Influence of cell deformation on leukocyte rolling adhesion in shear flow

Blood cell interaction with vascular endothelium is important in microcirculation, where rolling adhesion of circulating leukocytes along the surface of endothelial cells is a prerequisite for leukocyte emigration under flow conditions. HL-60 cell rolling adhesion to surface-immobilized P-selectin in shear flow was investigated using a side-view flow chamber, which permitted measurements of cell deformation and cell-substrate contact length as well as cell rolling velocity. A two-dimensional model was developed based on the assumption that fluid energy input to a rolling cell was essentially distributed into two parts: cytoplasmic viscous dissipation, and energy needed to break adhesion bonds between the rolling cell and its substrate. The flow fields of extracellular fluid and intracellular cytoplasm were solved using finite element methods with a deformable cell membrane represented by an elastic ring. The adhesion energy loss was calculated based on receptor-ligand kinetics equations. It was found that, as a result of shear-flow-induced cell deformation, cell-substrate contact area under high wall shear stresses (20 dyn/cm2) could be as much as twice of that under low stresses (0.5 dyn/cm2). An increase in contact area may cause more energy dissipation to both adhesion bonds and viscous cytoplasm, whereas the fluid energy input may decrease due to the flattened cell shape. Our model predicts that leukocyte rolling velocity will reach a plateau as shear stress increases, which agrees with both in vivo and in vitro experimental observations.     

Leukocyte rolling on P-selectin: a three-dimensional numerical study of the effect of cytoplasmic viscosity

Rolling leukocytes deform and show a large area of contact with endothelium under physiological flow conditions. We studied the effect of cytoplasmic viscosity on leukocyte rolling using our three-dimensional numerical algorithm that treats leukocyte as a compound droplet in which the core phase (nucleus) and the shell phase (cytoplasm) are viscoelastic fluids. The algorithm includes the mechanical properties of the cell cortex by cortical tension and considers leukocyte microvilli that deform viscoelastically and form viscous tethers at supercritical force. Stochastic binding kinetics describes binding of adhesion molecules. The leukocyte cytoplasmic viscosity plays a critical role in leukocyte rolling on an adhesive substrate. High-viscosity cells are characterized by high mean rolling velocities, increased temporal fluctuations in the instantaneous velocity, and a high probability for detachment from the substrate. A decrease in the rolling velocity, drag, and torque with the formation of a large, flat contact area in low-viscosity cells leads to a dramatic decrease in the bond force and stable rolling. Using values of viscosity consistent with step aspiration studies of human neutrophils (5-30 Pa·s), our computational model predicts the velocities and shape changes of rolling leukocytes as observed in vitro and in vivo.     

Leukocyte arrest during cytokine-dependent inflammation in vivo

Leukocyte rolling along the walls of inflamed venules precedes their adhesion during inflammation. Rolling leukocytes are thought to arrest by engaging beta2 integrins following cellular activation. In vitro studies suggest that chemoattractants may instantaneously activate and arrest rolling leukocytes. However, how leukocytes stop rolling and become adherent in inflamed venules in vivo has remained rather mysterious. In this paper we use a novel method of tracking individual leukocytes through the microcirculation to show that rolling neutrophils become progressively activated while rolling down the venular tree. On average, leukocytes in wild-type mice roll for 86 s (and cover 270 microm) before becoming adherent with an efficiency around 90%. These rolling leukocytes exhibit a gradual beta2 integrin-dependent decrease in rolling velocity that correlates with an increase in intracellular free calcium concentration before arrest. Similar tracking analyses in gene-targeted mice demonstrate that the arrest of rolling leukocytes is very rare when beta2 integrins are absent or blocked by a mAb. Arrest is approximately 50% less efficient in the absence of E-selectin. These data suggest a model of leukocyte recruitment in which beta2 integrins play a critical role in stabilizing leukocyte rolling during a protracted cellular activation period before arrest and firm adhesion.     

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

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

How do selectins mediate leukocyte rolling in venules?

At the onset of inflammation, 20-80% of all leukocytes passing postcapillary venules roll along the endothelium. Recent blocking experiments with antibodies and soluble adhesion receptor molecules, as well as in vitro reconstitution experiments, suggest that leukocyte rolling is mediated by adhesion molecules that belong to the selectin family. What differentiates a selectin-counterreceptor interaction that leads to leukocyte rolling from others that mediate firm adhesion after static incubation but no adhesion when incubated under flow conditions? Here, we explore this question by introducing a quantitative biophysical model that is compatible with the laws of mechanics as applied to rolling leukocytes and the present biochemical and biophysical data on selectin mediated interactions. Our computational experiments point to an adhesion mechanism in which the rate of bond formation is high and the detachment rate low, except at the rear of the contact area where the stretched bonds detach at a high uniform rate. The bond length and bond flexibility play a critical role in enhancing leukocyte rolling at a wide range of fluid shear rates.     

The LFA-1 integrin supports rolling adhesions on ICAM-1 under physiological shear flow in a permissive cellular environment

The LFA-1 integrin is crucial for the firm adhesion of circulating leukocytes to ICAM-1-expressing endothelial cells. In the present study, we demonstrate that LFA-1 can arrest unstimulated PBL subsets and lymphoblastoid Jurkat cells on immobilized ICAM-1 under subphysiological shear flow and mediate firm adhesion to ICAM-1 after short static contact. However, LFA-1 expressed in K562 cells failed to support firm adhesion to ICAM-1 but instead mediated K562 cell rolling on the endothelial ligand under physiological shear stress. LFA-1-mediated rolling required an intact LFA-1 I-domain, was enhanced by Mg2+, and was sharply dependent on ICAM-1 density. This is the first indication that LFA-1 can engage in rolling adhesions with ICAM-1 under physiological shear flow. The ability of LFA-1 to support rolling correlates with decreased avidity and impaired time-dependent adhesion strengthening. A beta2 cytoplasmic domain-deletion mutant of LFA-1, with high avidity to immobilized ICAM-1, mediated firm arrests of K562 cells interacting with ICAM-1 under shear flow. Our results suggest that restrictions in LFA-1 clustering mediated by cytoskeletal attachments may lock the integrin into low-avidity states in particular cellular environments. Although low-avidity LFA-1 states fail to undergo adhesion strengthening upon contact with ICAM-1 at stasis, these states are permissive for leukocyte rolling on ICAM-1 under physiological shear flow. Rolling mediated by low-avidity LFA-1 interactions with ICAM-1 may stabilize rolling initiated by specialized vascular rolling receptors and allow the leukocyte to arrest on vascular endothelium upon exposure to stimulatory endothelial signals.     

Simulation and Analysis of Tethering Behavior of Neutrophils with Pseudopods

P-selectin and P-selectin glycoprotein ligand-1 (PSGL-1) play important roles in mediating the inflammatory cascade. Selectin kinetics, together with neutrophil hydrodynamics, regulate the fundamental adhesion cascade of cell tethering and rolling on the endothelium. The current study uses the Multiscale Adhesive Dynamics computational model to simulate, for the first time, the tethering and rolling behavior of pseudopod-containing neutrophils as mediated by P-selectin/PSGL-1 bonds. This paper looks at the effect of including P-selectin/PSGL-1 adhesion kinetics. The parameters examined included the shear rate, adhesion on-rate, initial neutrophil position, and receptor number sensitivity. The outcomes analyzed included types of adhesive behavior observed, tether rolling distance and time, number of bonds formed during an adhesive event, contact area, and contact time. In contrast to the hydrodynamic model, P-selectin/PSGL-1 binding slows the neutrophil’s translation in the direction of flow and causes the neutrophil to swing around perpendicular to flow. Several behaviors were observed during the simulations, including tethering without firm adhesion, tethering with downstream firm adhesion, and firm adhesion upon first contact with the endothelium. These behaviors were qualitatively consistent with in vivo data of murine neutrophils with pseudopods. In the simulations, increasing shear rate, receptor count, and bond formation rate increased the incidence of firm adhesion upon first contact with the endothelium. Tethering was conserved across a range of physiological shear rates and was resistant to fluctuations in the number of surface PSGL-1 molecules. In simulations where bonding occurred, interaction with the side of the pseudopod, rather than the tip, afforded more surface area and greater contact time with the endothelial wall.     

The state diagram for cell adhesion mediated by two receptors

Leukocyte recruitment from the bloodstream to surrounding tissues is an essential component of the immune response. Capture of blood-borne leukocytes onto vascular endothelium proceeds via a two-step mechanism, with each step mediated by a distinct receptor-ligand pair. Cells first transiently adhere, or "roll" (via interactions between selectins and sialyl-Lewis-x), and then firmly adhere to the vascular wall (via interactions between integrins and ICAM-1). We have reported that a computational method called adhesive dynamics (AD) accurately reproduces the fine-scale dynamics of selectin-mediated rolling. This paper extends the use of AD simulations to model the dynamics of cell adhesion when two classes of receptors are simultaneously active: one class (selectins or selectin ligands) with weakly adhesive properties, and the other (integrins) with strongly adhesive properties. AD simulations predict synergistic functions of the two receptors in mediating adhesion. At a fixed density of surface ICAM-1, increasing selectin densities lead to greater pause times and an increased tendency toward firm adhesion; thus, selectins mechanistically facilitate firm adhesion mediated by integrins. Conversely, at a fixed density of surface selectin, increasing ICAM-1 densities lead to greater pause times and an increased tendency to firm adhesion. We present this relationship in a two-receptor state diagram, a map that relates the densities and properties of adhesion molecules to various adhesive behaviors that they code, such as rolling or firm adhesion. We also present a state diagram for neutrophil activation, which relates beta(2)-integrin density and integrin-ICAM-1 kinetic on rate to neutrophil adhesive behavior. The predictions of two-receptor adhesive dynamics are validated by the ability of the model to reproduce in vivo neutrophil rolling velocities from the literature.     

A 3-D computational model predicts that cell deformation affects selectin-mediated leukocyte rolling

Leukocyte recruitment to sites of inflammation is initiated by their tethering and rolling on the activated endothelium under flow. Even though the fast kinetics and high tensile strength of selectin-ligand bonds are primarily responsible for leukocyte rolling, experimental evidence suggests that cellular properties such as cell deformability and microvillus elasticity actively modulate leukocyte rolling behavior. Previous theoretical models either assumed cells as rigid spheres or were limited to two-dimensional representations of deformable cells with deterministic receptor-ligand kinetics, thereby failing to accurately predict leukocyte rolling. We therefore developed a three-dimensional computational model based on the immersed boundary method to predict receptor-mediated rolling of deformable cells in shear flow coupled to a Monte Carlo method simulating the stochastic receptor-ligand interactions. Our model predicts for the first time that the rolling of more compliant cells is relatively smoother and slower compared to cells with stiffer membranes, due to increased cell-substrate contact area. At the molecular level, we show that the average number of bonds per cell as well as per single microvillus decreases with increasing membrane stiffness. Moreover, the average bond lifetime decreases with increasing shear rate and with increasing membrane stiffness, due to higher hydrodynamic force experienced by the cell. Taken together, our model captures the effect of cellular properties on the coupling between hydrodynamic and receptor-ligand bond forces, and successfully explains the stable leukocyte rolling at a wide range of shear rates over that of rigid microspheres.     

High-temporal-resolution analysis demonstrates that ICAM-1 stabilizes WEHI 274.1 monocytic cell rolling on endothelium

Leukocyte rolling, adhesion, and migration on vascular endothelium involve several sets of adhesion molecules that interact simultaneously. Each of these receptor-ligand pairs may play multiple roles. We examined the role of ICAM-1 in adhesive interactions with mouse aortic endothelial cells (MAECs) in an in vitro flow system. Average rolling velocity of the monocytic cell line WEHI 274.1 was increased on ICAM-1-deficient MAECs compared with wild-type MAECs, both with and without TNF- stimulation. High-temporal-resolution analysis provided insights into the underlying basis for these differences. Without TNF- stimulation, average rolling velocity was slower on wild-type than on ICAM-1-deficient endothelium because of brief (<1 s) pauses. On TNF--stimulated ICAM-1-deficient endothelium, cells rolled faster because of transient accelerations, producing "jerky" rolling. Firm adhesion to ICAM-1-deficient MAECs was significantly reduced compared with wild-type MAECs, although the number of rolling cells was similar. These results demonstrate directly that ICAM-1 affects rolling velocity by stabilizing leukocyte rolling. intercellular adhesion molecule-1; cell adhesion; leukocytes; vascular endothelium; videomicroscopy     

Shear-driven rolling of DNA-adhesive microspheres

Many biologically important cell binding processes, such as the rolling of leukocytes in the vasculature, are multivalent, being mediated by large numbers of weak binding ligands. Quantitative agreement between experiments and models of rolling has been elusive and often limited by the poor understanding of the binding and unbinding kinetics of the ligands involved. Here, we present a cell-free experimental model for such rolling, consisting of polymer microspheres whose adhesion to a glass surface is mediated by ligands with well-understood force-dependent binding free energy—short complementary DNA strands. We observe robust rolling activity for certain values of the shear rate and the grafted DNA strands’ binding free energy and force sensitivity. The simulation framework developed to model leukocyte rolling, adhesive dynamics, quantitatively captures the mean rolling velocity and lateral diffusivity of the experimental particles using known values of the experimental parameters. Moreover, our model captures the velocity variations seen within the trajectories of single particles. Particle-to-particle variations can be attributed to small, plausible differences in particle characteristics. Overall, our findings confirm that state-of-the-art adhesive dynamics simulations are able to capture the complex physics of particle rolling, boding well for their extension to modeling more complex systems of rolling cells.     

Biomechanics of cell rolling: shear flow, cell-surface adhesion, and cell deformability

The mechanics of leukocyte (white blood cell; WBC) deformation and adhesion to endothelial cells (EC) has been investigated using a novel in vitro side-view flow assay. HL-60 cell rolling adhesion to surface-immobilized P-selectin was used to model the WBC-EC adhesion process. Changes in flow shear stress, cell deformability, or substrate ligand strength resulted in significant changes in the characteristic adhesion binding time, cell-surface contact and cell rolling velocity. A 2-D model indicated that cell-substrate contact area under a high wall shear stress (20 dyn/cm2) could be nearly twice of that under a low stress (0.5 dyn/cm2) due to shear flow-induced cell deformation. An increase in contact area resulted in more energy dissipation to both adhesion bonds and viscous cytoplasm, whereas the fluid energy that inputs to a cell decreased due to a flattened cell shape. The model also predicted a plateau of WBC rolling velocity as flow shear stresses further increased. Both experimental and computational studies have described how WBC deformation influences the WBC-EC adhesion process in shear flow.     

A computational study of leukocyte adhesion and its effect on flow pattern in microvessels

Three-dimensional computational modeling and simulation are presented on the adhesive rolling of deformable leukocytes over a P-selectin coated surface in parabolic shear flow in microchannels. The computational model is based on the immersed boundary method for cell deformation and Monte Carlo simulation for receptor/ligand interaction. The simulations are continued for at least 1 s of leukocyte rolling during which the instantaneous quantities such as cell deformation index, cell/substrate contact area, and fluid drag remain statistically stationary. The characteristic ‘stop-and-go’ motion of rolling leukocytes, and the ‘tear-drop’ shape of adherent leukocytes as observed in experiments are reproduced by the simulations. We first consider the role of cell deformation and cell concentration on rolling characteristics. We observe that compliant cells roll slower and more stably than rigid cells. Our simulations agree with previous in vivo observation that the hydrodynamic interactions between nearby leukocytes affect cell rolling, and that the rolling velocity decreases inversely with the separation distance, irrespective of cell deformability. We also find that cell deformation decreases, and the cells roll more stably with reduced velocity fluctuation, as the cell concentration is increased. However, the effect of nearby cells on the rolling characteristics is found to be more significant for rigid cells than compliant cells. We then address the effect of cell deformability and rolling velocity on the flow resistance due to, and the fluid drag on, adherent leukocytes. While several earlier computational works have addressed this problem, two key features of leukocyte adhesion, such as cell deformation and rolling, were often neglected. Our results suggest that neglecting cell deformability and rolling velocity may significantly overpredict the flow resistance and drag force. Increasing the cell concentration is shown to increase the flow resistance and reduce the fluid drag. The reduced drag then results in slower and more stable rolling of the leukocytes with longer pause time and shorter step distance. But the increase/decrease in the flow resistance/fluid drag due to the increase in the cell concentration is observed to be more significant in case of rigid cells than compliant cells.     

Simulation of cell rolling and adhesion on surfaces in shear flow: general results and analysis of selectin-mediated neutrophil adhesion.

The receptor-mediated adhesion of cells to ligand-coated surfaces in viscous shear flow is an important step in many physiological processes, such as the neutrophil-mediated inflammatory response, lymphocyte homing, and tumor cell metastasis. This paper describes a calculational method which simulates the interaction of a single cell with a ligand-coated surface under flow. The cell is idealized as a microvilli-coated hard sphere covered with adhesive springs. The distribution of microvilli on the cell surface, the distribution of receptors on microvilli tips, and the forward and reverse reaction between receptor and ligand are all simulated using random number sampling of appropriate probability functions. The velocity of the cell at each time step in the simulation results from a balance of hydrodynamic, colloidal and bonding forces; the bonding force is derived by summing the individual contributions of each receptor-ligand tether. The model can simulate the effect of many parameters on adhesion, such as the number of receptors on microvilli tips, the density of ligand, the rates of reaction between receptor and ligand, the stiffness of the resulting receptor-ligand springs, the response of springs to strain, and the magnitude of the bulk hydrodynamic stresses. The model can successfully recreate the entire range of expected and observed adhesive phenomena, from completely unencumbered motion, to rolling, to transient attachment, to firm adhesion. Also, the method can generate meaningful statistical measures of adhesion, including the mean and variance in velocity, rate constants for cell attachment and detachment, and the frequency of adhesion. We find a critical modulating parameter of adhesion is the fractional spring slippage, which relates the strain of a bond to its rate of breakage; the higher the slippage, the faster the breakage for the same strain. Our analysis of neutrophil adhesive behavior on selectin-coated (CD62-coated) surfaces in viscous shear flow reported by Lawrence and Springer (Lawrence, M.B., and T.A. Springer 1991. Cell. 65:859-874) shows the fractional spring slippage of the CD62-LECAM-1 bond is likely below 0.01. We conclude the unique ability of this selectin bond to cause neutrophil rolling under flow is a result of its unique response to strain. Furthermore, our model can successfully recreate data on neutrophil rolling as function of CD62 surface density.     

Role of shear forces and adhesion molecule distribution on P-selectin-mediated leukocyte rolling in postcapillary venules

Rolling on the venular endothelium is a critical step in the recruitment of leukocytes during the inflammatory response. P-selectin is a key mediator of leukocyte rolling, which is an early event in the inflammatory cascade; this rolling is likely to be directly regulated by both local fluid shear forces and P-selectin site densities in the microvasculature. However, neither the spatial pattern of P-selectin expression in postcapillary venules nor the effect of local expression patterns on rolling behavior in intact functional venules is known. We investigated the influence of local shear forces and the spatial distribution of endothelial P-selectin in intact blood perfused post capillary venules in anesthetized mice using intravital confocal microscopy, high temporal resolution particle tracking, and immunofluorescent labeling. We demonstrated a shear-dependent increase in average leukocyte rolling velocity that was attributable to a shear-dependent increase in the occurrence of transient leukocyte detachments from the endothelial surface: translational velocity during leukocyte contact with the vessel wall remained constant. P-selectin expression was not different in venules with characteristically different shear rates or diameters but varied significantly within individual venules. In postcapillary venules, regions of high P-selectin expression correlated with regions of slow leukocyte rolling. Thus the characteristically variable leukocyte rolling in vivo is a function of the spatial heterogeneity in P-selectin expression. The study shows how the local hydrodynamic forces and the nonuniform pattern of P-selectin expression affect the behavior of interacting leukocytes, providing direct evidence for the local variation of adhesion molecule expression as a mechanism for the regulation of leukocyte recruitment.     

Adhesive dynamics simulation of neutrophil arrest with deterministic activation

The transition from rolling to firm adhesion is a key element of neutrophil activation and essential to the inflammatory response. Although the molecular mediators of rolling and firm adhesion are known to be selectins and beta2 -integrins, respectively, the precise dynamic mechanism by which these ligands facilitate neutrophil arrest remains unknown. Recently, it has been shown that ligation of E-selectin can stimulate the firm adhesion of neutrophils via a MAP-kinase cascade. To study the possible mechanism by which neutrophil arrest could occur, we created an integrated model by combining two methodologies from computational biology: a mechanics-based modeling of leukocyte adhesion (adhesive dynamics) and signal transduction pathway modeling. Within adhesive dynamics, a computational method our group has shown to accurately recreate rolling dynamics, we include a generic, tunable integrin activation module that links selectin engagement to integrin and activity. This model allows us to relate properties of the activation function to the dynamics of rolling and the time and distance rolled before arrest. This integrated model allows us to understand how intracellular signaling activity can set the timescale of neutrophil activation, adhesion, and diapedesis.     

A role for ICAM-1 in maintenance of leukocyte-endothelial cell rolling interactions in inflamed arterioles

A key endothelial receptor in leukocyte-endothelial cell (EC) interactions is ICAM-1. ICAM-1 is constitutively expressed at low levels on vascular ECs, and its levels significantly increase following stimulation with many proinflammatory agents. This study provides evidence that in inflamed arterioles of anesthetized mice (65 mg/kg ip Nembutal), ICAM-1 mediates leukocyte rolling, in contrast to its expected role of mediating firm adhesion in venules. The number of leukocytes rolling on arteriolar ECs is decreased in ICAM-1 knockout (KO) compared with wild-type (WT) mice (KO, 6.0 +/- 0.9; WT, 12.0 +/- 1.0 leukocytes/40 s; P < 0.05), whereas the leukocyte-rolling number in venules remains unaffected (KO, 5.6 +/- 0.9; WT, 7.0 +/- 0.7 leukocytes/40 s; n = 13-15 sites). We also show that the fraction of leukocytes that is rolling on arteriolar ECs does so with a higher characteristic velocity (>70 microm/s), and, furthermore, that the distance over which rolling contacts with the arteriolar wall are maintained is ICAM-1 dependent. In ICAM-1 KO animals or in WT mice in the presence of ICAM-1-blocking antibody, leukocytes rolled significantly shorter distances over the sampled 200-microm vessel length compared with WT (68 +/- 6.7 and 55 +/- 9.4 vs. 85 +/- 12.9% total, respectively, n = 4 sites, P < 0.05). We also found evidence that in ICAM-1 KO mice, a significant fraction of leukocyte rolling and adhesive interactions with arteriolar ECs could be accounted for by upregulation of another adhesion molecule, VCAM-1, providing an important illustration of how expression of related proteins can be altered following genetic ablatement of a target molecule (in this case ICAM-1).     

Simulation of detachment of specifically bound particles from surfaces by shear flow.

The receptor-mediated adhesion of cells to ligand-coated surfaces is important in many physiological and biotechnological processes. Previously, we measured the detachment of antibody-coated spheres from counter-antibody- and protein A-coated substrates using a radial-flow detachment assay and were able to relate mechanical adhesion strength to chemical binding affinity (Kuo and Lauffenburger, Biophys. J. 65:2191-2200 (1993)). In this paper, we use "adhesive dynamics" to simulate the detachment of antibody-coated hard spheres from a ligand-coated substrate. We modeled the antibody-ligand (either counter-antibody or protein A) bonds as adhesive springs. In the simulation as in the experiments, beads attach to the substrate under static conditions. Flow is then initiated, and detachment is measured by the significant displacement of previously bound particles. The model can simulate the effects of many parameters on cell detachment, including hydrodynamic stresses, receptor number, ligand density, reaction rates between receptor and ligand, and stiffness and reactive compliance of the adhesive springs. The simulations are compared with experimental detachment data, thus relating measured bead adhesion strength to molecular properties of the adhesion molecules. The simulations accurately recreated the logarithmic dependence of adhesion strength on affinity of receptor-ligand recognition, which was seen in experiments and predicted by analytic theory. In addition, we find the value of the reactive compliance, the parameter which relates the strain of a bond to its rate of breakage, that gives the best match between theory and experiment to be 0.01. Finally, we analyzed the effect of varying either the forward or reverse rate constants as different ways to achieve the same affinity, and showed that adhesion strength depends uniquely on the equilibrium affinity, not on the kinetics of binding. Given that attachment is independent of affinity, detachment and attachment are distinct adhesive phenomena.     

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.     

A semianalytical model to study the effect of cortical tension on cell rolling

Cell rolling on the vascular endothelium plays an important role in trafficking of leukocytes, stem cells, and cancer cells. We describe a semianalytical model of cell rolling that focuses on the microvillus as the unit of cell-substrate interaction and integrates microvillus mechanics, receptor clustering, force-dependent receptor-ligand kinetics, and cortical tension that enables incorporation of cell body deformation. Using parameters obtained from independent experiments, the model showed excellent agreement with experimental studies of neutrophil rolling on P-selectin and predicted different regimes of cell rolling, including spreading of the cells on the substrate under high shear. The cortical tension affected the cell-surface contact area and influenced the rolling velocity, and modulated the dependence of rolling velocity on microvillus stiffness. Moreover, at the same shear stress, microvilli of cells with higher cortical tension carried a greater load compared to those with lower cortical tension. We also used the model to obtain a scaling dependence of the contact radius and cell rolling velocity under different conditions of shear stress, cortical tension, and ligand density. This model advances theoretical understanding of cell rolling by incorporating cortical tension and microvillus extension into a versatile, semianalytical framework.