A Numerical Method for Coupling Nano-Scale Molecular Binding With Mesoscale Cellular Deformation

Cell adhesion plays a pivotal role in diverse biological processes, including inflammation and thrombosis. Changes in cell adhesion can be the defining event in a wide range of diseases, including cancer, osteoporosis, atherosclerosis, 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. 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. Here, we review the development of a multi-scale model combining Monte-Carlo models of molecular binding with the Immersed Boundary Method for cellular-hydrodynamic interactions. This model predicted 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. The numerical model was modified to compare the effects of different kinetic models of molecular binding on cell rolling. Simulations predict that the catch-slip bond behavior and to a lesser extent bulk cell deformation are responsible for the shear threshold phenomenon. In bulk flow, shear rate has been shown to critically affect the kinetics and receptor specificity of cell-cell interactions. We are currently simulating the adhesion 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.