Non-linear stability analysis for animal cell adhesion to solid support

The interaction between cells and a solid support in aqueous solutions can be modeled by considering the stability of the thin aqueous film between them. This aqueous film is a viscous layer bounded by a free surface (the cell membrane) and a solid horizontal plane. In addition, the lateral diffusion of insoluble surfactants (adhesive molecules) at the free surface will be considered and surface tension varies in accordance with surface concentration (Marangoni effect). The viscous layer is subjected to a balance of forces: van der Waals attraction, repulsive electrostatic and steric/hydration interactions, formation of specific bonding at short distances. The movement of the free surface and of the adjacent fluids is described using a hydrodynamic approach. A systematic long-wave analysis is used to derive non-linear evolution equations governing the evolution of the position of the surface, coupled to the evolution of the concentration of surfactants. Numerical solutions are obtained by an implicit finite difference method. A set of different initial conditions is discussed, relevant to several experimental situations. Amongst them, a simulation for the formation of local contacts between an adhering cell and a solid support is presented. © 1994.SCOPUS: ar.j