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

Abstract

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.

Rolling and transient tethering of leukocytes on antibodies reveal specializations of selectins

“…Rolling and firmly adherent populations of cells often coexisted. These are the types of results that are predicted based on dynamic simulations of cell adhesive interactions in shear flow (12) or by some peeling models (21) and contrast with results with selectins. One remarkable property of selectins is the lack of development of firm adhesion in the absence of shear flow.…”

“…However, the interaction of CD2 with lymphocyte function-associated 3 (9, 10) and binding of an IgE antibody to its antigen (11) have similar kinetics but do not appear to support rolling. Another factor that may be important is the effect of force on bond association and dissociation kinetics (12). The effect of force has been measured on the duration of transient tethers of cells to the vessel wall, which occurs at selectin densities below the minimum required to support rolling.…”

Dynamic states of cells adhering in shear flow: From slipping to rolling

“…If molecular effects are of interest, then such modeling efforts typically start with physical models for bond association and dissociation [17]. Combined with the hydrodynamics of a sphere in front of a wall, they lead to algorithms known as adhesive dynamics [18]. This approach has been applied before to different aspects of rolling adhesion, e. g., the interplay of two receptor systems [19] or the effect of catch bonds [20].…”

“…For example, in physical terms cell rolling means that translation and rotation are synchronized. Although this fact was already noted in the pioneering paper on adhesive dynamics [18], it has not been systematically exploited due to the lack of experimental data. Here we present a detailed analysis of the different dynamic states of rolling adhesion which is based on the simultaneous tracking of both translational and rotational degrees of freedom.…”

“…In Sec. II we explain our numerical method, which is a combination of a Langevin equation accounting for hydrodynamic and thermal forces in the limit of small Reynolds numbers (Stokesian dynamics) [32] and adhesive dynamics accounting for the forces caused by the formation of adhesive bonds between cell and substrate [18]. By taking care of the diffusive motion of the sphere, we are able to explicitly resolve both receptor and ligand positions.…”