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. We therefore developed a three-dimensional computational model based on the immersed boundary method to investigate receptor-mediated rolling of deformable cells in shear flow coupled to a Monte Carlo method simulating the stochastic receptor-ligand interactions.

Containing most of the P-selectin glycoprotein ligand-1 (PSGL-1) on their tips, microvilli are believed to promote initial arrest of neutrophils on endothelium. Previous studies have modeled microvilli as inextensible rigid cylinders. However it has been observed that under a pulling force a microvillus can be extended (microvillus extension) or a long thin membrane cylinder (a tether) can be formed from it (tether formation). We therefore model microvilli as hookean springs if the pulling force is less than 45 pN and as viscoelastic tethers for pulling forces greater than 45 pN. Interestingly, our results show that at low selectin site densities of 15 molecules/μm2 microvillus viscoelasticity does not alter cell rolling velocity, cell deformation, or the bond lifetimes, presumably because of the lower forces acting on the microvillus. Furthermore, we compare two different receptor-ligand interaction models which hypothesize that the bond reverse rate constant is a function of bond length (Dembo model) or of bond force (Bell model). Our results show that both models exhibit similar behavior in the low shear regime (10-100 s^-1) at low selectin site densities (15 molecules/μm²).

Both in vivo and in vitro studies have documented the shear threshold phenomenon in which the number of rolling leukocytes first increases and then decreases with monotonically increasing wall shear stress. We use our model to simulate neutrophil rolling over endothelium in the low shear regime (10-100 s^-1) to capture the shear threshold effect. Our model predicts that the neutrophil rolling velocity remains virtually unchanged at shear rates below 50 s^-1. However beyond 50 s^-1 it increases dramatically, indicating that cell deformation plays a key role in explaining the shear threshold phenomenon. Furthermore, we observe that the bond lifetimes first increase and then decrease with increasing shear rates, consistent with experimental results obtained from single molecule probes such as AFM.