The Role of Mechanical and Biochemical Interactions in Focal Adhesion and Cellular Shapes

Abstract

We present findings from a two-dimensional mathematical model of a biological cell interacting with a soft substrate and focus on the role of the interaction of intracellular mechanical stresses and plaque protein concentrations on cell and focal adhesion shapes. 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. Focal adhesions connecting the cell and the substrate are modeled as a collection of discrete elastic springs. The model allows for the focal adhesion complexes to grow and shrink depending on mechanical forces that are acting on them and local concentrations of plaque protein. A model of stress-induced plaque protein dynamics, which is based on earlier work of Besser and Safran (2006), is coupled to the model of cell-substrate mechanics. Finite element simulations of the model allow us to explore the effects of original focal adhesion configuration, cytoskeletal dynamics, and focal adhesion strength on the shape evolution of individual focal adhesions and on overall cell shape.