A numerical study of the influence of cellular adhesion on prestress in Atomic Force Microscopy measurements

The effects of receptor number and cell membrane mechanical properties on cell-substrate adhesion and Atomic Force Microscopy indentation measurements in quiescent conditions are numerically investigated. A cell is modeled as an elastic membrane decorated with receptors that can form bonds with a ligand-coated substrate enclosing a Newtonian fluid. Bonds are modeled as elastic springs that cause cell deformation and fluid motion transiently during the adhesion process. After reaching steady-state, body forces are applied at an area of the cell surface to model Atomic Force Microscopy indentation measurements of apparent membrane stiffness. The governing equations are solved using the Immersed Boundary Method. Our simulations predict that at steady-state the highest elastic energy density is at the rim of binding region. For stiffer cells, high energy regions are localized to the edge of the binding region, whereas they are more diffuse for compliant cells. Increasing the number of receptors available for binding results in larger binding areas and number of bonds formed. Increasing membrane stiffness leads to decreasing characteristic exponential response time, since stiffer cells are less deformed at steady-state and thus initially closer to the equilibrium configuration. From the Atomic Force Microscopy indentation simulations we observe that number of receptors strongly affect the indentation depth that results in higher apparent membrane stiffness. Cumulatively, our studies reveal the interplay between receptor-ligand binding kinetics and cell mechanics in the regulation of cell-substrate adhesion. They also suggest that adhesion with the substrate must be considered when using Atomic Force Microscopy to measure cell stiffness.