Propagation of Forces in Epithelial Monolayer Is Highly Dependent on Substrate Stiffness

Mechanics and physical forces influence many epithelial processes, including epithelial formation and migration, as well as cell signaling via a process known as mechanotransduction. Many pathological conditions lead to changes in the epithelial mechanical homeostasis. For example, in tumors both the cells and the extracellular matrix become stiffer. Unfortunately, it is not well understood how these mechanical changes affect the signaling between cells. To study this, we used a computational approach to see how mechanical disturbances in the epithelia spread and how the stiffness of the substrate under the cells affects the force propagation.
Our cellular modeling approach uses a so-called boundary-based method, where the cells are represented by closed boundary polygons and the various cellular cytoskeletal components and processes are described by springs between or forces affecting the polygon vertices. The substrate is modeled as a mass-spring model, described by a hexagonal spring network. We mechanically disturbed the system by moving one cell to describe local micromanipulation of the epithelial monolayer. We simulated the micromanipulation for the epithelium-substrate system as well as for only the substrate.
We found that there is a dramatic difference on how the cell deformation spreads in the epithelia and in the substrate depending on the substrate stiffness. When the substrate is softer than the cells, the deformations caused by micromanipulation of a cell propagate across all the cells in the simulated area and the underlying substrate. However, with stiffer substrate, the deformations in both the other cells and substrate are local; only a few nearest neighbor layers deform and there is very little deformation in the substrate itself. We also simulated the deformation of only the substrate without the cells with similar micromanipulation and found that deformations in the soft substrate are local whereas the stiff substrate has more global deformations.
Our results indicate that the distance traveled by the mechanical deformations, and thus mechanical forces and signals, is highly dependent on the stiffness of the cell substrate. There is a major change in force propagation behavior as the substrate becomes stiffer than the epithelial monolayer, which may be extremely relevant especially in tumors due to the changes in mechanical properties.