Analyzing the interplay between single cell rheology and force generation through large deformation finite element models
Résumé
In this study, experimental results of single cell spreading between two parallel microplates are exploited through finite element modeling. Axisymmetric computations at finite strains are performed to extract the mechanical properties of the cell which can account for cell shape evolution and traction force generation. Our model includes two distinct components representing the cortex associated with the bilayer membrane on the one hand, and the rest of the cell on the other hand. The former is modeled as a homogeneous hyperelastic material described by a slightly compressible Gent strain energy function, while the latter is idealized either as a quasi-incompressible Newtonian fluid or as another homogeneous hyperelastic material. The kinetics of spreading is ensured by a stapling procedure defined from experimental observations. Material parameters are then optimized to match the simulation closely with the experimental data. In particular, the elastic modulus of the cortex is estimated at about 1,000 Pa in both models, while the cell interior is characterized by a viscosity of 1,000 Pa.s in the biphasic model, or by an elastic modulus of about 100 Pa in the hyperelastic one. These results are in good agreement with G' and G'' measurements carried out previously in the same parallel plates setup and estimated at the typical rate of cell straining. Moreover, stresses are found to concentrate at the edge of the cell-substrate contact area. These observations allow explaining the relationship between cell spreading and force increase since spreading and the consequent straining of the cell mechanical structure could be the source of the force applied by the cell on its substrate. They could also explain, in a very simple manner, why force-sensitive focal contacts concentrate at the cell edges.
