Vertex Modeling of Epithelial Tissues: Structural Changes from Out-of-plane Mechanics

Vertex models of domain systems have been used to model and understand mechanical properties of the entire system as a function of not only physical parameters, but of structural signatures of the domains. In two dimensions, in particular, quantification of polygonal domain shapes, as well as the statistical distribution of domain areas and topologies (numbers of neighbors) provides important information about the rigidity and mechanical response of the system, which may represent a single-layer biological tissue such as an epithelium.

We show here that the quantitative predictions of a two-dimensional approach fail to agree with experimental data on MDCK epithelia, predicting floppy mechanics where the tissues are stable and rigid. We identify the cause of this discrepancy as the presence of actin stress fiber bundles near the basement membrane, breaking the apical-basal symmetry and leading to significant, systematic changes in cell outline as a function of the apical-basal coordinate. The main effect on average cell shape is increased anisotropy related to the orientation of the fiber bundle. A modified 2D vertex model calibrates the strength of the effect on cell shape with the fiber bundle strength and correlates the bundle orientation and cell anisotropy orientation with the mechanical energy of the system, thus restoring the viability of diagnosing tissue mechanics from visual information only.