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| Cell shape and substrate properties have important implications in many contexts, and are particularly important in determining stem cell fate. We present a two-dimensional mathematical model and finite element simulations of a biological cell interacting with a deformable substrate and use this model to gain a better understanding of how the mechanical interaction between the cell and substrate affects cell shape and focal adhesion (FA) dynamics during cell spreading. The cell is treated as a hypoelastic actively-deforming continuum and the substrate is modeled as a linearly elastic continuum. The active deformation, captured by the addition of an active rate of deformation tensor, models local cytoskeletal reorganization. FAs connecting the cell and the substrate are modeled as a collection of discrete elastic springs, which can be dynamically added and removed. This model of mechanics is coupled to a model describing the intracellular stress-dependent evolution of the volume fraction of a single FA molecule representing all FA associated proteins. We investigate how cell mechanics and FA evolution should be coupled to obtain observable cell shapes. We also investigate how cell and substrate material properties affect cell and FA shapes, and how FA strength plays a role in FA dynamics. |
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