Elastic deformations of grafted layers with surface stress

We calculate the elastic response of thin films grafted to a solid substrate whose upper surface is subject to a stress. This issue is addressed in the context of biological cell adhesion where adhesive junctions consist of a thin layer of proteins grafted to the extracellular matrix and sheared by the cell contractility apparatus. We show that the finite thickness of the layer limits stress-induced deformations to short ranges proportional to the thickness of the film. In addition, we show that the attachment boundary condition creates an effective shear response to surface stresses that couples all the directions, even for fluidlike layers. We predict that perturbations with wavelengths of order of the film thickness induce resonancelike responses for isotropic rubberlike materials or anisotropic media with high shear moduli. We use these results to predict the elastic deformations of a layer of proteins under shear stress and propose that the resulting, polarized elastic response to local surface forces can explain the observed, anisotropic growth of cell-substrate junctions when subject to external stresses.