesion in shear flow. The stochastic reaction of bond formation and dissociation is described as a Markovian process, whereas the dynamic motion of cells follows classical analytical mechanics. The steady state of cells significantly depends on the shear rate of flow. The upper and lower critical shear rates required for cell detachment and attachment are extracted, respectively. When the shear rate increases from the lower threshold to the upper threshold, cell rolling became slower and more regular, implying the flow-enhanced adhesion phenomenon. Our results suggest that this flow-enhanced stability of rolling adhesion is attributed to the competition between stochastic reactions of bonds and dynamics of cell rolling, instead of force lengthening the lifetime of catch bonds, thereby challenging the current view in understanding the mechanism behind this flow-enhanced adhesion phenomenon. Moreover, the loading history of flow defining bistability of cell adhesion in shear flow is predicted. These theoretical predictions are verified by Monte Carlo simulations and are related to the experimental observations reported in literature.

A Theoretical Analysis of Receptor-Mediated Endocytosis of Nanoparticles in Wall Shear Flow

This study theoretically investigates receptor–ligand-mediated endocytosis of nanoparticles (NPs) in wall shear flow. The endocytosis is modeled as a birth–death process and relationships between coefficients in the model and the wall shear rate have been derived to deal with the effects of the shear flow. Model predictions show that flow-induced alteration in bond formation rates does not affect the endocytosis significantly, and the suppression of hydrodynamic load on endocytosis is eminent only when diameters of NPs are large (around 700[Formula: see text]nm) and the shear rate is sufficiently high. In the latter case, it is shown that the hydrodynamic load suppresses the initial attachment of NPs to cells more than the following internalization. The model also predicts that shear-promoted expression of certain ligands can lead to observable increase in the number of endocytozed NPs in typical flow-chamber experiments, and the promotion can also cause selective endocytosis of NPs by cells at high shear rate regions if the ligand surface density on NPs or the original expression of receptors on cells in the absence of flow is low.

Impact of real-time shedding on binding kinetics of membrane-remaining L-selectin to PSGL-1

L-selectin shedding induced by various cytokines is crucial in activating neutrophils (PMNs) in inflammatory cascade. While the real-time shedding in vivo lasts ~10 min after PMN activation, the impact of time-dependent shedding on binding kinetics of membrane-remaining L-selectins to its ligands is poorly understood at transient or steady state. Here, we developed an in vitro L-selectin shedding dynamics approach, together with competitive assays of cell adhesion, and proposed a theoretical model for quantifying the impact of real-time shedding on the binding kinetics of membrane-remaining L-selectins to P-selectin glycoprotein ligand-1 (PSGL-1). Our data indicated that the extent of L-selectin shedding on PMA activation is higher, but the terminating time is longer for Jurkat cells than those for human PMNs. Meanwhile, fMLF or IL-8 stimulation yields the longer terminating time than that on PMA stimulation but results in a similar shedding extent for PMNs. L-selectin shedding reduces L-selectin-PSGL-1-mediated cell adhesion in three ways: decreasing membrane-anchored L-selectins, increasing soluble L-selectins competitively binding to ligands, and presenting conformational alteration of membrane-remaining L-selectins themselves. Compared with those on intact cells, the binding affinities of membrane-remaining L-selectin-PSGL-1 pairs were all enhanced at initial and lowered at the late shedding phase for both PMN and Jurkat cells even with varied transition time points. The rolling velocities of both PMNs and Jurkat cells were increased following mechanically or biochemically induced shedding of L-selectin under shear flow. These findings help to further our understanding of the function of time-dependent L-selectin shedding during the inflammation cascade.

The glycocalyx promotes cooperative binding and clustering of adhesion receptors

Cell adhesion plays a pivotal role in various biological processes, e.g., immune responses, cancer metastasis, and stem cell differentiation. The adhesion behaviors depend subtly on the binding kinetics of receptors and ligands restricted at the cell-substrate interfaces. Although much effort has been directed toward investigating the kinetics of adhesion molecules, the role of the glycocalyx, anchored on cell surfaces as an exterior layer, is still unclear. In this paper, we propose a theoretical approach to study the collective binding kinetics of a few and a large number of binders in the presence of the glycocalyx, representing the cases of initial and mature adhesions of cells, respectively. The analytical results are validated by finding good agreement with our Monte Carlo simulations. In the force loading case, the on-rate and affinity increase as more bonds form, whereas this cooperative effect is not observed in the displacement loading case. The increased thickness and stiffness of the glycocalyx tend to decrease the affinity for a few bonds, while they have less influence on the affinity for a large number of bonds. Moreover, for a flexible membrane with thermally-excited shape fluctuations, the glycocalyx is exhibited to promote the formation of bond clusters, mainly due to the cooperative binding of binders. This study helps to understand the cooperative kinetics of adhesion receptors under physiologically relevant loading conditions and sheds light on the novel role of the glycocalyx in cell adhesion.

Analyses of movement and contact of two nucleated cells using a gas-driven micropipette aspiration technique

Adhesion between two nucleated cells undergoes specific significances in immune responses and tumor metastasis since cellular adhesive molecules usually express on two apposed cell membranes. However, quantification of the interactions between two nucleated cells is still challenging in microvasculature. Here distinct cell systems were used, including three types of human cells (Jurkat cell or PMN vs. MDA-MB-231 cell) and two kinds of murine native cells (PMN vs. liver sinusoidal endothelial cell). Cell movement, compression to, and relaxation from the counterpart cell were quantified using an in-house developed gas-driven micropipette aspiration technique (GDMAT). This assay is robust to quantify this process since cell movement and contact inside a pipette are independent of the repeated test cycles. Measured approaching or retraction velocity follows well a normal distribution, which is independent on the cycle period. Contact area or duration also fits a Gaussian distribution and moreover contact duration is linearly correlated with the cycle period. Cell movement is positively related to gas flux but negatively associated to medium viscosity. Cell adhesion tends to reach an equilibrium state with increase of cycle period or contact duration. These results further the understanding in the dynamics of cell movement and contact in microvasculature.

Biophysics of selectin-ligand interactions in inflammation and cancer

Selectins (L-, E- and P-selectin) are calcium-dependent transmembrane glycoproteins that are expressed on the surface of circulating leukocytes, activated platelets, and inflamed endothelial cells. Selectins bind predominantly to sialofucosylated glycoproteins and glycolipids (E-selectin only) present on the surface of apposing cells, and mediate transient adhesive interactions pertinent to inflammation and cancer metastasis. The rapid turnover of selectin-ligand bonds, due to their fast on- and off-rates along with their remarkably high tensile strengths, enables them to mediate cell tethering and rolling in shear flow. This paper presents the current body of knowledge regarding the role of selectins in inflammation and cancer metastasis, and discusses experimental methodologies and mathematical models used to resolve the biophysics of selectin-mediated cell adhesion. Understanding the biochemistry and biomechanics of selectin-ligand interactions pertinent to inflammatory disorders and cancer metastasis may provide insights for developing promising therapies and/or diagnostic tools to combat these disorders.

Application of Population Dynamics to Study Heterotypic Cell Aggregations in the Near-Wall Region of a Shear Flow

Our research focused on the polymorphonuclear neutrophils (PMNs) tethering to the vascular endothelial cells (EC) and the subsequent melanoma cell emboli formation in a shear flow, an important process of tumor cell extravasation from the circulation during metastasis. We applied population balance model based on Smoluchowski coagulation equation to study the heterotypic aggregation between PMNs and melanoma cells in the near-wall region of an in vitro parallel-plate flow chamber, which simulates in vivo cell-substrate adhesion from the vasculatures by combining mathematical modeling and numerical simulations with experimental observations. To the best of our knowledge, a multiscale near-wall aggregation model was developed, for the first time, which incorporated the effects of both cell deformation and general ratios of heterotypic cells on the cell aggregation process. Quantitative agreement was found between numerical predictions and in vitro experiments. The effects of factors, including: intrinsic binding molecule properties, near-wall heterotypic cell concentrations, and cell deformations on the coagulation process, are discussed. Several parameter identification approaches are proposed and validated which, in turn, demonstrate the importance of the reaction coefficient and the critical bond number on the aggregation process.

Lifetime and strength of periodic bond clusters between elastic media under inclined loading

Focal adhesions are clusters of specific receptor-ligand bonds that link an animal cell to an extracellular matrix. To understand the mechanical responses of focal adhesions, here we develop a stochastic-elasticity model of a periodic array of adhesion clusters between two dissimilar elastic media subjected to an inclined tensile stress, in which stochastic descriptions of molecular bonds and elastic descriptions of interfacial traction are unified in a single modeling framework. We first establish a fundamental scaling law of interfacial traction distribution and derive a stress concentration index that governs the transition between uniform and cracklike singular distributions of the interfacial traction within molecular bonds. Guided by this scaling law, we then perform Monte Carlo simulations to investigate the effects of cluster size, cell/extracellular matrix modulus, and loading direction on lifetime and strength of the adhesion clusters. The results show that intermediate adhesion size, stiff substrate, cytoskeleton stiffening, and low-angle pulling are factors that contribute to the stability of focal adhesions. The predictions of our model provide feasible explanations for a wide range of experimental observations and suggest possible mechanisms by which cells can modulate adhesion and deadhesion via cytoskeletal contractile machinery and sense mechanical properties of their surroundings.

A hybrid computational model for phagocyte transmigration

Phagocyte transmigration is the initiation of a series of phagocyte responses that are believed important in the formation of fibrotic capsules surrounding implanted medical devices. Understanding the molecular mechanisms governing phagocyte transmigration is highly desired in order to improve the stability and functionality of the implanted devices. A hybrid computational model that combines control theory and kinetics Monte Carlo (KMC) algorithm is proposed to simulate and predict phagocytes responses at molecular level. In order to mimic various biological knockout experiments, a general external control scenario is designed. The stochastic nature inherent to phagocyte transmigration is captured by KMC. A new formula is derived to calculate the transition rates as inputs to KMC. This formulation might quantify biological interactions in a general manner which is beyond the scope of the traditional chemical reaction kinetics.

Platelet adhesive dynamics. Part I: characterization of platelet hydrodynamic collisions and wall effects

Abnormally high shear stresses encountered in vivo induce spontaneous activation of blood platelets and formation of aggregates, even in the absence of vascular injury. A three-dimensional multiscale computational model-platelet adhesive dynamics-is developed and applied in Part I and Part II articles to elucidate key biophysical aspects of GPIbalpha-von-Willebrand-factor-mediated interplatelet binding that characterizes the onset of shear-induced platelet aggregation. In this article, the hydrodynamic effects of the oblate spheroidal shape of platelets and proximity of a plane wall on the nature of cell-cell collisions are systematically investigated. Physical quantities characterizing the adhesion probabilities between colliding platelet surfaces for the entire range of near-wall encounters between two platelets are obtained for application in platelet adhesive dynamics simulations of platelet aggregation explored in a companion article. The technique for matching simulation predictions of interplatelet binding efficiency to experimentally determined efficiencies is also described. Platelet collision behavior is found to be strikingly different from that of spheres, both close to and far from a bounding wall. Our results convey the significant effects that particle shape and presence of a bounding wall have on the particle trajectories and collision mechanisms, collision characteristics such as collision time and contact area, and collision frequency.

Two-dimensional kinetics of beta 2-integrin and ICAM-1 bindings between neutrophils and melanoma cells in a shear flow

Cell adhesion, mediated by specific receptor-ligand interactions, plays an important role in biological processes such as tumor metastasis and inflammatory cascade. For example, interactions between beta 2-integrin (lymphocyte function-associated antigen-1 and/or Mac-1) on polymorphonuclear neutrophils (PMNs) and ICAM-1 on melanoma cells initiate the bindings of melanoma cells to PMNs within the tumor microenvironment in blood flow, which in turn activate PMN-melanoma cell aggregation in a near-wall region of the vascular endothelium, therefore enhancing subsequent extravasation of melanoma cells in the microcirculations. Kinetics of integrin-ligand bindings in a shear flow is the determinant of such a process, which has not been well understood. In the present study, interactions of PMNs with WM9 melanoma cells were investigated to quantify the kinetics of beta 2-integrin and ICAM-1 bindings using a cone-plate viscometer that generates a linear shear flow combined with a two-color flow cytometry technique. Aggregation fractions exhibited a transition phase where it first increased before 60 s and then decreased with shear durations. Melanoma-PMN aggregation was also found to be inversely correlated with the shear rate. A previously developed probabilistic model was modified to predict the time dependence of aggregation fractions at different shear rates and medium viscosities. Kinetic parameters of beta 2-integrin and ICAM-1 bindings were obtained by individual or global fittings, which were comparable to respectively published values. These findings provide new quantitative understanding of the biophysical basis of leukocyte-tumor cell interactions mediated by specific receptor-ligand interactions under shear flow conditions.

Lifetime and strength of adhesive molecular bond clusters between elastic media

With a long-term objective toward a quantitative understanding of cell adhesion, we consider an idealized theoretical model of a cluster of molecular bonds between two dissimilar elastic media subjected to an applied tensile load. In this model, the distribution of interfacial traction is assumed to obey classical elastic equations whereas the rupture and rebinding of individual molecular bonds are governed by stochastic equations. Monte Carlo simulations that combine the elastic and stochastic equations are conducted to investigate the lifetime of the bond cluster as a function of the applied load. We show that the interfacial traction is generally nonuniform and for a given adhesion size the average cluster lifetime asymptotically approaches infinity as the applied load is reduced to below a critical value, defined as the strength of the cluster. The effects of elastic moduli, adhesion size, and rebinding rate on the cluster lifetime and strength are studied under strongly nonuniform distributions of interfacial traction. Although overly simplified in a number of aspects, our model seems to give predictions that are consistent with relevant experimental observations on focal adhesion dynamics.

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.

Impact of carrier stiffness and microtopology on two-dimensional kinetics of P-selectin and P-selectin glycoprotein ligand-1 (PSGL-1) interactions

Mechanics and surface microtopology of the molecular carrier influence cell adhesion, but the mechanisms underlying these effects are not well understood. We used a micropipette adhesion frequency assay to quantify how the carrier stiffness and microtopology affected two-dimensional kinetics of interacting adhesion molecules on two apposing surfaces. Interactions of P-selectin with P-selectin glycoprotein ligand-1 (PSGL-1) were used to demonstrate such effects by presenting the molecules on three carrier systems: human red blood cells (RBCs), human promyelocytic leukemia HL-60 cells, and polystyrene beads. Stiffening the carrier alone or in cooperation with roughing the surface lowered the two-dimensional affinity of interacting molecules by reducing the forward rate but not the reverse rate, whereas softening the carrier and roughing the surface had opposing effects in affecting two-dimensional kinetics. In contrast, the soluble antibody bound with similar three-dimensional affinity to surface-anchored P-selectin or PSGL-1 constructs regardless of carrier stiffness and microtopology. These results demonstrate that the carrier stiffness and microtopology of a receptor influences its rate of encountering and binding a surface ligand but does not subsequently affect the stability of binding. This provides new insights into understanding the rolling and tethering mechanism of leukocytes onto endothelium in both physiological and pathological processes.

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.

Flow-enhanced adhesion regulated by a selectin interdomain hinge

L-selectin requires a threshold shear to enable leukocytes to tether to and roll on vascular surfaces. Transport mechanisms govern flow-enhanced tethering, whereas force governs flow-enhanced rolling by prolonging the lifetimes of L-selectin–ligand complexes (catch bonds). Using selectin crystal structures, molecular dynamics simulations, site-directed mutagenesis, single-molecule force and kinetics experiments, Monte Carlo modeling, and flow chamber adhesion studies, we show that eliminating a hydrogen bond to increase the flexibility of an interdomain hinge in L-selectin reduced the shear threshold for adhesion via two mechanisms. One affects the on-rate by increasing tethering through greater rotational diffusion. The other affects the off-rate by strengthening rolling through augmented catch bonds with longer lifetimes at smaller forces. By forcing open the hinge angle, ligand may slide across its interface with L-selectin to promote rebinding, thereby providing a mechanism for catch bonds. Thus, allosteric changes remote from the ligand-binding interface regulate both bond formation and dissociation.

Similarities between heterophilic and homophilic cadherin adhesion

The mechanism that drives the segregation of cells into tissue-specific subpopulations during development is largely attributed to differences in intercellular adhesion. This process requires the cadherin family of calcium-dependent glycoproteins. A widely held view is that protein-level discrimination between different cadherins on cell surfaces drives this sorting process. Despite this postulated molecular selectivity, adhesion selectivity has not been quantitatively verified at the protein level. In this work, molecular force measurements and bead aggregation assays tested whether differences in cadherin bond strengths could account for cell sorting in vivo and in vitro. Studies were conducted with chicken N-cadherin, canine E-cadherin, and Xenopus C-cadherin. Both qualitative bead aggregation and quantitative force measurements show that the cadherins cross-react. Furthermore, heterophilic adhesion is not substantially weaker than homophilic adhesion, and the measured differences in adhesion do not correlate with cell sorting behavior. These results suggest that the basis for cell segregation during morphogenesis does not map exclusively to protein-level differences in cadherin adhesion.

Probabilistic modeling of rosette formation

Rosetting, or forming a cell aggregate between a single target nucleated cell and a number of red blood cells (RBCs), is a simple assay for cell adhesion mediated by specific receptor-ligand interaction. For example, rosette formation between sheep RBC and human lymphocytes has been used to differentiate T cells from B cells. Rosetting assay is commonly used to determine the interaction of Fc gamma-receptors (FcgammaR) expressed on inflammatory cells and IgG coated on RBCs. Despite its wide use in measuring cell adhesion, the biophysical parameters of rosette formation have not been well characterized. Here we developed a probabilistic model to describe the distribution of rosette sizes, which is Poissonian. The average rosette size is predicted to be proportional to the apparent two-dimensional binding affinity of the interacting receptor-ligand pair and their site densities. The model has been supported by experiments of rosettes mediated by four molecular interactions: FcgammaRIII interacting with IgG, T cell receptor and coreceptor CD8 interacting with antigen peptide presented by major histocompatibility molecule, P-selectin interacting with P-selectin glycoprotein ligand 1 (PSGL-1), and L-selectin interacting with PSGL-1. The latter two are structurally similar and are different from the former two. Fitting the model to data enabled us to evaluate the apparent effective two-dimensional binding affinity of the interacting molecular pairs: 7.19x10(-5) microm4 for FcgammaRIII-IgG interaction, 4.66x10(-3) microm4 for P-selectin-PSGL-1 interaction, and 0.94x10(-3) microm4 for L-selectin-PSGL-1 interaction. These results elucidate the biophysical mechanism of rosette formation and enable it to become a semiquantitative assay that relates the rosette size to the effective affinity for receptor-ligand binding.

Molecular bond formation between surfaces: anchoring and shearing effects

Specific molecular bonds between apposing surfaces play a central role in many biological structures and functions. They display a widely varying anchoring to the cell surface, and they are subject to forces that affect their binding characteristics due to their hydrodynamic environments. Here, we examine both anchoring and shearing aspects using simplified model systems aimed at gaining insight into the formation of a 2D bond collection under stress using two different surface anchors. The highly specific streptavidin-biotin molecular bond was chosen as the model receptor-ligand pair, and grafted colloids were used as model surfaces. To explore the role of the surface anchor, we grafted biotin onto the particle surface following two different approaches: first, the grafting was performed directly on the particle amine functions; second, a 35-nm-long PEG spacer was used. Hybrid particle classes were brought into contact in a homogeneous shear (between 200 s(-)(1) and 1200 s(-)(1)) using a cone plate geometry. The bond association and dissociation kinetics were given by the time course assemblage of hybrid particles into doublets. We observed saturating kinetics profiles that we interpreted as a linkage-breakage equilibrium, which yielded the on and off rates. We found that the biotin-PEG spacer was needed in order to observe significant binding at any shear rate. We also showed that only the number of collisions per unit time, generated by the shear, affected the on rate of the binding. Neither the exerted forces nor the collision lifetime had any effect. The off rate decreased with shear, possibly because of the shortening of the force duration, which results from the increasing shear rate.

Biomechanics of P-selectin PSGL-1 bonds: shear threshold and integrin-independent cell adhesion

Platelet-leukocyte adhesion may contribute to thrombosis and inflammation. We examined the heterotypic interaction between unactivated neutrophils and either thrombin receptor activating peptide (TRAP)-stimulated platelets or P-selectin-bearing beads (Ps-beads) in suspension. Cone-plate viscometers were used to apply controlled shear rates from 14 to 3000/s. Platelet-neutrophil and bead-neutrophil adhesion analysis was performed using both flow cytometry and high-speed videomicroscopy. We observed that although blocking antibodies against either P-selectin or P-selectin glycoprotein ligand-1 (PSGL-1) alone inhibited platelet-neutrophil adhesion by approximately 60% at 140/s, these reagents completely blocked adhesion at 3000/s. Anti-Mac-1 alone did not alter platelet-neutrophil adhesion rates at any shear rate, though in synergy with selectin antagonists it abrogated cell binding. Unstimulated neutrophils avidly bound Ps-beads and activated platelets in an integrin-independent manner, suggesting that purely selectin-dependent cell adhesion is possible. In support of this, antagonists against P-selectin or PSGL-1 caused dissociation of previously formed platelet-neutrophil and Ps-bead neutrophil aggregates under shear in a variety of experimental systems, including in assays performed with whole blood. In studies where medium viscosity and shear rate were varied, a shear threshold for P-selectin PSGL-1 binding was also noted at shear rates <100/s when Ps-beads collided with isolated neutrophils. Results are discussed in light of biophysical computations that characterize the collision between unequal-size particles in linear shear flow. Overall, our studies reveal an integrin-independent regime for cell adhesion and weak shear threshold for P-selectin PSGL-1 interactions that may be physiologically relevant.

Mechanics of transient platelet adhesion to von Willebrand factor under flow

A primary and critical step in platelet attachment to injured vascular endothelium is the formation of reversible tether bonds between the platelet glycoprotein receptor Ibalpha and the A1 domain of surface-bound von Willebrand factor (vWF). Due to the platelet's unique ellipsoidal shape, the force mechanics involved in its tether bond formation differs significantly from that of leukocytes and other spherical cells. We have investigated the mechanics of platelet tethering to surface-immobilized vWF-A1 under hydrodynamic shear flow. A computer algorithm was used to analyze digitized images recorded during flow-chamber experiments and track the microscale motions of platelets before, during, and after contact with the surface. An analytical two-dimensional model was developed to calculate the motion of a tethered platelet on a reactive surface in linear shear flow. Through comparison of the theoretical solution with experimental observations, we show that attachment of platelets occurs only in orientations that are predicted to result in compression along the length of the platelet and therefore on the bond being formed. These results suggest that hydrodynamic compressive forces may play an important role in initiating tether bond formation.

Relationship between molecular and cellular dissociation rates for VLA-4/VCAM-1 interaction in the absence of shear stress

The rate of leukocyte recruitment to and detachment from the vasculature contributes to cellular tethering, rolling, firm adherence, and migration across an endothelium layer. The molecular rates depend on the type and number of bound integrin or selectin adhesion molecules, shear force acting on the bound adhesion molecules, and affinity state of integrins. Although little is known of the effect that the number of adhesion molecules has on leukocyte recruitment, it has been shown that firm adhesion for cells in suspension may be mediated by small numbers of bound adhesion molecules. We studied the disaggregation of aggregates composed of B78H1 cells transfected with human vascular cell adhesion molecule-1 (VCAM-1) and human monoblastoid U937 cells expressing Very Late Antigen-4 (VLA-4). Aggregate disaggregation rates were obtained and compared to dissociation rates for soluble rhVCAM-1 ligand and monoblastoid U937 cells. Under conditions without shear stress, it was found that average cellular disaggregation rates were a factor of 1.3 +/- 0.4 times slower than molecular dissociation rates for the 1 mM Mn(2+) and 1 mM Mn(2+) + 1 mM Ca(2+) conditions. A simple mathematical model was used to predict how much smaller the dissociation constant would be if the number of bonds holding an aggregate varied from one bond to N bonds under conditions without shear stress. The average number of adhesion bonds holding the cell aggregates together was found to be 1.5 +/- 0.7. This suggests that a few bonds were needed to form cellular aggregates and that increased aggregation was related to integrin affinity changes and not due to clustering or increased bond numbers.

Cell mechanics: mechanical response, cell adhesion, and molecular deformation

As the basic unit of life, the cell is a biologically complex system, the understanding of which requires a combination of various approaches including biomechanics. With recent progress in cell and molecular biology, the field of cell mechanics has grown rapidly over the last few years. This review synthesizes some of these recent developments to foster new concepts and approaches, and it emphasizes molecular-level understanding. The focuses are on the common themes and interconnections in three related areas: (a) the responses of cells to mechanical forces, (b) the mechanics and kinetics of cell adhesion, and (c) the deformation of biomolecules. Specific examples are also given to illustrate the quantitative modeling used in analyzing biological processes and physiological functions.

Modeling of orthokinetic flocculation of Saccharomyces cerevisiae

This study examined the flocculation behavior of two Saccharomyces cerevisiae strains expressing either Flo1 (LCC1209) genotype or NewFlo (LCC125) phenotype in a laminar flow field by measurement of the fundamental flocculation parameter, the orthokinetic capture coefficient. This orthokinetic capture coefficient was measured as a function of shear rate (5.95-223 s(-1)) and temperature (5-45 degrees C). The capture coefficients of these suspensions were directly proportional to the inverse of shear rate, and exhibited an increase as the temperature was increased to 45 degrees C. The capture coefficient of pronase-treated cells was also measured over similar shear rate and temperature range. A theory, which predicts capture coefficient values due to zymolectin interactions, was simplified from that developed by Long et al. [Biophys. J. 76: (1999) 1112]. This new modified theory uses estimates of: (1) cell wall densities of zymolectins and carbohydrate ligands; (2) cell wall collision contact area; and (3) the forward rate coefficient of binding to predict theoretical capture coefficients. A second model that involves both zymolectin interactions and DLVO forces was used to describe the phenomenon of yeast flocculation at intermediate shear ranges, to explain yeast flocculation in laminar flow.

Dynamics of neutrophil aggregation in couette flow revealed by videomicroscopy: effect of shear rate on two-body collision efficiency and doublet lifetime

During inflammation, neutrophil capture by vascular endothelial cells is dependent on L-selectin and beta(2)-integrin adhesion receptors. One of us (S.I.S.) previously demonstrated that homotypic neutrophil aggregation is analogous to this process in that it is also mediated by these receptors, thus providing a model for studying the dynamics of neutrophil adhesion. In the present work, we set out to confirm the hypothesis that cell-cell adhesion via selectins serves to increase the lifetimes of neutrophil doublets formed through shear-induced two-body collisions. In turn, this would facilitate the engagement of more stable beta(2)-integrin bonds and thus increase the two-body collision efficiency (fraction of collisions resulting in the formation of nonseparating doublets). To this end, suspensions of unstimulated neutrophils were subjected to a uniform shear field in a transparent counter-rotating cone and plate rheoscope, and the formation of doublets and growth of aggregates recorded using high-speed videomicroscopy. The dependence of neutrophil doublet lifetime and two-body collision-capture efficiency on shear rate, G, from 14 to 220 s(-1) was investigated. Bond formation during a two-body collision was indicated by doublets rotating well past the orientation predicted for break-up of doublets of inert spheres. A striking dependence of doublet lifetime on shear rate was observed. At low shear (G = 14 s(-1)), no collision capture occurred, and doublet lifetimes were no different from those of neutrophils pretreated with a blocking antibody to L-selectin, or in Ca(++)-depleted EDTA buffers. At G > or = 66 s(-1), doublet lifetimes increased, with increasing G reaching values twice those for the L-selectin-blocked controls. This correlated with capture efficiencies in excess of 20%, and, at G > or = 110 s(-1), led to the rapid formation of large aggregates, and this in the absence of exogenous chemotactic stimuli. Moreover, the aggregates almost completely broke up when the shear rate was reduced below 66 s(-1). Partial inhibition of aggregate formation was achieved by blocking beta(2)-integrin receptors with antibody. By direct observation of the shear-induced interactions between neutrophils, these data reveal that steady application of a threshold level of shear rate is sufficient to support homotypic neutrophil aggregation.

Modeling concurrent binding of multiple molecular species in cell adhesion

Cell adhesion provides not only physical linkage but also communication between the cell and its environment. As such, it is important to many cellular functions. Recently, the probability distribution of forming a low number of specific adhesive bonds in a short-duration contact has been described (Chesla et al., Biophys. J. , 1998, 75:1553-1572). This model assumes that binding occurs between a single receptor species and a single ligand species. However, cell adhesion molecules rarely work alone in physiological settings. To account for these in vivo situations, we extended the previous model to include concurrent interactions of multiple receptor-ligand species, introducing the concept of independent binding. Closed-form solutions have been obtained for cases where competition is absent or can be neglected. In two companion papers (Williams et al., Biophys. J., 2000, 79:1858-1866; 2000, 79:1867-1875), the model developed herein has been applied to analyze two sets of experiments designed such that the validity of the theory was also tested.

Time and force dependence of the rupture of glycoprotein IIb-IIIa-fibrinogen bonds between latex spheres

We studied the shear-induced breakup of doublets of aldehyde/sulfate (A/S) latex spheres covalently linked with purified platelet GPIIb-IIIa receptor, and cross-linked by fibrinogen. Flow cytometry with fluorescein isothiocyanate-fibrinogen showed than an average of 22,500 molecules of active GPIIb-IIIa were captured per sphere, with a mean K(d) = 56 nM for fibrinogen binding. The spheres, suspended in buffered 19% Ficoll 400 containing 120 or 240 pM fibrinogen, were subjected to Couette flow in a counter-rotating cone-plate rheoscope. Doublets, formed by two-body collisions at low shear rate (G = 8 s(-1)) for < or =15 min, were subjected to shear stress from 0.6 to 2.9 Nm(-2), their rotations recorded until they broke up or were lost to view. Although breakup was time dependent, occurring mostly in the first 2 rotations after the onset of shear, the percentage of doublets broken up after 10 rotations were almost independent of normal hydrodynamic force, F(n): at 240 pN, 15.6, 16.0, and 17.0% broke up in the force range 70-150 pN, 150-230 pN, and 230-310 pN. Unexpectedly, at both [fibrinogen], the initial rate of breakup was highest in the lowest force range, and computer simulation using a stochastic model of breakup was unable to simulate the time course of breakup. When pre-sheared at low G for >15 min, no doublets broke up within 10 rotations at 70 < F(n) < 310 pN; it required >3 min shear (>1110 rotations) at F(n) = 210 pN for significant breakup to occur. Other published work has shown that binding of fibrinogen to GPIIb-IIIa immobilized on plane surfaces exhibits an initial fast reversible process with relative low affinity succeeded by transformation of GPIIb-IIIa to a stable high-affinity complex. We postulate that most doublet breakups observed within 10 rotations were from a population of young doublets having low numbers of bonds, by dissociation of the initial receptor complex relatively unresponsive to force. The remaining, older doublets with GPIIb-IIIa in the high-affinity complex were not broken up in the time or range of forces studied.

Kinetics and mechanics of cell adhesion

Cell adhesion is mediated by specific interaction between receptors and ligands. Such interaction provides not only physical linkage but also communication between the cell and its environment. The kinetics and mechanics of cell adhesion are coupled, because force can influence the formation and dissociation of receptor-ligand bonds. The kinetic rates and their force dependence determine how likely, how rapidly and how strongly cells bind as well as how long they remain bound. Since adhesion molecules are linked to apposing cellular membranes, their interaction is governed by two-dimensional (2D) kinetics. This is in contrast to the three-dimensional (3D) binding of soluble ligands to cell surface receptors. Unlike the 3D case in which many methods are available for measuring kinetic rates, not until recently have the 2D kinetic rates become experimentally measurable. In this review, I will discuss the recent progress in the experimental methods that enable quantification of the relevant kinetic and mechanical parameters, the fundamental concepts that underlie the physics of the biological phenomena, and the mathematical models that relate functions to the intrinsic properties of the adhesion molecules.

Analysis of competition binding between soluble and membrane-bound ligands for cell surface receptors

Binding of the Fc portion of IgG coated on targets to Fcgamma receptors (e.g., CD16) expressed on leukocytes (i.e., 2D binding) is an initiating step for immune responses such as phagocytosis or antibody-dependent cellular cytotoxicity. In vivo, circulating leukocytes are exposed to plasma IgG. The competition from soluble IgG (i.e., 3D binding) may affect the 2D binding. Many cell surface receptors, CD16 included, have soluble counterparts. While their physiological significance is not clear, receptor-based competitive inhibition therapy, in which soluble receptors, ligands, and their analogs are employed to compete with surface-bound receptors and ligands to prevent unwanted adhesion, is widely used to treat various diseases. To provide a quantitative basis for design of these therapeutic approaches, we developed a mathematical model for 2D and 3D competition binding. The model relates cell-surface adhesion (in the presence and absence of dislodging forces) to the concentration of the soluble competitor, the densities of the surface-bound receptors and ligands, as well as the binding affinities of the 2D and 3D interactions. Binding of CD16-expressing cells to an IgG-coated surface in the presence of a soluble competitor (IgG or anti-CD16 antibody) was quantified by a centrifugation assay. The agreement between experiment and theory supports the validity of the model, which could be useful in predicting the efficacy of the competitor.

Monte Carlo simulation of the heterotypic aggregation kinetics of platelets and neutrophils

The heterotypic aggregation of cell mixtures or colloidal particles such as proteins occurs in a variety of settings such as thrombosis, immunology, cell separations, and diagnostics. Using the set of population balance equations (PBEs) to predict dynamic aggregate size and composition distributions is not feasible. The stochastic algorithm of Gillespie for chemical reactions (. J. Comput. Phys. 22:403-434) was reformulated to simulate the kinetic behavior of aggregating systems. The resulting Monte Carlo (MC) algorithm permits exact calculation of the decay rates of monomers and the temporally evolving distribution of sizes and compositions of the aggregates. Moreover, it permits calculation of all moments of these distributions. Using this method, we explored the heterotypic aggregation of fully activated platelets and neutrophils in a linear shear flow of shear rate G = 335 s(-1). At plasma concentrations, the half-lives of homotypically aggregating platelet and neutrophil singlets were 8.5 and 2.4 s, respectively. However, for heterotypic aggregation, the half-lives for platelets and neutrophils decreased to 2.0 and 0.11 s, respectively, demonstrating that flowing neutrophils accelerate capture of platelets and growth of aggregates. The required number of calculations per time step of the MC algorithm was typically a small fraction of Omega(1/2), where Omega is the initial number of particles in the system, making this the fastest MC method available. The speed of the algorithm makes feasible the deconvolution of kernels for general biological heterotypic aggregation processes.