Influence of substrate thickness on cell-perceived stiffness: a computational study

Cell culturing on soft substrates has become a widely applied method towards mimicking the compliant mechanical environment of cells in vivo, and substrate stiffness was shown to influence cell behavior. The cell-perceived stiffness, however, does not only depend on the modulus of the substrate material, but also on its thickness. In the present work, we propose an in silico approach to quantify the effect of substrate thickness on cell-perceived substrate stiffness. We coupled a discrete network representation of the cellular cytoskeleton including subcellular cell-substrate connections, i.e. focal adhesions (FA), with a continuum model of the substrate, and simulated the contraction of individual cells and cell patches. The results indicate that for substrates of heights larger than a multiple of the FA size (i.e. in the range of 5-10  $\mu$ m) the cell-perceived displacements and forces depend only on the substrate material, i.e. the latter is perceived as a semi-infinite continuum. The FA displacements depend more strongly on substrate thickness than FA forces. Based on the present model with subcellular resolution, the length scale of FAs emerges as the governing length scale for depth sensing, which is independent of the dimensions of the cells or cell patches.