Kinetics of adhesion of IgE-sensitized rat basophilic leukemia cells to surface-immobilized antigen in Couette flow.

Antigen-antibody systems provide the flexibility of varying the kinetics and affinity of molecular interaction and studying the resulting effect on adhesion. In a parallel-plate flow chamber, we measured the extent and rate of adhesion of rat basophilic leukemia cells preincubated with anti-dinitrophenyl IgE clones SPE-7 or H1 26. 82 to dinitrophenyl-coated polyacrylamide gel substrates in a linear shear field. Both of these IgEs bind dinitrophenyl, but H1 26.82 has a 10-fold greater on rate and a 30-fold greater affinity. Adhesion was found to be binary; cells either arrested irreversibly or continued at their unencumbered hydrodynamic velocity. Under identical conditions, more adhesion was seen with the higher affinity (higher on rate) IgE clone. At some shear rates, adhesion was robust with H1 26.82, but negligible with SPE-7. Reduction in receptor number or ligand density reduced the maximum level of adhesion seen at any shear rate, but did not decrease the shear rate at which adhesion was first observed. The spatial pattern of adhesion for both IgE clones is well represented by the first-order kinetic rate constant kad, and we have determined how kad depends on ligand and receptor densities and shear rate. The rate constant kad found with H1 26.82 was approximately fivefold greater than with SPE-7. The dependence of kad on site density and shear rate for SPE-7 is complex: kad increases linearly with antigen site density at low to moderate shear rates, but is insensitive to site density at high shear. kad increases with shear rate at low site density but decreases with shear at high site density. With H1 26.82, the functional dependence of kad with shear rate was similar. Although these data are consistent with the hypothesis that we have sampled both transport and reaction-limited adhesion regimes, they point out deficiencies in current theories describing cell attachment under flow.     

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.     

Aggregation of IgE-receptor complexes on rat basophilic leukemia cells does not change the intrinsic affinity but can alter the kinetics of the ligand-IgE interaction.

The aggregation of IgE anchored to high-affinity Fc epsilon receptors on rat basophilic leukemia (RBL) cells by multivalent antigens initiates transmembrane signaling and ultimately cellular degranulation. Previous studies have shown that the rate of dissociation of bivalent and multivalent DNP ligands from RBL cells sensitized with anti-DNP IgE decreases with increasing ligand incubation times. One mechanism proposed for this effect is that when IgE molecules are aggregated, a conformational change occurs that results in an increase in the intrinsic affinity of IgE for antigen. This possibility was tested by measuring the equilibrium constant for the binding of monovalent DNP-lysine to anti-DNP IgE under two conditions, where the cell-bound IgE is dispersed and where it has been aggregated into visible patches on the cell surface using anti-IgE and a secondary antibody. No difference in the equilibrium constant in these two cases was observed. We also measured the rate of dissociation of a monovalent ligand from cell surface IgE under these two conditions. Whereas the affinity for monovalent ligand is not altered by IgE aggregation, we observe that the rate of ligand dissociation from IgE in clusters is slower than the rate of ligand dissociation from unaggregated IgE. These results are discussed in terms of recent theoretical developments concerning effects of receptor density on ligand binding to cell surfaces.     

Design of a side-view particle imaging velocimetry flow system for cell-substrate adhesion studies

Experimental models that mimic the flow conditions in microcapillaries have suggested that the local shear stresses and shear rates can mediate tumor cell and leukocyte arrest on the endothelium and subsequent sustained adhesion. However, further investigation has been limited by the lack of experimental models that allow quantitative measurement of the hydrodynamic environment over adherent cells. The purpose of this study was to develop a system capable of acquiring quantitative flow profiles over adherent cells. By combining the techniques of side-view imaging and particle image velocimetry (PIV), an in vitro model was constructed that is capable of obtaining quantitative flow data over cells adhering to the endothelium. The velocity over an adherent leukocyte was measured and the shear rate was calculated under low and high upstream wall shear. The microcapillary channel was modeled using computational fluid dynamics (CFD) and the calculated velocity profiles over cells under the low and high shear rates were compared to experimental results. The drag force applied to each cell by the fluid was then computed. This system provides a means for future study of the forces underlying adhesion by permitting characterization of the local hydrodynamic conditions over adherent cells.     

Study of local hydrodynamic environment in cell-substrate adhesion using side-view μPIV technology

Tumor cell adhesion to the endothelium under shear flow conditions is a critical step that results in circulation-mediated tumor metastasis. This study presents experimental and computational techniques for studying the local hydrodynamic environment around adherent cells and how local shear conditions affect cell-cell interactions on the endothelium in tumor cell adhesion. To study the local hydrodynamic profile around heterotypic adherent cells, a side-view flow chamber assay coupled with micro particle imaging velocimetry (μPIV) technique was developed, where interactions between leukocytes and tumor cells in the near-endothelial wall region and the local shear flow environment were characterized. Computational fluid dynamics (CFD) simulations were also used to obtain quantitative flow properties around those adherent cells. Results showed that cell dimension and relative cell-cell positions had strong influence on local shear rates. The velocity profile above leukocytes and tumor cells displayed very different patterns. Larger cell deformations led to less disturbance to the flow. Local shear rates above smaller cells were observed to be more affected by relative positions between two cells.     

Simulation of cell rolling and adhesion on surfaces in shear flow. Microvilli-coated hard spheres with adhesive springs.

The 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 article describes a calculational method that allows simulation of the interaction of a single cell with a ligand-coated surface. 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 springs, the response of springs to extension, and the magnitude of hydrodynamic stresses. By varying these parameters, 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 model can provide 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 extension of a bond to its rate of breakage; the higher the slippage, the faster the breakage for the same extension. Changes in the fractional spring slippage can radically change the adhesive behavior of a cell. We show that stiffer springs will only serve to increase adhesion if the fractional slippage remains small. In addition, our simulations emphasize the importance of reaction rates between receptor and ligand, rather than affinity, as being the key determinant of adhesion under flow. These results suggest reaction rates and response to stress of adhesion molecules must be independently measured to understand how adhesion is controlled at the molecular level.     

Simulation of cell rolling and adhesion on surfaces in shear flow

The 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 article describes a calculational method that allows simulation of the interaction of a single cell with a ligandcoated surface. 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 springs, the response of springs to extension, and the magnitude of hydrodynamic stresses. By varying these parameters, 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 model can provide meaningful statistical measures of adhesion, including the mean and variance in velocity, rate constants for ceil attachment and detachment, and the frequency of adhesion. We find a critical modulating parameter of adhesion is the fractional spring slippage, which relates the extension of a bond to its rate of breakage; the higher the slippage, the faster the breakage for the same extension. Changes in the fractional spring slippage can radically change the adhesive behavior of a cell. We show that stiffer springs will only serve to increase adhesion if the fractional slippage remains small. In addition, our simulations emphasize the importance of reaction rates between receptor and ligand, rather than affinity, as being the key determinant of adhesion under flow. These results suggest reaction rates and response to stress of adhesion molecules must be independently measured to understand how adhesion is controlled at the molecular level.     

Competition between solution and cell surface receptors for ligand. Dissociation of hapten bound to surface antibody in the presence of solution antibody.

We present a joint theoretical and experimental study on the effects of competition for ligand between receptors in solution and receptors on cell surfaces. We focus on the following experiment. After ligand and cell surface receptors equilibrate, solution receptors are introduced, and the dissociation of surface bound ligand is monitored. We derive theoretical expressions for the dissociation rate and compare with experiment. In a standard dissociation experiment (no solution receptors present) dissociation may be slowed by rebinding, i.e., at high receptor densities a ligand that dissociates from one receptor may rebind to other receptors before separating from the cell. Our theory predicts that rebinding will be prevented when S much greater than N2Kon/(16 pi 2D a4), where S is the free receptor site concentration in solution, N the number of free surface receptor sites per cell, Kon the forward rate constant for ligand-receptor binding in solution, D the diffusion coefficient of the ligand, and a the cell radius. The predicted concentration of solution receptors needed to prevent rebinding is proportional to the square of the cell surface receptor density. The experimental system used in these studies consists of a monovalent ligand, 2,4-dinitrophenyl (DNP)-aminocaproyl-L-tyrosine (DCT), that reversibly binds to a monoclonal anti-DNP immunoglobulin E (IgE). This IgE is both a solution receptor and, when anchored to its high affinity Fc epsilon receptor on rat basophilic leukemia (RBL) cells, a surface receptor. For RBL cells with 6 x 10(5) binding sites per cell, our theory predicts that to prevent DCT rebinding to cell surface IgE during dissociation requires S much greater than 2,400 nM. We show that for S = 200-1,700 nM, the dissociation rate of DCT from surface IgE is substantially slower than from solution IgE where no rebinding occurs. Other predictions are also tested and shown to be consistent with experiment.     

Shear modulation of intercellular contact area between two deformable cells colliding under flow

Shear rate has been shown to critically affect the kinetics and receptor specificity of cell-cell interactions. In this study, the collision process between two modeled cells interacting in a linear shear flow is numerically investigated. The two identical biological or artificial cells are modeled as deformable capsules composed of an elastic membrane. The cell deformation and trajectories are computed using the immersed boundary method (IBM) for shear rates of 100-400s(-1). As the two cells collide under hydrodynamic shear, large local cell deformations develop. The effective contact area between the two cells is modulated by the shear rate, and reaches a maximum value at intermediate levels of shear. At relatively low shear rate, the contact area is an enclosed region. As the shear rate increases, dimples form on the membrane surface, and the contact region becomes annular. The nonmonotonic increase of the contact area with the increase of shear rate from computational results implies that there is a maximum effective receptor-ligand binding area for cell adhesion. This finding suggests the existence of possible hydrodynamic mechanism that could be used to interpret the observed maximum leukocyte aggregation in shear flow. The critical shear rate for maximum intercellular contact area is shown to vary with cell properties such as radius and membrane elastic modulus.     

The forward rate of binding of surface-tethered reactants: effect of relative motion between two surfaces

The reaction of molecules confined to two dimensions is of interest in cell adhesion, specifically for the reaction between cell surface receptors and substrate-bound ligand. We have developed a model to describe the overall rate of reaction of species that are bound to surfaces under relative motion, such that the Peclet number is order one or greater. The encounter rate between reactive species is calculated from solution of the two-dimensional convection-diffusion equation. The probability that each encounter will lead to binding depends on the intrinsic rate of reaction and the encounter duration. The encounter duration is obtained from the theory of first passage times. We find that the binding rate increases with relative velocity between the two surfaces, then reaches a plateau. This plateau indicates that the increase in the encounter rate is counterbalanced by the decrease in the encounter duration as the relative velocity increases. The binding rate is fully described by two dimensionless parameters, the Peclet number and the Damk?hler number. We use this model to explain data from the cell adhesion literature by incorporating these rate laws into "adhesive dynamics" simulations to model the binding of a cell to a surface under flow. Leukocytes are known to display a "shear threshold effect" when binding selectin-coated surfaces under shear flow, defined as an increase in bind rate with shear; this effect, as calculated here, is due to an increase in collisions between receptor and ligand with increasing shear. The model can be used to explain other published data on the effect of wall shear rate on the binding of cells to surfaces, specifically the mild decrease in binding within a fixed area with increasing shear rate.     

Transport features, reaction kinetics and receptor biomechanics controlling selectin and integrin mediated cell adhesion

The distinct and overlapping roles of adhesion molecules belonging to the selectin and integrin families control the rate of leukocyte adhesion to stimulated vascular endothelial cells under hydrodynamic shear flow. Crystal structures have appeared for some of these interactions which complement molecular biology experiments, and clarify the molecular mechanism of the receptor-ligand binding interactions. Binding affinity data have also appeared using surface plasmon resonance and single-molecule biophysics experiments. These studies confirm and extend the predictions of previous experiments carried out in parallel-plate flow chambers, and cone and plate viscometers. This review discusses the current state of understanding on how molecular bond formation rates coupled with cellular and hydrodynamic features regulate leukocyte binding to endothelial cells.     

Modeling of cell adhesion and deformation mediated by receptor–ligand interactions

The current work is devoted to studying adhesion and deformation of biological cells mediated by receptors and ligands in order to enhance the existing models. Due to the sufficient in-plane continuity and fluidity of the phospholipid molecules, an isotropic continuum fluid membrane is proposed for modeling the cell membrane. The developed constitutive model accounts for the influence of the presence of receptors on the deformation and adhesion of the cell membrane through the introduction of spontaneous area dilation. Motivated by physics, a nonlinear receptor–ligand binding force is introduced based on charge-induced dipole interaction. Diffusion of the receptors on the membrane is governed by the receptor–ligand interaction via Fick’s Law and receptor-ligand interaction. The developed model is then applied to study the deformation and adhesion of a biological cell. The proposed model is used to study the role of the material, binding, spontaneous area dilation and environmental properties on the deformation and adhesion of the cell.     

Mast cell degranulating peptide binds to RBL-2H3 mast cell receptors and inhibits IgE binding

Fluorescent and biotinylated analogs of mast cell degranulating (MCD) peptide were synthesized and the labels fluoresceinisothiocyanate and N-hydroxysuccinimidobiotin were conjugated at position 1 in the MCD peptide sequence. The analogs with these moieties retained histamine-releasing activity as high as that of the parent MCD peptide in rat peritoneal mast cell assays. These labeled analogs were used in rat basophilic leukemia cells (RBL-2H3) to demonstrate by confocal microscopy and flow cytometry the specific binding of MCD peptide to mast cell receptors. Consequently MCD peptide was found to compete with and inhibit the binding of fluorescent IgE on RBL cells as monitored by flow cytometry. Thus MCD peptide may prove to be useful in the study of IgE receptor-bearing cells.     

Quantifying aggregation of IgE-FcepsilonRI by multivalent antigen

Aggregation of cell surface receptors by multivalent ligand can trigger a variety of cellular responses. A well-studied receptor that responds to aggregation is the high affinity receptor for IgE (FcepsilonRI), which is responsible for initiating allergic reactions. To quantify antigen-induced aggregation of IgE-FcepsilonRI complexes, we have developed a method based on multiparameter flow cytometry to monitor both occupancy of surface IgE combining sites and association of antigen with the cell surface. The number of bound IgE combining sites in excess of the number of bound antigens, the number of bridges between receptors, provides a quantitative measure of IgE-FcepsilonRI aggregation. We demonstrate our method by using it to study the equilibrium binding of a haptenated fluorescent protein, 2,4-dinitrophenol-coupled B-phycoerythrin (DNP25-PE), to fluorescein isothiocyanate-labeled anti-DNP IgE on the surface of rat basophilic leukemia cells. The results, which we analyze with the aid of a mathematical model, indicate how IgE-FcepsilonRI aggregation depends on the total concentrations of DNP25-PE and surface IgE. As expected, we find that maximal aggregation occurs at an optimal antigen concentration. We also find that aggregation varies qualitatively with the total concentration of surface IgE as predicted by an earlier theoretical analysis.     

Specific adhesion of glycophorin liposomes to a lectin surface in shear flow.

The adhesion of cells to other cells or to surfaces by receptor-ligand binding in a shear field is an important aspect of many different biological processes and various cell separation techniques. The purpose of this study was to observe the adhesion of model cells with receptor molecules embedded in their surfaces to a ligand-coated surface under well-defined flow conditions in a parallel plate flow chamber. Liposomes containing glycophorin were used as the model cells to permit a variation in the adhesion parameters and then to observe the effect on adhesion. A mathematical model for cell sedimentation was created to predict the deposition time and the velocity preceding adhesion for the selection of experimental operating conditions and the methods useful for data analysis. The likelihood of cell attachment was represented by a quantity called the sticking probability which was defined as the inverse of the number of times a liposome made contact with the surface before attachment occurred. The sticking probability decreased as the cell receptor concentration was lowered from approximately 10(4) to 10(2) receptors per 4-microns diam liposome and as the shear rate increased from 5 to 22 s-1. The effect of the wall shear rate and particle diameter on detachment of liposomes from a surface was also observed.     

The effect of receptor density on the forward rate constant for binding of ligands to cell surface receptors.

For monovalent ligands interacting with cell surface receptors we have directly observed the functional dependence of the forward rate constant on the number of receptors per cell (N). The experimental system we studied consisted of monovalent ligand, 2,4-dinitrophenyl (DNP)-aminocaproyl-L-tyrosine (DCT), binding to bivalent, monoclonal anti-DNP immunoglobulin E (IgE) anchored to its high affinity receptor on rat basophilic leukemia (RBL) cells. To measure the fractional occupation of antibody combining sites by DNP we employed a recently developed fluorescence technique (Erickson, J., Kane, B. Goldstein, D. Holowka, and B. Baird, 1986, Mol. Immunol., 72:769-781). Our results are well fitted by the equation (Berg and Purcell, 1977, Biophys. J., 20:193-219) konc = 4 pi DaN kappa on/[4 pi Da + N kappa on] where konc is the forward rate constant for binding to the cell, D is the diffusion constant of the ligand, a is the radius of the cell, and kappa on is the intrinsic forward rate constant describing a single IgE combining site-DNP interaction. If D is fixed at 10(-5) cm2/s, the best fit of accumulated data predicts an average cell radius of approximately 4 microns and kappa on of approximately 1.8 x 10(-13) cm3/s [1.1 x 10(8)(M . s)-1]; both in excellent agreement with RBL cell size and the single-site forward rate constant for the binding of DCT to IgE in solution, respectively. We believe this is the first report of experimental evidence that directly illustrates the effect of surface density in determining the rates of binding for small molecules to membrane receptors.     

Synthesis of surface immunoglobulin E receptor in Xenopus oocytes by translation of mRNA from rat basophilic leukemia cells

Immunoglobulin E-binding activity was expressed in Xenopus oocytes injected with mRNA from rat basophilic leukemia cells which possess abundant immunoglobulin E (IgE) receptor. Such activity was demonstrated with intact oocytes by their binding of 125I-labeled mouse monoclonal IgE. Binding activity was specific as shown by the total inhibition of 125I-IgE binding by unlabeled IgE but not by unlabeled IgG1. The relevance of the IgE-binding activity to the IgE receptor was also supported by the absence of this activity in oocytes injected with mRNA from cells lacking surface IgE receptors. mRNA coding for the IgE-binding activity was enriched in fractions sedimenting at 13.5 S in sucrose density gradients. From oocytes injected with rat basophilic leukemia mRNA, two major polypeptides were isolated by affinity purification on IgE immunoadsorbent. One (Mr = 31,000) is equivalent in size to the previously identified "receptor-associated protein;" the other (Mr = 40,000) is speculated to be a partially glycosylated or unglycosylated form of the alpha subunit of the IgE receptor. The binding of IgE-coated fluorescent microspheres by oocytes injected with rat basophilic leukemia mRNA demonstrated the surface expression of the IgE-binding proteins.     

A dynamical model for receptor-mediated cell adhesion to surfaces in viscous shear flow

We present a dynamical model for receptor-mediated cell adhesion to surfaces in viscous shear flow when the surfaces are coated with ligand molecules complementary to receptors in the cell membrane. This model considers the contact area between the cell and the surface to be a small, homogeneous region that mediates the initial attachment of the cell to the surface. Using a phase plane analysis for a system of nonlinear ordinary differential equations that govern the changes in free receptor density and bond density within the contact area with time, we can predict the conditions for which adhesion between the cell and the surface will take place. Whether adhesion occurs depends on values of dimensionless quantities that characterize the interaction of the cell and its receptors with the surface and its ligand, such as the bond formation rate, the receptor-ligand affinity, the fluid mechanical force, the receptor mobility, and the contact area. A key result is that there are two regimes in which different chemical and physical forces dominate: a rate-controlled high affinity regime and an affinity-controlled low affinity regime. Many experimental observations, including the effects of temperature and receptor mobility on adhesiveness, can be explained by understanding which of these regimes is appropriate. We also provide simple approximate analytical solutions, relating adhesiveness to cell and surface properties as well as fluid forces, which allow convenient testing of model predictions by experiment.     

A dynamical model for receptor-mediated cell adhesion to surfaces.

We present a dynamical model for receptor-mediated adhesion of cells in a shear field of viscous fluid to surfaces coated with ligand molecules complementary to receptors in the cell membrane. We refer to this model as the "point attachment model" because it considers the contact area between the cell and the surface to be a small, homogeneous region that mediates the initial attachment of the cell to the surface. Using a phase plane analysis of a system of nonlinear ordinary differential equations which govern the changes in free receptor density and bond density within the contact area with time, we can predict the conditions for which adhesion between the cell and the surface will take place. Whether adhesion occurs depends on values of dimensionless quantities that characterize the interaction of the cell and its receptors with the surface and its ligand, such as the bond formation rate, the receptor-ligand affinity, the fluid mechanical force, the receptor mobility, and the contact area. A key result is that there are two regimes in which different chemical and physical forces dominate: a rate-controlled high affinity regime and an affinity-controlled low-affinity regime. Many experimental observations can be explained by understanding which of these regimes is appropriate. We also provide simple approximate analytical solutions, relating adhesiveness to cell and surface properties as well as fluid forces, which allow convenient testing of model predictions by experiment.     

Effects of flowing RBCs on adhesion of a circulating tumor cell in microvessels

Adhesion of circulating tumor cells (CTCs) to the microvessel wall largely depends on the blood hydrodynamic conditions, one of which is the blood viscosity. Since blood is a non-Newtonian fluid, whose viscosity increases with hematocrit, in the microvessels at low shear rate. In this study, the effects of hematocrit, vessel size, flow rate and red blood cell (RBC) aggregation on adhesion of a CTC in the microvessels were numerically investigated using dissipative particle dynamics. The membrane of cells was represented by a spring-based network connected by elastic springs to characterize its deformation. RBC aggregation was modeled by a Morse potential function based on depletion-mediated assumption, and the adhesion of the CTC to the vessel wall was achieved by the interactions between receptors and ligands at the CTC and those at the endothelial cells forming the vessel wall. The results demonstrated that in the microvessel of \(15\,\upmu \hbox {m}\) diameter, the CTC has an increasing probability of adhesion with the hematocrit due to a growing wall-directed force, resulting in a larger number of receptor–ligand bonds formed on the cell surface. However, with the increase in microvessel size, an enhanced lift force at higher hematocrit detaches the initial adherent CTC quickly. If the microvessel is comparable to the CTC in diameter, CTC adhesion is independent of Hct. In addition, the velocity of CTC is larger than the average blood flow velocity in smaller microvessels and the relative velocity of CTC decreases with the increase in microvessel size. An increased blood flow resistance in the presence of CTC was also found. Moreover, it was found that the large deformation induced by high flow rate and the presence of aggregation promote the adhesion of CTC.