A multi-scale model for cell adhesion and deformation

A multi-scale computational approach for studying the adhesion kinetics and deformation of a cell on a substrate is presented. This method breaks the computational work into two separate but interrelated domains. At the cellular level, a continuum model satisfying the field equations for momentum transfer and mass continuity is adopted. At the receptor-ligand or molecular level, the bond force is mechanically represented by a spring, and the formation and dissociation of bonds are characterized by a reversible two-body kinetic model. The model demonstrates that as the reverse reaction rate increases, the receptor-ligand bonds break faster, and the opposite is observed when the forward reaction rate increases. As expected, the cell peeling time increases as the number of ligands increases until it equals the number of receptors. The peeling time becomes shorter when the spring constant or slippage constant is larger. Furthermore, as the cell velocity increases during the peeling process, the maximum bond length increases while the total peeling time decreases. Based on the information from the two modeling levels, dynamics of membrane movement can be computed, illustrating that the cell mechanical properties and surrounding fluid dynamics affect the receptor-ligand kinetics, and that these effects need to be included in any realistic cell-surface interaction models.