Mechanical link between durotaxis, cell polarity and anisotropy during cell migration

Cell migration, a fundamental mechanobiological process, is highly sensitive to the biochemical and mechanical properties of the environment. Efficient cell migration is ensured by the intrinsic polarity of the cell, which triggers a transition from an isotropic to an anisotropic configuration of the actomysion filaments responsible for the protrusion-contraction movement of the cell. Additionally, polarity may be highly influenced by the substrate rigidity, which results in a phenomenon called durotaxis. In the present work, we propose a two-dimensional finite element model able to capture three main features of cell migration: durotaxis, cell polarity and anisotropy. The cell is modelled as a continuum able to develop cyclic active strains regulated by the polymerization and depolymerization of the acto-myosin filaments and synchronized with the adhesion forces between the cell and the substrate underneath. A generalized Maxwell model is used to describe the viscoelastic behaviour of the cell constituted by a solid anisotropic branch with active strains (i.e. the acto-myosin filaments) and a fluid viscoelastic branch (i.e. the cytoplasm). Several types of substrate have been tested which are homogeneously soft or stiff or include both regions. The numerical results have been qualitatively compared with experimental observations showing a good agreement and have allowed us to find the mechanical link between durotaxis, cell polarity and anisotropy.