Leukocyte adhesion under flow in the microvasculature is mediated by binding between cell surface receptors and complementary ligands expressed on the surface of the endothelium. Leukocytes adhere to endothelium in a two-step mechanism: rolling (primarily mediated by selectins) followed by firm adhesion (primarily mediated by integrins). Using a computational method called ''Adhesive Dynamics,'' we have simulated the adhesion of a cell to a surface in flow, and elucidated the relationship between receptorligand functional properties and the dynamics of adhesion. We express this relationship in a state diagram, a one-to-one map between the biophysical properties of adhesion molecules and various adhesive behaviors. Behaviors that are observed in simulations include firm adhesion, transient adhesion (rolling), and no adhesion. We varied the dissociative properties, association rate, bond elasticity, and shear rate and found that the unstressed dissociation rate, k r o , and the bond interaction length, ␥, are the most important molecular properties controlling the dynamics of adhesion. Experimental k r o and ␥ values from the literature for molecules that are known to mediate rolling adhesion fall within the rolling region of the state diagram. We explain why L-selectinmediated rolling, which has faster k r o than other selectins, is accompanied by a smaller value for ␥. We also show how changes in association rate, shear rate, and bond elasticity alter the dynamics of adhesion. The state diagram (which must be mapped for each receptor-ligand system) presents a concise and comprehensive means of understanding the relationship between bond functional properties and the dynamics of adhesion mediated by receptor-ligand bonds.T rafficking of blood-borne cells into tissues is crucial to the proper function of the immune response. Inflammation, lymphocyte homing, and bone marrow replenishment after transplantation all depend on trafficking (1). Trafficking is mediated by receptor-mediated adhesion of blood-borne cells to the endothelial cells that line blood vessels. The transition from an unbound blood cell to an adherent one in flow involves a number of steps: initial tethering, transient ''rolling'' adhesion, and firm adhesion. Firm adhesion is usually followed by morphological changes and trans-endothelial migration into the tissue stroma, so that the cell can carry out its intended function within the tissue.Different adhesion molecules mediate different stages in this multistep adhesion process. Transient rolling adhesion occurs when receptor-ligand bonds between the leukocyte and endothelium exert a friction on the leukocyte, such that its velocity drops well below the hydrodynamic velocity for an unencumbered leukocyte at the same separation distance and wall shear rate. In the cell biology literature, rolling is often defined as a significant decrease in velocity, to perhaps 50% or less of the hydrodynamic velocity for cells near a surface, V H (2). Rolling is mediated by a variety of adhesion molecules, includ...

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 Damköhler 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.

Selectin-mediated leukocyte rolling is crucial for the proper function of the immune response. Recently, selectin-mediated rolling was recreated in a cell-free system (Biophysical Journal 71:2902-2907 (1996)); it was shown that sialyl Lewis(x) (sLe(x))-coated microspheres roll over E-selectin-coated surfaces under hydrodynamic flow. The cell-free system removes many confounding cellular features, such as cell deformability and signaling, allowing us to focus on the role of carbohydrate/selectin physical chemistry in mediating rolling. In this paper, we use adhesive dynamics, a computational method that allows us to simulate adhesion, to analyze the experimental data produced in the cell-free system. We simulate the effects of shear rate, ligand density, and number of receptors per particle on rolling velocity and compare them with experimental results obtained with the cell-free system. If we assume the population of particles is homogeneous in receptor density, we predict that particle rolling velocity calculated in simulations is more sensitive to shear rate than found in experiments. Also, the calculated rolling velocity is more sensitive to the number of receptors on the microspheres than to the ligand density on the surface, again in contrast to experiment. We argue that heterogeneity in the distribution of receptors throughout the particle population causes these discrepancies. We improve the agreement between experiment and simulation by calculating the average rolling velocity of a population whose receptors follow a normal distribution, suggesting heterogeneity among particles significantly affects the experimental results. Further comparison between theory and experiment yields an estimate of the reactive compliance of sLe(x)/E-selectin interactions of 0.25 A, close to that reported in the literature for E-selectin and its natural ligand (0.3 A). We also provide an estimate of the value of the intrinsic association rate (between 10(4) and 10(5) s(-1)) for the formation of sLe(x)/E-selectin bonds.

Leukocyte adhesion under flow in the microvasculature is a multistep process in which rolling adhesion is followed by firm arrest. These interactions are mediated by binding between receptors on the leukocyte surface and complementary ligands on the surface of endothelial cells. Previous work using a computational method called "adhesive dynamics" showed that the general shape of a state diagram for cell adhesive behavior in flow could be predicted by the bond reaction rates and their dependence on force. Other parameters, however, such as shear rate, particle size, and receptor and ligand density, determined the exact region of parameter space that corresponds to an adhesive behavior. In this paper, we present state diagrams for adhesion for a range of particle sizes to explain the rolling behavior for a wide range of cell diameters. Particle size is an easily controlled experimental variable, and if the locations of regions of desired adhesive behavior in the state diagram are known, then the size of particle needed to achieve a desired adhesive behavior can be predicted.