Spreading Out: Modeling the Physics of Cell-Substrate Interaction in Cell Spreading and Focal Adhesion Evolution

Abstract

Cell spread area and focal adhesion (FA) sizes are known to increase with substrate stiffness (Yeung et al., Cell Motil. Cytoskeleton., 2005). Different mathematical 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 describe a two-dimensional model of an actively spreading cell interacting with a deformable elastic substrate through spring-like FA complexes. The model couples FA evolution, intracellular stress, and active cell spreading. With these three components coupled, we demonstrate the ability of our model to qualitatively reproduce both, the increase in cell spread area and FA area with substrate stiffness that has been observed experimentally, as well as the temporal evolution of cell spread areas. To predict the stiffness dependence and the temporal evolution of cell spreading we find there are three key mechanisms: i) cell substrate attachments at the periphery, ii) attachments in the interior generating retrograde flow, and iii) the resistance to spreading from the tensile forces at the cell periphery due to the membrane. The 2D model allows us to capture the role of spatial localization of these different phenomena and the sensitivity of these mechanisms in enabling the observed global behaviors. Using this model, we generate insights on the role of both spatial coupling and integration of the signals to generate large scale changes in cellular dynamics. We also investigate the role of geometric anisotropy through non-circular shapes during spreading. The overarching aim of this work has been to specify what minimal physical mechanisms are required to recapitulate cellular spreading and FA evolution and their mechanical response to the underlying substrate.