A Breakdown of Cellular Mechanisms Required for Cell and Focal Adhesion Area Sensitivity to Substrate Stiffness

Abstract

Cell spread area and focal adhesion (FA) sizes are known to increase with substrate stiffness (Yeung et al., Cell Motil. Cytoskeleton., 2005). Different models have been developed, some of which can predict increases in cell spread area with substrate stiffness while others can predict increases in only the FA area. Here, we systematically add one mechanism at a time to start recapitulating both these behaviors together. We start with an adapted model (Walcott et. al. Biophysical J., 2011) of FA growth implemented in a 2D cell that spreads at a constant rate. This model demonstrates that while the total FA area increases with substrate stiffness the cell spread area is not sensitive to the stiffness. In order for the cell spread area to increase with substrate stiffness the spreading model must include a coupling between the spreading rate, the FA complex evolution, and intracellular stresses (Vernerey & Farsad, J. Math. Bio., 2013). When the spreading rate is coupled with cellular stresses and FA evolution, we demonstrate the ability of our model to qualitatively reproduce the increase in cell spread area and FA area with substrate stiffness. Further we try to generate biological insight on the role of the model parameters in their ability to reproduce cellular behavior for various experimentally studied cellular systems such as 3T3 fibroblasts and human mesenchymal stem cells. Based on this we also articulate the gaps in the current model and make a case for potentially bringing in additional mechanisms that can account for the role of stress fiber orientation (Deshpande et al, PNAS, 2006) which can enhance our ability to understand the interplay between the different mechanisms in predicting cellular responses across a broader range of cell types.