Mechanical properties of the substrate play a vital role in cell motility. Cells are shown to migrate up stiffness gradient (durotaxis) and along aligned fibers in the substrate (contact guidance). Here we present a simple mechanical model for cell migration, by placing a cell on lattice models for biopolymer gels and hydrogels. In our model cells attach to the substrate via focal adhesions (FAs). As the cells contract, forces are generated at the FAs, determining their maturation and detachment. At the same time, the cell also allowed to move and rotate to maintain force and torque balance. Our model, in which the cells only take the information of forces at the FAs, without a prior knowledge of the substrate stiffness or geometry, is able to reproduce both durotaxis and contact guidance.
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