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...