The Effect of Substratum Stiffness and Stochasticity on Cell Reorientation over a Stretched Substratum

It is observed that when cells are seeded on a substrate subject to a cyclic deformation, they tend to reorient their major axis either perpendicularly or forming an oblique angle with the main stretching direction. However, this does not occur any longer if the substrate is too soft, or if the frequency and amplitude of imposed deformation are too small. In order to explain these transitions, in this chapter we respectively schematize the cell as a set of discrete elements and deal with the random behaviour of cell response deducing a Fokker-Planck equation, that can be also related to an optimal control strategy the cell may wish to pursue.