Understanding the Role of Substrate Elasticity on Intracellular Stresses during Cell Spreading

Abstract

We present a two-dimensional mathematical model and finite element simulations of a cell interacting with a deformable substrate to better understand how substrate mechanical properties affect cellular mechanical response and spread areas. The cell is treated as an actively deforming hypoelastic material and the substrate is linearly elastic. The model predicts stress and displacement fields in both the cell and the substrate. This model of cell and substrate mechanics is coupled to models describing active cellular deformation due to stress fiber contraction and evolution of focal adhesions. In this work we compare cellular stresses and substrate displacements predicted by the model on substrates of increasing stiffness against two experimental works i) Hersh et. al. 20131 with cardiomyocytes and (ii) Marinkovic et. al. 20122 with hMSc's. The model predicts an increase in compressive stresses within the cell for the two cell types with increasing substrate stiffness between 1kPa-90kPa, which is in agreement with experimental results. Further model predictions of increase in substrate displacements with substrate stiffness are in good quantitative agreement with the experimental results. In addition on softer substrates we predict that increased stress fiber contraction due to a greater compliance of the substrate at the sites of attachment results in smaller spread areas.