A 3-D Computational Model Predicts that Cell Deformation Affects Selectin-Mediated Leukocyte Rolling

Abstract

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, thereby failing to accurately predict leukocyte rolling. We therefore developed a three-dimensional computational model based on the immersed boundary method to predict receptor-mediated rolling of deformable cells in shear flow coupled to a Monte Carlo method simulating the stochastic receptor-ligand interactions. Our model predicts for the first time that the rolling of more compliant cells is relatively smoother and slower compared to cells with stiffer membranes, due to increased cell-substrate contact area. At the molecular level, we show that the average number of bonds per cell as well as per single microvillus decreases with increasing membrane stiffness. Moreover, the average bond lifetime decreases with increasing shear rate and with increasing membrane stiffness, due to higher hydrodynamic force experienced by the cell. Taken together, our model captures the effect of cellular properties on the coupling between hydrodynamic and receptor-ligand bond forces, and successfully explains the stable leukocyte rolling at a wide range of shear rates over that of rigid microspheres.

Shear modulation of intercellular contact area between two deformable cells colliding under flow

“…Thus, a minimum separation distance between the two cells of about 800 nm or less is defined to be the contact area. This intercellular contact area represents the available area for cell adhesion; the larger the contact area the greater the possibility for the involvement of multiple receptor-ligand bonds and thus successful adhesion (Gourier, et al, 2004;Jadhav, et al, 2005;Lin, et al, 2006). The time evolution of the contact area with contact time is illustrated in Fig 2A. The contact area first increases, reaches a maximum, and then decreases back to zero when the cells separate at all capillary numbers examined here.…”

“…In our simulations, biological or artificial cells with a radius, a, of 3.75 µm, equivalent to that of a PMN, are modeled as elastic capsules whose membrane elasticity, Eh, varies from 0.03 -3 dynes/cm (Jadhav, et al, 2005), and are suspended in medium with fluid viscosity, µ, of 0.8 cP. The membrane stiffness values of 0.3-1.2 dynes/cm have been shown to match the extent of PMN deformation previously observed in vivo (Damiano, et al, 1996;Smith, et al, 2002), while higher values are used to observe the effects of membrane stiffening.…”

“…The cells are modeled as three-dimensional elastic capsules containing a Newtonian liquid, and the fluid flow is governed by the continuity and Stokes momentum balance equations (Eggleton and Popel, 1998;Jadhav, et al, 2005):…”

“…In the Immersed Boundary Method, the computational domain is comprised of an Eulerian Cartesian fluid grid x(x 1 , x 2 , x 3 ) and a Langragian triangular finite element grid X (X 1 , X 2 , X 3 ) that tracks cell motion and deformation (Eggleton and Popel, 1998;Jadhav, et al, 2005):…”

“…Periodic boundary conditions on the velocity and pressure are imposed, and the fast Fourier Transform method is used to solve the flow equations (Peskin and McQueen, 1989;Jadhav, et al, 2005).…”