A 3-D Computational Model of L-Selectin-PSGL-1 Dependent Homotypic Leukocyte Binding and Rupture in Shear Flow
Authors: Gupta Vijay K. , Eggleton Charles D. 
Published: July 2013

Cell adhesion plays a pivotal role in diverse biological processes, including inflammation, tumor metastasis, arteriosclerosis, and thrombosis. Changes in cell adhesion can be the defining event in a wide range of diseases, including cancer, atherosclerosis, osteoporosis, and arthritis. Cells are exposed constantly to hemodynamic/hydrodynamic forces and the balance between the dispersive hydrodynamic forces and the adhesive forces generated by the interactions of membrane-bound receptors and their ligands determines cell adhesion. Therefore to develop novel tissue engineering based approaches for therapeutic interventions in thrombotic disorders, inflammatory, and a wide range of other diseases, it is crucial to understand the complex interplay among blood flow, cell adhesion, and vascular biology at the molecular level.
In response to tissue injury or infection, polymorphonuclear (PMN) leukocytes are recruited from the bloodstream to the site of inflammation through interactions between cell surface receptors and complementary ligands expressed on the surface of the endothelium [1]. PMN-PMN interactions also contribute to the process of recruitment. It has been shown that PMNs rolling on activated endothelium cells can mediate secondary capture of PMNs flowing in the free blood stream through homotypic interactions [2]. This is mediated by L-selectin (ligand) binding to PSGL-1 (receptor) between a free-stream PMN and one already adherent to the endothelium cells [3]. Both PSGL-1 and L-selectin adhesion molecules are concentrated on tips of PMN microvilli [4]. Homotypic PMN aggregation in vivo or in vitro is supported by multiple L-selectin–PSGL-1 bondings between pairs of microvilli.
The ultimate objective of our work is to develop software that can simulate the adhesion of cells colliding under hydrodynamic forces that can be used to investigate the complex interplay among the physical mechanisms and scales involved in the adhesion process. However, cell-cell adhesion is a complex phenomenon involving the interplay of bond kinetics and hydrodynamics. Hence, as a first step we recently developed a 3-D computational model based on the Immersed Boundary Method to simulate adhesion-detachment of two PMN cells in quiescent conditions and the exposing the cells to external pulling forces and shear flow in order to investigate the behavior of the nano-scale molecular bonds to forces applied at the cellular scale [5]. Our simulations predicted that the total number of bonds formed is dependent on the number of available receptors (PSGL-1) when ligands (L-selectin) are in excess, while the excess amount of ligands controls the rate of bond formation [5]. Increasing equilibrium bond length causes an increased intercellular contact area hence results in a higher number of receptor-ligand bonds [5]. Off-rates control the average number of bonds by modulating bond lifetimes while On-rate constants determine the rate of bond formation [5]. An applied external pulling force leads to time-dependent on- and off-rates and causes bond rupture [5]. It was shown that the time required for bond rupture in response to an applied external force is inversely proportional to the applied external force and decreases with increasing offrate [5].
Fig. 1 shows the time evolution of the total number of bonds formed for various values of NRmv (number of receptor) and NLmv (number of ligand). As expected, the total number of bonds formed at equilibrium is dependent on NRmv when NLmv is in excess. In this particular case study since two pairs (or four) microvilli each with NRmv are involved in adhesion hence the equilibrium bond number is approximately 4NRmv. It is noticed that for NRmv = 50, as we vary NLmv the mean value of the total number of bonds at equilibrium does not change appreciably. However, it can be noticed from Fig. 1 that for NRmv = 50, as the excess number of ligands (NLmv) increases there is a slight increase in the rate of bond formation due to the increase in probability of bond formation.
Having developed confidence in the ability of the numerical method to simulate the adhesion of two cells that can form up to 200 bonds, we apply the method to study the effect of shear rate on the detachment of two cells. In particular, we first would like to establish the minimum shear rate needed for the two cells to detach for a given number of bonds between them. Fig. 2 shows the variation of force per bond at no rupture with number of bonds for various shear rates indicated. It is seen that at a given shear rate as the number of bonds increases the force per bond at no rupture decreases. This is attributed to the fact that force caused by shear flow is shared equally among the existing bonds. Further, it is seen that a given number of bonds as the shear rate increases the force per bond at no rupture increases. This is due to the fact that at a given number of bonds between the cells as we increase the shear rate the force caused by the flow increases hence the force per bond increases. We further notice that at shear rate = 3000 s−1 cells attached either by a single bond or by two bonds detach while they don’t for higher (> 2) number of bonds. This clearly demonstrate that there is a minimum shear rate needed to detach cells adhered by a given number of bonds. The higher the number of bonds, the higher the minimum shear rate for complete detachment of cells. For example, from Fig. 2 is it clear that for the cells adhered by two and five bonds the minimum shear rate needed for complete detachment of these two cells are 3000 s−1 and 6000 s−1, respectively.