  Mechanical cues like the rigidity of the substrate are main determinants for
the decision making of adherent cells. Here we use a mechano-chemical model to
predict the cellular response to varying substrate stiffness. The model
equations combine the mechanics of contractile actin filament bundles with a
model for the Rho-signaling pathway triggered by forces at cell-matrix
contacts. A bifurcation analysis of cellular contractility as a function of
substrate stiffness reveals a bistable response, thus defining a lower
threshold of stiffness, below which cells are not able to build up contractile
forces, and an upper threshold of stiffness, above which cells are always in a
strongly contracted state. Using the full dynamical model, we predict that
rate-dependent hysteresis will occur in the cellular traction forces when cells
are exposed to substrates of time-dependent stiffness.
