  Interfaces between stratified epithelia and their supporting stromas commonly
exhibit irregular shapes. Undulations are particularly pronounced in dysplastic
tissues and typically evolve into long, finger-like protrusions in carcinomas.
In a previous work (Basan et al., Phys. Rev. Lett. 106, 158101 (2011)), we
demonstrated that an instability arising from viscous shear stresses caused by
the constant flow due to cell turnover in the epithelium could drive this
phenomenon. While interfacial tension between the two tissues as well as
mechanical resistance of the stroma tend to maintain a flat interface, an
instability occurs for sufficiently large viscosity, cell-division rate and
thickness of the dividing region in the epithelium. Here, extensions of this
work are presented, where cell division in the epithelium is coupled to the
local concentration of nutrients or growth factors diffusing from the stroma.
This enhances the instability by a mechanism similar to that of the
Mullins-Sekerka instability in single-diffusion processes of crystal growth. We
furthermore present the instability for the generalized case of a viscoelastic
stroma.
