Hysteresis in the cell response to time-dependent substrate stiffness

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 stiffnesses. 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.