Modeling the Effects of Focal Adhesion Size Restriction on Cell Shape during Spreading

Abstract

Focal adhesions (FAs) are known to exhibit mechanosensitive properties. Changes in FA size, distribution, and dynamics is leveraged in controlling various signaling networks that enable a cell to demonstrate mechanochemical sensitivity to its environment. Here, we present a two-dimensional model and finite element simulations of a cell interacting with a deformable substrate through FA complexes. The cell is treated as a hypoelastic material that is allowed to undergo active deformation representative of spreading and localized actomyosin contractions, and the substrate is modeled as linearly elastic. FA complexes are modeled by collections of linear springs that can form and break dynamically. Our aim is to understand how controlling the size of FAs, either via disassembly by microtubules or by ligand patterning, affects cellular responses. We model microtubule induced FA disassembly by systematically removing FA springs from regions closest to the cell nucleus. Alternately we also examine control of FA size by ligand patterning using reaction-diffusion equations describing the interchange between bound and unbound integrins, which accounts for the conservation of the total number of integrins within the cell. We verify our model of the coupling between integrin activation and actomyosin contractions by demonstrating that stress fibers form between adhesive patches as reported in the experimental work of Thery et al [1]. In addition, we compare the effects of the proposed two models for controlling FA evolution on intracellular stresses, substrate displacement patterns, FA distribution, and cell shape for different substrate stiffnesses and ligand patterns.[1] M. Thery, A. Pepin, E. Dressaire,Y. Chen, and M. Bornens (2006). Cell Distribution of Stress Fibers in Response to the Geometry of the Adhesive Geometry, Cell Motility and the Cytoskeleton, 63, pp. 341-355.