Unexpected Tissue Surface Tension in Simple Models of Dense Biological Tissues

Tissue surface tension, the effective interfacial tension between two tissues composed of different cell types, has been a useful paradigm for explaining cell sorting, compartmentalization, and boundary maintenance in vivo or in co-culture. Different experimental techniques have been developed to measure tissue surface tension by analogy with the equilibrium behavior of molecular fluids. An important open question is whether these different techniques probe the same thing, since tissues are far from equilibrium and cells have different degrees of freedom and interactions compared to molecules. We extend existing vertex-based models for confluent tissues by allowing individual cells to regulate the tensions between neighboring cells of like or unlike type, and then numerically measure the effective surface tension between coexisting cell populations. Strikingly, we find that different methods which yield identical values of the tension in molecular fluids differ by more than an order magnitude in confluent models for tissue. We demonstrate that this difference stems from the topological nature of the interactions between cells, and speculate that similar interfacial sharpening may occur in other systems with topological interactions.