Interfacial friction and substrate deformation mediate long-range signal propagation in tissues

Tissue layers can generally slide at the interface, accompanied by the dissipation due to friction. Nevertheless, it remains elusive how force could propagate in a tissue with such interfacial friction. Here, we elaborate the force dynamics in a prototypical multilayer system in which an epithelial monolayer was cultivated upon an elastic substrate in contact with a hard surface, and discover a novel mechanism of pronounced force propagation over a long distance due to interfacial dynamics between substrate layers. We derived an analytical model for the dynamics of the elastic substrate under the shear stress provided by the cell layer at the surface boundary and the friction at bottom. The model reveals that sliding between substrate layers leads to an expanding stretch regime from a shear regime of substrate deformation in time and space. The regime boundary propagating diffusively with a speed depending on the stiffness, thickness, and slipperiness of the substrate, is a robust nature of a deformed elastic sheet with interfacial friction. These results shed new light on force propagation in tissues and our model could serve as a basis for studies of such propagation in a more complex tissue environment.