Continuum modeling and numerical simulation of cell motility

This work proposes a continuum-mechanical model of cell motility which accounts for the dynamics of motility-relevant protein species. For the special case of fish epidermal keratocytes, the stress and cell-substrate traction responses are postulated to depend on selected protein densities in accordance with the structural features of the cells. A one-dimensional version of the model is implemented using Arbitrary Lagrangian–Eulerian finite elements in conjunction with Lagrange multipliers for the treatment of kinematic constraints related to surface growth. Representative numerical tests demonstrate the capacity of the proposed model to simulate stationary and steady crawling states.