  How can dense biological tissue maintain sharp boundaries between coexisting
cell populations? We explore this question within a simple vertex model for
cells, focusing on the role of topology and tissue surface tension. We show
that the ability of cells to independently regulate adhesivity and tension,
together with neighbor-based interaction rules, lets them support strikingly
unusual interfaces. In particular, we show that mechanical- and
fluctuation-based measurements of the effective surface tension of a cellular
aggregate yield different results, leading to mechanically soft interfaces that
are nevertheless extremely sharp.
