Abstract
We present findings from a two dimensional mathematical model (adapted from Stolarska et. al., 2009) of a biological cell on a soft substrate focusing on the role of anisotropic growth of focal adhesions and its effect on the cellular tractions within the substrate and subsequent changes in cell shape. The cell is modeled as a two dimensional hypoelastic continuum and the substrate as a linear elastic continuum material. The model computes the displacements at each node constituting the cell and substrate and the stresses generated within cell and on the substrate. The cell-substrate interaction is modeled as being mediated by focal adhesion complexes. The focal adhesion complexes represented by small circular regions are allowed to grow in size or shrink in response to forces acting on them. The growth and shrinkage of the complexes is modeled using the approach proposed by Besser and Safran (2006) where the mechanical forces from intracellular contraction, cell elasticity, and adhesion size are coupled by force induced conformational changes of molecular sized mechanosensors located in the focal adhesions. Further the cytoskeletal reorganizations driving the intracellular deformations are captured by an empirical active deformation tensor.
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